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\begin{document}
\title{Sgr A*: observations, models, and imaging of the event horizon with VLBI}
 \author{Heino Falcke\altaffilmark{1}, Sera Markoff\altaffilmark{1},
 Peter L. Biermann\altaffilmark{1}, Thomas P.
Krichbaum\altaffilmark{1}, Fulvio Melia\altaffilmark{2}, Eric
Agol\altaffilmark{3}, Geoffrey Bower\altaffilmark{4}}
\altaffiltext{1}{Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel
69, D-53121, Bonn, Germany}
\altaffiltext{2}{Physics Department and Steward Observatory, The University of Arizona, Tucson, AZ 85721}
\altaffiltext{3}{Theoretical Astrophysics, Caltech MS 130-33, 1200 E. California
Blvd., Pasadena, CA 91125}
\altaffiltext{4}{Radio Astronomy Laboratory,
University of California, Berkeley, CA 94720}

\begin{abstract}
We show and discuss results and prospects of high-resolution imaging
of the supermassive black hole candidate Sgr A*.  We also briefly
review the latest observational and theoretical progress for this
source.  The latest millimeter-VLBI observations show compact radio
emission from within a region of about 15 Schwarzschild radii. This
compact component is most likely responsible for the so-called sub-mm
bump in the spectrum and perhaps even for the recently discovered
circular polarization discovered up to 43 GHz and some X-ray emission
through synchrotron self-Compton emission. Most importantly, however,
the sub-mm emission from Sgr A* opens the door to observe, for the
first time, the event horizon of a black hole directly with VLBI
at sub-mm wavelengths.
\end{abstract}

\section{Introduction}
The mass of Sgr~A* in the Galactic Center is by now relatively
securely determined to be $\sim3\cdot10^6M_\odot$
\cite{EckartGenzel1997,GhezKleinMorris1998}. While all evidence we
have so far points to the presence of a supermassive black hole, a
final proof is not yet available. Similarly, the nature of processes
producing the Sgr A*, radio and X-ray, emission is still under deliberation
(see \citeNP{MeliaFalcke2001} for a review). One important question is
whether the radiation from Sgr A* we see is actually produced in
plasma being accreted \cite{Melia1992a,NarayanMahadevanGrindlay1998}
or in plasma ejected via a jet
\cite{FalckeMannheimBiermann1993}. In either case Sgr A* will serve as 
an important test bed for the large number of low-luminosity accreting
black holes in general.

To learn more about the source, we need to intensify theoretical and
observational efforts. Indeed, substantial progress has again been
made in the recent past and, as we discuss later on, there is even
hope to eventually `see' the event horizon of the black hole with high
resolution imaging in the not--too--distant future and to uniquely
demonstrate its existence.

\begin{figure}
\hbox{\psfig{figure=geoff-spectrum.ps,width=0.48\textwidth}\hfill\vbox{\psfig{figure=fig-sgrx.ps,width=0.48\textwidth,angle=-90}\vspace{1cm}}}
\caption[]{\label{polarization}\label{sgrx}Left: 
Fractional linear (LP) and circular (CP) polarization in Sgr~A* from
1.4 to 86 GHz from the VLA (Bower et al., in prep.; see also Bower
2000) and from JCMT at higher frequencies as claimed by Aitken et
al. (2000). The sign of CP has been flipped.\break\hfill Right:
Broad-band spectrum of Sgr~A* produced by a jet model from synchrotron
and synchrotron self-Compton emission. The size of the jet nozzle is
$\sim 4$ Schwarzschild radii (cnf.~Falcke \& Markoff 2000).}
\end{figure}
\nocite{Bower2000}

\section{Observational and Theoretical Progress}
VLBI observations have continued to narrow the size and structure of
Sgr A*.  Radio proper motion studies of Sgr A*
\cite{BackerSramek1999a,ReidReadheadVermeulen1999} indicate that the
source is indeed at the Galactic Center and that it must have at least
several thousand solar masses. The source has been detected with VLBI
up to a frequency of 215 GHz \cite{KrichbaumGrahamWitzel1998} showing
that the radio emission in the mm-wave regime stems from a region just
tens of Schwarzschild radii across
\cite{KrichbaumGrahamWitzel1998}. Observations at 43 GHz have found
tentative evidence for an intrinsic north-south elongation and new 86
GHz observations \cite{DoelemanShenRogers2000} give an intrinsic
source size of $<0.25\times0.13$ mas. Consistent with this, the rising
spectrum at mm-to-sub-mm wavelengths indicates that the emission at
these wavelengths is extremely compact and becomes optically thin
somewhere in the sub-mm regime \cite{Melia1992a,FalckeGossMatsuo1998}.

Besides the new structural information, the discovery of circular
polarization in Sgr A* \cite{BowerFalckeBacker1999} has revived
interest in the polarization properties of Sgr A*. It seems that Sgr~
A* shows no linear polarization up to 112 GHz at limits ranging from
0.1--1\%, while circular polarization has now been detected up to 43
GHz (see
Fig.~\ref{polarization}). \citeN{AitkenGreavesChrysostomou2000} claim
a detection of linear polarization in the mm-wave regime which they
interpret as confirmation for a very compact, self-absorbed emission
region.

The level of circular polarization in Sgr A* is not unusual compared
to those found in compact radio cores of jets in quasars
\cite{WardleHoman2000}. However, the fact that circular polarization exceeds
linear by a large factor, is unusual.  The interpretation is unclear
but certainly implies a large number of low-energy electrons either in
the source (see for example the discussion in
\citeNP{BowerFalckeBacker1999}) or along the line of sight (Blandford,
this conference). In any case, \citeN{WardleHoman2000} find that the
circular polarization of AGN jets is always associated with the most
compact component, i.e. the core.

In addition to these new radio astronomical results, recently
\citeN{BaganoffBautzBrandt2000} detected Sgr A* with the X-ray
satellite Chandra. The emission is rather dim which reduces
significantly the accretion rates in various accretion models.  The
rather soft (steep) spectrum can be explained naturally in terms of
synchrotron self-Compton (SSC) emission from the sub-mm bump emission
region
\cite{BeckertDuschl1997,FalckeMarkoff2000,MeliaLiuCoker2000}. Within
the jet model for Sgr A* the sub-mm bump is attributed to radio
emission from the jet nozzle. SSC emission is then almost unavoidable
and follows naturally, given the small source size at these high
frequencies \cite{FalckeMarkoff2000}. A broadband spectrum produced by
such a jet+nozzle model is shown in Fig.~\ref{sgrx}. The `nozzle' has
several physical features in common with the inner region of an
accretion flow, so it is not yet possible to distinguish between these
two geometries on the basis of the sub-mm/X-ray emission alone (or to
say whether there is a difference at all).  It may eventually be
possible to do so when this is combined with the constraints due to
the polarization measurements.



\section{Imaging the Event Horizon}

As outlined above, various lines of arguments directly or indirectly
point to the mm and sub-mm emission of Sgr A* coming from a very
compact region. VLBI observations, modeling of radio and X-ray
emission, and tentatively also the polarization properties all point
to Sgr A* being only a few Schwarzschild radii in diameter. This is
certainly a regime where strong gravity effects are
important. \citeN{FalckeMeliaAgol2000} have shown that if Sgr A* is
surrounded by a transparent radiating plasma, the presence of an event
horizon will cast a shadow on the emission region, roughly 5
Schwarzschild radii in diameter. For a $\sim3\cdot10^6M_\odot$ black
hole at a distance of 8 kpc this corresponds to
$37\mu$-arcseconds. Current VLBI-experiments at 3mm have already
reached a resolution of 50$\mu$-arcseconds
\cite{RantakyroBaathBacker1998}. Given the expected resolution of mm-
and sub-mm VLBI-experiments and the extrapolated interstellar scatter
broadening one can show that the shadow of the event horizon will be
detectable with VLBI at wavelengths shortwards of 1.3
mm. Figure~\ref{eventhorizon} shows an example for a rotating black
hole with a very concentrated emission region.

Alternative suggestions to image this shadow with X-ray satellites
have been made at this conference \cite{CashShipleyOsterman2000}. If
the (faint) X-ray emission in Sgr A* is indeed due to SSC it will be
spatially coincident with the radio plasma and hence allow us to see
this effect perhaps even with the resolution of the first generation
of X-ray interferometers provided they will have the necessary
sensitivity. On the other hand, radio astronomers have a large head
start given the evolution of VLBI in the past decades. In any case,
detecting the `shadow' with the size predicted by General Relativity
will provide us with the final and an unambiguous proof for the
existence of an event horizon in Sgr~A*.

\begin{figure}
\centerline{\psfig{figure=fig-eventhorizon.ps,width=0.75\textwidth,bbllx=1.3cm,bblly=17.6cm,bburx=13.4cm,bbury=23cm}}
\caption[]{\label{eventhorizon}The shadow of the event horizon
calculated for Sgr A* in the Galactic Center smoothed to the
resolution of a VLBI array at 0.6 (left) and 1.3mm (right). Lines give
vertical (dashed) and horizontal (solid) cuts through the intensity
distribution. The vertical axis is in units of $GM/c^2$. The
simulations were made as in Falcke, Melia, Agol (2000), for a
maximally rotating black hole with rotating (``Keplerian'') shells and
an $r^{-2}$ emissivity seen at a 45$^\circ$ inclination angle.}
\end{figure}


%\bibliography{../../Review/review}
%\bibliographystyle{../../Review/apj} 
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\end{document}
