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\begin{huge}
The Silent Majority\\
\end{huge}

\vspace{0.35cm}

\begin{Large}
{Jets and Radio Cores from Weakly Active Black Holes}\\
\end{Large}
\vspace{1cm}

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\large {\bf Heino Falcke}
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\vspace{1cm}


\begin{huge}
The Silent Majority\\
\end{huge}


\begin{Large}
{Jets and Radio Cores from Weakly Active Black Holes}\\
\end{Large}
\vspace{0.3cm}

\centerline{\rule{7cm}{.3mm}}
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\begin{huge}
Die schweigende Mehrheit\\
\end{huge}

\begin{Large}
{Jets~und~Radiokerne~von~schwach-aktiven~schwarzen~L\"ochern}\\[4cm]
\end{Large}



\large {\bf Habilitationsschrift}\\
zur\\Erlangung\\
 der\\
Venia Legendi\\
der\\
Hohen Mathematisch-Naturwissenschaftlichen Fakult\"at\\
der\\
Rheinischen Friedrich-Wilhelms-Universit\"at Bonn\\[2.8cm]

\large vorgelegt von \\[1.5pc]
\large {\bf Dr. rer. nat. Heino Falcke} \\[1.5pc] 
\large aus K\"oln \\[1cm]
Bonn, im M\"arz $2000$\\
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%{\large\bf Math.-Nat. Fakult\"at der Universit\"at Bonn}\\[1cm]
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%\begin{trivlist}
%\item[] Referent: Prof.~Dr.~P.L.~Biermann
%\item[] Koreferent: Prof.~Dr.~H.J.~Fahr  
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%Tag der Promotion: 4. Juli 1994
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{\sf
This whole way of thinking and acting rests on the assumption that reality
 is reliable, not that disasters, and failures, and evil things will never
 happen, but that the world in which they happen ultimately makes sense. It
 is not just `buzzing, booming confusion' but springs from the will of a
 creator whose purposes are trustworthy and whose ultimate aim is glorious
 however dark and mysterious the way to it.
\bigskip

\hfill{} (John Habgod in ``Can Scientists Believe?'', Ed. Sir Nevill Mott, 1991)
}
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%La\ss{}t euch nicht von dem, was ihr am Himmel seht, beeindrucken! La\ss{}t euch nicht dazu verleiten, Sonne, Mond und Sterne als G\"otter zu verehren.
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%\hfill{} (5. Mose 4,19)
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\chapter*{Abstract}
\thispagestyle{empty}
They are weak, they are small, and they are often overlooked, but they
are numerous and an ubiquitous sign of accreting black holes: compact
radio cores and jets in radio-weak AGN.  Here I summarize our work
concerning these radio cores and jets in recent years, specifically
focusing on the large population of low-luminosity and radio-quiet
AGN. Special attention is given to Sgr A*, the supermassive black hole
candidate at the Galactic Center, whose radio properties are reviewed
in detail. This source exhibits a submm-bump, possibly from an
ultra-compact region around the black hole, has unusually high
circular but very low linear polarization and is variable at cm-waves
where it shows phases of quasi-periodic oscillation. Particularly the
compact submm emission is of great interest since it should allow
imaging of the event horizon of the black hole in the not too distant
future. A jet model is proposed which explains the basic feature of
Sgr A*: its slightly inverted radio spectrum, the submm-bump, the lack
of extended emission, and the X-ray emission.  This model is also
applied to famous sources like M81, NGC4258, and GRS1915+105 based on
the argument that radio cores are jets whose emission can be scaled
with the accretion power over many orders of magnitude. This scaling
is corroborated by the detection of many Sgr A*-like radio cores in
nearby Low-Luminosity AGN (LLAGN), many of which show jet structures
on the VLBI (Very Long Baseline Interferometry) scale. These cores
confirm an AGN origin of at least half of the known low-luminosity AGN
classified as LINERs and dwarf-Seyferts. It is argued that in fact
most of the compact radio emission in LLAGN is produced by a compact
radio jet and not an Advection Dominated Accretion Flow
(ADAF). Finally, we extend our view to compact radio cores and jets in
radio-`quiet' AGN such as Seyferts and radio-quiet quasars. Hubble
Space Telescope (HST) and Very Large Array (VLA) images show that jets
can have a significant impact on their environment even in these
sources. It is also suggested that basically all AGN contain
relativistic jets. This idea is strengthened by the first detection of
superluminal expansion in a spiral galaxy with a Seyfert nucleus. In
general one can say that compact radio cores are a genuine feature of
AGN, allowing one to precisely pinpoint black holes in many galaxies.

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\chapter*{Foreword}\thispagestyle{empty}\pagestyle{empty}
This review was written to fulfill the requirements for the
``Habilitation''-procedure at the University of Bonn. It summarizes a
big part of the research I have conducted over the recent years,
focusing on compact radio cores and jets. While I try to review what
has been done in the field where possible, this work is strongly
biased towards my own contributions. It therefore will not represent
the final wisdom but can just be a progress report that can help to
stimulate new research and perhaps sometimes different
answers. Naturally, in a rapidly evolving and highly competitive field
like astronomy and astrophysics many of the results presented here
have already been published in refereed journals and conference
proceedings, but some results are still unpublished and new. By
collating this material in one, hopefully homogeneous, publication
this review can perhaps provide a more comprehensive overview over the
questions and answers related to the given topic than a set of
individual publications could. The list of original publications used
as the basis for this work is given in the bibliography at the end.
It is certainly necessary, at this point, to thank all my
collaborators who contributed to many of the results presented here
and are listed as co-authors on the individual publications. In every
case it was a pleasure to work together with them. I think we are
truly blessed to have such an open and international scientific
community today which is connected through personal contacts and
electronic communications. Most of my research would not have been
possible without it, or at least would have taken much longer to
complete.

\bigskip
Heino Falcke, March 2000


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\chapter{Introduction}\label{intro}
\section{The Vocal Minority}
\citeme{Falcke1998c}
One of the main subjects for radio astronomers has been the study of
extragalactic radio jets. When observed at a higher resolution, many
of the first radio sources discovered in the early years of radio
astronomy later turned out to be powerful, collimated plasma flows of
relativistic plasma (called jets) which were ejected from the nucleus
of giant elliptical galaxies. These structures can reach sizes of
several million light years and hence extend well beyond their host
galaxies into the vastness of intergalactic space. This relative
isolation is ideal for studying the physics of astrophysical plasma flows
in great detail (see e.g.,
\citeNP{BridlePerley1984,BridleHoughLonsdale1994,KleinMackStrom1994,MartiMuellerFont1997})
and allows us to make some estimates of the properties of the IGM
(inter-galactic medium, e.g., \citeNP{SubrahmanyanSaripalli1993}).

An even more important aspect of radio jets, however, is that they are
the largest and most visible sign -- literally the "smoking gun" -- of
Active Galactic Nuclei (AGN). The standard model of an AGN consists of
a supermassive black hole at the center of a galaxy that accretes
matter via an accretion disk
\cite{vonWeizsaecker1948,Luest1952,ShakuraSunyaev1973,Lynden-BellPringle1974}.
The inflow of matter in the potential well leads to an enormous energy
production that is released through infrared (IR), optical, ultra-violet
(UV), and X-ray emission. In a fraction of sources one also sees very
strong $\gamma$-ray and TeV emission. Some of the energy is also
funneled into a relativistic radio jet along the rotation axis of the
disk (Fig.~\ref{AGN}). It was, in fact, the strong radio emission from
these jets which first led to the discovery of quasars (3C273,
\citeNP{HazardMackeyShimmins1963,Schmidt1963}).

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/britzen.cps,width=0.5\textwidth}}
\caption{\label{AGN}Schematic view of an AGN. An accretion disk
rotates around a central black hole and ejects a relativistic
magneto-hydrodynamic jet along its rotation axis. Jet and disk produce
emission across the entire electromagnetic spectrum from radio to TeV
photons. Surrounding ISM (interstellar medium) clouds are ionized by
strong UV flux from the disk and produce the visible emission-lines in
the optical spectra (Figure courtesy of Silke Britzen, MPG Jahrbuch
1995).}
\end{figure}

Jets have therefore been studied with great interest over many years
and in this time a huge zoo of different jet species has emerged. The main
characteristics of radio jets are the size (compact, i.e.~parsec to
kiloparsec scale, or extended, i.e.~tens to hundreds of kiloparsecs),
and the spectral index (flat or steep) of the radio sources. Steep
radio spectra ($\alpha<-0.5$, $S_\nu\propto\nu^{\alpha}$) are due to
optically thin synchrotron emission from large, extended radio
sources, while flat radio spectra can be produced if the source is
very compact and the spectrum is dominated by radiation from a number
of optically thick synchrotron components.

A typical powerful radio galaxy {}--{} a so called
\citeN{FanaroffRiley1974} type II radio galaxy (short
FR\,II) {}--{} consists of two steep-spectrum, extended lobes connected by
very faint (if visible at all), well-collimated plasma beams, and a
compact flat-spectrum core (which will be discussed in more detail
later). FR\,II jets are produced by the most powerful AGN, have the
largest kinetic powers of any jets observed
(i.e.~\citeNP{RawlingsSaunders1991}), and attain the absolute largest sizes
observed (see Fig.~\ref{cyga}).
\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/cyga.cps,width=\textwidth,angle=-90}}
\caption{\label{cyga}VLA image of the bright FR\,II radio galaxy Cygnus A (from
R. Perley et al.~1984, VLA/NRAO). One can see the bright lobes
connected by well-collimated jets emerging from a compact radio core
at the center. The jets expand over more than 600,000 lightyears.}
\end{figure}
Probably due to their huge powers FR\,II jets can plow with
relativistic speeds through the ambient medium, self-shielded by a
huge cocoon \cite{BegelmanCioffi1989}, until they slow down and
terminate in a massive shock {}--{} the hot spots. It is speculated that
these termination shocks are the site of intense acceleration of
electrons and protons (e.g., \citeNP{BiermannStrittmatter1987}),
possibly responsible for some of the ultra-high energy cosmic rays
observed at earth
\cite{RachenBiermann1993}. Behind the shock the jet material disperses
and at least a part of it flows back toward the galaxy it was ejected
from. This can be seen on many of the beautiful high dynamic-range VLA
maps made in recent years (e.g.,
\citeNP{BlackBaumLeahy1992,LeahyBlackDennett-Thorpe1997}).

Such beautiful structures, however, are not the rule but rather the
exception: at lower powers the jet morphology seems to change and
FR\,II radio galaxies suddenly turn into FR\,Is, where instead of a
well-collimated pencil-like beam with a well-defined terminus, the jet
has a larger opening angle, entrains material from the interstellar
medium (ISM)
\cite{DeYoung1993,Bicknell1994}, becomes bright, and then slowly fades
along the way (Fig.~\ref{3C296}). Clearly, in those cases the jet is
no longer independent of its environment but interacts with the ISM of
the host galaxy. Initially one was only able to see the effects of
this interaction on the radio jet itself, but now we can also see the
other side of this coin in X-ray observations, which indicate how the
radio plasma pushes against gas in the galaxy
(e.g.,~\citeNP{BoehringerVogesFabian1993,HollowaySteffenPedlar1996,ClarkTadhunterMorganti1997}).

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/3C296.ps,width=0.6\textwidth,angle=-90}}
\caption{\label{3C296}VLA map at 1.4 GHz obtained with the VLA of the FR\,I radio
galaxy 3C296 (from Leahy \& Perley 1991). In contrast to FR\,II
radio galaxies the jet is de-collimated very close to the nucleus and
is not able to produce hotspots at its terminus.}
\end{figure}
\nocite{LeahyPerley1991}

Not always, however, are we so fortunate to see all details of the
extended jets. If, for example, those jets happen to be seen under a
very small aspect angle with respect to the line of sight,
relativistic effects will become very important. Since the jet has
velocities close to the speed of light in the nucleus, the emission
from the flat-spectrum radio core will be boosted by the relativistic
Doppler effect and for small inclination angles will become so bright
that it dominates the entire radio emission, overwhelming even the
bright extended lobes (even though they still can be found in
high-dynamic range observations,
e.g.,~\citeNP{KollgaardWardleRoberts1992}). These galaxies appear as
compact, core-dominated flat-spectrum radio galaxies or quasars,
sometimes called Blazars. If observed at very high resolution Blazars
often show superluminal motion (an optical illusion caused by the
relativistic motion of bright features in the jet) which is
accompanied by strong flux variability down to scales of less than a
day
\cite{WagnerWitzel1995,Zensus1997}. In addition one finds luminous
high-energy emission, such as X-ray and $\gamma$-emission ($\ga10$ TeV,
\citeNP{AharonianAkhperjanianBarrio1999,ZweerinkAkerlofBiller1997}),
most certainly produced by scattering processes (e-$\gamma$,
p-$\gamma$, or p-p) from relativistic particles within the jet
\cite{MannheimBiermann1992,DermerSchlickeiser1993}.  In fact, for some
sources most of the observed luminosity is seen in $\gamma$-rays (e.g.,
\citeNP{vonMontignyBertschChiang1995}). 

The radio cores of Blazars are not only interesting because of their
astrophysics, but they are also used as beacons for a global
coordinate reference frame. Because of their compact bright radio
emission and cosmological distances, implying no significant proper
motion, their positions can be measured with radio-interferometers to
milli-arcsecond precisions. This not only allows extremely precise
astrometry on the sky, but it also can be used to determine fundamental
parameters of the earth orientation and even measure continental
drifts on earth (see \citeNP{Robertson1991}).

However, not all compact radio galaxies are Blazars. Some galaxies
show steep radio spectra (at least at high frequencies), yet, instead
of penetrating deep into the inter-galactic medium (IGM) as FR\,Is and
FR\,IIs do, they are stuck inside their host galaxies. The currently
favored idea is that these galaxies are very young and still need to
plow their way out through the ISM (see \citeNP{OwsianikConway1998}).
These sources are called CSS (compact steep-spectrum) or GPS
(Gigahertz-peaked spectrum) sources (see \citeNP{O'Dea1998} for a
recent review). Looking with higher resolution one can resolve the
jets and find extended lobes on scales of several kpc (for CSS) down
to hundreds of parsecs (GPS, needs Very Long Baseline Interferometry)
 {}--{}  at least some of them must be the predecessors of the large FR\,I
and FR\,II radio galaxies.

The main reason why all these radio galaxies and radio-loud quasars
have been studied in such detail so far is their large radio fluxes of
100 mJy up to several tens of Jansky, which makes them easily
accessible with current technology. On the other hand, it was noted
early on that the majority of quasars and AGN in the universe are {\it
not} radio-loud
\cite{StrittmatterHillPauliny-Toth1980,KellermannSramekSchmidt1989} and have in fact a
rather low radio flux, despite having very similar optical properties
compared to radio-loud quasars. Moreover, classical radio galaxies and
radio-loud quasars are among the most luminous AGN we know,
corresponding to black holes with the largest masses and the largest
accretion rates. Hence, when we discuss the properties of relativistic
jets in AGN, we usually tend to think exclusively about a relatively
small but vocal group of sources.  Is this the whole universe, or just
the tip of the iceberg?  Most likely there are many more, weaker black
holes and jets in the universe.

\section{The Silent Majority}
\citeme{FalckeNagarWilson2000}

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/NGC4261C.cps,width=0.5\textwidth,angle=0}}
\caption{\label{NGC4261}HST image of the galaxy NGC~4261 showing a
dark disk surrounding a bright nucleus (Ferrarese et al.~1996). A
black hole is suspected at the center producing a low-luminosity AGN,
a weak sibling of a quasar, surrounded by a dusty disk.}
\end{figure}
\nocite{FerrareseFordJaffe1996}

The evidence for supermassive black holes in the nuclei of most
galaxies has become much stronger recently. Some of the best cases are
the Milky Way \cite{EckartGenzel1997}, NGC~4258
\cite{MiyoshiMoranHerrnstein1995}, and a number of other nearby
galaxies
\cite{FaberTremaineAjhar1997,RichstoneBenderBower1998,MagorrianTremaineRichstone1998}
where convincing dynamical evidence for black holes exists. Hence, the
basic powerhouse for an AGN -- the black hole -- is built into almost
every galaxy, but compared to quasars and radio galaxies there is a
huge range in power output between the most luminous quasars and barely
active galaxies like the Milky Way.

For example in a spectroscopic survey of 486 nearby bright galaxies,
\citeN{HoFilippenkoSargent1997a}
found that a large fraction of these galaxies have optical
emission-line spectra. Roughly one third of the galaxies surveyed
showed spectra usually attributed to active galactic nuclei. The
energy output of these systems, is $10^{-6}-10^{-3}$ times lower than
in typical quasars \cite{Ho1999}. Consequently, these galaxies are
called low-luminosity AGN (LLAGN, see Fig.~\ref{NGC4261}).  The large
fraction of LLAGN already indicates that the number of AGN increases
with decreasing luminosity. This is, in fact, exactly what has been
found already in studies of the luminosity function of quasars and
Seyfert galaxies, namely a power-law distribution of AGN as a function
of luminosity with an index $\alpha\simeq-2.2$
(e.g.,~\citeNP{KoehlerGrooteReimers1997}, see Fig.~\ref{llf}). As in real
life, the majority of the entire population is rather quiet. To get a
complete view of the astrophysics of AGN and black holes one therefore
needs to look at this silent majority as well.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/llf.ps,width=0.75\textwidth,bbllx=2.5cm,bblly=3.0cm,bburx=12cm,bbury=9.1cm,clip=}}
\caption{\label{llf}Local luminosity function (number density as a
function of absolute magnitude) of $z<0.3$ quasars and Seyferts. The
number of AGN decreases with a power-law index of $\alpha\simeq-2.2$ as
the luminosity increases (from K\"ohler et al.~1997).}
\end{figure}
\nocite{KoehlerGrooteReimers1997}

The question of how the central engines in quasars and low-luminosity
AGN are related to each other and why they appear so different despite
being powered by the same type of object is therefore of major
interest. For many nearby galaxies with low luminosity nuclear
emission-lines, it is not even clear whether they are powered by an
AGN or by star formation. This is especially true for Low Ionization
Nuclear Emission Region (LINER) galaxies
\cite{Heckman1980,HeckmanvanBreugelMiley1983}, some of which can be
explained in terms of aging starbursts
(e.g.,~\citeNP{FilippenkoTerlevich1992,Alonso-HerreroRiekeRieke2000}).

One of the best ways to probe the very inner parts of these engines is
to study the compact radio sources found in many AGN. Indeed, despite
their low optical luminosity, quite a few nearby galaxies have such
radio sources in their nuclei, prominent cases being the Milky Way
(Sgr A*), and the galaxies M~104 and M~81
\cite{BietenholzBartelRupen1996}. These radio sources resemble the
cores of radio-loud quasars, showing a very high brightness
temperature and a flat to inverted radio spectrum that extends up to
sub-millimeter (submm) wavelengths.



\section{Radio Cores, Jets, and Accretion}
\citeme{FalckeBiermann1999}
What are these compact radio cores and how are they related to the
AGN?  Early on in the discussion about the existence of black holes,
\citeN{Lynden-BellRees1971} suggested that they would be accompanied by
compact radio nuclei, detectable by Very Long Baseline Interferometry
(VLBI), and predicted such a source for the Galactic Center. Indeed,
this source (Sgr A*) was then discovered by
\citeN{BalickBrown1974} and it became clear in later years that
compact radio cores are indeed good evidence for the existence of an
AGN or a black holes in a galaxy. For luminous radio galaxies and
radio-loud quasars the basic nature of these compact radio nuclei has
been clarified in the meantime through extensive and detailed VLBI
observations (see Zensus 1997 for a review) as being the inner regions
of relativistic jets emanating from the nucleus.

Despite this progress, a number of important questions remain when
looking back at the initial discussion. First of all, it is unclear
whether there indeed is a direct link between compact radio cores and
AGN, i.e.~whether compact radio cores and jets are just an accidental
by-product of black hole activity or a necessary
consequence. Secondly, for the lesser studied, low-luminosity AGN the
jet nature of compact radio nuclei has not yet been established beyond
any doubt, leaving the question open whether in fact a compact radio
core in a low-luminosity AGN is the same as in a high-luminosity AGN,
i.e.~a quasar.

The latter was exactly the claim made by
\cite{FalckeBiermann1995}, stimulated by the seminal paper from
\citeN{RawlingsSaunders1991}, where it was proposed that accretion disks and
jets form symbiotic systems. A scaling law was was proposed which connects
high-power and lower-power accretion disks and their associated radio
jets (cores). The scaling law was based on the assumption of an
equipartition between the energy released and radiated away through
dissipation processes in the accretion disk and the power put into the
formation of magnetically driven radio jets.

The question whether this scaling law holds all the way down to
LLAGN, as later claimed in \citeN{FalckeBiermann1996},
also has some very interesting implications for the current discussion
of accretion flows.  Since the early papers on the observational
appearance of black holes (e.g., \citeNP{ShakuraSunyaev1973}), it was
assumed that luminous, thermal emission at optical, UV, or X-ray
wavelengths was the primary sign for the presence of an accreting
black hole. It was argued that any matter falling onto the black hole
would likely form an accretion disk, if there was any residual angular
momentum, and hence would need to dissipate its potential energy into
heat by viscous processes allowing it to transport angular momentum
outwards while matter is falling inwards ($\alpha$-disk). This idea
was used successfully to explain the ``big blue bump'' in quasars
(e.g., \citeNP{SunMalkan1989}).

However, the view that the $\alpha$-disk can be extended to much lower
powers has been challenged
\cite{NarayanYi1994,NarayanYi1995a,NarayanYi1995b} and it was argued
that accretion disks will turn into Advection Dominated Accretion
Flows (ADAFs) if the accretion rate onto the black hole is
sufficiently sub-Eddington (see \citeNP{Meyer-HofmeisterMeyer2000}).
\citeN{NarayanYiMahadevan1995} and
\citeN{NarayanYiMahadevan1996} applied this idea to the Galactic
Center (see also \citeNP{Rees1982} and \citeNP{Melia1994}), trying to
explain the compact radio source Sgr A* and its faintness at other
wavelengths. \citeN{LasotaAbramowiczChen1996} used the ADAF model to
explain the broad-band spectrum of the nearby LLAGN and LINER galaxy
NGC~4258 which is famous for its megamaser emission from a molecular
disk (\citeNP{MiyoshiMoranHerrnstein1995}, see Fig.~\ref{NGC4258}).

An integral part of these ADAF models is the prediction of very
compact radio emission associated with the innermost part of the
accretion flow, providing an alternative explanation to the jet model
for compact radio nuclei in LLAGN. While initially the predicted,
highly inverted radio spectra of the ADAF model, did not fit the
observed characteristics of these radio cores very well,
\citeN{Mahadevan1998} presented a more recent version of this model
that was at least\footnote{It was never shown that also the size
predicted by this model is within the observationally allowed constraints.}
able to account for the correct radio spectrum of Sgr~A*. Still,
\citeN{diMatteoFabianRees1999} found a number of serious
constraints for ADAF models {}--{} at least for compact radio nuclei in
elliptical galaxies, casting some doubt on the applicability of the
ADAF model to compact radio cores in general. Hence, the question now
is whether indeed the radio emission from compact nuclei in
sub-Eddington accretion systems can be used as an argument for the
existence and necessity of ADAFs, or whether they are equally well, or
even better explained, in a scaled down AGN jet model.

The purpose of this work is therefore to describe a comprehensive
study of the radio emission from AGN operating at powers less than
those of typical quasars and to clarify their nature. Specifically we
will test the applicability of the standard AGN jet model to low-power
black holes.

By going to lower powers we want to understand how universal the
central engine really is. Are radio cores in LLAGN different from
those in quasars? How important is the formation of jets at lower
power and in radio-weak objects?  Are there classes of sources where
no jet is found? What happens with the jets in quasars if the power of
the engine becomes less and less? Will the jets die completely,
implying that accretion near the Eddington limit is required for the
jet formation, or will the jet just become proportionally weaker,
implying that jet formation is an integral part of accretion physics
and independent of the exact nature of the accretion disk itself?


\section{Outline}
In the next chapter, we will describe the jet-disk symbiosis model of
\citeN{FalckeBiermann1995} and \citeN{Falcke1996a}. Then we will apply
these solutions to some specific sources which are of particular
interest and check the basic predictions of the model.

In the subsequent chapters we will explore the applicability of the
model to a wider range of sources. In Chapter~\ref{SgrA*} we will
review in great detail the observational constraints on one of the
most famous and best studied radio cores -- Sgr A*, the supermassive
black hole candidate at the Galactic Center. We present a detailed
model of its emission characteristics within the frame work of the
radio core model described in Chapter~\ref{symbiosis}. This source is
of particular interest because general-relativistic ray tracing
calculations, presented at the end of this chapter, suggest that in
the near future the radio core could lead to the first detection and
imaging of the event horizon of a black hole.

In Chapter~\ref{llagn} we will extend our view again and present a
search for Sgr A*-like radio cores in low-luminosity AGN. This will
show that Sgr A*'s are a rather common phenomenon in the
universe. Finally, Chapter~\ref{seyferts} discusses the evidence we
have that the radio cores in radio-quiet  AGN, such as
radio-quiet quasars and Seyferts which make up the majority of
luminous AGN, can be explained in a very similar fashion. We will
present the first conclusive evidence for the existence of
relativistic jets in Seyfert galaxies.  Hubble Space Telescope (HST)
observations will show that, even after jets have been slowed-down
significantly, in Seyferts they can significantly effect their
environment -- despite being radio-quiet. In general, we will see that
in fact the majority of accreting black holes at the various levels of
accretion rates, despite being relatively silent in the radio regime,
can have quite active jets.

Given this finding, and with the ever-increasing sensitivity in radio
astronomy, one can foresee that these radio cores will become more and
more important as tracers of supermassive black holes in galaxies near
and far.

\chapter{The Jet-Disk Symbiosis Model}\label{symbiosis}
\section{The Universal Engine -- a {\it Simple} Ansatz}
\citeme{Falcke1996f}
If the central engine of an AGN is indeed associated with a black
hole, it has the unpleasant property of being so small that it is
almost inaccessible by observational means and hence open to wild
theoretical speculations.  Currently there is no way to prove or
disprove that all central engines are completely different or
absolutely identical and one is forced to choose a basic Ansatz for
the nature of the engine. This allows one to draw further conclusions
and test them against observational data.

Strangely, in Astronomy the burden of proof is usually on those who
postulate a simpler solution (like the unified schemes) while Occam's
Razor should force one to start with the simplest theory until
experimentally disproven. Consequently, our Ansatz for the nature of
the central engines in AGN should be that they are all very similar
and governed by a few parameters only, until forced to introduce more
parameters or a completely new theory. Such a simple engine is a black
hole accreting matter within an accretion disk and producing a jet at
the black hole/disk boundary layer, flowing out along the rotation
axis. As the escape speed from a black hole is relativistic, those
jets would have to be relativistic as well. Since the jets are
produced by the disk, one expects a strong coupling between jet and
disk. Since most of the power in an accretion disk is released close
to the center, the jet can be very powerful, and finally, because ``a
black hole has no hair'', there are not many parameters that can vary
from one engine to another. The main parameter of the engine is
therefore expected to be the accretion rate\footnote{The spin of the
black hole could be a secondary parameter, e.g., explaining the
radio-loudness}.  This ``simple Ansatz'' also implies that jets are a
natural companion to accretion disks, and both are necessary and
symbiotic features in the accretion process onto the compact central
object
\cite{FalckeBiermann1995}.

While this postulate sounds simple and almost trivial at first sight
it faces severe opposition if applied to individual sources,
i.e.~there is a trend to ``personalize'' models for each and every new
source and source class\footnote{This sometimes leads to the strange
effect that a model is not quoted and applied because it has the
`wrong' source name in the title, thus forcing theorists to publish
the same model over and over again for different source names.}. In
the following we will therefore try to go in the opposite direction
and describe a heterogeneous set of sources with just one model, based
on the principles discussed above.


\section{Radio Cores}
\citeme{Falcke1996f}
Jets in AGN are coherent structures with spatial scales from a few AU
up to several megaparsecs. Therefore we should be able to investigate
basic parameters of a jet at different scales and get similar
answers. For example, we can use the large, extended lobes of radio
jets in FR\,II radio galaxies to estimate their total power, e.g., by
calculating their minimum energy content from synchrotron theory or
from their interaction with hot, X-ray emitting gas and dividing by
the life time of the sources (e.g., derived from spectral aging). The
derived powers (which are often {\em lower} limits) are very high --
up to $10^{45-47}$ erg/sec
\cite{RawlingsSaunders1991} and thus larger than the total power output of 
a typical galaxy.  The only reasonable place where such enormous
amounts of energy can be released is deep in the potential well of a
supermassive black hole.

Even though at these larger distances the jet pressure has decreased
enough so that pressure balance between jet and external medium is
reached, it is believed that the implied adiabatic losses are largely
avoided by a constant re-collimation \cite{Sanders1983} of the jets:
the side-ways lateral expansion leads to a re-collimation shock which
in turn will focus the kinetic energy of the jet back into the forward
direction. Otherwise one would have to account for expansion factors
of $\ga10^6$ between launch and termination of powerful jets. For a
relativistic plasma where adiabatic losses scale as $r^{-2/3}$ this
would translate into an energy loss of four orders of magnitude and
require the jets to start with enormous initial powers of $10^{49-51}$
erg/sec, corresponding to accretion rates of $10^{2-4}M_\odot$/yr and
Eddington luminosities for black holes with a mass of
$10^{10-12}M_\odot$. From all what we know today, this seems to be too
high and one must conclude, that most of the way, the jet does not
suffer adiabatic losses.

The argument based on hotspots still has the problem that it depends
on parameters characterizing the external medium the jet is
interacting with. If we go to low-power jets we will find that most of
them (e.g., in FR\,I radio galaxies, Seyferts) do not even have
hotspots that would provide one with a well-defined, isolated
dissipation region to determine basic jet parameters
easily. Fortunately, every jet should also have an ``inflationary
phase'' close to the nucleus, after leaving the nozzle where the
energy density in powerful jets can be $1-100$ erg/cm$^3$ and above,
compared to $10^{-12}$ erg/cm$^{3}$ in the local ISM.  This is the
region, where flat spectrum radio cores are produced and which we will
use in the following to make more quantitative statements. The
advantage of radio cores is that they are largely independent of
external conditions and therefore should be visible in basically all
types of sources that produce relativistic jets. Their independence
comes for a price, since less interaction often means less shocks,
less energy dissipation, and less radio emission. Hence, compact radio
cores are much more difficult to observe than extended lobes and jets,
but modern radio astronomy is now sensitive enough to do just this.

\section{Jet-Disk Coupling}
\citeme{Falcke1996f}
In order to quantify the radio emission we expect from a radio jet
close to the nucleus we will make a few simple assumptions and resort
to the simple Ansatz made above, assuming that every jet is coupled to
an accretion disk. A coupled jet-disk system has to obey the same
conservation laws as all other physical systems, i.e.~at least energy
and mass conservation (other conservation laws we do not use yet). We
can express those constraints by specifying that the total jet power
$Q_{\rm jet}$ of the two oppositely directed beams is a fraction
$2q_{\rm j}<1$ of the accretion power $Q_{\rm disk}=\dot M_{\rm
disk}c^2$, the jet mass loss is a fraction $2q_{\rm m}<1$ of the disk
accretion rate $\dot M_{\rm disk}$, and the disk luminosity is a
fraction $q_{\rm l}<1$ of $Q_{\rm disk}$ ($q_{\rm l}=0.05-0.3$
depending on the spin of the black hole).  The dimensionless jet power
$q_{\rm j}$ and mass loss rate $q_{\rm m}$ are coupled by the
relativistic Bernoulli equation (\citeNP{FalckeBiermann1995}, see
Eq.~\ref{bernoulli}) for a jet/disk-system. For a large range in
parameter space the total jet energy is dominated by the kinetic
energy such that one has $\gamma_{\rm j}q_{\rm m}\simeq q_{\rm j}$, in
case the jet reaches its maximum sound speed, $c/\sqrt{3}$, the internal
energy becomes of equal importance and one has $2\gamma_{\rm j}q_{\rm
m}\simeq q_{\rm j}$ ('maximal jet'). The internal energy is assumed to
be dominated by the magnetic field, turbulence, and relativistic
particles. We will constrain the discussion here to the most efficient
type of jet where we have equipartition between the relativistic
particles and the magnetic field and also have equipartition between
the internal and kinetic energy (i.e.~bulk motion) -- one can show (see
\citeNP{FalckeBiermann1995}) that other, less efficient models would 
fail to explain the highly efficient radio-loud quasars.

Knowing the jet energetics, we can describe the longitudinal structure
of the jet by assuming a constant jet velocity (beyond a certain
point) and free expansion according to the maximal sound speed
($c_{\rm s}\la c/\sqrt{3}$). For such a jet, the equations become very
simple. The magnetic field is given by

\begin{equation}
B_{\rm j}=0.3\,G\;Z_{\rm pc}^{-1}\sqrt{q_{\rm
j/l}L_{46}}
\end{equation} 
and the particle number density is
\begin{equation}
n=11\,{\rm cm}^{-3} L_{46} q_{\rm j/l} Z_{\rm pc}^{-2}
\end{equation} 
(in the jet rest frame). Here $Z_{\rm pc}$ is the distance from the
origin in parsec (pc), $L_{\rm 46}$ is the disk luminosity in $10^{46}$
erg/sec, $2q_{\rm j/l}=2q_{\rm j}/q_{\rm l}=Q_{\rm jet}/L_{\rm disk}$
is the ratio between jet power (two cones) and disk luminosity which is
of the order 0.1--1 (FMB95) and $\gamma_{\rm j,5}=\gamma_{\rm j}/5$ ($\beta_{\rm
j}\simeq1$). If one calculates the synchrotron spectrum of such a jet,
one obtains locally a self-absorbed spectrum that peaks at

\begin{equation}
\nu_{\rm ssa}=20\,{\rm GHz}\;{\cal D}{\left(q_{\rm j/l}L_{46}\right)^{2/3}
\over Z_{\rm pc}}\,\left({\gamma_{\rm e,100} 
\over\gamma_{\rm j,5} \sin i}\right)^{1/3}.
\end{equation}
Integration over the whole jet yields a flat spectrum with a
monochromatic luminosity of

\begin{equation}\label{radioopt}
L_{\nu}={ 1.3\cdot 10^{33}}\,{{\rm erg}\over
{\rm s\, Hz}}\;\left({q_{\rm j/l} L_{46} }\right)^{17/12}
{\cal D}^{13/6}\sin i^{1/6} \gamma_{\rm
e,100}^{5/6} \gamma_{\rm j,5}^{11/6},
\end{equation}

where $\gamma_{\rm e,100}$ is the minimum {\it electron} Lorentz
factor divided by 100, and ${\cal D}$ is the {\it bulk} jet Doppler
factor. At a redshift of 0.5 this luminosity corresponds to an
un-boosted flux of $\sim100$ mJy. The brightness temperature of the jet
is

\begin{equation}
{T}_{\rm b}=1.2\cdot 10^{11}\, {\rm K}\; {\cal D}^{4/5}{\left({
{\gamma_{\rm e,100}}^2 q_{\rm j/l} L_{46} \over
\gamma_{\rm j,5}^2 \beta_{\rm j}}\right)^{1/12}\sin i^{5/6}}
\end{equation} 
which is almost independent of all parameters except the Doppler
factor. An important factor that governs the synchrotron emissivity
is, of course, the relativistic electron distribution, for which we
have assumed a power-law distribution with index $p=2$ and a ratio 100
between maximum and minimum electron Lorentz factor. As we are
discussing here the most efficient jet model we also assume that all
electrons are accelerated (i.e.~$x_{\rm e}=1$ in
\citeNP{FalckeBiermann1995}), hence the only remaining parameter is
the minimum Lorentz factor of the electron distribution $\gamma_{\rm
e,100}$ determining the total electron energy content. In order to
reach the magnetic field equipartition value, which is close to the
kinetic jet power governed by the protons, we have to require
$\gamma_{e,100}\sim1$. It cannot be higher because otherwise the power
in electrons would exceed the total jet power, and it cannot be much
lower because we would not reach equipartition. Such a high,
low-energy cut-off in the electron energy distribution was suggested
already by \citeN{Wardle1977} and
\citeN{CelottiFabian1993} for other reasons and could for example
be produced in hadronic processes (e.g.,
\citeNP{BiermannStromFalcke1995})\footnote{Only recently,
\citeN{WardleHomanOjha1998} argued for lower electron Lorentz factors
based on circular polarization observations, but their result depends
quite strongly on the exact shape of the electron distribution and
whether or not a second population of low-energy electrons is present
in these astrophysical plasmas. Therefore a conclusive answer to how
the low-energy electron distribution looks like cannot be given and we
have to live with some assumptions.}.

\medskip

If radio-interferometric techniques were not yet developed today, and
we would have been asked to predict what kind of jet sources we would
expect to see, we would have needed only very few
considerations:
\begin{itemize}
\item[a)] {\it `total equipartition' everywhere}, i.e.~equipartition between
the luminosity radiated by the disk and expelled by a jet,
equipartition between internal energy and kinetic energy, and
equipartition between relativistic particles and magnetic field
\item[b)] {\it relativistic speed}, because,  if the jet is  produced
close to the black hole, relativistic escape speeds are required,
\item[c)] {\it disk luminosity} (UV-bump), which is a measurable quantity.
\end{itemize}

Thus, using $L_{\rm disk}\sim10^{46}$ erg/sec (typical
optical/UV-luminosity) and $\gamma_{\rm j}\sim 5$ (a few times the
escape speed from a black hole), we could have predicted pc-scale
radio cores at cm-wavelengths, with brightness temperatures of
$10^{11}$ K and fluxes of 100 mJy and more.  But of course, nobody
would have believed us, as those assumptions are obviously too
simplified \dots

\section{UV/Radio Correlation}
\citeme{Falcke1996f}
Now, we will have to validate some of our assumptions and test the
jet-disk coupling derived above. To stay on safe grounds we will in
this section concentrate on the well-studied quasars. For these
sources we have to estimate the disk luminosity as
precisely as possible and compare it to their radio cores. The best
studied quasar sample so far is the PG quasar sample
\cite{SchmidtGreen1983}. For most sources in this sample
\citeN{SunMalkan1989}, using optical and IUE data, fitted the UV bump
with accretion-disk models and a few more were available in the
archive \cite{FalckeMalkanBiermann1995}. There are also excellent
photometric \cite{NeugebauerGreenMatthews1987} and spectroscopic data
\cite{BorosonGreen1992} available. Unlike the broadband UV-bump
fits, which give $L_{\rm disk}$ directly, emission-lines and continuum
colors do not give a direct estimate for the bolometric UV luminosity
and $L_{\rm disk}$. We will need to calibrate those values to obtain
an equivalent UV bump luminosity using the sources which have a
complete set of data available. This yields

\begin{equation}
\lg (L_{\rm disk}/{\rm erg\;s}^{-1})=2.85+\lg (L_{\rm [OIII]}/{\rm erg\;s}^{-1}),\label{oiii2uv}
\end{equation}
\begin{equation}
\lg (L_{\rm disk}/{\rm erg\;s}^{-1})=2.1+\lg (L_{\rm H{\beta}}/{\rm erg\;s}^{-1}),
\end{equation}
\begin{equation}
\lg (L_{\rm disk}/{\rm erg\;s}^{-1})=-0.4 M_{\rm b}+35.90.
\end{equation}

Here $L_{\rm [OIII]}$ and $L_{\rm H{\beta}}$ are the luminosities in
the [OIII]$\lambda5007$ and H$\beta$ (broad) emission-lines, $M_{\rm
b}$ is the absolute blue continuum magnitude as used by
\citeN{BorosonGreen1992}. The scatter in this relation, $\sim0.5$ in
the log, is shown in \citeN{FalckeMalkanBiermann1995}.

With these correlations one should be able to estimate the ``disk
luminosity'' for almost any quasar. If several indicators are
available, we can combine them (assigning appropriate weights) to get
the final estimate. This provides us with a fairly reliable estimate
of $L_{\rm disk}$ and reduces the scatter in the radio-optical
correlations considerably.  It also reduces the effects of the
orientation dependence of some lines (e.g., [OIII]).  In the next
step, we can compare those disk luminosities with VLA radio cores
\cite{KellermannSramekSchmidt1989,MillerRawlingsSaunders1993} and the total radio
emission of quasars. In addition to the optically selected sample in
\citeN{FalckeMalkanBiermann1995} we have now also included quasars from
the southern 2 Jansky sample
\cite{MorgantiKilleenTadhunter1993,TadhunterMorganti1993} which are
predominantly flat-spectrum quasars, and steep-spectrum, lobe
dominated quasars from
\citeN{BridleHoughLonsdale1994},
\citeN{AkujorLuedkeBrowne1994},
and \citeN{ReidShoneAkujor1995} which had emission-lines readily
available
\cite{Steiner1981,JacksonBrowne1991,WillsNetzerBrotherton1993}.
Thus, the number of radio-loud quasars is increased considerably --
the results are shown in Figure \ref{uvradioplot-qso1} \& \ref{uvradioplot-qso2}.

In Figure \ref{uvradioplot-qso1} we can see that the total radio
emission of radio-loud quasars with typical undisturbed FR\,II-type
radio structure correlates very well with their UV emission, while the
radio-emission of CSS and GPS sources does not. This emphasizes that
the interaction of the compact jets in CSS and GPS sources with the
ISM of the host galaxy significantly affects, i.e. increases, the
radio emissivity. Moreover, flat-spectrum radio-loud quasars also
spoil the correlation since their total radio flux is still dominated
by the relativistically boosted core, pointing towards the observer
and outshining emission from the extended jet. This makes a simple
derivation of jet powers based on the radio flux at one frequency
alone subject to large uncertainties, unless one concentrates on
isotropically radiating jets in `isolation'. Interestingly,
radio-quiet quasars show a relatively good correlation between radio
and UV luminosity (see also \citeNP{BaumHeckman1989}). This is a first
indication already that also in this radio-quiet AGN the radio emission
is directly linked to the central engine.

Figure \ref{uvradioplot-qso2}, demonstrates that the {\it cores} of
these quasars show the distribution expected within the jet-disk
model, assuming one has relativistic jets in radio-loud {\em and}
radio-quiet quasars operating at two basic levels of efficiency (see
\citeNP{FalckeBiermann1995} for a discussion of what these basic levels 
could be). In contrast to the total emission, this is true for the
cores of CSS and GPS sources as well, meaning that at the scales where
the cores are produced jet-ISM interactions are not so important. The
spread in the radio luminosity distribution is dominated by
relativistic boosting and random inclination angles. As expected, flat
spectrum radio-loud quasars, with the exception of a few
radio-intermediate quasars discussed in Chap.~\ref{seyferts}, are
found at the highest radio luminosities expected for jets with small
inclination angles. This spread can be translated into characteristic
bulk Lorentz factors for the jets, yielding a range between
$\gamma_{\rm j}=3-10$.


Being aware that the discussion of basic cosmological parameters
continues to evolve
(e.g., \citeNP{PerlmutterAlderingGoldhaber1999,PriesterHoell1996}) we
have in these figures still used the parameters from the original
publication for a then standard cosmology with $H_0=50$ km sec$^{-1}$
Mpc$^{-1}$, $q_0=0.5$, and $\Lambda=0$.  Different cosmologies would
show different behaviors in such a plot at high-redshifts and
luminosities. Once more radio data and optical data for high-z quasars
is available and the basic parameters of these radio cores are better
understood, constraining cosmological parameters with radio cores might
therefore not be impossible (see also
\citeNP{GurvitsKellermannFrey1999} and \citeNP{TaylorVermeulen1997}
). On the other hand it is not yet completely clear how well such a
method can compete with current supernova studies.


\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/uvradioplot-qso-total.ps,width=0.7\textwidth,bbllx=2.7cm,bblly=5.9cm,bburx=19.1cm,bbury=22.3cm}
}
\caption[]{\label{uvradioplot-qso1}
Total radio luminosity vs.~disk (UV-bump) luminosity for quasars
(including a complete optical and a radio-selected sample). The shaded
circles are core-dominated, flat-spectrum sources, open circles are
steep-spectrum (FR II type) sources, circles labeled 'c' are Compact
Steep-Spectrum (CSS) sour\-ces and filled points are radio-quiet
(diffuse or unresolved) sources. Only un\-dis\-turbed radio-loud FR II
type and radio-quiet sources show a tight correlation. Flat-spectrum
sources are boosted to the upper end of the distribution except six
radio-intermediate quasars which might be boosted radio-quiet quasars
(see Chap.~\ref{seyferts}). The total emission of CSS source does not
show a tight correlation with disk luminosity. The solid line is the
(oversimplified) model for the lobes from Falcke \& Biermann~(1995,
see also Falcke, Malkan, \& Biermann~1995).}
\end{figure}
\nocite{FalckeBiermann1995,FalckeMalkanBiermann1995}

\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/uvradioplot-qso-core.ps,width=0.7\textwidth,bbllx=2.7cm,bblly=5.9cm,bburx=19.1cm,bbury=22.3cm}
}
\caption[]{\label{uvradioplot-qso2}
The same as Fig.~\ref{uvradioplot-qso1} (CSS are not explicitly
marked), but now the radio core flux is plotted. The shaded bands
represent the radio-loud and radio-quiet jet models where the width is
determined by relativistic boosting. The jet velocity evolves with
luminosity as $\gamma_{\rm j}\beta_{\rm j}\propto L^{0.1}$, as
discussed in Falcke, Malkan, Biermann (1995). The dashed lines
represent the expected level of emission for sources just within the
boosting cone (i.e.~inclination $i=1/\gamma$) and the isolated solid
lines represent emission for $i=0^\circ$ inclination -- corresponding
to the maximally boosted flux. The position of flat-spectrum and
steep-spectrum sources and the ra\-dio-loud/radio-quiet separation can
be naturally accounted for with the coupled jet-disk model.}
\end{figure}



\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/theplot-pred.ps,width=0.7\textwidth,bbllx=3.4cm,bblly=17cm,bburx=13.7cm,bbury=27cm,clip=}
}
\caption[]{\label{theplot-pred}
The same as Fig.~\ref{uvradioplot-qso2}.  The shaded bands,
representing the radio-loud and radio-quiet jet models are extrapolated
to much lower jet powers while keeping the bulk Lorentz factors fixed
at $\gamma_{\rm j}=2$. To simplify the display, upper limits of the
radio-quiet quasars are no longer displayed as such. Small open
circles represent radio cores of FR\,I galaxies from Rawlings \&
Saunders (1991). At the lower end of the radio-quiet quasar
distribution radio cores of Seyfert galaxies from the CfA sample
(Kukula et al.~1995) are added. Finally, at the lowest accretion rates
we display radio cores of X-ray binaries as discussed in Falcke
\& Biermann (1996). Radio cores obviously decrease in luminosity 
as the accretion disk luminosity decreases, roughly along the lines
predicted by the jet-disk symbiosis model. The gap at intermediate
accretion luminosities implicitly predicts the presence of radio cores
in low-luminosity AGN. It is worth noting that the predicted relation
is not linear (see Eq.~\ref{radioopt}) and hence is not a simple
consequence of a luminosity-luminosity plot.  }
\end{figure}
\nocite{KukulaPedlarBaum1995}\nocite{RawlingsSaunders1991,FalckeBiermann1996}

One can extend this kind of plot also to lower luminosities {}--{} even
down to X-ray binaries. Already \citeN{HjellmingJohnston1988} had
suggested that the radio emission of some of these sources could be
explained as jet emission. Of course, for these stellar-mass systems
the peak in the spectral energy distribution is shifted from the UV to
the X-rays, as predicted by accretion disk theory. Hence, $L_{\rm
disk}$ is no longer given by the UV luminosity but by the X-ray
luminosity. This extension to lower mass and lower mass accretion
rates was done in
\citeN{FalckeBiermann1996}. The respective figure is shown here as
Fig.~\ref{theplot-pred}. It shows that basically all astrophysical
radio cores roughly fall along the lines predicted by the simple
jet-disk symbiosis model.

There are some notable exception though. Some FR\,I radio galaxies,
for example, seem to be somewhat above the line in cases where
relativistic boosting is not a dominant factor. This could mean that
these galaxies are underluminous in thermal emission or over-luminous
in non-thermal radio emission (see
\citeNP{FalckeGopal-KrishnaBiermann1995} for further
discussion). In any case, even those galaxies probably do not deviate
by many orders of magnitude from the general trend. The spread induced
by AGN being either radio-loud or radio-quiet and by relativistic
boosting is much larger. 

This kind of plot certainly has its limitations if it comes to
individual sources, however, it helps to obtain a broad\footnote{The
term ``global perspective'' I would have liked to use in this context
seems unfitting given the ``universal'' scale of the problem discussed
here.}  perspective and to place sources and source classes in a
proper context and relation.

For example, the plot published in \citeN{FalckeBiermann1996} was a
direct prediction of where radio cores at even lower-luminosities,
i.e.~in LLAGN, are expected if the basic theme of the jet-disk
symbiosis holds. These cores are now being discussed in the subsequent
sections.


\section[Radio Cores in LLAGN: Free Jets]{Radio Cores in LLAGN: Free Jet with Pressure Gradient}
\citeme{Falcke1996a}
Radio cores in quasars are quite well-studied and therefore one can
tolerate a number of free parameters in the jet model which are
constrained by additional observations. One of these parameter is the
jet speed which is generally believed to be in the range $\gamma_{\rm
jet}\sim5-10$ based on the observation of superluminal motion
(e.g., \citeNP{Zensus1997}). In LLAGN the situation is different and we
have no direct evidence whether they are highly-, moderately-, or
sub-relativistic. It is therefore useful to find a self-consistent
description of the velocity field in these radio cores mainly based on
first-principles. One possibly important inconsistency of the basic
jet model outlined above, which is based on
\cite{BlandfordKonigl1979}, is that it ignores the effects of any
pressure gradients along the jet. In the following we show that a
self-consistent treatment of the \citeN{BlandfordKonigl1979} model
implies a weak acceleration of the bulk jet flow due to its
longitudinal pressure gradient. This cannot only naturally explain why
the radio spectra of some LLAGN radio cores are slightly inverted
(e.g., Sgr A* \& M81; see
\citeNP{DuschlLesch1994,ReuterLesch1996,FalckeGossMatsuo1998}) rather
than just flat, it also provides one with a natural velocity field for
the jet, taking away $\gamma_{\rm jet}$ as a free parameter.

\subsection{Longitudinal Velocity Profile}
As in \citeN{FalckeBiermann1995}, we shall describe the jet core
within the framework of relativistic gas dynamics of a relativistic
gas with adiabatic index $\Gamma=4/3$. We consider only the supersonic
regime and impose as boundary condition, that the jet expands freely
with its initial sound speed $\beta_{\rm s}$ without any lateral
gradients behind the jet nozzle. This leads to the familiar conical
jet with $B^2/4\pi\propto z^{-2}$ \cite{BlandfordKonigl1979}, where
adiabatic losses due to lateral expansion need not be considered. For
a confined jet scenario at larger scales the adiabatic losses could,
however, be quite severe with energy densities scaling as
$z^{-2\Gamma}$ during phases of adiabatic expansion unless
reconfinement is important \cite{Sanders1983}.


Nonetheless, even in a simple, free jet at least some work due to
expansion will be done, because there is always a longitudinal
pressure gradient, which will 
%%
accelerate the jet along its axis. This acceleration 
%%
is described by the
z-component of the modified, relativistic Euler equation
(e.g., \citeNP{Pomraning1973}, Eq.~9.171) in cylindrical coordinates where we
set $\partial/\partial r=0$ and $\partial/\partial \theta=0$
\begin{equation}\label{euler1}
\gb {\partial\over\partial z}\left(\gb{\omega\over n}\right)=-{\partial\over\partial z}P.
\end{equation}
Here, $\omega=m_{\rm p}nc^2+U_{\rm j}+P_{\rm j}$ is the enthalpy
density of the jet, $U_{\rm j}$ is the internal energy density, $n$ is
the particle density, and $P_{\rm j}=(\Gamma-1)U_{\rm j}$ is the
pressure in the jet (all in the local rest frame). For `maximal
jets' -- the radiatively most efficient type of jet \cite{FalckeBiermann1995} -- to be
discussed here, we demand the equivalence of internal energy and
kinetic (or better rest mass) energy $U_{\rm j}\simeq m_{\rm p}nc^2$,
hence $\omega=(1+\Gamma)U_{\rm j}$ and ${\omega/n}=(1+\Gamma)m_{\rm p}
c^2=$ const at the sonic point $z=z_{0}$.  In a free jet with conical
shape the energy density evolves as $U_{\rm j}\propto
\left(\gb\right)^{-\Gamma}z^{-2}$ and we do not consider any loss
mechanisms other than adiabatic losses due to the longitudinal
expansion. Using the relations mentioned above, 
%%
the Euler equation becomes
%%

\begin{equation}\label{euler2}\label{v}
{\partial\gb\over\partial z}
\left({\left({\Gamma+\xi\over\Gamma-1}\right)(\gb)^2-\Gamma\over\gb}\right)={2\over z}
\end{equation}
with $\xi=\left(\gb/(\Gamma(\Gamma-1)/(\Gamma+1))\right)^{1-\Gamma}$.
For $\xi\sim1$ this is analogous to the well known Euler equation for
an isothermal, pressure driven wind, with the wind speed replaced by
the proper jet speed. The sound speed is fixed by the required
equivalence between internal and rest mass energy density at a value
$\beta_{\rm s}=\sqrt{(\Gamma-1)/(\Gamma+1)}\sim0.4$.

The asymptotic solution of Eq.~\ref{euler2} for $\xi=$const and
$z\rightarrow\infty$ is $\gb \propto 2\sqrt{\ln z}$. If we ignore
terms of the order $\ln \gb$ we could approximate the solution by $\gb
\simeq \sqrt{{\Gamma-1\over\Gamma+1}\left(\Gamma+4\ln
\left(z/z_{0}\right)\right)}$. For the following calculations we will,
however, use the exact, numerical solution to Eq.~\ref{euler2}
($\xi\neq$const), but the deviation from the approximate, asymptotic
solution is rather small.

\subsection{Plasma Properties}
The basic ideas how to derive the synchrotron emissivity and the basic
properties of a jet in a coupled jet-disk system have been described
extensively in \cite{FalckeBiermann1995}. The power 
%%
$Q_{\rm j}=q_{\rm j}\dot M_{\rm disk} c^2 = q_{\rm j/l} L_{\rm disk}$ 
%%
of {\em one} jet cone is
a fixed fraction of the disk luminosity, relativistic particles and
magnetic field $B$ are in equipartition within a factor $k_{\rm e+p}$
-- which we hereafter set to one, and the energy fluxes are conserved
along the conical jet (for a moment we will ignore the adiabatic
losses). Mass conservation requires that the mass loss in the jet
$\dot M_{\rm jet}$ is smaller than the mass accretion rate in the disk
$\dot M_{\rm disk}$, thus $q_{\rm m}=\dot M_{\rm jet}/\dot M_{\rm
disk} < 1$, while mass and energy of the jet are coupled by the
relativistic Bernoulli equation for a jet/disk-system
\cite{FalckeMannheimBiermann1993}.
\begin{equation}\label{bernoulli}
\gamma_{\rm j} q_{\rm m}\left(1+\beta_{\rm
s}^2/(\Gamma-1)\right)=q_{\rm j}.
\end{equation}

Here we will make use of the same logic and notation but with three
changes with respect to \citeN{FalckeBiermann1995}, namely (1) applying
the velocity law Eq.~\ref{v}, (2) neglecting the energy contents in
turbulence, and (3) considering only a quasi mono-energetic energy
distribution for the electrons at a Lorentz factor $\gamma_{\rm e}$
(usually $\ga100$). The latter is indicated by the steep submm-to-IR
cut-off found in Sgr A*
\cite{ZylkaMezgerWard-Thompson1995,SerabynCarlstromLay1997,FalckeGossMatsuo1998}
-- and probably also M81* \cite{ReuterLesch1996} -- which is different
from typical Blazar spectra and precludes an initial electron
power-law distribution (see Fig.~\ref{sgrx-pl}).

The semi-opening angle of the jet is $\phi=\arcsin\left(\gamma_{\rm
s}\beta_{\rm s}/\gb\right)$, and the magnetic field in the co-moving
frame of a maximal jet with the given sound speed, $L_{\rm
disk}=L_{41.5}10^{41.5}$ erg/sec, $q_{\rm j/l}=0.5 q_{0.5}$, and
$z_{16}=z/10^{16}$cm becomes (see Eq.~19 in \citeNP{FalckeBiermann1995})
\begin{equation}\label{b}
B=0.6\,{\rm G}\; \sqrt{\beta_{\rm j} L_{41.5} q_{0.5}}z_{16}^{-1}.
\end{equation}

The number of relativistic electrons that are to be in equipartition
with the magnetic field are a fraction $x_{\rm e}=n_{\rm e}/n$ of the
total particle number density, and the energy density ratio between
relativistic protons and electrons is $(\mu_{\rm p/e}-1)$. From the
energy equation $\gamma_{\rm j}\omega\gb c\pi r^2=q_{\rm j/l}L_{\rm
disk}$ we find that the characteristic Lorentz factor and electron
density required to achieve equipartition are
\begin{eqnarray}\label{gamma}
\gamma_{\rm e}&=&m_{\rm }/\left(4\Gamma m_{\rm e}\mu_{\rm p/e}x_{\rm e}\right)=344/\left(\mu_{\rm p/e}x_{\rm e}\right)\\
n_{\rm e}&=&45\,{\rm cm^{-3}}\;\beta_{\rm j} L_{41.5} q_{0.5} x_{\rm
e}z_{16}^{-2}.\label{n}
\end{eqnarray}
Finally, to incorporate adiabatic losses we now have to make the
following transitions with respect to the equations in \citeN{FalckeBiermann1995}
\begin{eqnarray}\label{adloss}
&&\gb\rightarrow\gb(z),\;\;\gamma_{\rm e}\rightarrow\gamma_{\rm e}\cdot(\gb(z)/\gb(z_{\rm 0}))^{1/3}\nonumber\\
&&B\rightarrow B\cdot(\gb(z)/\gb(z_{\rm 0}))^{1/6}.
\end{eqnarray} 

\subsection{Synchrotron Emission}
The local spectrum of the jet will be $F_{\nu}\propto\nu^{1/3}$
between the synchrotron self-absorption frequency $\nu_{\rm ssa}(z)$
and the characteristic frequency $\nu_{\rm c}(z)$ = $3 e \gamma_{\rm
e}^2 \sin\alpha_{\rm e} B(z) / 4 \pi m_{\rm e}c$ (here we will use
an average pitch angle $\alpha_{\rm e}=60^\circ$). For the maximal
jet using Equations \ref{b}, \ref{gamma}, \ref{n} and
\ref{adloss}, we have in the observers frame
\begin{equation}\label{nuc}
\nu_{\rm c}(z)=100\,{\rm GHz}\; {\cal D} {\sqrt{L_{41.5}
q_{0.5}}}/\left(
\sqrt{\beta_{\rm j}}\gamma_{\rm j} x_{\rm e}^2 \mu_{\rm p/e}
z_{16}\right)
\end{equation}
with the Doppler factor ${\cal D}=1/\gamma_{\rm j}\left(1-\beta_{\rm
j} \cos i\right)$ for an inclination $i$ of the jet axis to the line
of sight.

To find the local synchrotron self-absorption frequency $\nu_{\rm
ssa}$ we have to solve the approximate equation $\tau=n_{\rm e}
\sigma_{\rm sync}(\nu) \cdot 2 r_{\rm j}/\sin i=1$ and transform into
the observers frame. The jet radius is $r_{\rm j}\sim \phi z$ and the
synchrotron self-absorption cross section for a mono-energetic
electron distribution is given by $\sigma_{\rm sync}=$
$4.9\cdot10^{-13}\,{\rm cm}^2$ $(B/{\rm G})^{2/3}\gamma_{\rm
e}^{-5/3}(\nu/{\rm GHz})^{-5/3}$, yielding

\begin{equation}\label{nus}
\nu_{\rm ssa}=3.3\,{\rm GHz}\;{\cal D}{{\beta_{\rm
j}^{1/5}L_{41.5}^{4/5}q_{0.5}^{4/5}x_{\rm e}^{8/5}\mu_{\rm p/e}}\over
\gamma_{\rm j}^{3/5} ({\cal D}\sin i)^{3/5} z_{16}}.
\end{equation}

If we now use the velocity profile Eq.~\ref{v} we can invert
Eq.~\ref{nuc} to find the size of the jet as a function of observed
frequency. For the asymptotic regime $z\gg z_{\rm 0}$,  $\nu_{\rm c}$ is
approximated for a fixed inclination angle to within a few per-cent by
a power law in $z$, such that

\begin{eqnarray}\label{size}
z_{\rm c}&=(z_{{\rm c,0}}/\sin i)(\mu_{\rm p/e}x_{\rm e})^{-2\xi} \left(q_{0.5}L_{41.5}\right)^{\xi/2}z_{13.7}^{1-\xi}\nu_{10.3}^{-\xi}
\end{eqnarray}
where the parameters are $z_{13.7}=z_0/3$~AU, $\nu_{10.3}=\nu/22$~GHz,
$\xi=(0.99,0.95,0.9,0.89,0.88)$ and $z_{{\rm
c,0}}=(500,1200,1100,900,700)$ AU for $i=(5^\circ,20^\circ, 40^\circ,
60^\circ, 80^\circ)$.

The total spectrum of the jet is obtained by integrating the
synchrotron emissivity $\epsilon_{\rm sync}$ along the jet:
$F_\nu=(4\pi D^2)^{-1}\int_{z({\nu_{\rm ssa}})}^{z({\nu_{\rm c}})}
\epsilon_{\rm sync}\pi r^2 {\rm d}z$, which can again be 
approximated using power laws:

\begin{eqnarray}\label{flux}
F_{\nu}&=745\,{\rm mJy}(q_{0.5}L_{41.5})^{1.46}\mu_{\rm
p/e}^{.17}x_{\rm e}^{1.17}z_{13.7}^{0.08}\nu_{10.3}^{0.08}\nonumber\\
&-337\,{\rm mJy}(q_{0.5}L_{41.5})^{1.54}\mu_{\rm p/e}^{.92}x_{\rm
e}^{2.1}z_{13.7}^{0.08}\nu_{10.3}^{0.08},\\
F_{\nu}&=247\,{\rm mJy}(q_{0.5}L_{41.5})^{1.42}\mu_{\rm
p/e}^{.33}x_{\rm e}^{1.33}z_{13.7}^{0.16}\nu_{10.3}^{0.16}\nonumber\\
&-143\,{\rm mJy}(q_{0.5}L_{41.5})^{1.48}\mu_{\rm p/e}^{.85}x_{\rm
e}^{1.95}z_{13.7}^{0.15}\nu_{10.3}^{0.15},\\
F_{\nu}&=106\,{\rm mJy}(q_{0.5}L_{41.5})^{1.40}\mu_{\rm
p/e}^{.40}x_{\rm e}^{1.40}z_{13.7}^{0.20}\nu_{10.3}^{0.20}\nonumber\\
&-71\,{\rm mJy}(q_{0.5}L_{41.5})^{1.45}\mu_{\rm p/e}^{.81}x_{\rm
e}^{1.89}z_{13.7}^{0.19}\nu_{10.3}^{0.19},
\end{eqnarray}
for $D=3.25$ Mpc (using as an example the distance of M81 which
contains a 200 mJy radio core), and $i=(20^\circ,40^\circ,60^\circ$)
respectively. This means that the resulting spectrum is no longer flat
but tends to be inverted with $\alpha\sim0.15-0.27$ for
$i=30^\circ-90^\circ$. The spectral index, like the size index, is a
function of the inclination angle of the jet and tends to become
flatter for smaller $i$.


\section{Weeding Out Parameters}
\citeme{FalckeBiermann1999}

Unfortunately, the equations given above are not easy to handle since
the power-law indices are a function of the inclination angle. We
therefore derive here an approximate formula for the spectra and sizes
predicted by such a model.

We note here once more that Eq.~\ref{flux} has two inherent
constraints. First of all, by definition $\mu_{\rm p/e}$ cannot be
smaller than unity since it is defined as the ratio between the energy
densities in protons and electrons plus one. For the sake of
simplicity only, we will now ignore the relativistic proton content
and set $\mu_{\rm p/e}=1$, so that we can substitute the relativistic
electron fraction $x_{\rm e}$ with
\begin{equation}\label{xe}
x_{\rm e }=m_{\rm p}/\left(4\Gamma m_{\rm e}\gamma_{\rm e}\right)=344/\gamma_{\rm e}.
\end{equation}
Secondly, one cannot increase $\gamma_{\rm e}$ indefinitely since at
some point the flux would become negative, i.e.~the jet would become
completely self-absorbed and the simplifications would break
down\footnote{This is avoided when using numerical calculations as
presented in Chap.~\ref{jetmodel}}. 
Moreover, the equations are difficult to handle because of this sum,
since for large changes in $Q_{\rm jet}$ the sum also would become
negative.  Hence, we formally introduce an arbitrary scaling relation
\begin{equation}\label{gammae}
\gamma_{\rm e}=\gamma_{\rm e,0}\left({Q_{\rm jet}\over
10^{39}\mbox{erg/sec}}\right)^{0.09}
\end{equation}
which allows us to simplify the equations further. The physical
meaning is that electrons are pushed to somewhat higher energy with
increasing $Q_{\rm jet}$ to keep them in the optically thin part. A
mechanism which indeed could lead to such an effect is the
`synchrotron boiler' \cite{GhiselliniGuilbertSvensson1988} that
describes the evolution of low-energy electrons in a self-absorbed
system, but it is not clear whether this formally introduced relation
here has any significance in the real world and therefore we will
ignore it in the discussion of our results.

To further simplify the equations we have rounded the exponents
typically to the 2nd digit after the decimal and factorized the
equations. Even for the most strongly varying parameters, like $L_{\rm
disk}$ which can vary over 6 orders of magnitude, the resulting error
will be only some ten percent. Moreover, the exponents in the equations,
which are a function of the inclination angle $i$ of the jet, were
fitted by 2nd and 3rd order polynomials in $i$ to an accuracy of much
better than a few percent over a large range of angles.

All these simplifications lead to the following expressions for the
observed flux density and angular size of a radio core observed at a
frequency $\nu$ as a function of jet power. For a source at a distance
$D$, with black hole mass $M_\bullet$, size of nozzle region $Z_{\rm
nozz}$ (in $R_{\rm g}=G M_\bullet/c^2$), jet power $Q_{\rm jet}$,
inclination angle $i$, and characteristic electron Lorentz factor
$\gamma_{\rm e}$ (see Eq.~\ref{gammae}) the observed flux density
spectrum is given as

\begin{eqnarray}\label{simpleflux}
S_{\nu}&&=10^{2.06\cdot\xi_0}\;{\mbox mJy}\;\left({Q_{\rm jet}\over10^{39} \mbox{erg/sec}}\right)^{1.27\cdot\xi_1}
\nonumber\\&&\cdot
\left({D\over10{\rm kpc}}\right)^{-2}
\left({\nu\over8.5 {\rm GHz}}\right)^{0.20\cdot\xi_2}
\left({M_\bullet\over33 M_\odot}{Z_{\rm nozz}\over10 R_{\rm g}}\right)^{0.20\cdot\xi_2}
\nonumber\\&&\cdot
\left(3.9\cdot\xi_3\left(\gamma_{\rm e,0}\over200\right)^{-1.4\cdot\xi_4}
-2.9\cdot\xi_5\left(\gamma_{\rm e,0}\over200\right)^{-1.89\cdot\xi_6}\right),
\end{eqnarray}
with the correction factors $\xi_{0-6}$ depending on the
inclination angle $i$ (in radians):

\begin{eqnarray}
\xi_0&=&2.38 - 1.90\,i + 0.520\,{i^2}\\
\xi_1&=&1.12 - 0.19\,i + 0.067\,{i^2} \\
\xi_2&=&-0.155 + 1.79\,i - 0.634\,{i^2} \\
\xi_3&=&0.33 + 0.60\,i + 0.045\,{i^2} \\
\xi_4&=&0.68 + 0.50\,i - 0.177\,{i^2} \\
\xi_5&=&0.09 + 0.80\,i + 0.103\,{i^2}\\
\xi_6&=&1.19 - 0.29\,i + 0.101\,{i^2}.
\end{eqnarray}
Likewise, the characteristic angular size scale of the emission region
is given by

\begin{eqnarray}\label{simplesize}
\Phi_{\rm jet}&=&1.36\cdot\chi_0\,\mbox{mas}\,\sin{i}
\nonumber\\&\cdot&
\left(\gamma_{\rm e,0}\over200\right)^{1.77\cdot\chi_1}
\left({D\over10{\rm kpc}}\right)^{-1}
\left({\nu\over8.5 {\rm GHz}}\right)^{-0.89\cdot\chi_1}
\nonumber\\&\cdot&
\left({Q_{\rm jet}\over10^{39} \mbox{erg/sec}}\right)^{0.60\cdot\chi_1}
\left({M_\bullet\over33 M_\odot}{Z_{\rm nozz}\over10 R_{\rm g}}\right)^{0.11\cdot\chi_2},
\end{eqnarray}
with the correction factors

\begin{eqnarray}
\chi_0&=& 4.01 - 5.65\,i + 3.40\,{i^2} - 0.76\,{i^3}\\
\chi_1&=& 1.16 - 0.34\,i + 0.24\,{i^2} - 0.059\,{i^3}\\
\chi_2&=& -0.238 + 2.63\,i - 1.85\,{i^2} + 0.459\,{i^3},
\end{eqnarray}
where again the inclination angle $i$ is in radians. We point out that
in this model the characteristic size scale of the core region is
actually equivalent to the offset of the radio core from the
black hole. This does not exclude the existence of emission in
components further down the jet, which might be caused by shocks or
other processes.


\begin{figure}[t]
\centerline{\mbox{\psfig{figure=Figures/8090f1a.ps,width=8.2cm,bbllx=3.25cm,bburx=13.5cm,bblly=20.2cm,bbury=27cm}\hfill\psfig{figure=Figures/8090f1b.ps,width=8.2cm,bbllx=3.25cm,bburx=13.5cm,bblly=20.2cm,bbury=27cm}}}
\caption[]{Correction factors $\xi$ and $\chi$ for the exponents and
factors in Eqs.~\ref{simpleflux} \& \ref{simplesize} as a function of
inclination angle $i$ in radians, where $i=0$ corresponds to face-on
orientation. Note, however, that for $i\la10^\circ$ most
approximations fail.}
\end{figure}

The equations are now scaled to the typical values for Galactic jet
sources like GRS1915+105 and the correction factors are normalized to
an inclination angle of 1 rad ($\sim57^\circ$). We note that the
approximations fail at small inclination angles where the accretion
disk is seen face on and the jet points towards the observer
(i.e.~$i\la10^{\circ}$). The benefits of these equations now are that
they can be used to quickly compare observed radio core properties
with the model predictions, especially since we have reduced the
number of free parameters to the absolute minimum.

\section{Application to Individual Sources}
\citeme{FalckeBiermann1999}
Application of these simplified equations to real radio cores is
straight forward, the basic input parameters being the jet power, the
characteristic electron energy, the inclination to the line of sight,
the observed frequency, the distance, the black hole mass, and the
relative size of the nozzle region. The latter two enter only weakly
and hence need to be known only to an order of magnitude.

A few systems are so well studied that most of these parameters
(especially $i$, $D$, \& $M_\bullet$) can be fixed with some
confidence and where size and flux of their cores at a certain
frequency are well known through VLBI observations. Even though this
may be a subjective criterion, one can argue that the radio cores in
M81, NGC~4258, and GRS~1915+105 are, for various reasons, perhaps the
best studied and best constrained examples of low-power radio
cores. Following the convention in \citeN{Falcke1996a} and
\cite{Melia1992b} and in analogy to Sgr A*, we will identify the
radio cores in these sources by adding an asterisks to their host
galaxy or source name to clearly distinguish them from their hosts.

We have listed the sources and their parameters in
Table~\ref{famoustab}. The observed quantities we have used as input
parameters for the model are given in Columns 2-7. Since in all cases,
we have only two unknowns left (jet power and characteristic electron
energy) to describe the two observed quantities of the radio cores
(flux and size) we were able to solve the model equations for each
source completely and determine $Q_{\rm jet}$ and $\gamma_{\rm e}$
directly from the observations. These results and the predicted
spectral indices for the radio spectrum are given in the three
right-most columns of Table~\ref{famoustab}. For comparison with the
jet power, we also listed the accretion disk luminosity of each system
in Column 8. In the following we will briefly discuss the data and the
modeling of each source. A detailed discussion within this model of
the famous radio core Sgr A* in the Galactic Center is given in
Chapter~\ref{SgrA*}.

\subsection{NGC~4258}
The VLBI observations of megamaser emission has led to the detection
of a mo\-lecular disk in NGC~4258 \cite{MiyoshiMoranHerrnstein1995}
which can be used to determine the inclination angle $i=82^{\circ}$ of
the system, the black hole mass $M_\bullet=3.5\cdot10^7M_\odot$, and
the distance $D=7.3\pm0.3$ Mpc \cite{HerrnsteinMoranGreenhill1997,HerrnsteinMoranGreenhill1999} almost
directly from the observations. The variable central VLA radio core
\cite{TurnerHo1994}, here called NGC~4258*, has a flux of roughly 3
mJy and was interpreted by \citeN{LasotaAbramowiczChen1996} as
emission from an advection dominated accretion flow while
\citeN{Falcke1997b} suggested a scaled down AGN jet origin. The latter
picture was confirmed by
\citeN{HerrnsteinMoranGreenhill1997} and \citeN{HerrnsteinGreenhillMoran1998} who discovered a nuclear jet in NGC~4258 offset by
0.35 to 0.46 milli-arcsecond from the dynamical center (see
Fig.~\ref{NGC4258}). \citeN{HerrnsteinMoranGreenhill1997}
suggested that this offset could be interpreted within the framework
of the
\citeN{BlandfordKonigl1979} model as being due to self-absorption
in the inner jet cone. The search for radio emission directly at the
dynamical center remained unsuccessful
\cite{HerrnsteinGreenhillMoran1998} and
required a revision of the \citeN{LasotaAbramowiczChen1996} ADAF
model \cite{GammieNarayanBlandford1999}.

\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/n4258diska.plume.ps,width=0.9\textwidth,bbllx=5cm,bblly=2.2cm,bburx=14cm,bbury=25.2cm,angle=90,clip=}
}
\caption[]{\label{NGC4258}
VLBI results for the LLAGN NGC4258 (from Herrnstein et al.~1998). The
compact radio core is resolved by continuum VLBI into a jet-like
structure, slightly offset from the center. The red and blue points
mark the position of the red- and blue-shifted H$_2$O megamaser lines
in the molecular disk. Their velocity and position are modeled by a
warped disk shown as a mesh.}
\end{figure}
\nocite{HerrnsteinGreenhillMoran1998}


For our purposes NGC~4258* is an ideal system because all crucial
parameters, especially the inclination angle, seem to be fixed.  Using
an average radio flux of 3 mJy at 22 GHz and the offset of the core
from the dynamical center as the characteristic size scale of the
system we find a jet power of $10^{41.7}$ for the nuclear jet, a
characteristic electron Lorentz factor of $\sim630$, and predict an
average spectral index $\alpha=0.22$ ($S_\nu\propto\nu^\alpha$). The
jet-power of the nuclear jet is consistent with the large scale
emission-line jet in NGC~4258, since its kinetic power is also of the
order $10^{42}$ erg/sec  {}--{}  as derived from the mass ($2\cdot10^6
M_\odot$) and velocity ($\sim2000$ km/sec) of the emission-line gas
(Cecil et al.~1995). Moreover, this is also in line with the estimated
nuclear accretion disk luminosity of $\sim10^{42}$ erg/sec
(\citeNP{StueweSchulzHuehnermann1992,WilkesSchmidtSmith1995}; see also
discussions in \citeNP{HerrnsteinMoranGreenhill1997} and 
\citeNP{GammieNarayanBlandford1999}). Hence, all the activity in
NGC~4258 can be described in a consistent way by a low-luminosity
jet/disk-system and an accretion rate of the order $10^{-4}
M_{\sun}/$yr. One caveat exists, however, because the interpretation
of the offset of the core from the dynamical center as the
characteristic scale of the model (and not the self-absorption size
which is smaller) actually implies that also the core
size is of similar order. If it were smaller, e.g., 0.1
milli-arcsecond, this would reduce the relatively high value for
$\gamma_{\rm e}$ to around 200 without significantly reducing the
required jet power.  A difference between offset and actual core size
would occur if the jet were collimated more in the inner region than
assumed in our model (i.e.~were narrower than the Mach cone).


\subsection{GRS~1915+105}
\citeN{MirabelRodriguez1994} discovered a compact radio jet in the
Galactic X-ray source GRS~1915+105 with apparent superluminal motions,
for which they were able to determine the jet speed ($0.92c$) and the
inclination angle ($\sim70^\circ$) of the system. Moreover, in recent
papers
\cite{FenderPooleyBrocksopp1997,PooleyFender1997,MirabelDhawanChaty1998,EikenberryMatthewsMorgan1998}
an intriguing correlation between radio outbursts and X-ray flares was
found and hence a symbiotic jet/disk-system as proposed earlier
\cite{FalckeBiermann1996} seems to be a good description for
GRS~1915+105.  The parameters $L_{\rm disk}\sim10^{39}$ erg/sec and
$M_{\bullet}\sim33 M_{\sun}$ are discussed in the literature (e.g.,
\citeNP{MirabelBandyopadhyayCharles1997,MorganRemillardGreiner1997}) for
this source, but we point out that the mass determination is extremely
uncertain, yet is also not really critical for the modeling.

\citeN{DhawanMirabelRodriguez1998} observed the central radio core in a relatively
quiescent phase finding an intrinsic source size of $\sim2$
milli-arcsecond (major axis) at 15 GHz and fluxes around 40 mJy (flat
spectrum). For these parameters the jet model gives a jet power of
$10^{39.1}$ erg/sec and a $\gamma_{\rm e}$ of $\sim400$. In addition,
the predicted scaling of the core size ($\propto\nu^{-0.9}$) is
consistent with the observed one (roughly $\propto\nu^{-1}$, taking
out the scatter broadening).  The observed time delay of $\sim4$ min
between outburst peaks at 3.5 and and 2cm \cite{PooleyFender1997} can
be explained as the delay it takes for each outburst to reach the
optically thin regime ($\tau\simeq1$) at the angular distance
$\Phi_{\rm s}$ where the outburst first becomes visible. For the
parameters given here and in Table~\ref{famoustab} we
get\footnote{This is smaller than $\Phi$ where the spectrum should
peak. In the light curve the actual peak of an outburst could appear
somewhere between those scales if the duration of the outburst were
smaller than the travel time between $\Phi_{\rm s}$ and $\Phi$.}
$\Phi_{\rm s}=0.035$ milli-arcsecond and the time delay between 2 and
3.5 cm is predicted by the model to be of order 3 mins. The velocity
of the jet in the model grows asymptotically as determined by
Eq.~\ref{euler2}, yielding $\beta=$0.92 at $10^4 R_{\rm g}$ and
$\beta=0.96$ at the scale of a few milli-arcseconds, where the radio
emission is coming from. Considering that Eq.~\ref{euler2} is a no-fit
asymptotical description of the velocity field in the jet this is a
reasonably good prediction.  Apparently, the pressure gradient effect
must be at work at least to some degree here. However, it has to be
pointed out that recently \citeN{FenderGarringtonMcKay1999} claim that
the velocity is not as well constrained as initially thought. On the
other hand \citeN{MirabelRodriguez1994} found tentatively that {}--{}
in addition to their advance speed {}--{} the blobs may also expand
with $0.2c$ at larger scales, thus perhaps finding direct evidence for
a relativistic ``sound speed'' which is needed for the pressure
gradient effect to be important.  All in all the model seems to give a
remarkable good description of GRS~1915+105 as well.


\subsection{M81*}
For the nearby galaxy and LLAGN \cite{HoFilippenkoSargent1996} M81*
\citeN{BietenholzBartelRupen1996} and
\citeN{BietenholzBartelRupen1999}
presented some new measurements confirming that indeed it has a
core-jet structure as predicted in \citeN{Falcke1996a}. The
average flux and size of M81* at 8.5 GHz was $\sim120$ mJy and
$\sim0.5$ milli-arcsecond. \citeN{Falcke1996a} concluded that a range of inclinations
between $30-40^\circ$ fitted the radio observations best and this was
confirmed by the detection of a nuclear emission-line disk in M81 with
similar inclination \cite{DevereuxFordJacoby1997}. The jet power derived from
our model of M81* with these parameters is $10^{41.8}$ erg/sec and
$\gamma_{\rm e}=250$.  For comparison, \cite{HoFilippenkoSargent1996} give a
bolometric nuclear luminosity for M81 of $10^{41.5}$ erg/sec.

\setlength{\tabcolsep}{3pt}
%\begin{table*}
%\begin{center}
%\tiny
\begin{deluxetable}{lcccccccccc}
\scriptsize\tablecolumns{11}\tablewidth{0pt}
\tablecaption{PARAMETERS OF WELL-STUDIED JET-DISK SOURCES}
\tablehead{
\colhead{Source }&
\colhead{ $D$ }&
\colhead{ $i$ }&
\colhead{$\nu_{\rm obs}$ }&
\colhead{ $S_\nu$ }&
\colhead{ size }&
\colhead{ $M_\bullet$
}&
\colhead{$L_{\rm disk}$ }&
\colhead{ $Q_{\rm jet}$ }&
\colhead{ $\lg \gamma_{\rm e}$ }&
\colhead{ $\alpha$}\\
\colhead{       }&
\colhead{     }&
\colhead{  }&
\colhead{[GHz]              }&
\colhead{ [mJy]   }&
\colhead{ [mas]}&
\colhead{ [$M_\odot$]}&
\colhead{ [erg/sec]      }&
\colhead{ [erg/sec]     }&
\colhead{}&
\colhead{}
}
\startdata
GRS~1915+105*&12 kpc& 70$^\circ$& 15 & 40& 2 & (33) & $10^{39}$ &
$10^{39.1}$ & 2.6 & 0.21\\
NGC~4258*&7.3 Mpc& 82$^\circ$& 22 & 3 & 0.35& $3.5\cdot10^7$& $(10^{42})$ & $10^{41.7}$ & 2.8 &0.22\\
M81*     &3.25 Mpc& 35$^\circ$& 8.5& 100 & 0.5& $(10^6)$ & $10^{41.5}$
& $10^{41.8}$ & 2.4 & 0.14\\
\tablenotetext{}{\label{famoustab}Parameters for compact radio cores in various
sources. Columns 2-7 are observationally determined input parameters:
distance $D$, inclination angle $i$ of disk axis and jet to the line
of sight, observing frequency $\nu_{\rm obs}$, flux density of radio
core $S_\nu$, size of radio core, and black hole mass $M_\bullet$. The
inferred disk luminosity $L_{\rm disk}$ is not an input parameter here
and given in column 8 for comparison only. Uncertain values are given
in brackets, but since the black hole masses do not enter strongly the
uncertainties in the black hole mass for M81 and GRS~1915 are actually
irrelevant. Columns~9-11 are output parameters of the radio core
model: jet power $Q_{\rm jet}$, characteristic electron Lorentz factor
$\gamma_{\rm e}$, and average spectral index $\alpha$
($S_\nu\propto\nu^\alpha$) in the radio.}
\enddata
\end{deluxetable}


\section{Implications}
\citeme{Falcke1996a}
\subsection{Model Fitting}
The results of the model fitting in the previous section has a number
of interesting consequences and caveats. The fact that all radio cores
can be fitted with one simple model is already important, since the
sources discussed here are so well constrained that by far not all
combinations of size and flux could be fitted by the model. What is,
however, more striking is the fact that the parameters required to
explain sizes and fluxes are very similar. Firstly, in all sources the
typical Lorentz factor of the electrons is of the order of a few
hundred. Given the extreme simplicity of the model and the extensive
use of equipartition assumptions (departing from which would be
reflected in a change of $\gamma_{\rm e}$ as well) this similarity
points to a relatively similar internal structure of the radio cores.
Secondly, all sources have jet-powers very close to or larger than the
luminosity of their thermal radiation, i.e.~the suspected accretion
disk luminosity. Since the model was constructed such that the
radiative efficiency is maximal, applying more realistic models {}--{} for
example by including protons or using different equipartition factors,
velocity fields, or electron distributions {}--{} will therefore in almost
all cases only lead to an increased demand for jet power in these
sources.


The model fits perhaps most convincingly the jet in GRS~1915+105,
where it not only reproduces core size and flux very well, but
apparently also predicts radio time delay and jet velocity reasonably
well. The latter indicates that perhaps the pressure gradient in the
jet of GRS~1915+105 is mainly responsible for reaching its
asymptotical velocity {}--{} unless higher velocities are found in future
observations.


\subsection{Limitations}
We note that for determining $Q_{\rm jet}$ from the jet model, the
flux and to some degree the inclination angle (especially for small
$i$) are most important, while $\gamma_{\rm e}$ is mainly determined
by the size of the core. Consequently, the latter seems to be the most
uncertain part since it is often ambiguous how to define the core and
its characteristic size, especially when the resolution is of the
order of the core size. Moreover, we have introduced $\gamma_{\rm e}$
mainly to easily reflect the possibility of a low-energy cut-off or
break in the spectrum. This has the positive effect that cores can be
larger than their size purely given by the $\tau=1$ surface (which is
particularly useful in GRS~1915+105 and NGC~4258), however, it also
means that the core size may depend sensitively on the evolution of
the electron distribution which we have ignored almost
completely. Hence, the predictive power of this model for radio core
sizes is very limited and only good to an order of magnitude, so that
we will not base our interpretation heavily on the sizes. It should
also be noted that the jet model used here has been trimmed towards
LLAGN to achieve the greatest possible degree of simplification with
the assumption that their velocity field can be described by
Eq.~\ref{euler2}. We know that this does not apply to quasars where
the bulk Lorentz factor of the jets seems to be larger and the fully
parameterized equations (e.g., as in \citeNP{FalckeBiermann1995}) have
to be used.

However, taking all this into consideration we can give yet a more
simplified formula where we have fixed $\gamma_{\rm e}$ at an
intermediate value of 300 and which can be used to very roughly
estimate the jet power of a LLAGN from its flux and
presumed inclination angle alone:

\begin{equation}\label{jetpower}
Q_{\rm jet}=10^{37.6}\,\mbox{erg/sec}\;
{\frac{{{0.024}^
       {{\frac{{{\xi }_0}}{{{\xi }_1}}}}}\,
     {{1.56}^
       {{\frac{{{\xi }_4}}{{{\xi }_1}}}}}}{0.024\cdot1.56}}
{\frac{\,
     {{{\left({D\over10{\rm kpc}}\right)}}^
       {{\frac{1.6}{{{\xi }_1}}}}}\,
     {{{\left({S_\nu\over{\rm mJy}}\right)}}^
       {{\frac{0.79}{{{\xi }_1}}}}}}{
     {{{\left({M_\bullet\over33 M_\odot}\right)}}^
       {{\frac{0.15\,{{\xi }_2}}
          {{{\xi }_1}}}}}\,
     {{{\left({\nu\over8.5 {\rm GHz}}\right)}}^
       {{\frac{0.15\,{{\xi }_2}}
          {{{\xi }_1}}}}}\,
     {{{{\xi }_3}}^
       {{\frac{0.79}{{{\xi }_1}}}}}}}
\end{equation}

\subsection{Jet-Disk Symbiosis}
The main result of this work, however, is that in three very different
sources, with very different sizes and fluxes, we can explain the
central core with a single model by just scaling the jet power with
the accretion rate. This works because the three selected sources,
GRS~1915+105, NGC~4258, and M81*, all have some very important
ingredients in common. All three have clear evidence for a massive
black hole, signs of (large or small scale) accretion disks, jet
structures in their radio cores, and a good determination of the
inclination angle (important for the fitting of individual
sources). In GRS~1915+105 there is even direct evidence for a coupling
between jet and disk from the X-ray and radio light curves
\cite{EikenberryMatthewsMorgan1998}. The high jet power we derive for
the radio core in a relatively quiescent phase is quite consistent
with but lower than the power derived for the major outbursts (e.g.,
\citeNP{MirabelDhawanChaty1998}).

In hindsight this high power in the radio cores justifies the
assumptions we have made earlier that jet and disk can be
considered symbiotic systems and that {}--{} at least in a few
systems {}--{} the assumption of $Q_{\rm jet}/L_{\rm disk}\sim1$ (or even
larger) seems appropriate. This also strengthens the picture that the
jets are produced in the inner region of an accretion disk, where a
major fraction of the dissipated energy is channeled into the jet
\cite{FalckeBiermann1995,DoneaBiermann1996}. As a consequence,
modeling of accretion disks and X-ray light curves in jet systems
like GRS~1915+105 clearly requires taking the jet into account.



\subsection{Accretion Disks and ADAFs}
Another consequence from those radio cores is their amazing scale
invariance.  It seems that we can use the very same model for a
stellar mass black hole which is accreting near its Eddington limit
(GRS~1915+105) as well as for a supermassive black hole which is
presumably accreting at an extreme sub-Eddington rate (M81,
NGC~4258). Moreover, a very similar model was successfully applied to a
quasar sample earlier \cite{FalckeMalkanBiermann1995},
i.e.~supermassive black holes near the Eddington limit. That would
suggest that certain properties of an accretion disk/flow, namely jet
production, is very insensitive towards changes in accretion rate or
black hole mass, and that the 'common engine' mechanism of black hole
accretion and jet formation, suggested by
\citeN{RawlingsSaunders1991}, may include a much larger range of
AGN than only quasars and radio galaxies.

If this is so, it has to be asked whether indeed every accretion flow
necessarily has to make a transition from a thin $\alpha$-disk to an
ADAF when turning sub-Eddington \cite{Meyer-HofmeisterMeyer2000}. In
order to maintain this proposition one then needs to explain how the
accretion disk structure can change so drastically without affecting
its innermost region, where jets presumably are being produced. If one
asks what the arguments for ADAFs in low-power AGN really are, the
observational evidence remains thin. For NGC~4258 it is quite obvious
now that the radio core cannot serve to support an ADAF emission
model. Quite contrary the derived jet power is consistent with a low
accretion rate, which in turn is consistent with the low luminosity of
the nucleus and, of course, a thin disk is directly seen at least at
larger radii. With the radio emission gone the ADAF spectral energy
distribution, extending over many orders of magnitude, merely serves
to explain a single X-ray data point. Hence, it is currently not
obvious that an ADAF is really needed to explain this source at all.

The same seems to be true for M81, which is equally sub-Eddington as
NGC~4258. Here the situation is even worse, since
\citeN{IshisakiMakishimaIyomoto1996} also claim the
detection of a broad iron Fe-K line suggesting that probably the inner
disk cannot be as hot as required in an ADAF model. As similar broad
line has been tentatively claimed also for NGC~4258 by
\citeN{CannizzoGreenhillHerrnstein1998}. In any case the two
galaxies serve as a general warning to view the existence of a compact
radio core in low-luminosity AGN as prima facie evidence for an
ADAF {}--{} a jet origin may be a more natural explanation here and in
other cases. 

Of course, one could ask whether indeed the interpretation of $L_{\rm
disk}$ as emission from an accretion disk is correct in in each and
every case. \citeN{MannheimSchulteRachen1995}, for example, argue that
some of the ionizing emission can be produced in the base of the
jet. Moreover, already \citeN{Heckman1980} pointed to the possibility
of producing some of the optical line emission, used here to gauge the
accretion disk luminosity, by shock excitation. The latter could then
also be related to the jet who might be driving these shocks into the
ISM. So, while the radio core emission in the cases discussed here is
most likely not produced by an ADAF, the latter are not entirely
excluded either (see also discussion in Chap.~\ref{llagn}).

A much more detailed discussion of the properties of a specific
compact radio core, Sgr A*, where the jet-versus-ADAF discussion also
plays an important role, is presented in the next chapter.


\chapter{The Galactic Center -- Sgr A*}\label{SgrA*}

Sgr A* is the unique 1 Jy flat spectrum radio point source located at
the center of the Galaxy. Within the Sgr A complex (see
\citeNP{MezgerDuschlZylka1996} for a review) it is surrounded by a
thermal radio source Sgr A West and embedded in the non-thermal
``hypernova'' shell Sgr A East.  The presence of this compact source
was first predicted by
\citeN{Lynden-BellRees1971} and later indeed found with radio
interferometry
\cite{BalickBrown1974}. Due to its unusual appearance it has long been
speculated that this source is powered by a supermassive black
hole. Its mass was believed to be around
$M_\bullet\sim2\cdot10^6M_{\odot}$ (e.g., Genzel \& Townes 1987). In
recent years high-resolution imaging \cite{EckartGenzelHofmann1993}
and spectroscopy \cite{HallerRiekeRieke1996} in the near-infrared
(NIR) have made this case much stronger and the detection of proper
motions of stars around the Galactic Center has solidified this case
even further \cite{EckartGenzel1996,GhezKleinMorris1998} yielding an
enclosed mass of $2.6\cdot10^6 M_{\rm sun}$. The latest development in
this direction is that first signs of acceleration in the star's
motion have been found and that the determination of entire orbits
will be possible soon \cite{GhezMorrisBecklin2000}.  This will make
the mass determination yet more precise.  Moreover, since the relative
position of the radio source Sgr~A* in the NIR frame has now been well
determined
\cite{MentenReidEckart1997} one can also now state that Sgr A* is in
the dynamical center of the central star cluster of the Galaxy within
$0\farcs1$
\cite{GhezKleinMorris1998}. The constraints from the first
accelerations found in the stellar proper motions mentioned above seem
to have pushed this limit even further, indicating that the center of
mass is within 10 milli-acrsecond of Sgr A*. Corroborating evidence
that this radio source is associated with the large amount of dark
matter comes from the fact that, in great contrast to the surrounding
stars, Sgr A* does not show any random proper motion down to a limit
of 20 km/sec
\cite{ReidReadheadVermeulen1999,BackerSramek1999a}, while it does show
the apparent proper motion on the sky expected from the sun's rotation
around the Galactic Center. The lower limit placed on the mass of Sgr
A* from these observations is around 1000 $M_{\rm sun}$ {}--{} much larger
than any stellar object or remnant we know of in the Galaxy.

The enormous increase in observational data obtained for Sgr A* in
recent years has enabled us to develop, compare, and constrain a
variety of models for the emission characteristics of this source.
Because of its relative proximity and further observational input to
come Sgr A* may therefore become one of the best laboratories for
studying supermassive black hole candidates and basic AGN
physics. Hence it is worth to dedicate a separate chapter to this
radio source and briefly summarize what its radio properties are and
how we can model its emission.

\section{The Size of Sgr A*}
A problem in determining the size of Sgr A* is that its true structure
is washed out by scattering in the interstellar medium
\cite{DaviesWalshBooth1976,vanLangeveldeFrailCordes1992,Yusef-ZadehCottonWardle1994,LoShenZhao1998}
leading to a $\lambda^2$ dependence of the apparent size of Sgr A* as
a function of observed wavelength.
Nevertheless, the mm-to-submm size of Sgr A* is constrained at least
within one order of magnitude. From the absence of refractive
scintillation
\citeN{GwinnDanenTran1991} have argued that Sgr A* must be larger
than $10^{12}$ cm at $\lambda1.3$ and
$\lambda0.8$mm. \citeN{KrichbaumZensusWitzel1993} obtained a
source size for Sgr A* of $9.5\cdot10^{13}$cm at 43 GHz with VLBI --
well above the expected scattering size as extrapolated from lower
frequencies. This claim was challenged by
\citeN{RogersDoelemanWright1994} who only got $2\cdot 10^{13}$ cm
at 86 GHz consistent with the scattering size. 
\citeN{KrichbaumZensusWitzel1993} also
found an additional weak component and a somewhat elongated source
structure at 43 GHz not seen by
\citeN{BackerZensusKellermann1993}. A possibility to reconcile
the results could be source variability and elongation of the internal
structure which would lead to different sizes if observed with
differently oriented baselines. The problems of interpreting elongated
source structures in Sgr A* with insufficient baseline coverage was
discussed recently by \citeN{DoelemanRogersBacker1999}. The most
recent results are by \citeN{BowerBacker1998} who find a source
size of $6\cdot10^{13}$ cm at 43 GHz ($\lambda7$mm) -- a mere 2 $\sigma$ above the
scattering size, while \citeN{LoShenZhao1998} infer an elongated
source in North-South direction with a size of $5.5\times1.5\cdot
10^{13}$ cm. The latter result is a 4 $\sigma$ deviation from the
scattering size and would either confirm the basic results of
\citeN{KrichbaumZensusWitzel1993} of a jet-like structure 
or suffer the same problems as the earlier observations. Finally,
observations at 86 ($\lambda3$mm) and 215 GHz ($\lambda1.4$mm)
\cite{KrichbaumGrahamWitzel1998} demonstrate that Sgr A* is compact at
a scale at or below $10^{13}$ cm at the highest frequencies, i.e.~17
Schwarzschild radii for a $2.6\cdot10^6M_\odot$ black hole. While the
exact size of Sgr A* cannot yet be stated with absolute certainty, the
latest observations fuel hopes that somewhere in the millimeter wave
regime the intrinsic source size will finally dominate over
interstellar broadening.


\section{The Spectrum of Sgr~A*}\label{bump}
\citeme{Falcke1997b,FalckeGossMatsuo1998}
There also is some confusion in the current literature about the
actual spectrum of Sgr A*. \citeN{DuschlLesch1994} compiled an
average spectrum from the literature and claimed a $\nu^{1/3}$
spectrum indicative of optically thin emission from mono-energetic
electrons.  However, in early simultaneous multi-frequency VLA
observations
\cite{WrightBacker1993} the actual spectrum was bumpy and the
spectral index varied between $\alpha=0.19-0.34$
($S_{\nu}\propto\nu^\alpha$). \citeN{MorrisSerabyn1996} published
a more recent spectrum that was a smooth power law with $\alpha=0.25$
below 100 GHz. Moreover, in 24 simultaneous observations at 2.7 and 8
GHz between 1976 and 1978 the spectral index varied between
$\alpha_{2.7/8}=0.08$ and $\alpha_{2.7/8}=0.55$ with a mean value of
$\alpha_{2.7/8}=0.23\pm0.01$ \cite{BrownLo1982}. This data is
apparently affected (inverted) by a possible low-frequency turnover
of the spectrum around 1 GHz \cite{DaviesWalshBooth1976} which seems
to be variable in frequency with a time scale of several years: in 1976
the average 2.7 to 8 GHz spectral index was $\alpha_{2.7/8}=0.34$ wile
in the consecutive two years it was significantly lower at
$\alpha_{2.7/8}=0.23$.  The simultaneous VLA observations of Sgr A* in
1990/91 by
\citeN{ZhaoGossLo1992} indicate an average spectral index of
$\alpha_{8.4/15}\simeq0.22$ between 8.4 and 15 GHz and
$\alpha_{15/22}\simeq0.15$ between 15 and 22.5 GHz. The spectrum
changes once more if one looks at higher frequencies: the average flux
at 22.5 GHz is 1 Jy \cite{ZhaoGossLo1992} while it was 2.9$\pm0.3$ Jy at
230 GHz in the years 1987-1994 \cite{ZylkaMezgerWard-Thompson1995} yielding
$\alpha_{22/230}=0.45\pm0.5$.

So why do we have to mention all these numbers? Mainly because there
were heated debates in recent years about this spectrum. As Sgr A* may
be an archetype for compact radio cores in other galaxies, extreme
care has to go into the interpretation of its spectrum  {}--{}  most likely
any other radio core will have much less information available, and
any error we make here will propagate into endless space.

Of greatest interest for the future debate is the suggestion of a
sub-millimeter (submm) bump in the spectrum
\cite{ZylkaMezgerLesch1992,ZylkaMezgerWard-Thompson1995}, since in all
models the highest frequencies correspond to the smallest spatial
scales. In the case of Sgr A* one expects the sub-millimeter
emission to come directly from the vicinity of the black hole
\cite{Falcke1996b}.


The existence of this bump was, however, uncertain due to the
variability of Sgr A*. In order to determine the reality of this
crucial feature in the spectrum, we have conducted an experiment to
measure the spectrum of Sgr~A* simultaneously from $\lambda$20cm to
$\lambda$1mm. The Galactic Center (GC) was observed on three
consecutive days on 25-27 October 1996 with four different telescopes
(VLA, BIMA, Nobeyama 45 m, \& IRAM 30 m) on three continents. The
campaign was set up with redundancies in wavelengths and time
coverage. The observations were prepared, performed, and reduced
independently by four different groups and a description of
observations and data reduction is given in
\citeN{FalckeGossMatsuo1998}.

Despite several lost datasets we were able to obtain a spectrum of Sgr
A* which covers the range from 1.36 to 232 GHz (Fig.~\ref{sgrspec})
\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/sgrspec.ps,width=0.75\textwidth}}
\caption[]{\label{sgrspec}Quasi-simultaneous spectrum of Sgr~A* plotted as the
logarithm of the flux density vs.~the logarithm of the
frequency. Shown are the data averaged over the campaign period; flux
densities at neighboring frequencies were also combined from the
different mm-telescopes. Solid lines represent power law fits to the
low- and high-frequency VLA data.}
\end{figure}


\subsection{cm-Spectrum}
The spectrum at lower frequencies between 1.36 and 43 GHz was
successfully measured on two days by the VLA and is described by two
power laws with spectral indices $\alpha=0.17$
($S_\nu\propto\nu^\alpha$) below and $\alpha=0.30$ above 10 GHz, while
there is a marked break between 8.5 and 15 GHz with $\alpha=0.77$
(Fig.~\ref{sgrspec}). We did not find any variability at and below 8.5
GHz between the two days (at the 1\% level for 8.5 GHz). We find an
increase by $\sim$15\% in flux at 15 GHz between 26 \& 27 Oct.~1996,
however, in addition to the statistical errors, we may have a
systematic error of up to $\sim$10\% at frequencies 15 GHz and higher
in the observations on 26 Oct 1996 due to possible improper correction
of different air masses. Thus we cannot claim any significant
intra-day variability of Sgr A* from our data at cm wavelengths.

\subsection{mm-Spectrum}
The errors of the mm-telescopes are much larger than those of the VLA
and comparison of various data-sets indicate that the variability at
$\lambda$3 \& 2mm is not larger than 20\% over a period of three days
during the campaign at all frequencies below 150 GHz (see also
\citeNP{GwinnDanenTran1991}). We therefore first
combined all available data for each telescope to obtain an average
flux density measurement of Sgr~A* over the campaign period. 

Since the individual flux densities from the three mm-telescopes agree
within the errors with each other we then combined the flux density
measurements from the different telescopes at $\lambda$3 \& 2mm and
compared it with the time-averaged VLA flux densities.

First of all, we notice that the $\lambda$3mm flux density is only
slightly above the extrapolation from the VLA observations which is
reassuring concerning the possible systematic uncertainties in the
thermal background subtraction. Hence, the fact that the $\lambda$2mm
flux density  {}--{}  measured by the same telescopes  {}--{}  lies
substantially (0.8Jy, $\sim4\sigma$) above the extrapolation from the
VLA cm data becomes even more significant. If we only consider
$\lambda$7, 3, \& 2mm we find that the spectral index of Sgr A*
increases to $\alpha=0.52$ in the mm-range, while the
$\lambda$3-to-2mm spectral index even becomes $\alpha=0.76$, hence
we conclude that there is a {\em significant mm-excess in the spectrum
of Sgr A~*}. The $\lambda$1.3mm measurement is consistent with such an
excess but, because of the large errors, has no significance for this
discussion.

\section{Implications of the Sgr A* Spectrum}
\citeme{FalckeGossMatsuo1998,Falcke1996b}
A major problem in discussing the spectrum of Sgr A* and the reality
of the mm-excess has been the non-simultaneity of the measurements and
the comparison of array (low frequencies) and single dish (high
frequencies) flux densities. Our simultaneous observations now show a
smooth transition from the VLA to the mm-telescopes and an upturn in
the spectrum of Sgr~A* between $\lambda$3mm and $\lambda$2mm in the
single dish observations alone. The results of all telescopes were
consistent with each other and we conclude that the observed mm-excess
is not due to variability or technical artifacts.

A concern that needs to be addressed in more detailed when studying
the spectrum of Sgr A~* is, however, confusion by other sources. The
diffuse free-free emission in the GC obviously is a major source of
confusion for single dish observations of Sgr A* and subtraction of
this component was taken care of. Optically thick thermal emission,
e.g., from cold dust, on a scale of a few arcseconds and beyond seems
to be negligible in the mm-regime \cite{ZylkaMezgerWard-Thompson1995} and comparison
of single-dish and high-resolution interferometer flux density
measurements (with OVRO) do not indicate the presence of such
components at smaller scales as discussed by
\citeN{SerabynCarlstromScoville1992} and 
\citeN{SerabynCarlstromLay1997}.


Finally, a major contribution of a yet unknown non-variable point
source in the very vicinity of Sgr A* can also be ruled out.  Based on
high resolution VLA images with a resolution of 0\farcs1 at
$\lambda$13 and $\lambda$7 mm, the peak flux density for such a
hypothetical source is below 5 mJy at $\lambda$7mm.  The brightest
regions near Sgr A* are IRS 13 (3\arcsec{} SW to Sgr A*) which
contributes 100 mJy (integrated within a 3\arcsec$\times$3\arcsec{}
area) and IRS 2 (1-2\arcsec{} south to IRS 13) which contributes 85
mJy (within a 2\arcsec$\times$2\arcsec area) {}--{} the spectra of these
sources are consistent with optically thin free-free emission. From
the upper limits at lower frequencies it follows that any source which
might be confused with Sgr~A* would contribute negligibly to the total
flux density of Sgr A* at mm-wavelengths. For a source with optically
thick, thermal emission, for example, the contribution has to be less
than 50 mJy at $\lambda$2mm in order to be below the upper limits at
$\lambda$7mm. We therefore conclude that the mm-excess is indeed an
intrinsic feature of Sgr A*.


The submm-bump causing this excess is, in fact, very well explained
by assuming the presence of a compact, self-absorbed synchrotron
component in Sgr~A*. As outlined in Falcke (1996b; see also
\citeNP{BeckertDuschl1997}) this submm component can be described in
its most simple minded form by four parameters: magnetic field $B$,
electron density $n$, electron Lorentz factor $\gamma_{\rm e}$, and
volume $V=\pi R^2 Z$, using for simplicity a one-temperature
(i.e.~quasi mono-energetic) electron distribution and the distance
being set to 8.5 kpc.  On the other side we have three measurable
input parameters: the peak frequency $\nu_{\rm max}\sim\nu_{\rm
c}/3.5$ of a mono-energetic synchrotron spectrum (characteristic
frequency $\nu_{\rm c}$), the peak flux $S_{\nu_{\rm max}}$, and the
VLBI source size (see above). A fourth parameter can be gained if one
assumes that magnetic field and relativistic electrons are in
equipartition, i.e.~$B^2/8\pi=k^{-1} n_{\rm e} \gamma_{\rm e} m_{\rm e}
c^2$ with $k\sim1$. With this condition we obtain (averaged over pitch
angle) that
 
\begin{equation}
\gamma_{\rm e}=326 \; k^{1/7}\left({F_{\nu_{\max}}\over 3.5 {\rm
Jy}}\right)^{-1/7}  
\left({\nu_{\rm max}\over 10^{12} 
{\rm Hz}}\right)^{3/7} 
\left({R\over 10^{13}{\rm cm}}\right)^{2/7}
\left({Z\over 4\cdot 10^{13}{\rm cm}}\right)^{1/7}
\end{equation}


\begin{equation}
B=10\,{\rm G}\; k^{-2/7}\left({F_{\nu_{\max}}\over 3.5 {\rm
Jy}}\right)^{2/7}  
\left({\nu_{\rm max}\over 10^{12} 
{\rm Hz}}\right)^{1/7}
\left({R\over 10^{13}{\rm cm}}\right)^{-4/7}
\left({Z\over 4\cdot 10^{13}{\rm cm}}\right)^{-2/7}
\end{equation}


\begin{equation}
n_{\rm e}={ 1.4\!\cdot\!10^4\over {\rm cm^{3}}}k^{2/7}\!\left({F_{\nu_{\max}}\over 3.5 {\rm
Jy}}\right)^{5/7}  \!\!
\left({\nu_{\rm max}\over 10^{12} 
{\rm Hz}}\right)^{-1/7}\!\!
\left({R\over  10^{13}{\rm cm}}\right)^{-10/7}\!\!
\left({Z\over 4\!\cdot\! 10^{13}{\rm cm}}\right)^{-5/7}\!\!\!.
\end{equation}

Apparently the `non'-equipartition parameter $k$ enters only weakly
 and as long as one is not very far from equipartition the parameters
 are basically fixed: $\nu_{\max}$ is known within a factor
 three, $S_{\nu_{\max}}$ within $50\%$, and the source size within a
 factor of ten. 

Because of the high compactness of Sgr A* synchrotron self-absorption
becomes another important point to be considered. Using an absorption
coefficient of $\kappa_{\rm sync}=1.4\cdot10^{-9} {\rm cm}^{-1}
(n_{\rm e}/{\rm cm}^{-3}) (B/{\rm G})
\gamma_{\rm e}^{-5} \left(\nu/\nu_{\rm c}\right)^{-5/3}$ 
one finds the synchrotron self-absorption frequency to be
\begin{equation}
\nu_{\rm ssa}={2.5\,{\rm GHz}\over k^{0.09}}\left({F_{\nu_{\max}}\over 3.5 {\rm
Jy}}\right)^{0.69}  
\left({\nu_{\rm max}\over 10^{12} 
{\rm Hz}}\right)^{-.46}
\left({R\over 10^{13}{\rm cm}}\right)^{-.77}
\left({Z\over 4\cdot 10^{13}{\rm cm}}\right)^{-.69}\!.
\end{equation} 


We can now make very solid arguments about the possible source size of
Sgr A* at submm wavelengths. As VLBI measurements are only available
at longer wavelengths one could still postulate arbitrarily large
submm source sizes.  However, if Sgr A*(submm) were optically thin and
larger than $4\cdot10^{13}$ cm we should have seen the low frequency
$\nu^{1/3}$ part of its spectrum with 3mm VLBI already. This could
only be avoided if the submm component becomes optically thick below
$\sim100$ GHz. As shown above this is possible only for a very compact
source where the dimensions of Sgr A* at submm wavelengths are
substantially {\it smaller} than at $\lambda$3mm. Consequently Sgr A*
has to be of the same size or smaller at submm wavelengths than at
$\lambda$3mm.
 
If we now turn the argument around and assume a spherical source structure,
we can calculate the actual size of the submm component to be

\begin{equation}\label{submmsize}\label{sgrsizeeq}
R\sim1.5\cdot10^{12}{\rm cm}\quad
k^{-1/17} \left({S_{\nu_{\max}}\over 3.5 {\rm Jy}}\right)^{8/17}
\left({\nu_{\rm max}\over 10^{12} {\rm Hz}}\right)^{-16/51}
\left({\nu_{\rm ssa}\over 100{\rm GHz}}\right)^{-35/51}.
\end{equation}

This size is consistent with the upper limits ($\sim$1~AU) from VLBI
\cite{RogersDoelemanWright1994,KrichbaumGrahamWitzel1998} 
and lower limits ($\sim10^{12}$cm) from scintillation experiments
\cite{GwinnDanenTran1991}, as discussed above. In comparison we also
note that the Schwarzschild radius ($R_{\rm S}$) of the putative
$2.6\cdot10^6 M_{\sun}$ black hole in the GC is already $R_{\rm
S}=0.77\cdot10^{12}$ cm and thus the compact submm component should
correspond to a region in the very vicinity of the black hole. Most
interesting is the possibility that this region is directly affected
by general relativistic effects, and could for example be
gravitationally amplified if the radiation is intrinsically
anisotropic (e.g., similar to \citeNP{Cunningham1975a}).


Finally, a compact component with the parameters as in
Eq.~\ref{sgrsizeeq} would be very interesting for mm-VLBI, since the
black hole horizon could be imaged against the background of this
submm emission. This will be discussed in greater detail below
(Sec.~\ref{bhimage}).


\section{Radio Variability}
\citeme{Falcke1999a}
An important parameter for constraining the spectrum and nature of Sgr
A* should be its variability. A major observational problem, however,
is the relatively low elevation of Sgr A*, the large confusing
structure of the Sgr A complex, and the scatter-broadening at low
frequencies. The confusion is a major problem especially for
single-baseline interferometers with short baselines like the Green
Bank Interferometer (GBI) that is often used for variability
studies. For this reason the exact nature of the variability of Sgr~A*
has remained inconclusive. Flux density variations are clearly seen
between different epochs, but the time scale of the variability at
various frequencies is not well determined and it is not clear whether
some of the more extreme claims of variability are real or
instrumental artifacts. So far,
\citeN{ZhaoEkersGoss1989} and \citeN{ZhaoGossLo1992} probably have 
presented the largest database of Sgr A* flux-density measurements
with the VLA. They found a number of outbursts at higher
frequencies and tentatively concluded that the small-amplitude
variability at longer wavelengths is caused by scattering effects in
the ISM while the variability at higher frequencies is intrinsic. 

An alternative way to look at flux density variations is to use the
GBI interferometer, which performs daily observations at two different
frequencies. First results of this interferometer have been published
in \citeN{Falcke1999a}. This paper also gives a short description of
observation and data reduction techniques. It is important to note
that all the observations were made at the same hourangle thus
avoiding the problems mentioned before with spurious variability due
to confusing flux. The database used consisted of about 540 days of
continuous monitoring. Here we can now present the results of an
expanded database, including 845 daily observations. The light curves
have been smoothed with a moving average of three days and a secular
increase in flux density of about 50 mJy and 100 mJy during the entire
observing campaign at 2.3 GHz and 8.3 GHz respectively has been
subtracted.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/gbi-lightcurve2a.ps,width=0.48\textwidth}\hfill\psfig{figure=Figures/gbi-lightcurve2b.ps,width=0.48\textwidth}}
\caption[]{\label{gbi-lightcurve}Radio light curves of Sgr A* at 8.3 GHz (left panel) and
2.3 GHz (right panel) measured with the GBI (dots). The solid line is
the interpolated light curve for three-day averages. The straight line 
is a linear fit to the data to take out a long-term secular increase
in the flux density}
\end{figure}


The light curves, before subtraction of the secular increase, are
shown in Figure~\ref{gbi-lightcurve}. One can see a peak-to-peak
variability of 250 mJy and 60 mJy with an RMS (i.e.~modulation index)
of 6\% and 2.5\% at 8.3 \& 2.3 GHz, respectively. The median spectral
index between the two frequencies for the whole period is
$\alpha=0.28$ ($S_\nu\propto\nu^\alpha$), varying between 0.2 and
0.4. These number are basically unchanged with respect to our earlier
results.  Interestingly, there is still a clear trend for the spectral
index to become larger when the flux density in both bands
increases. This is shown in Figure~\ref{gbi-alpha}. The spectral index
vs.~flux correlation and the different modulation indices at the two
frequencies simply imply that outbursts in Sgr A* are more pronounced
at higher and more damped at lower frequencies. The secular increase
in flux density over the entire monitoring period shows a similar
behavior.


\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/gbi-alpha.ps,width=0.48\textwidth}\hfill\psfig{figure=Figures/gbi-color.ps,width=0.48\textwidth}}
\caption[]{\label{gbi-alpha}Left: Spectral index variation of Sgr A*
between 2.3 and 8.3 GHz as a function of time. Right: Spectral index
evolution as a function of combined flux density at 2.3 and 8.3 GHz --
the higher the flux the more inverted the spectrum.}
\end{figure}

\subsection{Autocorrelation, Structure Function, and Power Spectrum}
To characterize the variability pattern better,
Fig.~\ref{gbi-structuref} shows the structure function $D(\tau)$ of
the two light curves as a function of the time delay $\tau$, where
\begin{equation}
D(\tau)=\sqrt{\left<\left(S_\nu(t)-S_\nu(t\pm\tau)\right)^2\right>}\quad.
\end{equation}

A maximum in the structure function indicates a characteristic
time scale, a minimum indicates a characteristic period. A
characteristic period in radio light curves usually does not persist
for a long time, and hence, similar to X-ray astronomy, is commonly
called a quasi-periodicity, even though the underlying physical
processes are probably very different from those seen in X-ray
binaries.

At both frequencies the characteristic time scale is somewhere between
50 and 250 days. The steepest increase and hence the time scale where
the variability amplitude rises most rapidly is around a few ten days.
During the period discussed in \citeN{Falcke1999a} one could see a
strong signal of a quasi-periodic variability with a period of 60 days
over one year. As expected this periodicity has subsided, even though
the structure function is still rather 'bumpy' at 2.3 GHz compared to
8.3 GHz. In contrast to this behavior we now find a minimum of the
structure function at 8.3 GHz around 250 days that is also visible at
2.3 GHz  {}--{}  again a quasi-periodic behavior during a certain time range
but now with a much longer period.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/gbi-structx.ps,width=0.48\textwidth}\hfill\psfig{figure=Figures/gbi-structs.ps,width=0.48\textwidth}}
\caption[]{\label{gbi-structuref}Structure function of the radio light curves of Sgr A* at
8.3 GHz (left panel) and 2.3 GHz (right panel). Maxima indicate a
characteristic times scale, minima indicate a characteristic period}
\end{figure}

This quasi-periodicity is also visible in the power spectra -- the
Fourier transform of the light curves multiplied by their complex
conjugates (Fig.~\ref{gbi-pow}). At 8.3 GHz we find a peak again at
250 days, indicating a periodicity. At 2.3 GHz we also see a
flattening of the power spectrum but a clear location of the peak is
difficult. At short delays of one to three days we see the effect
of smoothing the data. If one subtracts a polynomial from the two
power spectra one can also identify a peak around some ten days,
corresponding to the onset of variability seen already in the
structure function.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/gbi-powx.ps,width=0.48\textwidth}\hfill\psfig{figure=Figures/gbi-pows.ps,width=0.48\textwidth}}
\caption[]{\label{gbi-pow}Power spectrum of the radio light curves of Sgr A* at
8.3 GHz (left panel) and 2.3 GHz (right panel). The spectra were
bined in logarithmic intervals to reduce the scatter. The solid lines 
are 4th and 2nd order polynomial fits to the data.}
\end{figure}


Finally, we can look at the cross correlation between the two
frequencies to see whether the variations are correlated or not.  The
resulting cross correlation in Fig.~\ref{gbi-cross} has a marked peak
at zero-lag indicating that indeed the variability is strongly
correlated: both frequencies rise and fall together but with different
amplitudes as already discussed in the context of the spectral index
variations. In addition we see a second strong peak at the 250 day
period indicating that the quasi-periodicity is recovered in both
light curves.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/gbi-cross.ps,width=0.48\textwidth}}
\caption[]{\label{gbi-cross}Cross correlation of 8.3 GHz and 2.3 GHz radio light curves
of Sgr A*. Positive and negative time lags have been
co-added.}
\end{figure}

\subsection{Implications}
To summarize the results one can say that there is clear evidence for
variability of a few percent at cm wavelengths in Sgr A*. The
variability does not seem to be consistent with a simple model of
refractive interstellar scintillation (RISS) as suggested by
\citeN{ZhaoGossLo1992}. The time scales at 2.3 GHz and 8.3 GHz both
seem to be comparable to the one found at 5 GHz by
\citeN{ZhaoGossLo1992} and does not follow a $t\propto\lambda^2$
law. Moreover, the modulation index apparently decreases towards lower
frequencies.

The quasi-periodicity is reminiscent to those in some quasar
cores. For example the QSO 0917+624 is know to show episodes of
quasi-periodicity \cite{KrausWitzelKrichbaum1999}. Unfortunately the
frequency of these quasi-periodicities in quasar cores, and perhaps
also in Sgr A*, may not be related to a well defined and constant
(e.g., precession) frequency like the QPOs in X-ray binaries, but
could simply be due to intermittent periodic phenomena in the
accretion disk (e.g., waves) or the jet (e.g., helical motion). In the
case of Sgr A* all characteristic time scales associated with a black
hole or a relativistic outflow at these frequencies are less than a
day and hence one might consider global accretion flow instabilities
for such a behavior. On the other hand, the possibility that the
quasi-periodicity could be produced by interstellar scattering needs
to be explored as well. It remains to be seen whether any of the
periods found so far will persist over longer periods of time. This
can be done, e.g., by utilizing the treasures of the VLA archive
(Bower et al., in prep.).

The most direct conclusion we can draw from the variability data is
the high degree of correlation between 2.3 and 8.3 GHz. The lag is
apparently less than three days which corresponds to a light travel
distance of $\la10^{16}$ days ($\sim60$ milli-arcsecond at the Galactic Center
and less than the scattering size). For models which a have
frequency-dependent structure (e.g., the jet model) this will be an
upper limit to the size scale at these frequencies. In models where
the radio emission is produced in the accretion flow and where the
travel time is given by the accretion velocity those scales would be
much smaller.

\section{Linear Polarization}\label{linpol}
\citeme{BowerBackerZhao1999,BowerWrightBacker1999}
The final parameter to be discussed in the context of the Sgr A* radio
emission is its polarization. Early papers that looked into the
radio emission of Sgr A did not find any significant
polarization. \citeN{EkersGossSchwarz1975} gave an upper limit of 1\%
linear polarization for the peak of Sgr A which was not well resolved
in their 5 GHz Westerbork observations. Similarly,
\citeN{Yusef-ZadehMorris1987} did not find any significant polarization 
in Sgr A with the VLA. In contrast to this, polarization measurements
of AGN, where the linear polarization is typically a few percent, have
been an important tool in understanding radiation mechanisms and basic
processes governing the radio emitting plasmas, such as shock
acceleration \cite{HughesAllerAller1985,MarscherGear1985}. So, while
polarization promises interesting insight, the early negative results
on Sgr A* made this a non-issue for over a decade. Only recently, in
a series of papers has polarization been revisited with some surprising
answers
\cite{BowerFalckeBacker1999,BowerBackerZhao1999,BowerWrightBacker1999}.

Of course, one important question is, if indeed linear polarization in
Sgr A* is low, why is this so? Two possibilities that come immediately
to mind are that perhaps the scattering screen between the Galactic
Center and the observer de-polarizes any radiation. One can imagine
two possibilities: a) the Faraday rotation of the homogeneous medium
is so high that within the bandwidth of the observation the
polarization vector is rotated by more than 180 degrees and therefore
is largely canceling itself. Or b) there is considerable variation of
the Faraday rotation in the scattering screen so that every ray that
reaches the observer gets rotated differently and hence the overall
polarization is reduced significantly. Finally, one could wonder
whether any such effect could lead to a conversion of linear
polarization to circular polarization, after all we have an
anisotropic scattering screen permeated by a large scale magnetic
field \cite{Yusef-ZadehCottonWardle1994}. This question will be
discussed in the subsequent section.


To investigate the linear polarization -- or its lack thereof -- two
different approaches have been followed. First, one needs to measure
the linear polarization with high accuracy and then check whether a
large Faraday rotation is present. This was done by
\citeN{BowerBackerZhao1999} where continuum polarimetry at 4.8 GHz and
spectro-polarimetric observations with the VLA of Sgr A* at 4.8 and
8.4 GHz were presented.  The spectro-polarimetric observations were
made to exclude strong Faraday rotation in the Galactic Center that
could lead to a de-polarization of the radiation when observed in
continuum mode integrating over a large bandwidth.

Faraday rotation is produced when radio waves pass trough an ionized
and magnetized medium. Since left and right circularly polarized waves
have different refractive indices for a given magnetic field
orientation, a wavelength-dependent delay is induced which rotates the
position angle $\phi_{\rm LP}$ of the linear polarization vector,
yielding

\begin{equation}
\phi_{\rm LP}={\rm RM}\lambda^2.
\end{equation}
The parameter RM is called the rotation measure and can be determined
by measuring the position angle of the linear polarization vector
$\phi_{\rm LP}$ at different wavelengths $\lambda$. For a given
frequency bandwidth $\Delta \nu$ significant de-polarization is
obtained if $\phi_{\rm LP}$ changes by more than one radian, i.e.~if

\begin{equation}
{\rm RM}>0.5 {\nu\over\lambda^2\Delta\nu}.
\end{equation}
This means that for a typical VLA bandwidth of 50 MHz at 4.8 GHz the
critical rotation measure is $\sim10^4$ rad m$^{-2}$. This value is
not deemed to be so excessively high that it could not be present in
the Galactic Center.

The results of the broad-band continuum polarimetry indeed confirmed
the absence of linear polarization with a rather low upper limit of
$<0.1\%$ fractional polarization. In order to detect whether RM in
excess of $\sim10^4$ rad m$^{-2}$ could cause this non-detection the
spectro-polarimetric data, where $\Delta\nu$ is much smaller, was
Fourier transformed to detect multiple rotations of the polarization
vector across the entire band. While the resulting Fourier amplitude
spectra (Fig.~\ref{pol-fourier}) do show significant peaks for the two
calibrator sources at zero RM, the spectrum for Sgr A* is almost
indistinguishable from a noise data set. Hence one can exclude that
Faraday rotation by a plasma with rotation measures up to $10^{7}$ rad
m$^{-2}$ is responsible for a de-polarization of Sgr A* for an upper
limit of $0.2\%$ percent linear polarization.


\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/pol-fourier6cm.ps,width=0.48\textwidth}\hfill\psfig{figure=Figures/pol-fourier3cm.ps,width=0.48\textwidth}}
\caption[]{\label{pol-fourier}Fourier amplitude for 3C286, NRAO 530,
Sgr A*, and a noise data set at 4.8 GHz (left) and 8.4 GHz
(right). The Fourier amplitude is given in mJy and as a fraction of
the total flux for each source. The scaling of the Gaussian noise data 
is set to match that of Sgr A*. There is no significant peak in Sgr A* 
for RMs within $\pm3.5\cdot10^6$ rad m$^{-2}$ at 4.8 GHz and within 
$\pm1.5\cdot10^7$ rad m$^{-2}$ at 8.4 GHz. The figures are taken from
Bower, Zhao, Goss, \& Falcke (1999).
}
\end{figure}
\nocite{BowerBackerZhao1999}

In order to clarify whether RM fluctuations in the scattering medium
could de-polarize the radiation of Sgr A* one could simply try to
measure the linear polarization at progressively higher
frequencies. Since the scattering size decreases with $\nu^{-2}$ the
differential changes in the angles to the line of sight for light rays
from Sgr A* will rapidly become smaller and smaller with increasing
wavelength. In addition the Faraday rotation itself will also decrease
with $\nu^{-2}$. \citeN{BowerWrightBacker1999} have therefore
investigated high-frequency polarization of Sgr A* with the VLA and
found only upper limits. Figure \ref{pol-spec} shows the upper limits
for the fractional linear polarization of Sgr A* as a function of
frequency. Since the sensitivity for observations at higher
frequencies decreases the upper limits at 43 and 86 GHz are not as
strict as at 4.8 GHz. However, in most AGN the linear polarization
seems to rise towards higher frequencies \cite{AllerAllerHughes1992}
and given the strong frequency dependence of Faraday rotation,
de-polarization by the scattering medium becomes
rather unlikely at present.

The very latest information now comes from linear polarization
observations made with the SCUBA camera at the James Clerk Maxwell
Telescope (JCMT) at 0.75, 0.85, 1.35, and 2 mm wavelengths
\cite{AitkenGreavesChrysostomou2000}. The authors claim to have found
fractional linear polarization at these wavelengths as high as 10\%
and above. One problem in these low-resolution observations is the
strong confusion of the Sgr A* flux with dust emission from the
surrounding circum-nuclear disk (CND). It is also difficult to
reconcile the strong upper limits at $\lambda$3.5mm reported above and
this new detection. On the other hand, for an ultra-compact region
with a strong low-frequency cut-off at these wavelengths due to
self-absorption (see Eq.~\ref{submmsize}) this may be possible. In any
case this result will need further confirmation but is potentially
very interesting.

 
\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/pol-spec.ps,width=0.48\textwidth,bbllx=0.8cm,bblly=5.8cm,bburx=19.8cm,bbury=24.2cm}}
\caption[]{\label{pol-spec}Upper limits to the linear polarization
of Sgr A* measured with the VLA and BIMA (86 GHz). The figure is taken
from Bower, Wright, Backer \& Falcke (1999).  }
\end{figure}
\nocite{BowerWrightBacker1999}

\section{Circular Polarization}
\citeme{BowerFalckeBacker1999}
\subsection{First Detection of Circular Polarization}
Another less well studied aspect of synchrotron radiation is circular
polarization. Typically, the degree of circular polarization is $m_c <
0.1\%$ with only a few cases where $m_c$ approaches $0.5\%$
\cite{WeilerdePater1983}.  The degree of circular polarization usually
peaks near 1.4 GHz and decreases strongly with increasing frequency.


Recently, VLBI imaging of 3C 279 has found 
$m_{\rm c}\simeq1\%$ 
in an individual radio component with a fractional linear polarization
of 10\% \cite{WardleHomanOjha1998}.
The integrated circular
polarization, however, is less than 0.5\%. 
The circular polarization is probably produced through the conversion
of linear to circular polarization by low-energy electrons in the 
synchrotron source.  This process is also known as re-polarization 
\cite{Pacholczyk1977}.


Given the stringent limits on linear polarization of Sgr A* at
cm-waves discussed in the previous section, the presence of circular
polarization was not expected. Yet \citeN{BowerFalckeBacker1999} have
detected circular polarization in this source at a surprisingly high
level.

\begin{figure}%%%[htb]
\centerline{\rotate[r]{\mbox{\psfig{figure=Figures/pol-cp.ps,bbllx=36pt,bblly=91pt,bburx=576pt,bbury=701pt,width=0.48\textwidth}}}}
\caption{\label{pol-cp.ps}The Stokes $V$ map for Sgr A* 
on 10 April 1998 at 4.8 GHz.
The peak intensity is -1798 $\mu {\rm Jy\ beam^{-1}}$ .
The rms noise is 68 $\mu {\rm Jy\ beam^{-1}}$.
Contour levels are -16, -8, -4, -2, -1, 1, 2, 4, 8 
and 16 times 175 $\mu {\rm Jy\ beam^{-1}}$.  Negative contours are shown
with dashed lines.}
\end{figure}


Figure~\ref{pol-cp.ps} shows the Stokes $V$ image of Sgr A* at 4.8 GHz
from 10 April 1998.  The peak at -1.8 mJy is more than 20 times the
noise level of 68 $\mu {\rm Jy}\ {\rm beam^{-1}}$.  For the same
epoch, the calibrator B1748-253 had a peak flux of 262 $\mu {\rm Jy}$
in a map with a noise level of 58 $\mu {\rm Jy}\ {\rm beam^{-1}}$.


The circular polarization was found to be $m_c=-0.36 \pm 0.05\%$ and
$m_c=-0.26 \pm 0.06\%$ at 4.8 and 8.4 GHz, respectively.  The errors
are estimated from the variance of the three separate measurements for
each frequency.  These errors set an upper limit to the variability,
as well.  The average spectral index of the fractional circular
polarization is $\alpha=-0.6 \pm 0.3$ for $m_c \propto \nu^\alpha$.
The error in $\alpha$ is less than that expected from the errors in
$m_c$.  This is due to the fact that variations in $m_c$ between
epochs appear to be due to systematic errors that are common to both
frequencies.

In the mean time the initial detection was confirmed by an Australian
group \cite{SaultMacquart1999} with a different telescope (Australia
Telescope Compact Array) at 4.8 GHz.

Most recently the circular polarization observations of Sgr A* have
been extended up to frequencies of 15 GHz and monitoring of the
variability of the polarized flux has been performed with the VLA
\cite{BowerFalckeBacker1999c}. The first results indicate that
circular polarization is detected even at 15 GHz and that during
certain periods the polarized flux is rising towards the highest
frequencies. While the polarized flux density at 1.4 GHz and 4.86 GHz
is relatively stable over two months, the variability amplitude seems
to rise at 8.4 and 15 GHz. Figure \ref{gccp} shows the light curves of
the relative circular polarization in Sgr A* as measured with the
VLA. For the monitoring period the mean spectrum is in fact highly
inverted with a spectral index $\alpha\sim0.6$ ($m_{\rm
c}\propto\nu^{\alpha}$). It has to be noted, however, that this data
is still being worked on and that supplementing higher frequency data
is expected in the near future.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/gccp.ps,bbllx=0.8cm,bblly=6.5cm,bburx=19.9cm,bbury=24.2cm,width=0.75\textwidth}}
\caption{\label{gccp} Light curves of fractional circular polarization 
in Sgr A* (solid lines), the calibrator J1744-312 (short-dashed), and
the calibrator J1751-258 (long-dashed line) from VLA measurements at
1.4, 4.8, 8.4, and 14.9 GHz (Bower, Falcke, \& Backer 1999c).}
\end{figure}
\nocite{BowerFalckeBacker1999c}

\subsection{Mechanisms for the Production of Circular Polarization}

While the detection of circular polarization for Sgr A* is in itself
an unexpected result, two additional properties set this source apart
from any other radio core and make the result very puzzling: the fact
that circular polarization exceeds linear by more than a factor of two
at cm-waves and the flatness (or inversion) of the circularly
polarized spectrum.

One can consider now whether the circular polarization is produced not
in the source, but in the intervening scattering screen.  A
birefringent scattering medium may produce scintillating circular
polarization from an unpolarized background source.  This effect is
presently being studied in detail (Macquart \& Melrose, in prep.).
It requires a scattering region with a fluctuating rotation measure
gradient.  Such a mechanism is appealing due to the strong scattering
medium and the strong observed gradients in RM in the GC region
\cite{Yusef-ZadehWardleParastaran1997}.  The fact that the scattered
image of Sgr A* itself is anisotropic might also indicate an
anisotropic scattering medium.  However, the diffractive effect has
$\alpha=-4$ or steeper, which is not at all consistent with the
measured spectral index. Further calculations of this relatively
unexplored issue should show whether such a scattering model could
nevertheless be made consistent with the observations.


Alternatively, one can ask whether the conversion mechanism
or intrinsic synchrotron circular polarization could be at work in Sgr A* 
\cite{Pacholczyk1977,JonesODell1977}. 
Here, the main problem is the low level of linear
polarization. Magnetic field reversals would reduce linear
polarization, but most likely would affect circular polarization in
the same way \cite{WilsonWeiler1997}.  However, one
important factor in the relative level of linear to circular
polarization is the electron energy distribution, since low-energy
electrons (with Lorentz factors less than 100) can lead to
Faraday de-polarization of linear and/or conversion of linear to
circular polarization.


As model calculations show (\citeNP{JonesODell1977}, their Fig.~1)
circular polarization of a radio component peaks near the
self-absorption frequency $\nu_{\rm ssa}$, where linear polarization
drops to a minimum. In typical radio core components the strongest
contribution to linear polarization therefore comes from the
optically-thin power-law part of its spectrum. However, in Sgr A* such
a power law is most likely absent or already ends at a frequency
$\nu_{\rm max}\sim\nu_{\rm ssa}$, as indicated by the steep
high-frequency cut-off in its spectrum towards the infrared
\cite{SerabynCarlstromLay1997,FalckeGossMatsuo1998}.


Such a situation has not yet been considered in synchrotron
propagation calculations involving conversion. However, it may result
in a high $m_{\rm c}$-to-$m_{\rm l}$ ratio if $\nu_{\rm
max}\sim\nu_{\rm ssa}$ is true for the electrons that produce the low
frequency spectrum.  For example, Jones \& O'Dell show that for a
power law of electron energies with characteristic frequencies
$\nu_{\rm min}$ extending at least a factor thirty below $\nu_{\rm
ssa}$, circular polarization around $\nu_{\rm ssa}$ can exceed $m_{\rm
l}$. With the absence of any higher frequency emission, linear
polarization could be quenched.  On the other hand, a narrow
distribution with $\nu_{\rm min}\sim\nu_{\rm ssa}\sim\nu_{\rm max}$
would again lead to significant linear polarization even at the
self-absorption frequency \cite{JonesHardee1979}.

We consider here a simple synchrotron model of Sgr A*, where the flux
density at 5 GHz is produced in a spherical component by a flat
electron distribution with a power law index of $p=1$ ranging over
electron energies that correspond to the characteristic frequencies
$\nu_{\rm max}=\nu_{\rm ssa}=5$ GHz and $\nu_{\rm min}=\nu_{\rm
max}/30$.  This model corresponds to a single zone of a complete
inhomogeneous model (e.g., \citeNP{BlandfordKonigl1979}, also
Chap.~\ref{symbiosis}).  The low and high energy electrons are fully
mixed.  Assuming equipartition, we find a magnetic field of 0.4 Gauss
and a maximum electron Lorentz factor of 60.  The electron
distribution chosen here has an equal number of low- and high-energy
electrons per logarithmic interval.  According to Pacholczyk (1977,
Eq. 3.152), such a power law will contain enough low-energy electrons
near $\gamma_{\min}$ to produce the observed circular polarization
through re-polarization.  Intrinsic circular polarization could be as
important as conversion in this model.  The intrinsic synchrotron
circular polarization is given by $m_{\rm c}=3\%\,(B/{\rm
Gauss})^{1/2}(\nu/{\rm GHz})^{-1/2}=0.9\%$, assuming an angle of
$60^\circ$ between the magnetic field and the line of sight
\cite{LeggWestfold1968}.  However, field reversals and optical depth
effects will decrease that number.


The polarization properties of models (e.g., ADAF and Bondi-Hoyle)
that produce gyro-synchrotron emission with low temperature electrons
are largely unexplored.  However, \citeN{Ramaty1969} did show that
circular polarization may dominate linear polarization in some simple
gyro-synchrotron sources.


Obviously, a more self-consistent treatment of these problems is
required. The circular and linear polarization spectrum will depend on
the electron distribution and the temperature and magnetic field
stratification in the source.  Nevertheless, it seems as if a highly
self-absorbed source with a low high-energy cut-off and a modest
amount of low-energy electrons might explain the observed properties
of Sgr A*.

The rise of the fractional circular polarization and its variability
towards higher frequencies is another important clue. It is not clear
whether this indicates that the circular polarization is mainly
associated with the submm-bump since this is expected to cut-off
rather sharply towards low frequencies. It could well be that this is
another indication of hidden intrinsic structure within Sgr A*.  In a
model, where the Sgr A* spectrum is produced by a combination of
self-absorbed components, such as in the jet model discussed below, a
rather flat or even inverted spectrum is expected since the
time-averaged fractional polarization at the self-absorption frequency
should not change drastically when going from one spatial scale (and
one peak frequency) to the next. In any case, this discovery opens a
significant new parameter space for the study of the nearest
supermassive black hole candidate and its environment.

\section{Accretion Models -- An Overview}
\citeme{Falcke1996b} If we now want to go beyond a mere description of
Sgr A*, we have to ask how this source is powered and what the
underlying engine producing the radio and X-ray emission actually is?
One idea is that, if Sgr A* is a black hole, it should swallow some
fraction of the strong stellar winds seen in the GC through spherical
(Bondi-Hoyle) accretion.

The rate of infall depends only on the mass of the black hole and the
wind parameters. Once we know the latter we can determine the black
hole mass from the estimated accretion rate, which in turn could be
derived from the spectrum of Sgr A*. The general validity of the
Bondi-Hoyle accretion (without angular momentum) under these
assumptions was demonstrated by 3D numerical calculations (Ruffert \&
Melia 1994) and the main uncertainties are related to the
plasmaphysical effects associated with the infall. It is usually
assumed that the magnetic field in the accreted plasma is amplified by
compression up to a point where it reaches the equipartition value.
Beyond this point the excess magnetic field is assumed to be
dissipated and used to heat the plasma.  The electron temperature is
determined by the equilibrium between heating and cooling via
cyclo-synchrotron radiation where one has to consider two domains for
the solution of this problem: (1) hot electrons, where the typical
electron Lorentz factors are of the order 100-1000 and (2) warm
electrons, where the electron Lorentz factor is still close to unity.

The first domain is in a regime where synchrotron emission is
important and also very effective. This requires only low accretion
rates ($\dot M\sim10^{-10} M_{\odot}/{\rm yr}$) and hence permits only
moderately high black hole masses of the order
$M_{\bullet}\simeq10^{3-5} M_{\odot}$
\cite{Ozernoy1992,MastichiadisOzernoy1992}. The radio spectrum in such
a configuration is mainly due to the optically thin part of a quasi
mono-energetic (or Maxwellian) electron distribution and was
calculated also by \citeN{DuschlLesch1994},
\citeN{BeckertDuschl1997}, and used with in the jet model \cite{Falcke1996b}.

The second domain is in the transition regime between cyclotron and
synchrotron radiation, which is less effective than pure synchrotron
radiation and hence requires higher accretion rates ($\dot
M\sim10^{-4} M_{\odot}/{\rm yr}$) and a higher black hole mass of the
order $M_{\bullet}\simeq10^6M_{\odot}$
\cite{MeliaJokipiiNarayanan1992,Melia1992a,Melia1994}.

The big advantage of the wind-accretion approach is that it, firstly,
appears unavoidable and, secondly, self-consistently ties observable
parameters and accretion rate to the mass of the central object.

On the other hand there are several problems to be considered:
firstly, it is not at all clear that the wind-producing stars, as an
ensemble, have zero angular momentum, thus producing a non-zero
angular momentum of the winds to be accreted. This would diminish the
accretion rate as pointed out by
\citeN{Falcke1996b}. Hydrodynamical simulations show that the exact
distribution and velocity of stellar wind sources within the
observationally allowed range indeed can change the expected accretion
rate \cite{CokerMelia1997}. Another question is whether the stellar
winds are indeed isotropic. The only resolved stellar wind seen in the
Galactic Center so far, the wind of IRS 7
\cite{Yusef-ZadehMorris1991}, looks like a cometary tail pointing {\em 
away} from Sgr A*. This raises the question whether there is a wind
\cite{Chevalier1992} or expanding bubble pushing gas out of the
Galactic Center.


There also could be residual angular momentum in Sgr A* itself,
e.g.,~because of a fossil accretion disk which could catch the inflow
further out, filling a reservoir of rather dense matter instead of
directly feeding the black hole. The viscous time scales of such a
disk can be very long -- up to $10^7$ years \cite{FalckeHeinrich1994}.
However, detailed calculations of such a process
\cite{FalckeMelia1997,CokerMeliaFalcke1999} indicate that the impact
of the wind onto the fossil disk should produce a non-negligible IR
emission that is not seen.

An alternative to the models mentioned above was proposed by
\citeN{NarayanYiMahadevan1995} and
\citeN{NarayanMahadevanGrindlay1998}, who explain the discrepancy
between high accretion rate and low luminosity by the effects of an
advection dominated accretion flow (ADAF) or disk. In this model more
than $99.9\%$ of the energy is not radiated but transported through
the disk by advection and finally swallowed by the black hole. And, in
fact, it appears as if advection is non-negligible in many accretion
disks, but whether indeed such a high fraction of the energy is
transported by advection alone is not at all clear. One also has to
make sure that not a substantial fraction of the energy is released in
the inner parts of the disk and that the energy is swallowed quietly
by the black hole. Even if an advection dominated accretion flow is
not the whole story, it may be an interesting part of it.

A major problem of the ADAF model is that it under-predicts the cm-wave
emission in the spectrum of Sgr A* by more than an order of
magnitude. In \citeN{NarayanMahadevanGrindlay1998} this is fixed by
artificially assuming a constant electron temperature in the accretion
flow over a particular range in radius $r$. The range was hand-picked
such that the cm-wave spectrum is fitted by a $\nu^{1/3}$ spectrum,
reminiscent of the spectra produced by \citeN{Ozernoy1992} and
\citeN{BeckertDuschl1997}. Another fix was proposed by
\citeN{Mahadevan1998} who added a power-law distribution of protons
producing high-energy pairs in hadronic interactions. The proton power
law would require shock acceleration in the accretion flow which
requires turbulent plasma waves
(e.g.,~\citeNP{SchlickeiserCampeanuLerche1993,Schneider1993}). It has
to be ensured that these waves do not couple to electrons as well,
otherwise this would lead to heating and shock acceleration of
electrons. In this case the basic assumption of a two-temperature
plasma, a fundamental assumption of ADAFs, would break down. In
astrophysical plasmas we generally do see that electrons are
accelerated at shocks {}--{} after all, this is the basic explanation
for the power-law radio spectra one sees in AGN. Therefore, the
predictions of the ADAF model in terms of the spectral characteristics
of Sgr A* are less than satisfying at present. In the following
section we will discuss as an alternative the application of the jet
model to the observed characteristics of Sgr A*.


\section{The Jet Model}\label{jetmodel}
\citeme{FalckeMarkoff2000}
The latest information for Sgr A* comes from the possible detection of
Sgr A* at X-ray wavelengths with the satellite Chandra
\cite{BaganoffAngeliniBautz1999}.  The first epoch data show a point
source at the location of Sgr A* with a rather low X-ray luminosity
around $0.5-1\cdot10^{34}$ erg s$^{-1}$ in the 0.5-10 keV band
(Baganoff et al., priv. comm.) {}--{} even lower than the earlier
ROSAT limit of $\sim2\cdot10^{34}$ erg s$^{-1}$
\cite{PredehlTruemper1994}.  This new measurement provides a crucial
constraint for any model of radiative emission from Sgr A*.

Given these new observations and the possible recent mm-VLBI detection
of a small-scale jet \cite{LoShenZhao1998}, it is perhaps timely to
revisit the jet model for Sgr A* \cite{FalckeMannheimBiermann1993}
with the additional constraints provided by the Chandra observations.
Here, we will therefore look at refined numerical calculations
developed by \citeN{FalckeMarkoff2000} for the jet model using more
realistic electron distributions also including the contribution of
synchrotron self-Compton (SSC) emission.  Thus, we will be able to
show that the jet model can account in detail for the observed
properties of Sgr A*, specifically the spectrum from cm- to mm-waves,
the low X-ray emission, the apparent lack of extended emission in VLBI
observations, and the possibly frequency-dependent size of the radio
core.

The basic model is already outlined in Chapter~\ref{symbiosis}, for a
magnetized, relativistic proton and electron plasma leaving a nozzle
close to the black hole. The velocity field is described by
Eq.~\ref{euler2}.  As before, the gravitational potential is ignored
since its influence is rather small in the supersonic regime
considered here. The size of the nozzle $z_0$, i.e.~the location of
the sonic point, remains a free parameter, since an undisputed model
for the launching mechanism of astrophysical jets has not been found
yet even though we know that they launch.

Given an initial magnetic field $B_0$, a relativistic electron total
number density $n_0$ with a characteristic electron energy
$\gamma_{\rm e,0}m_{\rm e}c^2$, radius $r_0$ of the nozzle, and taking
only adiabatic cooling due to the longitudinal pressure gradient
(i.e.~$\propto {\cal M}^{\Gamma-1}$, where ${\cal M}$ is the Mach
number) and dilution by the lateral expansion into account, one can
determine the magnetic field $B(z_*)$, particle density $n(z_*)$,
electron Lorentz factor $\gamma_{\rm e,0}(z_*)$, and jet radius as a
function of the dimensionless distance from the nozzle
$z_*=(z-z_0)/r_0$:
\begin{eqnarray}
{\cal M}(z_*)&=&{\gb\over\gamma_{\rm s,0}\beta_{\rm s,0}},\\
n(z_*)&=&n_0\cdot\left({r(z_*)/ r_0}\right)^{-2}{\cal M}^{-1}(z_*),\\
r(z_*)&=&r_0+z_*/{\cal M}(z_*),\\
\gamma_{\rm e}(z_*)&=&\gamma_{\rm e,0}\cdot{\cal M}^{-1/3}(z_*),\\
B(z_*)&=&B_0\cdot\left({r(z_*)/r_0}\right)^{-1}{\cal M}^{-2/3}(z_*).
\end{eqnarray}
This fixes the basic parameters for synchrotron and SSC emission along
the entire jet.

We assume that magnetic field and relativistic electrons are in
approximate equipartition, with $k(B^2/8\pi)=\int E_e n_e(E_e) dE_e$,
where $n_e(E_e)$ is the energy-dependent electron number density, and
$k\approx 1$.  The form of the electron distribution will be discussed
below.

By approximating the jet as a series of cylindrical sections, we can
calculate the total emission by integrating over the contributions
from each component.  For each segment the optical depth to
synchrotron absorption is $\tau_\nu=\frac{\pi}{2} \alpha_\nu
r(z_*)/D\sin{\theta_i}$, where $\theta_i$ is the angle between the jet
axis and the line of sight, $\alpha_\nu$ is the absorption
coefficient, $D=[\gamma(1-\beta\cos{\theta_i})]^{-1}$ is the Doppler
factor accounting for the angle aberration (e.g.,
\citeNP{LindBlandford1985}) due to the relativistic bulk velocity,
$\beta(z_*) c$, in the jet.  Using the transfer equation for
source-only emission, assumed constant within the segment, we get
$I_\nu(\tau_\nu)=(1-{\rm e}^{-\tau_\nu})S_\nu$ where
$S_\nu=j_\nu/\alpha_\nu$ is the source function.  Assuming isotropic
emission in the rest frame of the cylindrical shell, the net flux out
of the component is $F_\nu=4\pi I_\nu$.  The observed flux density is
then $F'_{\nu'}=D^2 2 r (D\sin{\theta_i}) \Delta z F_\nu/4 \pi
d_{gc}^2$, where the distance to the Galactic Center is assumed to be
$d_{gc}=8.5$ kpc and the $2 r (D\sin{\theta_i})\Delta z$ factor is the
approximate projected surface area of the radiating cylinder. The
$D\sin{\theta_i}$ term cancels in the optically thin regime and in the
limits of $\tau\to0$ and $\tau\to\infty$, we recover the correct
optically thin and optically thick solutions.

To calculate the inverse-Compton up-scattered emission for the same
segment, we can ignore projection effects since the optical depth for
Compton scattering is small and use the self-absorbed synchrotron
emission in the component frame calculated above.  Then, using the
general expression for Compton scattering \cite{BlumenthalGould1970}
by a distribution of electrons (including the Klein-Nishina limit), we
find the SSC emission in the frame of the component which then is
transformed into the observers frame as before.

\subsection{Radio Spectrum}

The basic parameters for the jet {}--{} $B_0$, $\gamma_{\rm e,0}$, and
$r_0$  {}--{} are fixed within a factor of a few by the location of the
submm-bump in the spectrum and which, in this model, is mainly
produced by emission from the nozzle \cite{Falcke1996b}. The steep
spectral cut-off towards the IR further constrains the electron
distribution. It indicates the lack of a power-law tail of high-energy
electrons, which usually produces the optically thin high-frequency
emission seen, for example, in Blazars. Here, we explore two seemingly
prevalent possibilities for the electron distribution.  First, we
consider a narrow power law with a sharp cut-off at roughly
$5\gamma_{\rm e,0}$.  Alternatively we consider a relativistic thermal
Maxwellian distribution with $\gamma_{\rm
e,0}\approx3.5\frac{kT}{m_{\rm e}c^2}$.  Since the allowed width of
the electron distribution is very narrow in all cases, the different
distributions do not produce a significantly different cm- to mm-wave
radio spectrum, but slightly affect the high-energy cut-off and the
SSC spectrum.

Figure \ref{sgrx-pl} shows a fit to the submm and cm radio spectrum
for the two electron distributions with the nozzle parameters given in
the plot. We are plotting $F_\nu$ rather than $\nu F_\nu$ thus
allowing one to better judge the quality of the spectral fit at
cm-waves. The nozzle component accounts for most of the submm-bump, as
well as the main Compton component, and the low-frequency spectrum
stems from the emission of the more distant parts along the
jet. Within the model, the slope of the cm-wave spectrum and the ratio
between cm and submm emission is mainly determined by the inclination
angle. The parameters we obtain for jet and nozzle are very close
to those used by \citeN{Falcke1996b}, \citeN{BeckertDuschl1997}, and
\citeN{FalckeBiermann1999}.  The jet-specific parameters appear reasonable: the
inclination angle is rather average, size of the nozzle is a few times
$R_s$, and the system is very close to equipartition.

\begin{figure}
\centerline{\psfig{figure=Figures/sgrx-spec.ps,width=0.75\textwidth,angle=-90}}
\caption[]{\label{sgrx-pl}Broad-band spectrum of Sgr A* for a power-law distribution
of electrons (PL) and a relativistic Maxwellian distribution (MW). The
width of the nozzle is $r_0=4R_{\rm s}$ and $r_0=3 R_{\rm s}$
respectively, while its height is $z_0=3r_0$. The dots are the
simultaneous spectrum measured by Falcke et al.~(1998) with additional
high-frequency data discussed by Serabyn et al.~(1997). In the hard
X-rays we show the possible detection of Sgr A* with Chandra as a
short straight line (Baganoff, Morris, priv.~comm.).  At this point
the spectral index is not yet well determined and could possibly
become steeper. For the MW, we can also obtain a similar fit as the
PL, but we show one with no hard X-rays in order to indicate the
flexibility in the X-ray fluxes.}
\end{figure}
\nocite{FalckeGossMatsuo1998}\nocite{SerabynCarlstromLay1997}

\subsection{X-ray Flux}
Once the radio spectrum due to synchrotron emission is fixed, so is
the Compton up-scattered spectrum. The peak frequency of the latter is
$\sim4\gamma_{\rm e}^2$ times the peak frequency of the synchrotron
emission being up-scattered. Hence, in order to produce soft X-ray
emission from 1 THz synchrotron emission one needs electron Lorentz
factors in the range of a few hundred. This is just the range required
to produce the correct radio emission from the nozzle.

In Figure~\ref{sgrx-pl}, we compare the SSC spectrum with the
currently available data for Sgr A* from the X-ray satellite Chandra
(Baganoff, Morris, priv.~comm.). Since it is not clear at present
whether this flux is entirely from a point source or contains extended
emission as well this again should be taken as a tentative number or
possibly an upper limit. For a narrow power-law distribution we get
roughly the correct X-ray luminosity and a slightly steeper slope than
the reported value. However, at the time of writing the spectral shape
of the observed X-ray emission was still subject to scrutiny. For a
Maxwellian distribution the predicted slope in the model is slightly
steeper. By changing the nozzle parameters within the range allowed by
the radio data, the X-ray spectrum can be shifted around the measured
value, as demonstrated in the figure.

The predictions from this model are clear: we would expect significant
SSC emission in the EUV and the softer X-ray band.  Given the
variability of the radio emission we also expect to see correlated
submm and X-ray variability. The spectral shape in the X-rays is not
expected to be a perfect power law. It remains to be seen, how much of
the observed X-ray emission is from extended hot gas in and outside the
accretion region and how much is SSC emission from Sgr A* itself. A
mixture of both components is certainly possible; in that case the
nozzle should most likely reveal itself through variability in the
soft X-ray bands. Complete absence of X-ray variability would argue
against SSC emission giving a major contribution. This is possible if
the width of the electron distribution is even narrower thus cutting
off the SSC X-ray spectrum at even lower energies.


\subsection{VLBI Size and Extended Emission}
Possibly the most important constraints for any model are the VLBI
measurements of the size of Sgr A*. Since most models have a
stratified structure, the size of Sgr A* is expected to be a function
of frequency.  We note that for a given observing frequency the
emission in the jet model is highly concentrated to one spatial scale.
The emission from the jet at a particular frequency is self-absorbed
at small distances from the origin and cuts off at large distances
where the decreased magnetic field shifts the synchrotron cut-off
frequency below the observing frequency.  This is illustrated in
Fig.~\ref{size.ps}, where we show a longitudinal cut through the jet
based on our model. Each line corresponds to a different observing
frequency and one can see that the flux towards larger distances from
the core falls off rather steeply, i.e.~exponentially rather than with
a power law.

\begin{figure}
\centerline{\psfig{figure=Figures/size.ps,width=0.75\textwidth,angle=-90}}
\caption[]{\label{size.ps}Longitudinal cuts along the jet axis for
our model (Maxwellian electron distribution) at various
frequencies. Plotted are the observed flux per segment in arbitrary
units versus the observed separation in milli-arcseconds (mas) from
the black hole. Curves to the left represent higher frequencies and
the spikes in the left-most flux distributions are due to the nozzle.}
\end{figure}
\nocite{LoShenZhao1998,KrichbaumGrahamWitzel1998}


Thus, extended emission from the jet is highly (almost exponentially)
suppressed and the size of the detectable core will be a power law
$z\propto\nu^{-\aleph}$ with $\aleph$ in the range 0.9 to 1. This also
implies a shift of the location of the core with frequency. Figure
\ref{sgrx-size} compares the predicted full width at half maximum
(FWHM) of major and minor axis of the emission predicted by the jet
model with the constraints imposed by high-frequency VLBI
observations. Throughout the cm-wave range the emission basically
resembles one elliptical component decreasing in size with wavelength
and only at mm-waves (i.e.~above 30 GHz) an even more compact
core-component, the nozzle, appears. Hence, as long as the FWHM
predicted in the model is compatible with the observed values it will
be difficult to distinguish the Sgr A* source structure at one
frequency from a Gaussian VLBI component.

\begin{figure}
\centerline{\psfig{figure=Figures/sgrx-size.ps,width=0.75\textwidth,angle=-90}}
\caption[]{\label{sgrx-size}FWHM of the major and minor axis of the
jet model as a function of frequency. The filled dots mark the FWHM as
measured by Lo et al.~(1998; 43 GHz) and Krichbaum et al.~(1998; 86
\& 215 GHz). At frequencies above 30 GHz one obtains a two component
structure with an increasingly stronger core (nozzle, solid dashed
line) and a fainter jet component (dotted line).}
\end{figure}
\nocite{LoShenZhao1998,KrichbaumGrahamWitzel1998}



\subsection{Conclusions from Applying the Jet Model}
The spectrum of Sgr A*, including the new X-ray observations from
Chandra, can be modeled entirely by emission from this jet alone. We
can also show that the radio emission satisfies all constraints
imposed by VLBI observations. This shows that the basic model
introduced by \citeN{FalckeMannheimBiermann1993} can provide a
detailed explanation of the Sgr A* radio and X-ray spectrum. It also
fits Sgr~A* within the frame work of compact radio cores discussed in
Chapters~\ref{symbiosis} and \ref{llagn}.

One counter argument often heard in the context of modeling Sgr A* as
a jet is that one does not {\bf see} a jet.  However, in typical AGN
core-jet sources the extended jet structure is due to an optically
thin power law. Here this extended emission is greatly suppressed due
to the steep cut-off in the electron spectrum, required by the IR
limits. This naturally can explain the compact jet structure as seen
by \citeN{LoShenZhao1998}. Sgr A*, basically is a naked core without
much jet emission. The lack of optically thin emission could also help
to reduce the level of linear polarization in Sgr A* compared to more
powerful AGN (see Sec.~\ref{linpol}), since the degree of polarization
decreases to zero near the self-absorption frequency due to radiation
transfer effects.

The main assumption of the model is the presence of a nozzle close to
the central black hole collimating a relativistic plasma with
approximate equipartition between the magnetic field and relativistic
particles. The evolution of magnetic field and particle density is
calculated self-consistently and does not require additional
parameters beyond those fixed for the nozzle. The spectra we obtain
are therefore generic for collimated outflows from any accretion
flow {}--{} whether a magneto-hydrodynamical jet from a standard accretion
disk or an outflow from an ADAF {}--{} provided the accretion flow can
produce the required magnetic field, electron temperature, and density
near its inner edge. For an ADAF or Bondi-Hoyle type accretion the
presence of a jet near the black hole could thus aid those models in
accounting for the cm-wave radio emission, which is especially
difficult. The energy requirements to produce such a jet (see
\citeNP{FalckeBiermann1999}) are rather small compared to the power
available through accretion of nearby winds \cite{CokerMelia1997}.

It remains to be seen whether one can construct a self-consistent
model which couples an outflow as described here together with, for
example, an ADAF model. Particularly interesting in this context is
whether one could reproduce the unusual electron distribution found in
Sgr A*. As pointed out in \citeN{Falcke1996b} the typical electron
Lorentz factors required in the nozzle are close to those expected
from pair production in proton-proton (pp)
collisions. \citeN{Mahadevan1998} showed that an ADAF could in
principle provide the environment where pp-collisions could play an
important role even though in this paper a power-law distribution of
protons had to be artificially added. More detailed calculations in
this direction should therefore be undertaken in the future.

\section{Future Prospects - Imaging of the Event Horizon}\label{shadow}
\citeme{FalckeMeliaAgol2000}
As one can easily see from the previous sections the ever growing
interest in Sgr A* has already yielded a number of tantalizing
results, the most important being that Sgr A* is the best
supermassive black hole candidate we know. VLBI observations are
already approaching scales which are not far from the actual scale of
the black hole and the presence of the submm-bump indicates that even
more compact emission is present at yet smaller scales -- possibly as
close in as the event horizon of the black hole. It is therefore worth
exploring whether we have in principal a chance to actually approach
this scale with imaging techniques and to ask what we would expect to
see. This naturally will have to be done at the highest radio
frequencies where the resolution is highest and the scatter-broadening of
Sgr A* is the lowest.

At submm wavelengths, the various models indeed predict that the
synchrotron emission of Sgr A* is not self-absorbed, allowing a view
into the region near the event horizon. The size of this event horizon
is $(1+\sqrt{1-a_*^2})R_g$, where $R_g\equiv GM/c^2$, $M$ is the mass
of the black hole, $G$ is Newton's constant, $c$ the speed of light,
$a_*\equiv Jc/(GM^2)$ is the dimensionless spin of the black hole in
the range 0 to 1, and $J$ is the angular momentum of the black hole.

\citeN{Bardeen1973} described the idealized appearance of a black
hole in front of a planar emitting source, showing that it literally
would appear as a `black hole'. At that time such a calculation was of
mere theoretical interest and limited to just calculating the envelope
of the apparent black hole. \citeN{FalckeGossMatsuo1998} suggested to
apply this basic idea also to Sgr A* where it could possibly be
tested with submm-VLBI. To further check whether there is indeed a
realistic chance of seeing this `black hole' in Sgr A*
\cite{FalckeMeliaAgol2000} reported calculations obtained with a
general relativistic (GR) ray-tracing code that allows one to simulate
observed images of Sgr A* for various combinations of black hole spin,
inclination angle, and morphology of the emission region directly
surrounding the black hole and not just for a background source.


\subsection{The Appearance of a Black Hole}
The appearance of the emitting region around a black hole was
determined by \citeN{FalckeMeliaAgol2000} under the condition that it
is optically thin.  For Sgr A* this might be the case for the
submm-bump \cite{FalckeGossMatsuo1998} indicated by the turnover in
the spectrum, and can always be achieved by going to a suitably high
frequency.  For the qualitative discussion the emissivity was assumed
to be frequency independent and to be either spatially uniform or to
scale as $r^{-2}$.  These two cases cover a large range of conditions
expected under several reasonable scenarios, be it a quasi-spherical
infall, a rotating thick disk, or the base of an outflow.

The calculations took into account all the well-known relativistic
effects, e.g., frame dragging, gravitational redshift, light bending,
and Doppler boosting.  The code is valid for all possible spins of the
black hole and for any arbitrary velocity field of the emission
region.

For a planar emitting source behind a black hole, a closed curve on
the sky plane divides a region where geodesics intersect the horizon
from a region whose geodesics miss the horizon \cite{Bardeen1973}.
This curve, which is referred to as the ``apparent boundary'' of the
black hole, is a circle of radius $\sqrt{27} R_g$ in the Schwarzschild
case ($a_*=0$), but has a more flattened shape of similar size for a
Kerr black hole, slightly dependent on inclination.  The size of the
apparent boundary is much larger than the event horizon due to strong
bending of light by the black hole.  When the emission occurs in an
optically thin region {\em surrounding} the black hole, the case of
interest here, the apparent boundary has the same exact shape since
the properties of the geodesics are independent of where the sources
are located.  However, photons on geodesics located within the
apparent boundary that can still escape to the observer experience
strong gravitational redshift and a shorter total path length, leading
to a smaller integrated emissivity, while photons just outside the
apparent boundary can orbit the black hole near the circular photon
radius several times, adding to the observed intensity
\cite{JaroszynskiKurpiewski1997}.  This produces a marked deficit of the
observed intensity inside the apparent boundary {}--{} the ``shadow'' of
the black hole.

We here consider a compact, optically-thin emitting region surrounding
a black hole with spin parameter $a_*=0$ (i.e., a Schwarzschild black
hole) and a maximally spinning Kerr hole with $a_*=0.998$.  In the set
of simulations shown in Fig.~\ref{bhimage},  the viewing angle $i$ was taken to be $45^\circ$ with respect to the spin axis (when it is
present) with two distributions of the gas velocity $v$. The
first has the plasma in free-fall, i.e.,
$v^r=-\sqrt{2r(a^2+r^2)}\Delta/A$ and $\Omega = 2ar/A$, where $v^r$ is
the Boyer-Lindquist radial velocity, $\Omega$ is the orbital
frequency, $\Delta\equiv r^2-2r+a^2$, and
$A\equiv(r^2+a^2)^2-a^2\Delta\sin^2{\theta}$. (We have set $G=M=c=1$
in this paragraph.)  The second has the plasma orbiting in rigidly
rotating shells with the equatorial Keplerian frequency $\Omega =
1/(r^{3/2}+a)$ for $r>r_{ms}$ with $v^r=0$, and infalling with
constant angular momentum inside $r<r_{ms}$
\cite{Cunningham1975a}, with $v^\theta=0$ for all $r$.


In order to display concrete examples of how realistic the proposed
measurements of these effects with VLBI will be, the expected images
were simulated for the massive black hole candidate Sgr A* at the
Galactic Center.  For its measured mass
\cite{EckartGenzel1996,GhezKleinMorris1998} $M = 2.6\times
10^6\;M_\odot$, the scale size for this object is the gravitational
radius $R_g=3.9\times 10^{11}$ cm, which is half of the Schwarzschild
radius $R_s\equiv 2GM/c^2$.

To simulate an observed image one has to take two additional effects
into account: interstellar scattering and the finite telescope
resolution achievable from the ground. Scatter-broadening at the
Galactic Center is incorporated by smoothing the image with an
elliptical Gaussian with a FWHM of 24.2
$\mu$arcsecond$\times(\lambda/1.3\,\mbox{mm})^{2}$ along the major axis
and 12.8 $\mu$arcsecond$\times(\lambda/1.3\,\mbox{mm})^{2}$ along the
minor axis \cite{LoShenZhao1998}. The position angle of this
ellipse is arbitrary since one does not know yet the spin axis of the
black hole on the sky and PA=$90^\circ$ was assumed for the major
axis. The telescope resolution {}--{} in an idealized form {}--{} is then added by
convolving the smoothed image with a spherical Gaussian point-spread
function of FWHM 33.5 $\mu$arcsecond$\times(\lambda/1.3\,\mbox{mm})^{-1}
(l/8000\mbox{km})^{-1}$ {}--{} the possible resolution of a global
interferometer with 8000 km baselines \cite{Kri1996}. In reality the
exact point-spread-function will of course depend on the number and
placement of the participating telescopes.

\begin{figure}[h]
\centerline{\psfig{figure=Figures/bhimage.cps,width=\textwidth,bblly=11.2cm,bbury=21.5cm,bbllx=0.8cm,bburx=18.2cm}}
\caption{\label{bhimage}
An image of an optically thin emission region surrounding a black hole
with the characteristics of Sgr A* at the Galactic Center.  The black
hole is here either maximally rotating ($a_* = 0.998 $, panels a-c) or
non-rotating ($a_*=0$, panels d-f). The emitting gas is assumed to be
in free fall with an emissivity $\propto r^{-2}$ (top) or on Keplerian
shells (bottom) with a uniform emissivity (viewing angle
$i=45^\circ$). Panels a\&d show the GR ray-tracing calculations,
panels b\&e are the images seen by an idealized VLBI array at 0.6 mm
wavelength taking interstellar scattering into account, and panels
c\&f are those for a wavelength of 1.3 mm. The intensity variations
along the $x$-axis (solid green curve) and the $y$-axis (dashed
purple/blue curve) are overlayed. The vertical axes show the intensity
of the curves in arbitrary units and the horizontal axes show the
distance from the black hole in units of $R_{\rm g}$ which for Sgr~A*
is $3.9\times 10^{11}$ cm $\sim3\;\mu$arcseconds.}
\end{figure}

The results of the two different models with and without scattering at
two different observing wavelengths are shown in Fig.~\ref{bhimage}.
The two distinct features that are evident in the top panel for a
rotating black hole are (1) the clear depression in $I_\nu$ {}--{} the
shadow {}--{} produced near the black hole, which in this particular
example represents a modulation of up to 90\% in intensity from peak
to trough, and (2) the size of the shadow, which here is $9.2R_{\rm
g}$ in diameter.  This represents a projected size of 27
$\mu$arcseconds, which is already within a factor of two of the
current VLBI resolution \cite{Kri1995}.  The shadow is a generic
feature of various other models one can look at, including those
with outflows, cylindrical emissivity, and various inclinations or
spins.

This black hole shadow is also visible in the second illustrated case
for a non-rotating black hole with a modulation in $I_\nu$ in the
range of 50-75\% from peak to trough, and with a diameter of roughly
$10.4\,R_g$.  In this case, the emission is asymmetric due to the
strong Doppler shifts associated with the emission by a rapidly moving
plasma along the line-of-sight (with velocity $v_\phi$).


The important conclusion is that the diameter of the shadow {}--{} in
marked contrast to the event horizon {}--{} is fairly independent of the
black hole spin and is always of order 10$R_{\rm g}$.  Indeed, this is
consistent with the observed 0.8 mm size limit $>4 R_g$ of Sgr A* from
a lack of scintillation \cite{GwinnDanenTran1991}.  The presence of
a rotating hole viewed edge-on will lead to a shifting of the apparent
boundary (by as much as 2.5 $R_g$, or 8 $\mu$arcseconds) with respect
to the center of mass, or the centroid of the outer emission region.

Interestingly, the scattering size of Sgr A* and the resolution of
global VLBI arrays become comparable to the size of the shadow at a
wavelength of about 1.3 mm. As one can see from Figures
\ref{bhimage}c\&f the shadow is still almost completely washed out for
VLBI observations at 1.3 mm, while it is very apparent at a factor two
shorter wavelength (Figures \ref{bhimage}b\&e). In fact, already at
0.8 mm (not shown here) the shadow can be easily seen. Under certain
conditions, i.e., a very homogeneous emission region, the shadow would
be visible even at 1.3 mm (Fig.~\ref{bhimage}f).


\subsection{How Realistic is Such an Experiment?}

The arguments for the feasibility of such an experiment are rather
compelling. First of all, the mass of Sgr A* is known within 20\%, the
main uncertainty being the exact distance to the Galactic Center and
the exact choice of the mass estimator to interpret the stellar proper
motions. Since, as shown, the unknown spin of the suspected black hole
contributes only another 10\% uncertainty, one can conservatively
predict the angular diameter of the shadow in Sgr A* from the GR
calculations alone to be $\sim30\pm7\,
\mu$arcseconds independent of wavelength. As seen in
Fig.~\ref{bhimage}, the finite telescope resolution and the scatter
broadening will make the detectability of the shadow a function of
wavelength and emissivity; however, the size of the shadow will remain
of similar order of magnitude and cannot become smaller under any
circumstance.

The technical methods to achieve such a resolution at wavelengths
shortwards of 1.3 mm are currently being developed and a first
detection of Sgr A* at 1.4 mm with VLBI has already been reported. The
challenge will be to push this tech\-nology even further towards 0.8
or even 0.6 mm VLBI. Over the next decade many more telescopes are
expected to operate at these wavelengths.  Depending on how short a
wavelength is required, the projected time scale for developing the
necessary VLBI techniques may be about ten years.  A fundamental
problem preventing such an experiment is not now apparent, but in
light of our results, planning of the new submm-telescopes should
include sufficient provisions for VLBI experiments.


A potential problem with the model could be the unknown morphology of
the emission region. Strong velocity fields and density
inhomogeneities would make an identification of the shadow in an
observed image more difficult. However, inhomogeneities are unlikely
to be a major issue, since the time scale for rotation around the
black hole in the Galactic Center is only a few hundred seconds and
hence much less than the typical duration of a VLBI observation. The
strong shear near the black hole would tend to smooth out any
inhomogeneities very quickly. Indeed, submm variability studies on
such short time scales \cite{GwinnDanenTran1991} have yielded negative
results. The same argument applies to emission models which are offset
from the black hole, e.g., are one-sided. Since the shadow of the
black hole has a very well defined shape it would under any conditions
appear as a distinct feature, given that the dynamic range of the map
is large enough (i.e., $\ga$100:1, considering a range of emission
models, Agol et al., in prep.).

Finally, synchrotron self-absorption could pose a problem. So far the
available submm spectra show a flattening of the spectrum around
1.3-0.6 mm indicating a turnover towards an optically thin spectrum.

The importance of the proposed imaging of Sgr A* at submm wavelengths
with VLBI cannot be overemphasized.  The bump in the spectrum of Sgr
A* (Sec.~\ref{bump} strongly suggests the presence of a compact
component whose proximity to the event horizon is predicted to result
in a shadow of measurable dimensions in the intensity map. Such a
feature seems unique and Sgr~A* seems to have all the right parameters
to make it observable.  The observation of this shadow would confirm
the widely held belief that most of the dark mass concentration in the
nuclei of galaxies such as ours is contained within a black hole, and
it would be the first direct evidence for the existence of an event
horizon largely independent of any modelling. A non-detection with
sufficiently developed techniques, on the other hand, might pose a
major problem for the standard black hole paradigm. Because of this
fundamental importance, the experiment proposed here should be a major
motivation for intensifying the current development of submm astronomy
in general and mm- and submm-VLBI in particular.

This result also shows the outstanding position Sgr A* has among known
radio cores. For other supermassive black holes, with the exception
perhaps of the very massive black hole in M87, the shadow will be much
smaller than in Sgr A* because of the much larger distances.


\chapter{Low-Luminosity AGN}\label{llagn}
In Chapter \ref{symbiosis} we have discussed the general theory of
compact radio cores and the jet-disk symbiosis. The conclusion was
that compact radio cores are rather scale invariant and only subject
to changes in the accretion rate onto the central black hole. As a
consequence, the paper by \citeN{FalckeBiermann1996} basically
predicted the presence of a large number of galaxies with faint radio
cores at low levels of activity.  With the finding of black holes in
many nearby galaxies and the identification of a huge crowd of
low-luminosity AGN, many of them compiled in the spectroscopic atlas
by \citeN{HoFilippenkoSargent1995}, it was clear that from this theory
one would expect a large number of galaxies with compact radio cores
(see also \citeNP{Perez-FournonBiermann1984}). These radio cores
should bridge the gap between Sgr A* and quasars.  The imperative then
was to find them in a significant number and compare their properties
with more luminous counter parts.

This comparison is also important since the question of how central
engines in high and low-luminosity AGN are related to each other and
why they appear so different despite being powered by the same type of
object is of major interest. For many nearby galaxies with
low-luminosity nuclear emission-lines, it is not even clear whether
they are indeed powered by an AGN or by star formation {}--{} despite
many of them being dubbed LLAGN.

Earlier surveys have shown that E and S0 galaxies often have compact,
flat-spectrum radio sources in their nuclei
\cite{WrobelHeeschen1984,SleeSadlerReynolds1994}.  Some of the most
prominent flat-spectrum nuclear radio sources in nearby galaxies are
found in galaxies with LINER nuclear spectra
\cite{O'ConnellDressel1978}, but so far there has been no
comprehensive study of radio nuclei in a significant sample of LINER
galaxies, which make up the majority of galaxies with low-level
nuclear activity. We have, therefore, recently conducted a survey of
LINER galaxies with the Very Large Array (VLA;
\citeNP{ThompsonClarkWade1980}) in its A configuration at 15 GHz
(resolution $\sim$0\farcs15) and the VLBA \cite{NapierBagriClark1994}
at 5 GHz (resolution $\sim$0\farcs002) to search for compact radio
emission (\citeNP{NagarFalckeWilson2000,FalckeNagarWilson2000}).  In
the following sections the results of this search for ``siblings of
Sgr A*'' and their interpretation are presented.


\section[VLA Detection of Radio Cores]{Detection of Flat-Spectrum Radio Cores with the VLA}
\citeme{NagarFalckeWilson2000}
Observations were made of two samples
\cite{NagarFalckeWilson2000,FalckeNagarWilson2000}. All sources were
drawn from the extensive and sensitive spectroscopic study of the
complete, magnitude-limited sample of 486 nearby galaxies mentioned
above
\cite{HoFilippenkoSargent1995}, one third of which showed LINER-like
activity \cite{HoFilippenkoSargent1997a}. From these active galaxies
with a LINER spectrum a subsample (dubbed ``48 LINERs'' sample) of 48
bright sources was drawn with no well-defined selection criterion
other than that they had been observed with other telescopes as well,
e.g., ROSAT, the HST (UV imaging,
\citeNP{MaozFilippenkoHo1996,BarthHoFilippenko1998}), and the VLA at
1.4 and 8.4 GHz in A and B configuration
\cite{vanDykHo1998}.  The sample also included so-called transition
objects which have spectra intermediate between LINER and \ion{H}{2}
region galaxies. While the project was being conducted a few sources
in the original LINER sample were re-classified as low-luminosity
Seyfert galaxies. Transition objects were included because for these
objects it was not clear whether their emission-line spectrum is
produced by intense star formation or whether they are simply LINERs
with a very faint AGN.

In a second step we compiled a distance limited sample (dubbed ``96
LLAGN'' sample) from the \cite{HoFilippenkoSargent1995} atlas,
selecting all galaxies with LINER, Seyfert, and transition spectra
within 19 Mpc. This will reduce the effects of any bias that might
have come from the rather ill-defined selection criterion of the first
sample.  By including LINERs, Seyferts, and Transition objects we will
also be able to see possible differences in the detection rates
between the different types. By choosing a distance limited sample,
constrained to the very local universe, we also make sure to study the
faintest AGN we can find today.

Both samples were observed with the VLA at 15 GHz in its largest
configuration (A) providing maximal resolution, i.e.~up to 0\farcs15
corresponding to a linear scale of 14 pc at a distance of 19 Mpc. The
$5\sigma$ detection limit was around 1 mJy.

The rationale behind going to this setup is that the extended emission
from AGN is optically thin and steep-spectrum. Radio cores, on the
other hand -- if they are produced on scales very close to the AGN --
are optically thick, and compact at milli-arcsecond scales. This means
that by going to the configuration with the highest resolution one
will resolve out most of the extended emission and get a clearer view
on the compact structure. At higher frequencies this effect is even
stronger since the beam size is inversely proportional to the
frequency, reducing the extended flux per beam. The steep spectrum
will diminish the flux density of the extended emission even further.
The reason that one does not go to even higher frequencies is simply a
technical one, since the achievable sensitivity with the current
instrumentation of the VLA becomes increasingly worse at 22 and 43
GHz.

The results of the first survey for the 48 LINERs is summarized in
Table~\ref{48tab}. The first striking result is that we detected
relatively many, namely 18 out of 48 galaxies (37\%). Split into
the different groups we detected only 1 out of 18 transition objects,
but 6 out of 8 Seyferts and 11 out of 22 LINERs, yielding a combined
detection rate for Seyferts and LINERs of 57\% compared to only 6\%
for transition objects.

Using literature data (the VLA data at lower frequencies is still
being processed by another group) it was possible to determine whether
the detected cores should be considered as flat- or steep-spectrum
cores.  Out of the 18 detected cores only two apparently had a steep
radio spectrum. Hence, the 15 GHz VLA observations were indeed
properly designed to discriminate against steep-spectrum emission and
to pick out the flat-spectrum cores.

The high detection rate is confirmed by observations of the second
sample summarized in Table~\ref{96tab}. Since this is a distance
limited sample selection effects should be minimized. The detection
rate is 40 out of 96 galaxies, i.e.~42\%. In the sample we detected
only 5 out of 28 transition galaxies (18\%), while we detected 35 out
of 68 Seyferts and LINERs (51\%). At least 28 out of 68 Seyferts and
LINERs have flat-spectrum cores (41\%), while only 3 out of 28
transition objects do (11\%), two of which are in doubt.

We can therefore conclude that galaxies with Seyfert and LINER spectra
are much more likely to contain flat-spectrum radio cores than
transition objects. The latter are therefore probably significantly
weaker AGN or are largely dominated by starbursts. On the other hand,
if one considers flat-spectrum cores as evidence for a black hole
powered AGN, we can conclude that at least about half of LINERs and
Seyferts are indeed genuine AGN.  If we can combine both samples we
find no significant difference in the detection rates between Seyferts
and LINERs. Given the difficulty of finding clear AGN evidence in
these weakly active galaxies by looking for broad emission-lines
\cite{HoFilippenkoSargent1997c} the VLA survey at 15 GHz seems to be a
relatively efficient way of identifying AGN.

However, these conclusions all rest on the assumption of flat-spectrum
cores being AGN related. In principle the flat spectrum could also be
produced by a giant free-free emission region in a star forming
region. To exclude this possibility one needs to go to even higher
resolution and observe the respective galaxies with VLBI. This will
allow one to probe brightness temperatures around $10^8$ K for the
cores of interest here and distinguish between the two cases. The
attempt to do this is described in the next chapter.




\begin{deluxetable}{llrrrrrrrcl}
\tablecolumns{11}
\scriptsize
%\tablenum{1}
\tablewidth{0pt}
\tablecaption{NEW 2~CM VLA OBSERVATIONS OF LOW-LUMINOSITY AGNs}
\tablehead{
\colhead{Name} & \colhead{Activity}  & \colhead{T} & \colhead{R.A.} &
     \colhead{Dec.}  & \colhead{$\Delta$} & \colhead{Peak A} &
     \colhead{Total A} & 
   \colhead{Dist.} & 
     \colhead{Log P$_{2cm}^{core}$} & \colhead{$\alpha$} \\
\colhead{}     & \colhead{Type}      & \colhead{ } & \colhead{(B1950)} &
     \colhead{(B1950)} & \colhead{($\arcsec$)} & \colhead{(mJy)} &
     \colhead{(mJy)} &
     \colhead{(Mpc)} &
     \colhead{(W Hz$^{-1}$)}         & \colhead{ } \\
\colhead{(1)}     & \colhead{(2)}      & \colhead{(3)} & \colhead{(4)} &
     \colhead{(5)}   & \colhead{(6)} & \colhead{(7)} &
     \colhead{(8)} &        \colhead{(9)}        & \colhead{(10)} &
     \colhead{(11)} 
     }
\startdata
   NGC 185 & S2          & -5.0 & 00 36 09.993 &  48 03 50.20 &       14.5 &       0.8 &       0.8 &    0.7 &      16.67 & ?       \nl 
   NGC 266 & L1.9        &  2.0 & 00 47 05.247 &  32 00 20.04 &        1.9 &       4.1 &       4.1 &   62.4 &      21.28 & F       \nl 
   NGC 404 & L2          & -3.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.3 & $<$   1.3 &    2.4 & $<$  17.95 & \nodata \nl 
  NGC 2655 & S2          &  0.0 & 08 49 08.450 &  78 24 48.31 &        2.4 &       6.0 &       6.0 &   24.4 &      20.63 & S       \nl 
  NGC 2681 & L1.9        &  0.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.4 & $<$   1.4 &   13.3 & $<$  19.48 & \nodata \nl 
  NGC 2787 & L1.9        & -1.0 & 09 14 49.468 &  69 24 50.81 &        1.6 &       7.0 &       7.0 &   13.0 &      20.15 & F       \nl 
  NGC 3147 & S2          &  4.0 & 10 12 39.818 &  73 39 00.79 &        1.6 &       8.0 &       8.1 &   40.9 &      21.21 & F       \nl 
  NGC 3169 & L2          &  1.0 & 10 11 39.413 &  03 42 52.60 &        3.5 &       6.8 &       6.8 &   19.7 &      20.50 & F       \nl 
  NGC 3226 & L1.9        & -5.0 & 10 20 43.173 &  20 09 06.52 &        0.9 &       5.0 &       5.4 &   23.4 &      20.55 & F       \nl 
  NGC 3642 & L1.9        &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.3 & $<$   1.3 &   27.5 & $<$  20.06 & \nodata \nl 
  NGC 3692 & T2          &  3.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.2 & $<$   1.2 &   29.8 & $<$  20.09 & \nodata \nl 
  NGC 3705 & T2          &  2.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.2 & $<$   1.2 &   17.0 & $<$  19.61 & \nodata \nl 
  NGC 3917 & T2    :     &  6.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.2 & $<$   1.2 &   17.0 & $<$  19.63 & \nodata \nl 
  NGC 3953 & T2          &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.3 & $<$   1.3 &   17.0 & $<$  19.64 & \nodata \nl 
  NGC 3992 & T2    :     &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.3 & $<$   1.3 &   17.0 & $<$  19.64 & \nodata \nl 
  NGC 4036 & L1.9        & -3.0 & 11 58 52.765 &  62 10 27.73 &        2.4 & $<$   1.5 & $<$   1.5 &   24.6 & $<$  20.04 & \nodata \nl 
  NGC 4111 & L2          & -1.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.3 & $<$   1.3 &   17.0 & $<$  19.64 & \nodata \nl 
  NGC 4143 & L1.9        & -2.0 & 12 07 04.547 &  42 48 44.27 &        1.5 &       3.3 &       3.3 &   17.0 &      20.06 & F       \nl 
  NGC 4145 & T2    :     &  7.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.3 & $<$   1.3 &   20.7 & $<$  19.81 & \nodata \nl 
  NGC 4192 & T2          &  2.0 & 12 11 15.488 &  15 10 39.62 &        1.5 & $<$   1.3 & $<$   1.3 &   16.8 & $<$  19.64 & \nodata \nl 
  NGC 4203 & L1.9        & -3.0 & 12 12 33.943 &  33 28 30.35 &        1.0 &       9.5 &       9.5 &    9.7 &      20.03 & F       \nl 
  NGC 4216 & T2          &  3.0 & 12 13 21.559 &  13 25 38.16 &        0.5 & $<$   2.0 & $<$   2.0 &   16.8 & $<$  19.83 & \nodata \nl 
  NGC 4220 & T2          & -1.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.4 & $<$   1.4 &   17.0 & $<$  19.70 & \nodata \nl 
  NGC 4278 & L1.9        & -5.0 & 12 17 36.307 &  29 33 29.56 &        0.5 &      88.3 &      89.7 &    9.7 &      21.00 & F       \nl 
  NGC 4419 & T2          &  1.0 & 12 24 24.661 &  15 19 25.84 &        3.2 & $<$   2.8 & $<$   2.8 &   16.8 & $<$  19.98 & \nodata \nl 
  NGC 4429 & T2          & -1.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   16.8 & $<$  19.57 & \nodata \nl 
  NGC 4435 & T2/H:       & -2.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   16.8 & $<$  19.57 & \nodata \nl
  NGC 4527 & T2          &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   13.5 & $<$  19.38 & \nodata \nl 
  NGC 4548 & L2          &  3.0 & 12 32 55.276 &  14 46 17.60 &        1.8 &       1.2 &       1.2 &   16.8 &      19.61 & F       \nl 
  NGC 4550 & L2          & -1.5 & 12 32 58.493 &  12 29 49.50 &        9.3 &       0.7 &       0.7 &   16.8 &      19.37 & F       \nl 
  NGC 4565 & S1.9        &  3.0 & 12 33 52.014 &  26 15 45.87 &        3.9 &       3.7 &       3.7 &    9.7 &      19.62 & F       \nl 
  NGC 4569 & T2          &  2.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   16.8 & $<$  19.57 & \nodata \nl 
  NGC 4579 & S1.9/L1.9   &  3.0 & 12 35 12.000 &  12 05 34.85 &        0.7 &      27.6 &      28.3 &   16.8 &      20.98 & F       \nl 
  NGC 4636 & L1.9        & -5.0 & 12 40 16.660 &  02 57 41.64 &        2.5 &       1.6 &       1.9 &   17.0 &      19.82 & S       \nl 
  NGC 4639 & S1.0        &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   16.8 & $<$  19.57 & \nodata \nl 
  NGC 4651 & L2          &  5.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   16.8 & $<$  19.57 & \nodata \nl 
  NGC 4866 & L2          & -1.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   16.0 & $<$  19.53 & \nodata \nl 
  NGC 5005 & L1.9        &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   21.3 & $<$  19.78 & \nodata \nl 
  NGC 5033 & S1.5        &  5.0 & 13 11 09.169 &  36 51 30.37 &        1.3 &       1.4 &       1.4 &   18.7 &      19.77 & F       \nl 
  NGC 5055 & T2          &  4.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &    7.2 & $<$  18.83 & \nodata \nl 
  NGC 5273 & S1.5        & -2.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   21.3 & $<$  19.78 & \nodata \nl 
  NGC 5566 & L2          &  2.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   26.4 & $<$  19.96 & \nodata \nl 
  NGC 5701 & T2    :     &  0.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   26.1 & $<$  19.95 & \nodata \nl 
  NGC 5866 & T2          & -1.0 & 15 05 07.121 &  55 57 17.77 &        0.3 &       7.1 &       7.5 &   15.3 &      20.32 & F       \nl 
  NGC 6500 & L2          &  1.7 & 17 53 48.137 &  18 20 39.90 &        1.5 &      83.5 &      85.0 &   39.7 &      22.21 & F       \nl 
  NGC 7217 & L2          &  2.0 & 22 05 37.830 &  31 06 51.50 &        2.7 & $<$   0.6 & $<$   0.6 &   16.0 & $<$  19.23 & \nodata \nl 
  NGC 7742 & T2/L2       &  3.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   22.2 & $<$  19.81 & \nodata \nl
  NGC 7814 & L2    ::    &  2.0 &    \nodata   &    \nodata   &    \nodata & $<$   1.1 & $<$   1.1 &   15.1 & $<$  19.48 & \nodata \nl 
 
\tablenotetext{}{\label{48tab}Columns are: (1)~galaxy name;
(2)~nuclear activity type as given by H97a.
`L' represents LINER, `S' represents Seyfert,
`H' represents an H~II region type spectrum, and
`T' represents objects with transitional `L' + `H' spectra.
%The numbers are classification`2' implies that no broad H$\alpha$ is detected,
%`1.9' implies that broad H$\alpha$ is present, but
%not broad H$\beta$,
%and `1.0' or `1.5' implies that both broad H$\alpha$ and
%broad H$\beta$ are detected, with the specific type depending
%on the ratio of
%the flux in [O~III]~$\lambda$5007 to the flux in
%broad + narrow H$\beta$ (e.g., Osterbrock 1981).
The `:' and `::' symbols represent uncertain, and highly uncertain,
classifications, respectively;
(3)~Hubble morphological parameter T as listed in H97a;
(4) and (5)~2~cm radio position, from our maps;
(6)~offset, in arcsec, between the 2~cm radio position and the position of
the galaxy optical nucleus listed in Cotton et al. 2000;
(7) and (8)~peak and total flux density, obtained by fitting a single Gaussian,
using task JMFIT, to the radio peak in the A-array image;
(9)~distance in Mpc to galaxy, as listed in H97a;
(10)~the logarithm of the core radio power (derived from the {\it{peak}}
radio flux in the A-array image);
(11)~indication of whether the radio spectrum of the A-array 2~cm  
detected core is {\textbf{S}}teep or {\textbf{F}}lat;
%($\alpha <~-$0.3; S$_\nu \propto \nu^{\alpha}$), 
%($\alpha \geq~-$0.3);
(H97a=Ho, Filippenko, Sargent 1997a)}
\enddata
\end{deluxetable}



\begin{deluxetable}{llrrrrrrrrcc}
\tablecolumns{12}
\tiny
%\tablenum{1}
\tablewidth{0pt}
\tablecaption{NEW 2~CM VLA OBSERVATIONS OF A DISTANCE-LIMITED LLAGN SAMPLE}
\tablehead{
\colhead{Source }&
\colhead{ Typ }&
\colhead{ $T$ }&
\colhead{ $D$   }&
\colhead{ log H$\alpha$    }&
\colhead{ $S_{\rm 15 GHz,p}$ }&
\colhead{ $S_{\rm 15 GHz,t}$ }&
\colhead{ $S_{\rm 1.4 GHz}$ }&
\colhead{ $\alpha$ }&
\colhead{ }&
\colhead{RA     }&
\colhead{ DEC}\\
\colhead{       }&
\colhead{     }&
\colhead{     }&
\colhead{ [Mpc] }&
\colhead{ [erg/sec/cm$^2$] }&
\colhead{ [mJy]              }&
\colhead{  [mJy]             }&
\colhead{ [mJy]             }&
\colhead{          }&
\colhead{ }&
\colhead{(B1950) }&
\colhead{(B1950)}\\
\colhead{(1)}     & \colhead{(2)}      & \colhead{(3)} & \colhead{(4)} &
     \colhead{(5)}   & \colhead{(6)} & \colhead{(7)} &
     \colhead{(8)} &        \colhead{(9)}        & \colhead{(10)} &
     \colhead{(11)}               & \colhead{(12)} 
     }
\startdata
NGC2541 & T2/H:     &  6 & 10.6 & -14.9 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC2683 & L2/S2     &  3 &  5.7 & -14.4 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC2685 & S2/T2:    & -1 & 16.2 & -13.8 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC2787 & L1.9      & -1 & 13.0 & -13.8 &   11.1 &      11.4 &      11.3 &    -0.01 &  F & 09:14:49.47 &  69:24:50.82 \\
NGC2841 & L2        &  3 & 12.0 & -13.7 &    1.1 &       2.1 &      35.9 &    -1.34 &  F & 09:18:35.84 &  51:11:24.11 \\
NGC3031 & S1.5      &  2 &  3.3 & -12.7 &  164.1 &     164.8 &      88.9 &     0.25 &  F & 09:51:27.31 &  69:18:08.15 \\
NGC3368 & L2        &  2 &  8.1 & -13.6 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC3379 & L2/T2::   & -5 &  8.1 & -13.9 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC3486 & S2        &  5 &  7.4 & -14.0 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC3489 & T2/S2     & -1 &  6.4 & -13.5 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC3623 & L2:       &  1 &  7.3 & -14.0 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC3627 & T2/S2     &  3 &  6.6 & -13.2 &    1.1 &       2.9 & $<$ 324.9 & $>$-2.27 &    & 11:17:38.48 &  13:15:55.74 \\
NGC3628 & T2        &  3 &  7.7 & -15.0 &    1.5 &      28.0 &     291.7 &    -1.96 & $*$& 11:17:40.34 &  13:51:46.10 \\
NGC3675 & T2        &  3 & 12.8 & -14.1 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC3718 & L1.9      &  1 & 17.0 & -14.1 &   10.5 &      10.8 &      16.5 &    -0.19 &  F & 11:29:49.91 &  53:20:38.47 \\
NGC3982 & S1.9      &  3 & 17.0 & -13.3 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4013 & T2        &  3 & 17.0 & -14.7 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4051 & S1.2      &  4 & 17.0 & -12.5 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4138 & S1.9      & -1 & 17.0 & -14.0 &    1.5 &       1.3 &      20.5 &    -1.15 &  F & 12:06:58.34 &  43:57:48.12 \\
NGC4143 & L1.9      & -2 & 17.0 & -13.8 &    9.8 &      10.0 &      10.8 &    -0.03 &  F & 12:07:04.55 &  42:48:44.26 \\
NGC4150 & T2        & -2 &  9.7 & -13.9 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4168 & S1.9:     & -5 & 16.8 & -14.9 &    3.0 &       3.1 &       6.0 &    -0.29 &  F & 12:09:44.27 &  13:28:59.62 \\
NGC4203 & L1.9      & -3 &  9.7 & -13.7 &    8.8 &       9.0 &       6.6 &     0.13 &  F & 12:12:33.94 &  33:28:30.48 \\
NGC4216 & T2        &  3 & 16.8 & -14.0 &    1.2 &       1.3 &       6.9 &    -0.73 & F? & 12:13:21.62 &  13:25:38.11 \\
NGC4258 & S1.9      &  4 &  6.8 & -13.4 &    2.6 &       3.0 & $<$   2.5 & $>$ 0.04 &  F & 12:16:29.37 &  47:34:53.19 \\
NGC4278 & L1.9      & -5 &  9.7 & -12.9 &   83.8 &      87.7 &     385.5 &    -0.63 &  F & 12:17:36.16 &  29:33:29.27 \\
NGC4293 & L2        &  0 & 17.0 & -13.8 &    0.7 &       1.4 &      19.3 &    -1.26 &    & 12:18:41.00 &  18:39:35.31 \\
NGC4314 & L2        &  1 &  9.7 & -13.6 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4321 & T2        &  4 & 16.8 & -13.5 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4346 & L2::      & -2 & 17.0 & -15.0 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4350 & T2::      & -2 & 16.8 & -14.3 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4374 & L2        & -5 & 16.8 & -13.6 &  180.7 &     183.7 & $<$3179.4 & $>$-1.21 &  F & 12:22:31.58 &  13:09:49.82 \\
NGC4388 & S1.9      &  3 & 16.8 & -12.5 &    2.2 &       3.7 &     120.4 &    -1.59 &    & 12:23:14.64 &  12:56:20.10 \\
NGC4394 & L2        &  3 & 16.8 & -14.2 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4395 & S1.8      &  9 &  3.6 & -13.3 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4414 & T2:       &  5 &  9.7 & -14.0 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4419 & T2        &  1 & 16.8 & -13.3 &    2.7 &       3.6 &      55.4 &    -1.24 &    & 12:24:24.72 &  15:19:26.54 \\
NGC4438 & L1.9      &  0 & 16.8 & -13.2 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4450 & L1.9      &  2 & 16.8 & -13.7 &    2.0 &       2.7 &      10.3 &    -0.64 & F? & 12:25:58.28 &  17:21:40.94 \\
NGC4457 & L2        &  0 & 17.4 & -13.0 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4459 & T2:       & -1 & 16.8 & -13.8 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4472 & S2::      & -5 & 16.8 & -14.9 &    3.7 &       4.1 &     221.3 &    -1.74 &    & 12:27:14.18 &  08:16:36.00 \\
NGC4477 & S2        & -2 & 16.8 & -13.7 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4486 & L2        & -4 & 16.8 & -13.1 & 2725.7 &    2835.7 &    138488.0 &    -1.67 &  F & 12:28:17.57 &  12:40:01.74 \\
NGC4494 & L2::      & -5 &  9.7 & -14.5 &        & $<$   0.8 &           &          &    & --          & --           \\
NGC4501 & S2        &  3 & 16.8 & -13.6 &        & $<$   1.1 &           &          &    & --          & --           \\
NGC4548 & L2        &  3 & 16.8 & -14.1 &    1.4 &       1.6 & $<$   2.5 & $>$-0.24 &  F & 12:32:55.28 &  14:46:17.65 \\
NGC4552 & T2:       & -5 & 16.8 & -14.0 &   58.1 &      58.6 &     103.1 &    -0.25 &  F & 12:33:08.29 &  12:49:53.58 \\
NGC4565 & S1.9      &  3 &  9.7 & -14.1 &    3.1 &       3.1 &      58.3 &    -1.23 &    & 12:33:52.02 &  26:15:45.89 \\
NGC4579 & S/L1.9 &  3 & 16.8 & -13.1 &   20.8 &      20.6 &      98.2 &    -0.66 &  F & 12:35:12.00 &  12:05:34.85 \\
NGC4596 & L2::      & -1 & 16.8 & -14.6 &        & $<$   1.1 &           &          &    & --          & --           \\
NGC4636 & L1.9      & -5 & 17.0 & -14.3 &    1.6 &       1.8 &      78.7 &    -1.63 &  F & 12:40:16.66 &  02:57:41.58 \\
NGC4698 & S2        &  2 & 16.8 & -13.8 &        & $<$   1.0 &           &          &    & --          & --           \\
NGC4713 & T2        &  7 & 17.9 & -14.4 &        &       1.1 &           &          &    & --          & --           \\
NGC4725 & S2:       &  2 & 12.4 & -14.1 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC4736 & L2        &  2 &  4.3 & -13.6 &    1.9 &       1.7 &     269.9 &    -2.13 &  F & 12:48:31.92 &  41:23:31.36 \\
NGC4762 & L2:       & -2 & 16.8 & -15.0 &    0.9 &       1.3 & $<$   2.5 & $>$-0.38 &  F & 12:50:25.14 &  11:30:03.27 \\
NGC4772 & L1.9      &  1 & 16.3 & -14.0 &    3.3 &       3.4 & $<$   2.5 & $>$ 0.13 &  F & 12:50:56.00 &  02:26:22.36 \\
NGC4826 & T2        &  2 &  4.1 & -13.1 &        & $<$   0.9 &           &          &    & --          & --           \\
NGC5194 & S2        &  4 &  7.7 & -13.0 &        & $<$   1.1 &           &          &    & --          & --           \\
NGC5195 & L2:       & 10 &  9.3 & -14.1 &        & $<$   1.1 &           &          &    & --          & --           \\
NGC5879 & T2/L2     &  4 & 16.8 & -14.2 &        & $<$   1.1 &           &          &    & --          & --           \\
NGC6503 & T2/S2:    &  6 &  6.1 & -14.1 &        & $<$   1.0 &           &          &    & --          & --           \\
\tablenotetext{}{\label{96tab}Here we only list the galaxies not yet listed in
Table~\ref{48tab}. The distance-limited sample consists of all
galaxies with D$<$19 Mpc in Table~\ref{48tab} and Table~\ref{96tab}. Columns are: (1)~galaxy name;
(2)~nuclear activity type as given by H97a.
`L' represents LINER, `S' represents Seyfert,
`H' represents an H~II region type spectrum, and
`T' represents objects with transitional `L' + `H' spectra.
`2' implies that no broad H$\alpha$ is detected,
`1.9' implies that broad H$\alpha$ is present, but
not broad H$\beta$,
and `1.0' or `1.5' implies that both broad H$\alpha$ and
broad H$\beta$ are detected, with the specific type depending
on the ratio of
the flux in [O~III]~$\lambda$5007 to the flux in
broad + narrow H$\beta$ (e.g., Osterbrock 1981).
The `:' and `::' symbols represent uncertain, and highly uncertain,
classifications, respectively;
(3)~Hubble morphological parameter T as listed in H97a;
(4)~distance in Mpc to galaxy, as listed in H97a;
(5)~H$\alpha$-luminosity as listed in H97a;
(6) and (7)~peak and total flux density, obtained by fitting a single Gaussian,
using task JMFIT, to the radio peak in the A-array image;
(8)~flux density at 1.4 GHz obtained from the NVSS survey {}--{} the beam
is more than a hundred times larger than at 15 GHz and can include a lot of
extended emission;
(9)~spectral index between 1.4 GHz (NVSS) and 15 GHz {}--{} is meaningless
for sources with a large extended emission but useful for finding flat 
spectrum cores;
(10)~spectral index flat: ``F'' marks sources where comparison with
data from the literature at other frequencies indicates a
flat-spectrum core in conjunction with our 15 GHz data, $*$NGC3628 has very
extended 15 GHz emission belonging to a known star forming region;
(11) and (12)~15~GHz radio position, from our maps;
(H97a=Ho, Filippenko, Sargent 1997a)
}
\enddata
\end{deluxetable}
\nocite{Osterbrock1981}



\section[VLBA Detection of Radio Cores]{Detection of Flat-Spectrum Radio Cores with the VLBA}
\citeme{FalckeNagarWilson2000}


Our 15~GHz VLA survey found a surprisingly large number of galaxies
with compact radio cores and flat spectral indices.  The prediction
from this VLA study and from our theoretical modeling was that this
radio emission comes from high brightness temperature radio cores
produced by genuine AGN. In this section we present Very Long Baseline
Array (VLBA) observations of these galaxies to test this notion and to
investigate the central region of LINER galaxies at the sub-parsec
scale. Such investigations were made for both samples described
above. Data reduction and evaluation for the distance limited sample
is still going on and here we will concentrate on observations of the
48 LINERs.


From our 48 LINERs sample (previous chapter), we selected all eleven
galaxies with both nuclear flux densities above 3.5 mJy at 15 GHz and
a flat spectrum ($\alpha>-0.5,\; S_\nu\propto\nu^\alpha$). Only one
source, NGC~2655, was above the flux density limit and was excluded
because of its steep spectrum. The flux density limit was chosen so
that we could detect all sources with the VLBA in snapshot mode in a
single 12 hr observation if most of the 15 GHz emission were indeed
compact on milli-arcsecond (mas) scales. Because of the low flux
densities the phase-referencing technique had to be used. The
observations of NGC~3147 failed since the phase-calibrator was not
detected, thus reducing our sample to ten sources.  The data reduction
is more extensively described in \citeN{FalckeNagarWilson2000}.

\begin{deluxetable}{lrrcllrrrrrrr}
\scriptsize
\tablecolumns{13}
\tablewidth{0pt}
\tablecaption{Properties of VLBA LINER sample}
\tablehead{
\colhead{(1)}&\colhead{(2)}&\colhead{(3)}&\colhead{(4)}&\colhead{(5)}&\colhead{(6)}&\colhead{(7)}&\colhead{(8)} & \colhead{(9)}&\colhead{(10)}&\colhead{(11)}&\colhead{(12)}&\colhead{(13)}\\
\colhead{Name}&\colhead{D}&
\colhead{T}&\colhead{spec.}&\colhead{R.A.}&\colhead{Dec.}&\colhead{$\Delta_{\rm 
pos}$}&\colhead{$S_{\rm 5 GHz}^{\rm total}$}&\colhead{$S_{\rm 5
GHz}^{\rm peak}$}&\colhead{$T_{\rm b}$}
& P.A.&\colhead{$S_{\rm 15 GHz}^{\rm VLA}$}&\colhead{$\alpha$}\\
\colhead{}&\colhead{[Mpc]}&\colhead{}&\colhead{}&\colhead{(J2000)}&\colhead{(J2000)}&\colhead{[mas]}&\colhead{[mJy]}&\colhead{[mJy]}&\colhead{[$10^8$K]}&\colhead{[$^\circ$]}&\colhead{[mJy]}&\colhead{}}
\startdata
NGC~266  &62.4& 2&L1.9& 00 49 47.8174  &+32 16 39.749& 55 &3.8  &3.2  & 0.25 &    & 4.1  & 0.07 \\
NGC~2787 &13.0&-1&L1.9& 09 19 18.6095  &+69 12 11.690& 10 &11.5 &11.2 & 0.87 &    & 7.0  &-0.45\\
NGC~3169 &19.7& 1&L2.0& 10 14 15.0500  &+03 27 57.844& 14 &6.6  &6.2  & 0.48 &    & 6.8  & 0.03 \\
NGC~3226 &23.4&-5&L1.9& 10 23 27.0113  &+19 53 54.496& 150&4.8  &3.5  & 0.27 &(64)& 5.0  & 0.04\\
NGC~4203 &9.7 &-3&L1.9& 12 15 05.0519  &+33 11 50.359& 55 &8.9  &8.9  & 0.69 &    & 9.5  & 0.06\\
NGC~4278 &9.7 &-5&L1.9& 12 20 06.8254  &+29 16 50.715& 1  &87.3 &37.2 & 2.9  &163 & 88.3 & 0.01\\%
NGC~4565 &9.7 & 3&S1.9& 12 36 20.7820  &+25 59 15.632& 55 &3.1  &3.2  & 0.25 &    & 3.7  & 0.16\\
NGC~4579 &16.8& 3&L1.9& 12 37 43.5222  &+11 49 05.488& 1  &21.3 &21.3 & 1.7  &    & 27.6 & 0.23\\%
NGC~5866 &15.3&-1&T2.0& 15 06 29.4989  &+55 45 47.568& 1  &8.4  &7.0  & 0.55 &(11)& 7.1  &-0.15\\
NGC~6500 &39.7& 2&L2.0& 17 55 59.7827  &+18 20 17.661& 14 &83.6 &35.8 & 2.8  & 39 & 83.5 & 0.00\\%
\enddata

\tablecomments{\label{48VLBA}The columns are: (1) galaxy name; (2) distance in Mpc; 
(3) host galaxy morphological type from RC3; 
(4) spectroscopical AGN classification:
L=LINER, S=Seyfert, T=H II Transition galaxy; (5~\&~6) VLBI J2000 coordinates; 
(7) position uncertainty of phase referencing calibrator in
milli-arcsecond (mas);
(8) total flux
density at 5~GHz (VLBA); (9) peak flux density at 5~GHz (VLBA); 
(10) brightness temperature in $10^8$ K;
(11)
position angle, measured N through E, of 5~GHz radio core if extended; 
values in brackets are very uncertain;
(12) peak VLA flux density at 15~GHz (Nagar et al. 2000); 
(13) spectral index between peak 15~GHz (VLA) and total 5~GHz (VLBA) flux
     densities. 
Columns 2-4 are from Ho et al.~(1997).}
\end{deluxetable}

In the observations all ten remaining sources were detected with the
VLBA.  The results are shown in Table~\ref{48VLBA}, where we list the
galaxy names, distances (from Ho et al.~1997), Hubble galaxy type from
RC3 (de Vaucouleurs et al. 1991) and spectroscopic classification from
Ho et al.~(1997) in columns 1 - 4.  The detected sources are equally
distributed between early- and late-type galaxies. We also give the
positions of the radio sources (columns 5 and 6). The internal errors
of the positions should be about the beam size (2.5 milli-arcsecond) or better for
the stronger ones, but the absolute astrometric accuracy is limited by
the uncertainty in the positions of the phase calibrators, (listed in
column 7). In addition, we list the total and peak flux densities in
the VLBA maps and the brightness temperature (column 10, defined
below).  Our $1\sigma$ rms noise is typically 0.2 mJy and hence for
the weakest source we obtain a dynamic range of 15:1. For extended
sources we give the position angle (column 11) of an elliptical
Gaussian component fitted to the core. For comparison we also list the
peak VLA flux density at 15 GHz (column 12) from our previous survey
and the (non-simultaneous) spectral index $\alpha$ between the peak
VLA 15 GHz and total VLBA 5 GHz flux densities (column 13).

\begin{figure}
\centerline{\psfig{figure=Figures/NGC4278.ps,height=0.35\textwidth,bbllx=2.1cm,bburx=19.2cm,bblly=4.9cm,bbury=25.4cm,clip=}\quad\psfig{figure=Figures/NGC6500.ps,height=0.35\textwidth,bbllx=1.425cm,bburx=19.95cm,bblly=5.2cm,bbury=25.05cm,clip=}}
\caption[]{\label{LINVLBA}VLBA maps of NGC~4278 (left) and NGC~6500 (right). The beam is 2.5 milli-arcsecond and contours are integer powers
of $\sqrt{2}$, multiplied by the $\sim5\,\sigma$ noise level of 0.9
mJy.  The peak flux densities are 37.3 mJy and 35.8 mJy respectively.}
\end{figure}

The two brightest sources in our sample, NGC~4278 \& NGC~6500, for
which we have the largest dynamic range, show core plus jet structures
(Fig.~\ref{LINVLBA}). NGC~6500 has a core and a symmetric two-sided
jet, while NGC~4278 has an extended core and an elongated lobe
towards the SE. The other sources are point-like with the possible
exceptions of NGC~3226 and NGC~5866, although phase errors may be
responsible for the extension in these faint sources.  The spectral
indices range from $\alpha=-0.5$ to $\alpha=0.2$, with an average
$\left<\alpha\right>=0.0\pm0.2$. We note that the VLBA does not
provide spacings as short as the VLA. The VLBA measurements at 5 GHz
may then underestimate the true flux density if the sources are
extended below the 150 milli-arcsecond scale, so the actual spectrum might be less
inverted (i.e.~the spectral index smaller) than we measure here.

From the flux densities and the sizes we have measured, we can
calculate the brightness temperatures for a Gaussian flux density
distribution with the following equation


\begin{equation}
T_{\rm b}=7.8\times10^6\;{\rm K} \left({S_{\nu}\over{\rm mJy}}\right)\left({\theta\over{\rm 2.5\,mas}}\right)^{-2}\left({\nu\over{\rm 5\,GHz}}\right)^{-2}
\end{equation}
where $\theta$ is the FWHM of the Gaussian beam
(e.g., \citeNP{CondonCondonGisler1982}). Using our beam size of 2.5 milli-arcsecond
and the peak 5 GHz flux densities in Table~\ref{48VLBA}, we find
brightness temperatures in the range $T=0.25-2.9\times10^8$ K for our
sample, with an average brightness temperature for all sources of
$\left<T_{\rm b}\right>=1.0\times10^8$ K. Since most of our sources
are unresolved, these values are usually lower limits.


Our result has a number of interesting implications. The presence of
high brightness temperature radio cores in our LINER sample confirms
the presence of AGN-like activity in these galaxies. It is unlikely
that the radio sources represent free-free emission, as has been
claimed for example in NGC~1068 \cite{GallimoreBaumO'Dea1997}, since a
much higher soft X-ray luminosity than is typically observed in
low-luminosity AGN would result.  The emission coefficient for thermal
bremsstrahlung from a gas at temperature $T$ is (e.g., \citeNP{Longair1992},
eq.~3.43)
\begin{equation}\label{VLBA-ff}
\epsilon_\nu~= 6.8 \times 10^{-51} Z^2 T^{{\small{-\onehalf}}} N_p N_e
	      g(\nu, T) exp(- h\nu/kT)\, {\rm W m^{-3} Hz}^{-1}
\end{equation}
where $g(\nu, T)$ is the Gaunt factor.  If we consider a plasma at
temperature $T\simeq10^8$~K, then at 5~GHz, the exponential factor in
Eq.~(\ref{VLBA-ff}) is 1, while the Gaunt factor is $\sim$12.  In the soft X-ray
regime, taken as 0.4~keV to 2~keV, the Gaunt factor varies between 1.7
and 0.8, respectively, while the exponential factor in Eq.~\ref{VLBA-ff} varies
between 0.95 and 0.8, respectively.  Therefore, the luminosity, per
Hertz, at 0.4~keV and 2~keV is $\sim$0.25 times and $\sim$0.05 times
that at 5~GHz, respectively.  The geometric mean monochromatic
luminosities of the nuclei observed by us is 10$^{27.5\pm0.6}$ erg
sec$^{-1}$ Hz$^{-1}$ at 5~GHz. If this emission traces thermal
bremsstrahlung we would expect the total 0.4--2~keV luminosity of
these nuclei to be 10$^{43.9}$ erg s$^{-1}$.  However, the observed
0.4-2~keV luminosities for low-luminosity AGN tend to be of the order
of 10$^{39-40}$ erg s$^{-1}$ (e.g., \citeNP{PtakSerlemitsosYaqoob1999}) {}--{} many orders of
magnitude lower and thus rendering a thermal origin of the radio
emission very unlikely. Of course photo-electric absorption could
attenuate some of the soft X-ray emission, however, since seven of our
galaxies show broad H$\alpha$ emission (spectral type 1.9) the
absorption should only be moderate. To make this argument more
watertight one will need to investigate multiwavelength data for our
galaxies on a case-by-case basis.


On the other hand, the compact, flat-spectrum cores we have found are
similar to those typically produced in many AGN. Hence we can take the
presence of compact, non-thermal radio emission as good evidence for
the presence of an AGN in our galaxies.  The 100\% detection rate with
the VLBA, based on our selection of flat-spectrum cores found in a 15
GHz VLA survey, shows that for statistical purposes we could have
relied on the VLA alone for identification of these compact, high
brightness radio sources.  Hence, with 15 GHz VLA surveys of nearby
galaxies one has an efficient tool for identifying low-luminosity
AGN. This complements other methods for identifying AGN, such as
searching for broad emission-lines or hard X-rays, and has the
advantage of not being affected by obscuration. 

If we only consider galaxies with a LINER spectrum, we found at least
eleven flat-spectrum radio cores at 15 GHz in a sub-sample of 24
LINERs observed in the ``48 LINERs'' sample.  Eight of these eleven
LINERs are included in our sample here, yielding a lower limit to the
AGN fraction for LINERs of at least $33\pm12$\% (8/24). Based on our
100\% detection rate of these flat-spectrum cores with the VLBA, we
can, however, argue that all eleven flat spectrum sources found in the
VLA study are likely to be AGN, raising the AGN fraction of LINERs to
at least $46\pm14$\% (11/24). These ratios do not change significantly
if we include the galaxies classified as Seyferts. Since the selection
of our parent sample is not very well defined, we could still be
subject to an unquantifiable bias. However, the VLA observations of
the distance-limited sample reported above seem to indicate that the
bias is not large.

The two brightest radio sources in our sample show extended structure
suggestive of jet-like outflows, and the other seven sources are
unresolved or slightly resolved.  Our very limited dynamic range is
not good enough to prove or exclude the presence of jets for the
latter. VLBA observations of M81 \cite{BietenholzBartelRupen1999} have
shown that jets in low-luminosity AGN can be very compact and
difficult to detect. The only clue we therefore have is the spectrum
which is flat or slightly inverted. Such a behavior is predicted by
simple jet models \cite{Falcke1996a,FalckeBiermann1999}, where the
spectral index ranges from $\alpha=0.0$ to 0.23 as a function of
inclination angle to the line-of-sight. In no case do we find a
spectral index as high as $\alpha=0.4$ as predicted in the ADAF model
\cite{YiBoughn1998}. This does not necessarily exclude the ADAF model,
but argues for the parsec scale radio emission at centimeter radio
waves being dominated by another component, such as a radio jet or a
wind. A combination of an underluminous disk or an ADAF and a radio
jet is one possibility (e.g., \citeNP{DoneaFalckeBiermann1999}).

Finally, it is worth pointing out that Nagar et al.~(2000, in prep.) have
started to extend the VLBI sample to all galaxies in our two samples
with detected compact cores above 3 mJy. Preliminary data reduction
indicates that all galaxies, with the exception of NGC2655 which has a
steep-spectrum core, were detected at the level expected from our 15 GHz
VLA observations by assuming a flat spectrum. Among these, two
galaxies show again jet-like structures and since M87 and M81 are
well-known jet sources belonging to our sample, the six brightest
radio cores in our combined samples all have core-jet structures.

\section{Radio Cores in LLAGN  -- the Grand Perspective}
\citeme{FalckeNagarWilson2000,FalckeNagarWilson2000b}
Assuming the cores detected in the VLA \& VLBA survey are produced by
randomly oriented, maximally efficient jets from supermassive black
holes (of order $10^8 M_\odot$) we can use Eq.~\ref{jetpower} to
calculate that for an average monochromatic luminosity of $10^{27.5}$
erg sec$^{-1}$ Hz$^{-1}$ at 5 GHz the jets would require a minimum
{\em total} jet power of order $Q_{\rm jet}\ga10^{42.5}$ erg
sec$^{-1}$. The way the model was constructed one has to consider this
a minimum energy estimate. Compared to quasars this is a rather low
value and supports the conclusion, based on their low UV and
emission-line luminosities, that the cores are powered by under-fed
black holes. On the other hand this jet power is well within the range
of the bolometric luminosity of typical low-luminosity AGN
($10^{41-43}$ erg sec$^{-1}$;~\citeNP{Ho1999}) and, compared to
radiation, jets should be a significant energy loss channel for the
accretion flow.

This similarity between jet power and (accretion) luminosity, of
course, appeals again to the jet-disk symbiosis picture discussed at the
beginning of this work. We can now take the radio cores detected in
our survey and put them on the correlation predicted in
\citeN{FalckeBiermann1996}. A problem one encounters is how to
estimate the accretion disk luminosity. To make the different AGN
comparable we will use the narrow H$\alpha$ line that is measurable in
all AGN, and apply the same conversion factor between H$\alpha$ and
$L_{\rm disk}$ as used for quasars. For narrow H$\alpha$
Eq.~\ref{oiii2uv} then reads

\begin{equation}
\lg (L_{\rm disk}/{\rm erg\;s}^{-1})=4.85+\lg (L_{\rm H\alpha,n}/{\rm erg\;s}^{-1}).
\end{equation}
Figure \ref{theplot-all} shows the predicted Radio/$L_{\rm disk}$
correlation together with LLAGN found in our survey. The galaxies
almost fill the gap between quasars and X-ray binaries on this
absolute scale and fall in the predicted range. This illustrates that
we have a continuation from high-luminosity to low-luminosity AGN, {\em the
latter being the silent majority within the AGN family}.

\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/theplot-all.ps,width=0.7\textwidth,bbllx=3.4cm,bblly=17cm,bburx=13.7cm,bbury=27cm,clip=}
}
\caption[]{\label{theplot-all}
The same as Fig.~\ref{theplot-pred}, showing the correlation between
thermal emission from the accretion disk (with the exception of X-rays
this is basically normalized to their narrow H$\alpha$ emission) and
the monochromatic luminosity of AGN radio cores. Open circles:
Radio-loud quasars; small open circles: FR\,I radio galaxies; open
gray circles: Blazars and radio-intermediate quasars (dark grey);
black dots: radio-quiet quasars and Seyferts; small dots: X-ray
binaries; small boxes: detected sources from the from the ``48
LINERs'' sample. The latter apparently confirm the basic prediction of
Falcke \& Biermann (1996) and almost close the gap between very low
(on an absolute scale) accretion rate objects and high accretion rate
objects.  The shaded bands represent the radio-loud and radio-quiet jet
models as a function of accretion as shown in the aforementioned
paper.}
\end{figure}

We can investigate the optical/radio correlation in greater detail.
For the VLBI-sample, i.e.~the well-detected cores above 3 mJy in both
samples, for which we have basically established that the radio
emission is AGN-related, we can look at correlations between radio,
emission-line, and bulge luminosities. Figure \ref{LLAGN-ha} (right
panel) shows that there is a trend for galaxies with higher H$\alpha$
emission to have more luminous radio cores. Interestingly, elliptical
and spiral host galaxies are offset from each other.  The same effect
can be seen in Fig.~\ref{theplot-all} where one finds a string of
sources connecting to FR\,I radio galaxies and falling somewhat above
the top line predicted by the model. This are the large elliptical
galaxies which are probably faint versions of radio galaxies. Does
this reflect a radio-loud/radio-quiet dichotomy for LLAGN?


\begin{figure}%%%[htb]
\centering
\noindent
\psfig{figure=Figures/spectralindex.ps,width=0.49\textwidth,bbllx=3.1cm,bblly=18.1cm,bburx=17.8cm,bbury=27cm,clip=}\psfig{figure=Figures/halpha-radio.ps,width=0.49\textwidth,bbllx=3.8cm,bblly=20.8cm,bburx=13.8cm,bbury=27cm,clip=}
\caption[]{Left: Spectral indices of LLAGN in our two samples with $S_{\rm 15 GHz}>3$
 mJy between 5 GHz (VLBI) and 15 GHz (VLA) as a function of radio core
flux at 5 GHz. Right: $S_{\rm 15 GHz}$ plotted versus narrow H$\alpha$
flux for the same sample; ellipticals and spirals are distinguished by
big and small dots respectively.}
\label{LLAGN-ha}
\end{figure}

There is another important factor: the galaxy bulge luminosity. We do
see a weak trend for the radio luminosity to be related to bulge
luminosity; also the ratio between radio and H$\alpha$ luminosity
tends to increase with increasing bulge luminosity. Hence, galaxies
apparently become more efficient in producing radio emission relative
to H$\alpha$ in bigger bulges. This also holds if we look at the
entire VLA detected sample (Fig.~\ref{LLAGN-Mb}). Whether this is due
to increasing obscuration, effects intrinsic to the AGN, or a
selection effect is unclear.  In any case, we are comparing here
pumpkins with apples. Since ellipticals and spirals in our sample are
nicely separated between the top and bottom end of the bulge
luminosity distribution, an apparent dichotomy in Fig.~\ref{LLAGN-ha}
is a natural consequence of this trend.

If the bulge luminosity is proportional to the central black hole mass
\cite{KormendyRichstone1995}, the ellipticals in our sample are more
likely to have larger black hole masses. This means they have a larger
'headroom' with respect to their Eddington limit and are more likely
to have larger accretion rates. Moreover, if an accretion disk becomes
radiatively less efficient the further away it is from the Eddington
limit, we could reproduce the scaling of the
Radio/H$\alpha$-ratio. Another explanation for the latter could be
that the larger bulges of these ellipticals contain more obscuring
material towards our line of sight and hence optical emission is more
strongly suppressed.


\begin{figure}%%%[htb]
\centering
\noindent
\psfig{figure=Figures/radio-mb.ps,width=0.475\textwidth,bbllx=3.8cm,bblly=20.8cm,bburx=13.4cm,bbury=27cm,clip=}\psfig{figure=Figures/mball.ps,width=0.505\textwidth,bbllx=3.5cm,bblly=20.9cm,bburx=13.7cm,bbury=27cm,clip=}
\caption[]{Left: Radio luminosity ($\nu L_\nu$) at 15 GHz of LLAGN in our sample 
with $S_{\rm 15 GHz}>1.5$ mJy as a function of blue bulge
magnitude. Right: Ratio between 15 GHz radio core and narrow H$\alpha$
flux as a function of blue bulge magnitude in the same sample.
Ellipticals and spirals are distinguished by big and small dots
respectively.}
\label{LLAGN-Mb}
\end{figure}

To summarize: we find that at least 40\% of optically selected LLAGN
with Seyfert and LINER spectra have compact radio cores.  VLBI
observations show that these cores are similar to radio jets in more
luminous AGN with high brightness temperatures, jet-like structures,
and flat radio spectra. The radio emission seems to be related to the
luminosity of the emission-line gas and hence both are probably
powered by genuine AGN operating at low powers. We found no evidence
for high frequency components with highly inverted spectra as predicted
in ADAF models. Hence, for these models one should probably not
include radio fluxes in broad-band spectral fits. 

We also find only a weak correlation between radio and bulge
luminosity, which could imply a scaling of radio emission with black
hole masses.  Such an effect was claimed earlier and interpreted
within the ADAF models as a possibility to measure black hole masses
with the radio data \cite{FranceschiniVercelloneFabian1998}. However,
this result was based on a much smaller, ill-selected sample and gave
a much steeper dependence which we cannot confirm. Strangely, this
sample even included galaxies like M87  {}--{}  one of the most famous
radio galaxies, where we know for many decades now that the radio
emission is produced by a radio jet and not an ADAF. As we have seen
here, the radio-H$\alpha$ correlation is a much stronger effect. If
the H$\alpha$ is a tracer of the accretion disk luminosity, this most
likely means that the radio power is much more dependent on the
accretion rate than on the black hole mass. One will therefore have to
continue to measure black hole masses in the traditional way, mainly
through spectroscopy.



\chapter{Jets and Radio Cores in Radio-Quiet AGN}\label{seyferts}
\citeme{Falcke1998c} In the last two chapters we have moved from an
almost inactive galaxy, like the Milky Way, to weakly active galaxies
such as LINERs and dwarf-Seyferts. In both classes we find strong
radio cores. If we move up to even higher luminosities we arrive at
Seyfert galaxies and quasars.  As outlined in the introduction
already, at this luminosity level radio cores in radio-loud quasars
are relatively well understood and studied in great detail. However,
the majority of quasars are radio-quiet, i.e.~they have very little
radio emission.  We have argued in passing (Chap.~\ref{symbiosis};
esp.~Fig.~\ref{uvradioplot-qso1} \& \ref{uvradioplot-qso2}) that also
in these radio-quiet quasars, which one should rather call radio-weak
quasars, the radio emission is also produced by jets and consequently
its flux was treated within the framework of the jet-disk symbiosis
model. But, is it really true that all AGN have jets {}--{} even the
radio-quiet ones? And, if it is true, what kind of jets are these?

In comparison to stellar winds it is often argued that the escape
speed from the central object is an important factor that determines
the terminal jet speed. If that is true and since we believe that most
of the AGN are powered by a black hole one should assume that if an
AGN produces a jet it should {\it always} be
relativistic. Consequently the crucial question then becomes: Do all
AGN have relativistic jets including those deemed radio-quiet? In
\citeN{Falcke1994} and \citeN{FalckeBiermann1995} we proposed that,
since black holes do not have many free parameters, AGN should be
similar in their basic properties (``the universal engine'') and hence
one should {\it ab initio} assume that all AGN, rather than only a few
sub-classes, have relativistic jets. Using Occam's razor we also
suggested that jets and accretion process (accretion disk) should form
a symbiotic system in the sense that both are always required for an
AGN. As it turned out, this hypothesis, in its simplicity, was
surprisingly successful and has motivated most of the research
presented here. In a review \citeN{Livio1997} comes to a similar
conclusion, i.e.~that a majority of accretion disk systems produce
jet-like outflows.

\section{Radio-Quiet Quasars}
\citeme{Falcke1998c,FalckeSherwoodPatnaik1996,FalckeBowerLobanov1999,BrunthalerFalckeBower2000}
One class of sources where the jet-disk symbiosis principle was used
first was the UV/radio-correlation of quasars
(Fig.~\ref{uvradioplot-qso1} \& \ref{uvradioplot-qso2}).  If one looks
at the distribution of the radio-to-optical flux ratios
($R$-parameter) of an optically selected quasar sample (here the PG
quasar sample) one finds a clear dichotomy between radio-loud and
radio-quiet sources. This is especially true if one selects only
steep-spectrum quasars, which are supposedly unaffected by orientation
effects (see Fig.~\ref{fig-riq}). VLA observations of the
steep-spectrum radio-loud PG quasars
\cite{MillerRawlingsSaunders1993,KellermannSramekSchmidt1994} have
clearly established, that they have FR$\,$II-type radio jets.  The
radio dichotomy was occasionally attributed to the fact that
radio-quiet quasars do not show and do not have radio-jets at
all. However, as we all know, `absence of evidence is not evidence of
absence'  {}--{}  especially not, if one has not even looked yet.
Following the jet-disk symbiosis principle, one would rather think
that radio-quiet quasars should have jets as well.

\subsection{Predictions for Boosted Radio-Quiet Jets}

We therefore have to ask: How can we obtain evidence for or against
the presence of jets in radio-quiet quasars? One direction to go would
be to look for relativistic boosting. In an optically selected sample,
we would expect that, if radio-quiet quasars have relativistic jets,
some of these quasars are accidentally pointing towards us, thus
producing a population of `weak Blazars' with the following
properties:
\begin{itemize}
\item[a)]  similar to flat-spectrum, core-dominated, variable radio
quasars but with relative low radio-to-optical flux ratio ($R$),

\item[b)] apparent brightness temperatures close to $\sim10^{12}$K or above,

\item[c)] superluminal motion,

\item[d)] very faint (i.e.~radio-quiet) extended radio emission,

\item[e)] number of sources in a well selected sample, and their
Doppler-boosting relative to radio-quiet quasars both imply the same
Lorentz factor,

\item[f)] luminosity- and redshift-distribution consistent with radio-quiet
parent population,

\item[g)] host galaxies compatible with those of radio-quiet quasars.
\end{itemize}

This list is quite helpful, as it allows an either/or decision: if we
do not find a population of weak Blazars, we can exclude that
relativistic jets in radio-quiet quasars exist (or one would have to
invent an argument why these jets never point towards us); if we find
them, we can prove that radio-quiet quasars must have relativistic
jets. Interestingly, in the PG quasar sample we indeed find a
population of quasars, which at least partially fulfill most of the
criteria listed above and most likely are such weak Blazars.

\subsection{Radio-Intermediate Quasars}
\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/fig-riq.ps,height=0.5\textheight,bbllx=4.3cm,bblly=3.2cm,bburx=18.7cm,bbury=24.1cm}
}
\caption[]{\label{fig-riq}Distribution of the $R$-parameter (ratio between radio and
optical flux) for an optically selected sample of quasars with steep
radio spectra (from Falcke et al.~1996a). The RIQ are added with gray
shades. While in total flux they rival some of the fainter radio-loud
quasars with their bright, flat-spectrum radio core, their extended
emission is comparable only to radio-quiet quasars.}
\end{figure}



\citeN{MillerRawlingsSaunders1993}, \citeN{Falcke1994}, and
\citeN{FalckeSherwoodPatnaik1996} identified a small sample of
radio-intermediate quasars (RIQ) which sparsely fill the space in $R$
between radio-loud and radio-quiet quasars. They have optical+UV
luminosities between $10^{45}$ and $10^{47}$ erg/sec, just like the
bulk of the radio-quiet quasars and unlike radio-loud quasars which
can be found only above $10^{46}$ erg/sec in the PG sample. They are
typical flat-spectrum, core-dominated quasars, but their $R$ parameter
is too low for them to be boosted radio-loud quasars. If they were
boosted radio-quiet quasars instead, their number and $R$-distribution
would indicate a bulk Lorentz factor of $\gamma_{\rm j}$=2-4.  For at
least the three low-redshift RIQ, there is no extended emission above
a level of a few mJy {}--{} far below what is expected for any radio-loud
quasar {}--{} neither on the VLA A- \& D-array
\cite{KellermannSramekSchmidt1994} nor on the EVN \& MERLIN scales
\cite{FalckePatnaikSherwood1996}. At least one source, III Zw~2, has
shown outbursts indicating a brightness temperature of $10^{12}$ K
\cite{TerasrantaValtaoja1994} which requires relativistic boosting,
while VLBI observations of the three low-$z$ sources indicate at least
lower limits of several $10^{10}$ K. III~Zw~2 is the most interesting
source in this respect since it is the most variable source with a
huge outburst every few years but which has for a long time resisted
attempts to resolve any structure with VLBI (e.g.,
\citeNP{KellermannVermeulenZensus1998}). Here we will now focus on
most recent results for this galaxy.

III~Zw~2 was classified as a Seyfert I galaxy (e.g.,
\citeNP{Arp1968,Osterbrock1977}), 
and was later also included in the PG quasar sample 
\cite{SchmidtGreen1983}. The host galaxy was classified as a
spiral (e.g., \citeNP{HutchingsCampbell1983}) and a spiral arm was found
\cite{Hutchings1983}. A galaxy disk model was later confirmed by fitting of
model isophotes to near-IR images \cite{TaylorDunlopHughes1996}.

Because of its frequent outbursts the flux-density of III~Zw~2 was
monitored frequently, leading to the discovery of a new outburst in
1997.  A first VLBA observations in the early phase of the outburst
then revealed a high-brightness temperature around $3\cdot10^{11}$ K,
a very compact double structure, and a highly inverted spectrum with
a peak at 43 GHz \cite{FalckeBowerLobanov1999}. Continued monitoring
of the outburst with the VLBA then finally led to the detection of
superluminal motion in this source
\cite{BrunthalerFalckeBower2000} {}--{} the first time superluminal motion
was ever found in a spiral galaxy (later than S0) and which, judged
from its extended radio emission, is clearly not a radio galaxy.

Figure~\ref{iiizw2-vlba} shows four epochs of VLBA observations. In
the last two epochs the source clearly starts to expand. If one
considers the expansion speed of the blob one finds basically no
expansion in the early phase of the outburst, but a rapid expansion
with apparent velocity $1.25\pm0.09$~c at the end. This apparent
superluminal motion -- an optical illusion -- can only occur, if the
underlying jet itself expands with a velocity close to the speed of
light. Hence, one can conclude that at least III Zw 2 contains a
relativistic jet.

Key to this success was the frequent monitoring of the source with the
VLBA. In a parallel program \cite{UlvestadWrobelRoy1998} we have been
studying the expansion velocity of two other Seyfert galaxies, Mrk 348
and Mrk 231, and found only sub-relativistic expansion speeds. It
could well be, that those sources could also show phases of faster
expansion that we have missed so far.

\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/iiizw2-vlba.ps,width=0.75\textwidth,bbllx=2.3cm,bburx=18.7cm,bblly=7.8cm,bbury=23.7cm}}
\caption{Four epochs of VLBA maps of III~Zw~2 at 43 GHz convolved with a super-resolved beam of 150 $\mu$as. The original beam sizes were $0.29\times 0.12$ milli-arcsecond at a position angle (P.A.) of $-5^{\circ}$ in June 1998, $0.31\times 0.16$ at a P.A. of $11^{\circ}$ in September 1998, $0.38\times0.17$ at a P.A. of $-4^{\circ}$ in December 1998 and $0.5\times0.14$ at a P.A. of $-18^{\circ}$ in June 1999.}
\label{iiizw2-vlba}
\end{figure}


\begin{figure}%%%[htb]
 \centerline{\psfig{figure=Figures/expand.ps,width=0.75\textwidth,angle=-90}}
 \caption[]{\label{iiizw2-expand}Component separation from model
 fitting of point-like components to the closure phases and amplitudes
 of III Zw 2 at 43 GHz. The separation of the first three epochs is
 consistent with an expansion speed $\le0.04~c$ (solid line). The
 expansion speed between the fourth and fifth epoch is
 $1.25\pm0.09~c$. Formal error bars are a few $\mu$arcseconds only for
 the first four epochs.}
\end{figure}


It is known that radio-loud AGN almost never reside in spiral galaxies
(e.g., \citeNP{BahcallKirhakosSaxe1997},
\citeNP{KirhakosBahcallSchneider1999}) whereas radio-quiet quasars
appear both in spiral and in elliptical host galaxies.  Furthermore,
all relativistically boosted jets with superluminal motion and typical
Blazars have been detected in early type galaxies
(e.g., \citeNP{UrryScarpaO'Dowd1999}). Therefore, the detection of
superluminal motion in III~Zw~2 provides a significant breakthrough.


In addition, one of three low-redshift RIQs, PG 1309+355, was part of
recent HST host galaxy study \cite{BahcallKirhakosSaxe1997} and found
to be a spiral as well.  Hence, together with III Zw 2 at least two of
the three RIQs are in spiral galaxies, confirming the prediction that
host galaxies of RIQs should resemble those of radio-quiet quasars
rather than those of radio-loud quasars.

In summary, the so far identified and studied RIQ meet all the
requirements for intrinsically radio-quiet quasars, whose relativistic
jets accidentally point towards us. Moreover, since only a very small
fraction of quasars will point towards us, one can infer also that a
large number {}--{} if not all {}--{} of the remaining radio-quiet quasars must
harbor relativistic jets. Further VLBI studies of radio-quiet quasars
\cite{BlundellBeasley1998} indeed conclude that also radio-quiet
quasars with weaker radio emission have compact cores resembling those of
radio-loud quasars, albeit at a much fainter level. Therefore, we have
direct evidence that fainter, un-boosted counterparts do exist and the
idea of radio-quiet AGN having relativistic jets has made a big step
towards becoming an established view. It also strengthens the notion
that all black holes are equal.


\section{Imaging of Large-Scale Jets in Radio-Quiet AGN}
\citeme{Falcke1998c,FalckeWilsonSimpson1998,FalckeWilsonHenkel2000}
A second route to establish that jets play a significant role in
radio-quiet AGN is deep, high-resolution VLA imaging of the extended
radio structures which were seen already in some snapshot maps. First
results of such a project seem to indicate that radio-quiet quasars
indeed harbor Seyfert-like jets \cite{KukulaDunlopHughes1998}.

Fortunately, already now are results available which can, at least in
part, answer whether direct evidence for jets in radio-quiet quasars
exists at all. First of all VLA observations of
\citeN{KellermannSramekSchmidt1994} have already revealed a number of
radio-quiet quasars with weak, bi-polar radio-structure. Secondly,
there is a large regime, where the Seyfert galaxies and quasar
classifications blend into each other and it may be useful to study
Seyferts rather than radio-quiet quasars and their jets in greater
detail. Seyferts are closer and appear brighter on the sky. In this
section we will discuss some results we have obtained using the HST
and the VLA for Seyfert galaxies and which might be helpful for the
interpretation of quasars as well.

\subsection{Seyferts}
Seyfert galaxies were first noted because of their strong
emission-lines coming from their nucleus, which is emission of hot gas
ionized by an AGN. After the advent of the VLA a number of radio
surveys have shown that, besides their extended emission-line regions,
Seyferts also possess -- sometimes very faint -- radio emission which
is very often bi-polar (\citeNP{UlvestadWilson1984}, and previous
papers). Seen at higher resolution one finds a strong tendency for the
circumnuclear emission-line and radio morphologies to be aligned in
Seyfert galaxies
\cite{UngerPedlarAxon1987,Pogge1988,HaniffWilsonWard1988}.  This
strongly suggested that the ejection of the radio plasma and the
excitation of the emission-line gas were related and that the ionizing
radiation escapes preferentially from the active nucleus along the
radio axis. Here the Hubble Space Telescope (HST) has made an enormous
impact: seen with the superior resolution of this telescope the
structure of the emission-lines gas was revealed and in some cases
shown to be well-defined cones (e.g.\ NGC~1068,
\citeNP{EvansFordKinney1991}; NGC~5728,
\citeNP{WilsonBraatzHeckman1993}; NGC~5643,
\citeNP{SimpsonWilsonBower1997}), which seemed to confirm an
anisotropic escape of ionizing photons from the nucleus. This is most
popularly explained by the presence of an optically thick `obscuring
torus' \cite{Antonucci1993}, which is able to collimate the
intrinsically isotropic ionizing radiation (see, e.g.,
\citeNP{Storchi-BergmannMulchaeyWilson1992}) from the AGN. In
addition, a number of galaxies display the `ionization cone'
morphology when an excitation map is made, e.g.\ in
[\ion{O}{3}]/(H$\alpha$+[\ion{N}{2}]).

\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/fig-syo.ps,width=0.95\textwidth,bbllx=1.2cm,bblly=7.3cm,bburx=19.6cm,bbury=25.4cm}
}
\caption[]{\label{fig-syo}Narrow band HST images of Seyfert 2 galaxies in the H$\alpha$ emission
line from Falcke et al.~(1998)
}
\end{figure}
\nocite{FalckeWilsonSimpson1998}

The close connection between the radio ejecta of Seyfert nuclei and
their narrow-line regions (NLRs) initially became apparent from their
similar spatial extents and from strong correlations between radio
luminosities and [\ion{O}{3}]$\lambda$5007 luminosity and line width
\cite{deBruynWilson1978,WilsonWillis1980,Whittle1985,Whittle1992b}.
Spectroscopic studies of the NLR
\cite{BaldwinWilsonWhittle1987,WhittlePedlarMeurs1988},
 have revealed that the kinematics of the gas are often clearly
 affected by the radio jets. Such interactions could play a role in
 determining the structure of the NLR within the region ionized by the
 nucleus. In a handful of cases, HST has shown a clear spatial
 correspondence between the radio and emission-line distributions
 (e.g., NGC~5929, \citeNP{BowerWilsonMulchaey1994}; Mrk~78,
 \citeNP{CapettiMacchettoSparks1994} \&
 \citeNP{CapettiAxonMacchetto1996}; Mrk~1066,
 \citeNP{BowerWilsonMorse1995}; Mrk~3,
 \citeNP{CapettiAxonMacchetto1996}; ESO~428--G14,
 \citeNP{FalckeWilsonSimpson1996}), indicating that the radio ejecta
 strongly perturb the ionized gas, at least in these objects. It has
 also been suggested that the hot gas associated with the shocks
 generated by the interaction between the radio ejecta and the ambient
 medium is a significant source of ionizing radiation
 (e.g., \citeNP{DopitaSutherland1995} or
 \citeNP{BicknellDopitaTsvetanov1998}).


It is therefore of great importance to study more Seyfert galaxies at
the high spatial resolution which only HST can provide, to determine
whether the morphology of the NLR is determined by the
nuclear ionizing radiation or by the interaction of radio jets with
the interstellar medium, or by a combination of both.

\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/fig-syion.ps,width=0.95\textwidth,bbllx=1.2cm,bblly=7.3cm,bburx=19.6cm,bbury=25.4cm}
}
\caption[]{\label{fig-syion}Excitation maps (\ion{O}{3}/H$\alpha$) for the galaxies in
Fig.~\ref{fig-syo}. Dark shades indicate higher excitation. The overall structure
of the highly excited gas resembles cones and bi-cones.}
\end{figure}

In Falcke, Wilson, \& Simpson (1998) \nocite{FalckeWilsonSimpson1998}
we presented images taken with the Wide Field and Planetary Camera 2
(WFPC2) of seven Seyfert~2 galaxies (see Fig.~\ref{fig-syo}), selected
on the basis of possessing either extended emission-line regions (as
seen in ground-based images) or broad emission-lines in polarized
light. For each galaxy images in the light of the
[\ion{O}{3}]~$\lambda$5007 line and the
H$\alpha$+[\ion{N}{2}]~$\lambda\lambda$6548,6583 blend were taken. In
addition we also obtained new radio maps taken with the Very Large
Array (VLA), almost all in `A-configuration', providing an angular
resolution comparable with that of the HST images. Taken together,
these allowed us to compare directly the structures of the
line-emitting gas and the radio plasma on scales of tens of parsecs.

And indeed in four of the seven galaxies (Mrk~573, ESO~428$-$G14,
Mrk~34, NGC~4388) we found bi-polar structures in the excitation maps
(i.e.~the maps obtained by dividing the [\ion{O}{3}] by the
H$\alpha$+[\ion{N}{2}] map, Fig.~\ref{fig-syion}) and a number of
finer structures in the emission-line regions of all galaxies (with
the exception of one, Mrk 1210, which was basically unresolved).  In
addition, the high quality radio maps of the galaxies we obtained,
show the considerable diversity one can find in the radio structure of
Seyferts, all of which indicate the presence of a jet outflow: narrow,
filamentary jets (ESO~428$-$G14), triple structures with a core and
two hotspots (Mrk~573), jets plus two hotspots (Mrk~34), radio plumes
and limb-brightened lobes (NGC~4388), etc. (Fig.~\ref{fig-syo+r}).

Even though the dynamic range of Seyfert radio maps is naturally lower
than what one can obtain for the much brighter radio galaxies, this
diversity is much larger than what we find in the latter. This is of
course readily understood, since Seyfert jets are much more subject to
jet-ISM interaction than FR\,II radio galaxies, because of their
orders of magnitude lower absolute jet powers and smaller
extents. Morphologically, this interaction can be seen in many images
of the HST: e.g., in Mrk~573 and Mrk~34 the radio hotspots coincide
with regions of reduced excitation, the bow-shock structure in the
emission-line gas of Mrk~573 is most certainly caused by the action of
an outflow as indicated by the presence of the radio hotspots, and the
filamentary emission-line structure in ESO~428--G14 finds its detailed
counterpart in the filamentary radio jet.

\begin{figure}%%%[htb]
\centerline{
\psfig{figure=Figures/fig-syo+r.ps,width=0.95\textwidth,bbllx=1.2cm,bblly=7.3cm,bburx=19.6cm,bbury=25.4cm}
}
\caption[]{\label{fig-syo+r}The same images as in Fig.~\ref{fig-syo} with the VLA
radio contours overlaid. The observed wavelengths are 3.5cm for Mrk~34
and NGC~4388 and 2 cm for Mrk~573 and ESO428--G14. The direct relation
between radio and optical emission is obvious.}
\end{figure}


It is quite obvious from this data that there is not only a close
correlation between the radio and the emission-line morphologies, but
that {\it the radio jet-ISM interaction is an important effect which
strongly influences the excitation and morphology of the NLR}.
 
Does this mean the unified scheme is wrong? Is the bi-polarity of the
NLR and are the ionization cones just illusions of a weary
astronomer's soul longing for a simple scheme to explain the Seyfert
world? Are {\rm all} the structures seen in the NLR produced by
widening, self-excited matter outflows as Dopita and others suggest?

Fortunately, in at least two cases we can find good arguments, that
the anisotropic photon escape scheme remains still valid: In Mrk~573
and NGC~4388 `ionization cones'
\cite{PoggeDeRobertis1995,CapettiAxonMacchetto1996,Pogge1988,CorbinBaldwinWilson1988}
were already known from ground-based observations on the arcsecond
scale and we found an equivalent counterpart on the sub-arcsecond
scale with identical opening angle. This continuation and the
straightness of the cones clearly favor some kind of obscuring `torus'
with well defined inner edges around the nucleus that leads to a
beamed ionizing continuum. Attributing these cones to the action of an
outflow seems unreasonable, since the radio ejecta we do see have not
only a very different appearance in both galaxies despite similar cone
structures, the jets are also themselves subject to collimation by the
galaxy, e.g.,~as seen in the constriction of the northern lobe of
NGC~4388, and therefore are nothing like the proposed freely
expanding, conical outflows. On the other hand, Mrk~573 has not only a
straight `excitation cone' but, with its bow-shaped emission-line
strands, is also the clearest example of a jet-shaped
NLR. Consequently, any successful model of the NLR of this galaxy will
require a {\it composite model that includes photo-ionization from a
central source {\rm and} the impact of a radio jet} (see
\citeNP{FerruitWilsonFalcke1999}).

Other examples for the shaping of the NLR by the jet are ESO~428$-$G14
and NGC~4388. The former exhibits well collimated, irregular
emission-line strands on one side and a figure ``eight'' morphology on
the other. The latter has been interpreted as two helical
emission-line strands wrapping around a radio jet
\cite{FalckeWilsonSimpson1996}. The overall structure of the NLR and
of the radio jet in ESO~428--G14 is perhaps the most bizarre case one can
find.  In NGC~4388 a bright spike is seen in the ionized gas at the
end of the southern jet, while the radio plasma to the north flows
apparently unhampered out of the galaxy disk and forms a large ($\sim$
1 kpc) radio plume. This structure is reminiscent of the radio lobe
found, for example, in NGC~3079 \cite{SeaquistDavisBignell1978} and a
few other galaxies \cite{FordDahariJacoby1986}. This kind of
limb-brightened radio lobe stands in marked contrast to the
well-collimated, stranded jets in ESO~428$-$G14 and NGC~4258
(e.g., \citeNP{CecilWilsonTully1992}). An important difference is that
NGC~3079 and NGC~4388 have jets which escape almost perpendicular to
the galaxy plane, while in NGC~4258 and perhaps ESO~428--G14 the jet
appears to be directed into the disk of the galaxy. The difference in
radio morphology may then be ascribed to the much higher external gas
density when the jet is in the disk rather than in the galaxy halo.


What remains unclear, however, is the exact nature of the jet-ISM
interaction in our Seyferts. To what degree are jet-induced shocks
responsible for the excitation of the gas? Are there regions, where
shock excitation dominates the photo-ionization from the nucleus? What
amount of energy is locally dissipated in the jets due to this
interaction? To answer these questions the observation of only two
emission-lines is not enough and long-slit spectroscopy will be
needed. For ESO~428--G14, the necessary HST time for such observations
has been allocated, and other projects will address similar questions
in the future. Moreover, some recent results obtained with the FOC
on board the HST already now strongly support the jet-ISM interaction
picture \cite{WingeAxonMacchetto1997}.

At least in a very simple way the jets must have an influence on the
excitation of the gas: e.g., the reduced excitation
(i.e.~[\ion{O}{3}]/(H$\alpha$+[\ion{N}{2}]) ratio) of the inner
emission-line arcs in Mrk~573 is consistent with a lower ionization
parameter which can be understood if the arcs represent gas which has
passed through a radiative bow shock, cooled and increased in
density. A similar effect is seen in Mrk~34, in which the radio lobes
coincide with a low-excitation region, while the jet itself is
surrounded by high-excitation gas. The wiggles seen in the radio jet
of this galaxy could possibly be interpreted as some kind of
Kelvin-Helmholtz instabilities between the radio plasma and the
surrounding, ionized gas. Looking at all the galaxies in our sample,
there seems to be indeed a tendency for radio lobes to coincide with
lower excitation regions, presumably a result of compression of the
ambient gas.

Finally, we can now come back to our initial question about the
presence and importance of jets in general. Especially with respect to
the situation in radio-quiet quasars, we are now much more prepared to
give a positive answer. Some of our galaxies (e.g., Mrk~34 and Mrk~573)
have [\ion{O}{3}] luminosities comparable to radio-quiet, low-redshift
quasars. Hence, for such objects, we are discussing a regime in which
the quasar and Seyfert classifications indeed overlap. From their
radio flux it is clear that the Seyferts in our sample belong to the
radio-quiet class of AGN, yet they not only show jets, but the jets
are also kinematically important for the emission-line gas.  The jets
we find in Mrk~34 and Mrk~573 would in fact resemble some of the
double structures seen by \citeN{KellermannSramekSchmidt1994} in
radio-quiet quasars, if placed at a larger distance and observed with
lower sensitivity.

\subsection{Megamaser Galaxies}
When looking at the large-scale jet structure in Seyferts there remains
one important question to be solved: how are the large-scale jets and
the central AGN with its alleged torus and compact radio core
connected? Clearly, if, as seen in III Zw 2, jets start out
relativistically, they have to slow down on their way out to explain
the rather diffuse radio ejecta discussed in the previous section. The
slow expansion in the early phase of the III Zw 2 outburst and the
sub-relativistic expansion we found in Mrk 348 and Mrk 231
\cite{UlvestadWrobelRoy1998} seems to indicate that a significant
slow-down is happening already at the sub-parsec scale and may
possibly be related to the obscuring torus itself. An excellent way to
get information about molecular gas at this scale is through water
megamasers.

In recent years a number of active galaxies have been found to have
powerful H$_2$O maser emission in their nuclei
\cite{BraatzWilsonHenkel1994,BraatzWilsonHenkel1994}. It is known that
the H$_2$O megamaser phenomenon is associated with nuclear activity
since all such megamaser sources are in either Seyfert 2 or LINER
nuclei.

It appears reasonable to infer that the masers trace molecular
material associated with the obscuring torus or an accretion disk that
feeds the nucleus.  This notion was confirmed in great detail by VLBI
observations of the megamaser in NGC 4258
(\citeNP{MiyoshiMoranHerrnstein1995} \&
\citeNP{GreenhillJiangMoran1995}, see also Fig.~\ref{NGC4258}). 
The positions and velocities of the H$_2$O maser lines show that the
masing region is a thin disk in Keplerian rotation around a central
mass of $3.9\cdot10^7M_\odot$ at a distance of $\approx$0.16 pc from
that mass \cite{HerrnsteinMoranGreenhill1999}.

Although plausible scenarios for the megamaser phenomenon exist
(e.g., \citeNP{NeufeldMaloney1995}), it is by no means clear how the
material which obscures the nucleus (the ``obscuring torus'') and the
masing disk are related. The masing disk may be part of a
geometrically thin, molecular accretion disk at smaller radii than the
torus, or the thin, central plane of a thick torus in which the column
density is high enough for strong amplification. Alternatively, the
whole structure could be a warped thin disk, so the masing gas might
be misaligned with the central accretion disk. The most
straightforward picture consistent with current data would, however,
have the masing disk, obscuring torus and any more extended molecular
cloud distribution as one coherent accretion structure feeding the
central engine, with the ionized thermal and non-thermal radio plasma
roughly along the rotation axis.

We have therefore started a program to observe the narrow-line regions
(NLR) of all known megamaser galaxies with the Hubble Space Telescope
(HST) to establish this often suggested link between the molecular
disk responsible for the maser emission and the obscuring torus
responsible for the ionization cones. We are also obtaining continuum
color images to search for the obscuring material directly.

The most luminous known H$_2$O maser source is found in the galaxy
TXS2226-184 (IRAS F22265-1826; \citeNP{KoekemoerHenkelGreenhill1995}),
at a redshift of z=0.025 (luminosity distance D=101 Mpc for $H_0=75$
km sec$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$; in the images 0\farcs1
correspond to 46 pc). Here we present
H$\alpha$+[\ion{N}{2}]$\lambda\lambda$6548,6583 and broad-band
radio continuum observations of TXS2226-184 obtained with the HST and the
VLA. Our results indeed show a linear H$\alpha$+[\ion{N}{2}] structure
along the radio axis and perpendicular to a dust lane. This supports
the connection between megamaser emission, dusty disk, obscuring
torus, and the narrow-line region discussed above. Observational
details are given in \citeN{FalckeWilsonHenkel2000}.


A slightly super-resolved map of TXS 2226-184 at 8.46 GHz using a
circular restoring beam of 0.2\arcsec{} is shown in Figure
\ref{txfs-images} (right) where we have subtracted the central point
source to show the extended emission more clearly. The source is
resolved with a peak flux density of 15 mJy and a total flux density
of 23 mJy. The emission is elongated in PA $-37^\circ$ towards the NW
and in PA $146^\circ$ towards the SE. The position of the central
radio component is $\alpha=22^h26^m30\fs07$,
$\delta=-18\arcdeg26^\prime09\farcs6$ (B1950).


\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/txfs-images.cps,width=\textwidth,bbllx=0.9cm,bburx=20.4cm,bblly=20.1cm,bbury=24.9cm}}
\caption[]{\label{txfs-images} Left: continuum map
obtained by averaging the red and green images taken with the
Planetary Camera (0\farcs0455 pixel size). The centroid of the
continuum in the inner part of the galaxy (see text) is marked here
and in the following panels by a cross, and the B1950 coordinates are
from the VLA astrometry (assuming the radio nucleus and the optical
centroid are coincident). Middle: color map obtained by dividing the
green by the red continuum image (same spatial scale as left).  The
flux density ratio ranges from 0.4 (red colors) to 1.5 (blue colors)
which roughly corresponds to V--I colors ranging from 2.2 to 0.8. The
gray areas are around V--I$\sim$1.3.  Contours overlaid are of the
H$\alpha$+[\ion{N}{2}] image (right).  Right: continuum subtracted
H$\alpha$+[\ion{N}{2}] image of TXS2226-184. The
H$\alpha$+[\ion{N}{2}] flux in a rectangular
1.7\arcsec{}$\times$3.2\arcsec{} aperture is $2.5\times10^{-14}$ erg
s$^{-1}$ cm$^{-2}$ and the intensity scale is proportional to the
square root of the brightness. Contours overlaid are of the 8.46 GHz
VLA radio continuum (contours starting at 0.3 mJy and increasing by
factors of $\sqrt{2}$). We have subtracted the central point source
from the radio map to show the extended structure more clearly.}
\end{figure}

Our HST images are shown in Figure~\ref{txfs-images}. The continuum
map, which is the combination of the red and green filters used also
for off-band subtraction, reveals a highly elongated galaxy along PA
$55^\circ$. The inner region (1\arcsec{} diameter) is bisected by a
dark band, presumably a nuclear dust lane.  The presence of this dust
lane is further strengthened by the color map, which shows a region of
high reddening along PA 60$^\circ$ extending roughly 1\arcsec{} across
the nucleus. 

The H$\alpha$+[\ion{N}{2}] map shows a highly elongated structure
roughly along PA $-40^\circ\pm5^\circ$, i.e.~in the same direction as
the radio emission, with a bright spot 0\farcs2 NW of the supposed
nucleus. The emission extends further towards the SE, with a broad,
``wiggly'' structure near the nucleus and a ``plume'' 1\farcs5 from
the nucleus.  The adopted nucleus in the HST images is within
1\farcs5 {}--{} the typical error in absolute HST astro\-metry {}--{} of the
radio nucleus.


We have fitted elliptical isophotes to the red continuum image of the
galaxy ignoring the innermost few pixels which are heavily affected by
the dust lane.  For a disk + bulge model (a) we obtained a good fit (reduced
$\chi^2=0.86$) with the parameters $\mu_0=18.0$ mag arcsec$^{-2}$,
$R_0=2\farcs4$ (1.1 kpc), $\mu_{\rm e}=19.7$ mag arcsec$^{-2}$, and
$R_{\rm e}=0\farcs6$ (0.29 kpc). For a bulge component only (b),
i.e.~an elliptical galaxy profile, the fit is much worse (reduced
$\chi^2=4.9$). The ellipticity of
TXS2226-184 ($e=1-b/a=0.61$ at 2\farcs7$<R<$6\farcs0) indicates an
inclination of the galaxy to the line of sight of 70$^\circ$ (using
$i=\arcsin{\sqrt{(1-(b/a)^2)/0.96}}$, e.g., \citeNP{Whittle1992a}).

Koekemoer et al.~(1995) have classified this galaxy as an elliptical
or S0 and speculated whether the unusually broad line-width of the
megamaser emission seen in this galaxy and in NGC1052 might be typical
of elliptical galaxies. Our HST images reveal that TXS2226-184 is
almost certainly not an elliptical, so NGC1052 remains the only known
megamaser in an elliptical galaxy \cite{BraatzWilsonHenkel1994}.  On
the other hand, the high inclination of TXS2226-184 strengthens the
tentative conclusion of \citeN{BraatzWilsonHenkel1997} that megamasers
are preferentially found in highly inclined galaxies. This excess
suggests that nuclear and large scale dust disks in many active spiral
galaxies are indeed related.

The NLR in TXS2226-184 is very elongated and reminiscent of the
jet-like NLR seen in many Seyfert galaxies, as imaged by HST (see
previous section).  These gaseous structures are believed to be
produced in the interaction between outflowing radio ejecta and the
ISM. The fact that our radio map is elongated along exactly the same
direction as the NLR supports this view.

In addition to the NLR and radio jet, we find a dust lane in the
nucleus which aligns with the galaxy major axis and presumably
represents its normal interstellar medium. The elongation of the NLR
and the radio source perpendicular to the NE-SW dust lane suggests
that the nuclear accretion disk and the obscuring torus are more or
less coplanar with the stellar disk in TXS2226-184. Preliminary
results of VLBA observations of the masers in this galaxy indeed seem
to roughly show a NE-SW orientation along PA 20$^\circ$ (Greenhill,
priv.~comm.).  

However, if one interprets this megamaser structure in analogy to
NGC~4258 as a molecular disk it would indicate a certain degree of
warping between large-scale and small-scale disks and jets. The same
is seen in the galaxy NGC~3079 (Fig.~\ref{NGC3079}) -- another galaxy
in our HST program -- where the masing ``disk'' and the nuclear radio
jet are inclined by 45$^\circ$. On even larger scales the axis of the
outflow is determined by huge bubbles seen in radio and H$\alpha$ (see
\citeNP{SeaquistDavisBignell1978}, also Fig.~\ref{NGC3079}) along the
minor axis of the galaxy.  If one looks at Seyfert galaxies as a
whole, however, there is quite a distribution of misalignments between
AGN axes and galaxy minor axes (e.g., \citeNP{NagarWilson1999} an
refs.~therein). These few examples already indicate that the radio
jets in these radio-quiet objects apparently encounter many obstacles
on their way out. Already on the parsec-scale the ``torus'' or just a
molecular gas layer could have its rotation axes misaligned with the
jet axis and deflect or slow down the jet. Further out, the
interaction with the gas in the ISM, that we see as the NLR, further
impacts the jet structure and can lead to a diverse morphological
appearance at random angles. While this can produce spectacular
structures it will make quantitative studies of jets in radio-quiet AGN
difficult. Hence, only at the very smallest scales where radio cores
are produced, and possibly at the highest frequencies, do we stand a
chance to study the AGN practically in isolation. This, to some
degree, justifies the special attention those cores have received in
the previous chapters and sections.

\paragraph{Note added in Proof:} As a postscriptum and late addition to this 
chapter, it should be mentioned that on 17 March 2000 we
(i.e.~together with C. Henkel, A. Peck, and Y. Hagiwara) discovered
yet another megamaser galaxy with the Effelsberg 100 m dish. This in
itself is exciting, since megamasers are rare and of great scientific
interest. What makes this new discovery even more interesting is that
the galaxy, Mrk 348, is one of the Seyferts with the brightest and
most variable radio cores. Though not as extreme, it is comparable in
spectrum and variability to III Zw 2 discussed in the previous
section. The radio core flux in Mrk 348 now underwent a similarly
strong outburst as III Zw 2 with a radio flux exceeding 1 Jy at high
frequencies. At the same time the previously undetected megamaser
emission appeared. It should warrant some curiosity that even though
only 5\% of Seyferts show megamaser emission, among those 19
discovered so far quite a few belong to the small class of Seyferts
with relatively bright (several tens of mJy) radio cores. Mrk 348 is
the most recent example of a growing list that also includes NGC 2639,
NGC 1068, NGC 3079, and Mrk 1210.  Clearly the radio cores are needed
to provide seed photons for the megamaser, but is there another,
deeper connection we do not understand yet? This question will be left
to future research.


\begin{figure}%%%[htb]
\centerline{\psfig{figure=Figures/NGC3079.cps,width=\textwidth}}
%,bbllx=0.9cm,bburx=20.4cm,bblly=20.1cm,bbury=24.9cm}}
\caption[]{\label{NGC3079}Composite (false-color) HST image of the megamaser galaxy
NGC~3079. Green colors represent the H$\alpha$ emission and red and
blue colors represent the emission seen in the two continuum
filters. Aside from many star forming regions one can see a faint
``bubble'' of ionized H$\alpha$-emitting gas emerging from the
center. The center is obscured by a highly reddened dust lane. The
nuclear maser ``disk'' seems to align with this dust disk, while the
central radio jet is inclined by roughly 45$^\circ$ to this disk
(Trotter et al.~1998), pointing towards one of the arms of
the bubble.}
\end{figure}
\nocite{TrotterGreenhillMoran1998}

\chapter{Conclusions and Outlook}
After many pages of a detailed analysis of black holes, radio cores,
and jets, summarizing many years of research, it is now time to
reflect on the results. ``The universe is simple, it just looks
complicated'' could be one of the messages. AGN can come in many
different disguises, producing a large variety of classifications, yet
the underlying astrophysical scheme remains the same. Whether we talk
about quasars, Blazars, radio galaxies, CSOs, Seyferts, LINERs, or
even some X-ray binaries, the common engine seems to be an accreting
black hole.

Of course, we are still far from understanding how these black holes
work and what physical processes play which role. There is certainly
significant plasma physics involved which is a great challenge for a
distant observer. One should just imagine how difficult it would be
for an alien astronomer to predict something like lightning on a
planet called Earth with a piece of paper and a telescope -- without
being able to be in the midst of a thunderstorm.

So, while some of the ripples we see in the emission from black holes
may just be space weather, there are some fundamental constants as
well. Radio cores and jets are one example. In part based on the
findings presented here, we can say that in all types of active
sources with a black hole, radio cores have been found. While this
cannot yet be claimed for every single black hole, it is still true
that there is no region of the explored parameter space where not at
least one black hole produces such a radio core. We find them in high-
or low-luminous, radio-loud or radio-quiet, supermassive or even
stellar mass black holes. The intermediate radio cores we have found
in LLAGN illustrates this huge range: it would be equally correct to
call them ``giant Sgr A*'s'' or ``dwarf quasars''. The radio cores in
the different objects all have very similar properties: high
brightness temperatures, flat radio spectrum, variable emission, and
in many cases a jet structure. This homogeneity makes it very likely
that they are all produced by one basic process.

The theoretical foundation to explain the emission from these cores
has been described at the beginning of this work. The basic idea being
a flow of relativistic plasma collimated near the black hole and
ejected along the rotation axis of the disk. When calculated it
turns out that this can reproduce the observed properties of radio
cores in great detail. The emission is produced close to the black
hole where it dominates its environment. Moreover, a black hole has
only two basic parameters: the mass and the angular momentum. In
addition we only have the mass accretion rate as a major free
parameter, thus explaining why radio cores are so similar over an
amazingly large range of astrophysical situations. While it is not
yet proven that all these jets are relativistic it is certainly
implied by the model. The finding of the first superluminal jet in a
Seyfert galaxy presented here could be the first step in establishing
this idea.

In general, the existence of radio cores at all scales also shows that
jet formation is apparently possible under all circumstances. Even
though we do not exactly know why and how jets are formed, it seems
that nature always finds a way to make them. This suggests that jets
are an integral part of accretion physics and thus also of black hole
physics. It should no longer be possible to just calculate how much
matter is flowing into the black hole, one should always also have to
consider how much is flowing out. The drain of mass and energy,
presumably near the inner edge of the accretion flow, is an important
boundary condition for all accretion models. The idea of a ``jet-disk
symbiosis'' formulated in our earlier papers therefore seems an
appropriate description of this relation.

What else can the radio cores offer for the future? First, it is
important to have established the clear link between radio cores and
black holes/AGN. Black holes may be black, but they are not dark -- at
least not in the radio regime. In the optical, searching for a black
hole can often be a search for a needle in a haystack. In the Galactic
Center it certainly is. With radio interferometers at high frequencies
the haystack is gone and only the needle remains. Consequently, with
more sensitive arrays we will be easily able to pinpoint black holes
in the local and distant universe. Telescopes like the planned
Square-Kilometer-Array with a hundred-fold increase in sensitivity
over the VLA will therefore pick out literally thousands of new black
hole candidates.

Among other things this will provide us with the most accurate
measurement of the center of mass of galaxies, assuming that
supermassive black holes are just this. The astrometric precision
reached with VLBI is now approaching 100 $\mu$arcseconds and in some
cases can already be pushed to tens of $\mu$arcseconds. With such
precision and enough sensitivity, one could in principle detect the
proper motion of the center of M31 rotating around the Milky Way
within a few years. Even slightly more distant galaxies, like M81 with
its bright radio nucleus, are not completely out of reach for such a
project, given somewhat longer time scales. Like the stellar proper
motions in the Galactic Center this would allow one to more reliably
determine the large scale gravitational potential, e.g., of the Local
Group, and confirm the presence of dark matter.

As outlined in Chap.~\ref{shadow}, radio cores can also serve to
illuminate the immediate surroundings of a black hole, thus probing
the smallest scales of a gravitational potential -- the event horizon.
For the Galactic Center the shadow of the black hole is already within
reach of current and planned radio-interferometers at mm- and
submm-wavelengths. If not achieved earlier, this will be an important
project for the upcoming ALMA (Atacama Large Millimeter Array)
telescope. With its high sensitivity at the highest frequencies in a
southern location it is an ideal backbone for a submm-VLBI array
imaging the event horizon in Sgr A*. With the exception perhaps of
M87, we may have to wait much longer to do a similar experiment in any
other compact radio core. However, in principle it is just a question
of technological progress until even this will be possible in other
sources as well.

Finally, with a better understanding of the physics of radio cores and
the detection of more faint ones, we will also pick out more cores at
higher redshifts and perhaps be able to use them as cosmological
probes. So far we are biased towards the brightest objects, i.e.~those
which are relativistically boosted and pointing towards us. Once we
see the entire range of radio cores and can get a better estimate of
their apparent sizes and luminosities we should be able to distinguish
between different cosmologies.

These ideas just summarize what is possible in principle. Many other,
perhaps more ordinary, applications may follow. Radioastronomy with
its interferometric technique provides a unique tool, making black
holes readily accessible. Perhaps, some day, black hole physics will
almost become an ordinary experimental science. At least we know:
their radio cores are out there, waiting to be explored.


\chapter{Summary}
Radio jets are the ``smoking guns'' of active galactic nuclei
(AGN). They are also the site of many high-energy processes, including
X-ray and $\gamma$-ray emission as well as high-energy particle
acceleration. Early on it was the radio emission from these jets which
drew people's attention to quasars and led to their discovery. Today
we know that radio jets are relativistic, magnetized plasma flows
ejected at velocities close to the speed of light most likely from the
immediate vicinity of black holes. At the smallest scales, the radio
emission from these jets appears as very compact radio cores with a
flat and variable radio spectrum. With Very Long Baseline
Inter\-ferometry this emission can often be resolved into a core-jet
structure sometimes showing apparent superluminal motion caused by the
relativistic ejection velocity.

However, similar radio cores have also been found in quite a number of
other sources, including the center of the Milky Way (Sgr A*), X-ray
binaries (stellar mass black holes and neutron stars), and some nearby
galaxies. Despite being interesting in their own right, none of these
sources can compare in their power output and violence with
quasars. On the other hand it is thought that in all these cases black
holes (and in a few cases also neutron stars) are involved as well,
possibly accreting at much lower levels -- in absolute terms -- than
quasars.

In this review we investigate how these low-luminosity radio cores are
related to their much more powerful siblings in quasars, radio
galaxies, and Blazars. It is suggested that all radio cores can be
described in a very similar fashion as jets coupled to an accretion
disk, with jet and disk being symbiotic features in an accretion
scenario of black holes. At some level every black hole will accrete
material and only a minority of sources reach the enormous power
levels of quasars. The ``silent majority'' of black holes therefore
operates at much lower levels producing much fainter radio cores.

Based on this idea of a ``jet-disk symbiosis'' a general emission
model for radio cores is presented which describes the radio emission
of a collimated relativistic plasma flow after leaving its collimation
region -- the nozzle. This part of the jet is most likely dominated
entirely by free expansion and is relatively independent of
environmental influences. This leads to a relatively homogeneous
appearance of compact radio cores in different sources with the jet
power or the accretion rate being the main parameter.

The model is used to describe some ``famous'' and relatively
well-constrained radio cores, ranging from a Galactic X-ray binary to
a megamaser galaxy. One can show that despite the vastly different
scales in accretion rates and black hole masses the model describes radio
cores properties, i.e.~size and flux as a function of frequency,
correctly.

An even more detailed investigation is presented of the radio core and
supermassive black hole candidate Sgr A* in the Galactic Center. Its
quasi-simultaneous radio spectrum was determined in an international
observing campaign, confirming the existence of an inverted cm-wave
spectrum and a ``submm-bump''. Daily flux density monitoring over more
than two years reveal variations on characteristic time scales of ten
to hundred days and phases of quasi-periodic oscillations which are
possibly related to variations intrinsic to the accretion flow. The
polarization of the Sgr A* radio spectrum is rather unusual with only
upper limits for linear polarization but an unexpected new discovery
of circular polarization. The entire spectrum can be described very
well by the jet model mentioned before, including the most recent
X-ray observations, and taking new high-frequency VLBI limits on the
extended structure into account.  Finally, it is pointed out that the
submm-bump in the spectrum, which is most certainly produced on the
smallest scales in the system, can be used as a background against
which one could image the event horizon of the black hole. Using 3D
general relativistic ray-tracing calculations one can show that the
shadow cast by the event horizon onto the submm-emitting region has a
size of $30\,\mu$arcseconds -- a size within reach of the currently
developed new generation of high-frequency VLBI arrays.

To extend the view further, results of a search for Sgr A*-like radio
cores in a sample of nearby Low-Luminosity AGN (LLAGN) is
presented. Almost half of the surveyed LINER and dwarf-Seyfert
galaxies indeed show compact flat-spectrum radio emission. The AGN
nature is confirmed by high-resolution VLBI observations. The
brightest sources do show core-jet structures and the spectral index
is within the range expected from a jet model, while being too flat
for emission from an Advection Dominated Accretion Flow (ADAF).  The
measured radio fluxes as a function of optical luminosity fall just
within the range predicted by the jet-disk symbiosis model and confirm
that these radio cores are the faint counterparts to radio cores in
quasars.

Finally, the radio emission from radio-quiet AGN -- which make up the
majority of quasars and Seyferts -- are considered. Hubble Space
Telescope and Very Large Array observations of Seyfert and megamaser
galaxies reveal that even in radio-quiet AGN jets are powerful enough
to significantly shape their environment. VLBI observations of one
particular spiral galaxy with a bright Seyfert nucleus show for the
first time superluminal motion in a galaxy type which usually is
exclusively associated with radio-quiet AGN. This galaxy was considered
to be a part of a small sample of radio-intermediate quasars which
were proposed to be relativistically boosted radio-quiet quasars or
Seyferts. The observations confirm that even in radio-quiet AGN
relativistic jets are present and validates the use of the radio
core/jet model also for these sources.

To conclude, one can say that the production of a relativistic jets
seems to be an inevitable consequence of accreting black holes and is
possible even at very low accretion rates. Therefore, compact radio
cores are an ideal tracer of black holes in the near and distant
universe. With the increasingly higher resolution and sensitivity of
radiointerferometers, they allow an intimate look at how black
holes work at various scales and in different contexts. In the future,
radio cores could also be used as cosmological probes and as reference
points to precisely measure even the proper motions of entire galaxies
in search for dark matter.

\chapter{Zusammenfassung}
\footnotetext[1]{Dieser Abschnitt benutzt die neue deutsche Rechtschreibung.}Radiojets sind, im wahrsten Sinne des Wortes, die herausragendsten
Zeichen aktiver galaktischer Kerne (AGN). Sie sind auch verantwortlich
f\"ur viele Hochenergieprozesse in der Astrophysik, von der
R\"ontgenemission, \"uber $\gamma$-Emission bis hin zur
Teilchenbeschleunigung bei h\"ochsten Energien. Schon ganz am Anfang
zog die Radioemission der Jets die Aufmerksamkeit von Wissenschaftlern
auf sich, was zur Entdeckung der Quasare f\"uhrte. Heute wissen wir,
dass es sich dabei um relativistische, magnetisierte Plasmastrahlen
handelt, die mit nahezu Lichtgeschwindigkeit aus der unmittelbaren
Umgebung eines schwarzen Lochs hinaus geschleudert werden. Auf den
kleinsten Skalen erscheint die Radioemission dieser Jets als kompakter
Kern mit einem flachen und variablen Radiospektrum. Mit Hilfe der Very
Long Baseline Interferometry (VLBI) kann diese Emission meistens in
eine Kern-Jet-Struktur aufgel\"ost werden, die in einigen Quellen
scheinbar
\"uberlichtschnelle Bewegungen zeigt. Letzteres ist eine optische T\"auschung, die
durch die relativistische Str\"omungsgeschwindigkeit verursacht wird.

Man kann allerdings sehr \"ahnliche Radiokerne auch in einer ganzen
Reihe anderer Quelle entdecken, z.B.~im Zentrum der Milchstra\ss{}e
(Sgr A*), in galaktischen R\"ontgen-Doppelsternen (stellare schwarze
L\"ocher oder Neutronensterne) und auch in einigen nahen
Gala\-xien. Obwohl f\"ur sich genommen interessant, k\"onnen diese
Quellen doch nicht die unglaublichen Energieausst\"o\ss{}e erreichen, wie
sie Quasare zeigen. Immerhin geht man auch in diesen F\"allen davon
aus, dass hier ein schwarzes Loch (in einigen F\"allen auch ein
Neutronenstern) eine entscheidende Rolle spielt, wobei es scheint, als
ob diese schwarzen L\"ocher auf einem, in absoluten Einheiten, viel
niedrigeren Niveau akkretieren.

In dieser Arbeit wird untersucht, ob und in welcher Weise
leuchtschwache und radio-leise Radiokerne mit ihren gro\ss{}en
Geschwistern in Quasaren, Radiogala\-xien und Blazaren verwandt sind.
Es wird vorgeschlagen, dass alle Radiokerne in einem einheitlichen
Bild beschrieben werden k\"onnen, bei dem Jet und Scheibe ein
symbiotisches System innerhalb eines Akkretionsmodells f\"ur schwarze
L\"ocher bilden. Auf irgendeinem, wenn auch noch so kleinen, Niveau
wird jedes schwarze Loch akkretieren, aber nur eine kleine Minderheit
erreicht die enormen Leistungen eines Quasars. Die ``schweigende
Mehrheit'' der schwarzen L\"ocher arbeitet daher auf einem niedrigen
Niveau mit entsprechend leuchtschwachen Radiokernen.

Basierend auf dieser Idee einer ``Jet-Scheiben-Symbiose'' wird ein
allgemeines Emissionsmodell f\"ur Radiokerne hergeleitet, das die
Radioemission eines kolli\-mierten, relativistischen Plasmastromes
beschreibt, der die Kollimationszone -- die D\"use -- verlassen hat und
sich frei ausdehnt. Dieser Teil des Jets ist, wegen des gro\ss{}en
\"Uberdrucks, mit aller Wahrscheinlichkeit relativ
unab\"angig von Umgebungseinfl\"ussen. Dies f\"uhrt zu einem relativ
homogenen Erscheinungsbild kompakter Radiokerne in unterschiedlichen
Quellen, wobei die Leistung im Jet bzw.~der Akkretionscheibe der
entscheidende freie Parameter ist.

Das Modell wird zun\"achst benutzt, um einige bekannte und gut
bestimmte Radiokerne zu beschreiben. Dabei wird der Bereich von
galaktischen R\"ontgen-Doppelsternen bis hin zu einer nahen
Megamaser-Galaxie abgedeckt. Es kann gezeigt werden, dass trotz der
sehr unterschiedlichen Skalen bez\"uglich Akkre\-tionsrate und zentraler
Masse das Modell die Eigenschaften des Kernes, d.h.~Gr\"o\ss{}e und Fluss
als Funktion der Frequenz, sehr gut beschreibt.

Dar\"uberhinaus wird eine detailliertere Untersuchung des Radiokerns
und vermutlichen schwarzen Lochs im Zentrum der Milchstra\ss{}e
vorgelegt. Dessen quasi-simultanes Radiospektrum wurde in einer
internationalen Kampagne bestimmt. Die Beobachtungen best\"atigten ein
leicht invertiertes Spektrum und die Existenz eines
``submm-Buckels''. T\"agliche Flussdichtemessungen \"uber mehr als
zwei Jahre zeigen Variabilit\"at mit charakteristischen Zeitskalen von
einigen zehn bis hundert Tagen und Phasen quasi-periodischer
Aktivit\"aten, die wahrscheinlich auf Insta\-bilit\"aten im
Akkretionsfluss zur\"uckzuf\"uhren sind. Die Polarisation von Sgr A*
ist
ausgesprochen ungew\"ohnlich, mit niedrigen oberen Grenzwerten f\"ur
die lineare Polarisation und einer \"uberraschenden Entdeckung von
zirkularer Polarisation. Das gesamte Radiospektrum kann mit einem
Jetmodell im Detail reproduziert werden. Dies schlie\ss{}t auch die
neuesten R\"ontgenmessungen ein und ber\"ucksichtigt die oberen
Grenzen f\"ur die ausgedehnte Emission, die mit VLBI-Beobachtungen im
Hochfrequenzbereich bestimmt worden sind. Schlie\ss{}lich wird darauf
hingewiesen, dass der submm-Buckel im Spektrum, welcher
h\"ochstwahrscheinlich auf den kleinsten r\"aumlichen Skalen
produziert wird, eine ideale Hintergrundquelle bildet, gegen den man
den Ereignishorizont des schwarzen Lochs abbilden kann. Mit Hilfe von
dreidimensionalen allgemeinrelativistischen Ray-Tracing Rechnungen
kann gezeigt werden, dass der vom Ereignishorizont produzierte
``Schatten'' eine Gr\"o\ss{}e von c.a.~$30\,\mu$-Bogensekunden haben muss
und somit im Aufl\"osungsbereich der n\"achsten Generation von
VLBI-Arrays bei hohen Frequenzen liegt.

Um das Blickfeld noch mehr zu erweitern werden die Ergebnisse einer
Suche nach Sgr A*-\"ahnlichen Radiokernen in einer Stichprobe
leuchtschwacher AGN (LLAGN) vorgestellt. Fast die H\"alfte aller
untersuchten LINER und Seyfert-Galaxien zeigen dabei kompakte,
flachspektrum Emission. Durch VLBI-Beobachtungen wird nachgewiesen,
dass es sich dabei tats\"achlich um Emission von einem AGN
handelt. Dabei zeigen die hellsten Quellen eine Kern-Jet-Struktur. Die
gemessenen Spektren sind kompatibel mit den Voraussagen des Jetmodels
und zu flach, um von einem advektionsdominierten Akkretionsfluss
(ADAF) zu stammen. Die gemessenen Radiofl\"usse, im Verh\"altnis zu
den optischen Helligkeiten, bewegen sich ebenfalls im Bereich der
Voraussagen des Jet-Scheiben-Symbiose-Modells und best\"atigen, dass
es sich bei diesen Quellen um die leuchtschwachen Gegenst\"ucke zu
Quasaren handelt.

Schlie\ss{}lich wird im Rahmen dieser Arbeit auf die Radioemission
radio-leiser AGN eingegangen, die den weitaus gr\"o\ss{}ten Teil von
Quasaren und Seyfert-Galaxien ausmachen. Beobachtungen von Seyfert-
und Megamaser-Galaxien mit dem Hubble-Space-Teleskop und dem
Very-Large-Array zeigen, dass es auch in radio-leisen AGN Jets
gibt, die ihre Umgebung signifikant beeinflussen
k\"onnen. VLBI-Beobachtungen einer speziellen Spiralgalaxie mit hellem
Seyfert\-kern zeigen dar\"uberhinaus zum erstenmal scheinbare
\"Uberlichtgeschwindigkeiten in einem Galaxientyp, der normalerweise
ausschlie\ss{}lich mit radio-leisen AGN in Verbindung gebracht
wird. Die Galaxie war Teil einer Gruppe von soge\-nannten
radio-intermedi\"aren Quasaren bei denen man vermutete, dass es sich
um relativistisch geboostete radio-leise Quasare oder
Seyfert-Galaxien handelte. Die Beobachtungen best\"atigen nun, dass es
auch in radio-leisen AGN relativistische Jets gibt und somit auch
dort das Jetmodell zur Anwendung kommen kann.

Zusammenfassend kann man sagen, dass die Produktion eines
relativistischen Jets wahrscheinlich eine unausweichliche Konsequenz
akkretierender schwarzer L\"ocher ist -- selbst bei den niedrigsten
Akkretionsraten. Daher sind kompakte Radiokerne ein idealer Indikator
f\"ur schwarze L\"ocher im nahen und fernen Universum. Mit der sich
immer noch steigernden Aufl\"osung und Empfindlichkeit von
Radiointerferometern erlauben sie einen genauen Einblick in die
Arbeitsweise von schwarzen L\"ochern auf den verschie\-dens\-ten Skalen
und in den verschiedensten Zusammenh\"angen. In der Zukunft k\"onnten
Radiokerne f\"ur kosmologische Fragestellungen und als Referenzpunkte
zur genauen Bestimmung extragalak\-tischer Eigenbewegungen im Rahmen der
Suche nach dunkler Materie dienen.


\chapter{Bibliography}
The material presented in the previous chapters -- texts and figures --
was taken in part from the publications listed below. The initial
number refers to the section number used here, followed by the short
references to the original papers. The full reference is given in
the ``Reference'' section. Parts of text from a previous publication
were used only where the lead author of the publication and the author
of this review were identical. In all cases the text was modified and
adapted for this review. Some of the material will become part of a
review for ``Annual Reviews of Astronomy \& Astrophysics''.


\begin{itemize}
\@starttoc{cit}
\end{itemize}


\chapter{References}
\bibliographystyle{apj}
\bibliography{apjmnemonic,ref0}

\chapter*{Danksagungen}\addcontentsline{toc}{chapter}{Danksagungen/Acknowledgements}
Mein ganz besonderer Dank gilt an dieser Stelle meinem Mentor
Prof.~Peter Biermann. Er hat mir schon fr\"uh die notwendige Freiheit
und den Ansporn f\"ur meine wissenschaftliche Arbeit gegeben und mich
immer wieder durch viele Diskussionen, Ratschl\"age und Ideen
begleitet.

Ich danke auch dem Max-Planck-Institut, und insbesondere seinem
Direktor Dr. Anton Zensus, f\"ur die bereitwillige Unterst\"utzung
meiner Arbeit und das hervorragende Arbeitsumfeld.

Von den vielen Kollegen, m\"ochte ich dar\"uberhinaus ganz besonders
Prof. F. Melia, Prof. A.S. Wilson, Prof. P.G. Mezger, Prof. K. Menten,
Dr. S. Markoff, Dr. G. Bower, Dr. A. Roy, Dr. T. Krichbaum,
Dr. A. Lobanov, Dr. E. Agol, Dr. C. Henkel, Dr. A. Patnaik,
Prof.~Dr. W. Duschl, Dr. R. Zylka, Dr. I. Owsianik, Dr. C. Simpson,
Frau G. Pugliese, und Herrn A. Brunthaler hervorheben, von denen ich
in intensiven Diskussionen sehr viel gelernt habe.

Schlie\ss{}lich bedanke ich mich bei meiner Familie, insbesondere bei
meiner Frau Dagmar und meinen Kindern Jana, Lukas und Niklas f\"ur die
gro\ss{}e Geduld und das Verst\"andnis mir gegen\"uber, sowie f\"ur
die fortw\"ahrende Erinnerung daran, dass es auch wichtigeres im Leben
gibt als die Wissenschaft.


\medskip
Teile der Arbeit sind bei Aufenthalten an der University of Maryland
und der University of Arizona enstanden f\"ur deren Gastfreundlichkeit
ich mich bedanke.

\medskip
Viele der gezeigten Beobachtungen sind mit Teleskopen des
NRAO\footnote{The National Radio Astronomy Observatory is a facility
of the National Science Foundation, operated under cooperative
agreement by Associated Universities, Inc.} und mit dem
Hubble-Space-Teleskop\footnote{Observations with the NASA/ESA Hubble
Space Telescope were obtained at the Space Telescope Science
Institute, which is operated by AURA, Inc., under NASA contract NAS
5-26555} gemacht worden.

\medskip
Diese Arbeit wurde durch ein Habilitationsstipendium und eine
Sachbeihilfe der Deutschen Forschungsgemeinschaft (Fa 358/1-1 \& 2)
unterst\"utzt.

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