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\begin{document}
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   \title{Constraints on the circumnuclear absorber in NGC\,1052 from Radio and X-ray observations}

   \author{M. Kadler\inst{1}
          \and
	  E. Ros\inst{1}
	  \and
          J. Kerp\inst{2}
	  \and
	  A.\,P. Lobanov\inst{1}
	  \and
	  H. Falcke\inst{1}
	  \and
	  J.\,A. Zensus\inst{1}
          }

   \institute{Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel 69, D-53121 Bonn, Germany 
         \and
             Radioastronomisches Institut der Universit\"at Bonn, Auf dem H\"ugel 71, D-53121 Bonn, Germany
             }

   \abstract{
Multi-frequency studies of the pc-scale twin-jet in NGC\,1052 have revealed
the presence of a dense circumnuclear absorber obscuring the central engine.
We analyze the brightness temperature distribution along the approaching, eastern
pc-scale jet of NGC\,1052 based on observational data obtained with the VLBA at 
5, 8.4, 22 and 43\,GHz. We present evidence for a geometry in which the central
absorber covers also $\sim$0.3\,pc of the approaching jet in addition to
the previously known obscuration of the receding jet. 
Further constraints on the properties of the circumnuclear absorber in
NGC\,1052 are obtained using the CHANDRA X-ray observatory. A rather moderate
X-ray absorbing column density, substantially lower than previously published values,
is derived from the nuclear X-ray spectrum.
Imaging the extended X-ray
emission reveals the presence of various jet-related X-ray emitting regions in
NGC\,1052: a bright compact core, unresolved knots in the jet structure, and
an elongated, diffuse emission region whose spectrum can be described by a thermal model.  
We compare the spatial distribution of the
diffuse X-ray emission on kpc-scales with the radio structure derived from a
MERLIN observation and an optical image taken by the Hubble Space Telescope.
   }

   \maketitle
%
%________________________________________________________________

\section{Introduction}
NGC\,1052 has become one of the most promising candidates for probing
the physical properties of a circumnuclear absorber around a supermassive
black hole predicted by the AGN standard model. The presence of such a
central absorber in this elliptical galaxy is indicated by various observations 
of the pc-scale
twin-jet using VLBI techniques, e.g. by \cite{Kel99},
\cite{Kam01}, \cite{Kad02}.
Strong free-free absorption towards the receding western
jet has been established by these authors. The obscuration of the jet by a
circumnuclear disk or torus is sustained by the presence of water maser emission
distributed along the western jet suggesting an interaction between the
jet radiation field and circumnuclear, molecular matter (\cite{Cla98}).\\
Evidence for the existence of a central absorber in NGC\,1052 also comes from observations in the
X-ray regime (\cite{Wea99}, \cite{Gua99}, \cite{Gua00}). 
While free-free absorption at radio wavelangths is an indicator of ionized matter,
absorption at X-ray frequencies can give information about neutral
hydrogen (HI).
The spectral analysis of the spatially 
unresolved X-ray spectrum suggests an obscuring neutral gas component with
an absorbing column density of $N_{\rm H} \sim 10^{23}$\,cm$^{-2}$.
CHANDRA is the first X-ray imaging facility with an angular resolution
high enough to separate the X-ray core and diffuse, extended emission.
It is thus better suited to obtain an unpolluted nuclear spectrum than
earlier missions.\\
In this work we  use the high angular resolution of CHANDRA combined 
with VLBI observations in the radio regime 
to better constrain the physical properties of the central absorber in NGC\,1052. 
%________________________________________________________________

\section{Evidence for free-free absorption towards the eastern jet}
Figure \ref{fig1} shows VLBA images of NGC\,1052 in total 
intensity at 5, 8.4, 22 and 43\,GHz obtained from our observations on 
December 28th 1998. In Kadler et al. (2002) we described the mapping and
registration of the images.
The spectral indices at the core of the western jet are larger than
2.5 indicating free-free absorption.
The core position in both jets changes with frequency.
The core-shift analysis suggests that the cores of both
jets are covered by the central absorber and that the shift rates
with frequency have also to be explained in terms of free-free absorption
in conjunction with steep pressure gradients along both jets.\\ 
To clarify the geometry of the central absorber, we analyze the brightness temperature
distribution along the approaching, eastern jet of NGC\,1052.
The brightness temperature associated with a circular Gaussian component is
(e.g. Condon et al. 1982)
\begin{equation}
T_b=1.22\cdot10^{12} {\rm K} \left(\frac{S_\nu}{\rm Jy}\right)\left(\frac{\nu}{\rm GHz}\right)^{-2}\left(\frac{\Theta}{\rm mas}\right)^{-2}
\end{equation}
   \begin{figure}
   \centering
   \includegraphics[width=\columnwidth]{kadler_fig1}
      \caption{The twin jet of NGC\,1052 at 5, 8.4, 22 and 43\,GHz at epoch 1998.99
observed with the VLBA (Kadler et al. 2002). The outer parts of both jets
fade away towards higher frequencies, indicating optically thin synchrotron
emission.
The gap between both jets (presumably caused by the obscuring torus) becomes
smaller at higher frequencies but stays prominent up to 43\,GHz. There is no
true core detectable, even at the smallest beam-size (corresponding to the highest
resolution), at 43\,GHz. Component B is totally absorbed at 5\,GHz, indicating
the presence of an obscuring torus, located in this region. A detailed analysis
gives a
spectral index well above 2.5, ruling out synchrotron self--absorption.
              }
         \label{fig1}
   \end{figure}
\begin{figure}
   \centering
   \includegraphics[width=\columnwidth,clip]{kadler_fig2}
      \caption{Brightness temperature distribution along the eastern jet of
NGC\,1052. Farther out than $\sim$3\,mas the data (solid symbols) can be approximated by a
power-law
of the form $T_b \propto r^{-4}$. The offsets between the four frequency-data sets
reflects the frequency dependence of $T_b$. Inside a radius of 3\,mas ($\sim$0.3\,pc) the
brightness temperature of the jet is substantially reduced (open symbols). The location of
the cutoff can be
interpreted as the edge of the central absorber covering the core of the approaching,
eastern jet.
              }
         \label{fig2}
   \end{figure}
where $S_\nu$ is the flux density of the component, $\nu$ is the observing frequency
and $\Theta$ is the FWHM of the model component.
In Figure 
\ref{fig2}, the brightness temperatures of the components along the eastern jet are plotted as a function 
of distance from the central
engine, which is assumed to be located at the center between the innermost model components 
(see Kadler et al. 2002 for a detailed discussion).
A conspicuous cutoff around 3\,mas east of the center is present at all four 
frequencies\footnote{At the distance of NGC\,1052 ($D = 22.6$\,Mpc) 
1\,mas corresponds to $\sim$0.11\,pc (assuming H$_0 = 65$\,km\,s$^{-1}$\,Mpc$^{-1}$).}. Farther out, the data points can well be 
approximated by
a power law of the form $\log T_b  = A + B \cdot \log r $.
A linear regression for the
fit parameters gives at all four frequencies a $T_b \propto r^{-4}$ law. 
The frequency independence of the cutoff distance implies
an external effect suggesting that at this
position the influence of the nuclear absorber 
starts to affect substantially the jet and the brightness
temperature of the components in it.
This suggests the existence of an obscuring torus around the central
engine of NGC\,1052 with a sharp edge rather than a 
circumnuclear cloud system. 
In the case of free-free absorption, the observed flux
density $S_{\nu , abs}$ should depend on the intrinsic flux density $S_\nu$, the
optical depth of the absorber $\tau_f$ and the observing frequency $\nu$ as
\begin{equation}
S_{\nu , abs}=S_\nu \cdot e^{-\tau_f} {\rm \quad .}
\end{equation}
Extrapolating the power--law dependence for each of the four frequency data
sets to smaller distances ($< 3$\,mas) we can calculate an optical depth
for each data point that can explain the degradation of the brightness temperature
with respect to the extrapolated value. 
The resulting values for $\tau_f$ are very similar and lie between 2 and 3. 
Assuming an absorbing path length of 0.3\,pc 
(comparable to the extent of the absorbing region in the plane of
the sky), the 
optical depth can be determined from (compare e.g. Rybicki \& Lightman 1979) 
\begin{eqnarray}
&\tau_f = 30 \cdot 10^{16}\,L\,T^{-1.35}\,\nu^{-2.1}\,n_{mean}^2 \\
\Rightarrow &T^{-1.35}\,n_{mean}^2 = 3.33 \cdot 10^{-18} \, L^{-1} \tau_f \, \nu^{2.1}
\end{eqnarray}
with a length $L=\int dl$ and an average density $n_{mean}$.
For $\tau_f \sim 2.5$ at $\nu = 22$\,GHz and a temperature of $T=10^4$\,K, 
this gives a density of
$n_{mean}=6 \cdot 10^5$\,cm$^{-3}$ and an absorbing column density of 
$5.6 \cdot 10^{22}$\,cm$^{-2}$. This value is consistent with the implications
of the X-ray observations of NGC\,1052, which find a (model-dependent)
column density of $10^{22}$-$10^{23}$\,cm$^{-2}$ (\cite{Wea99}, \cite{Gua99},
and section 4 ) towards the unresolved nuclear X-ray core.
 
%________________________________________________________________

\section{The X-ray jet of NGC\,1052}
   \begin{figure}
   \centering
   \includegraphics[clip,width=\columnwidth]{kadler_fig3}
%\vspace{230pt}
   \caption{The X-ray jet of NGC\,1052 imaged by CHANDRA. The grey scale image has been
smoothed to a resolution of 4\,$^{\prime\prime}$ within the CSMOOTH program,
which is part of the CIAO software, to increase sensitivity. Each tick corresponds
to 2\,$^{\prime\prime}$.
The clipping level is 3$\sigma$.
Overlaid are the radio contours from a 1.4\/GHz MERLIN map at epoch 1995.9\,.
The enclosed panel shows the
HST image from \cite{Pog00} at the same scale. Two knots
appear at the same positions as the corresponding X-ray features.}
            \label{fig3}
    \end{figure}
CHANDRA observed NGC\,1052 on August 29/30, 2000\footnote{The CHANDRA data were 
taken from the public archive ({\tt http://cxc.harvard.edu/cda/chaser.html}) 
and analyzed using standard methods within the software package CIAO 2.2. The
observation was planned and scheduled by G. P. Garmire.}.
During the 2342 sec. observation, the Advanced CCD Imaging Spectrometer 
(ACIS) Chip S3 was in focus of the High Resolution Mirror Assembly (HRMA).
The ACIS--S3 detector offers $0\rlap{.}^{\prime\prime}$5 angular resolution as well as information on 
the X-ray source spectrum because of its intrinsic energy resolution.\\
The nucleus of NGC\,1052 is the brightest X-ray source within the field of 
interest. During the rather short X-ray observation about 280 photons from the
nucleus were detected. This value corresponds to a count rate of 
0.12\,${\rm cts\,s^{-1}}$.\\
The CHANDRA image of NGC\,1052 is
shown in Figure \ref{fig3}.
Strong X-ray emission from the AGN is seen in this image as well as diffuse
extended emission well aligned with the radio jet,
whose MERLIN image is superimposed in contours\footnote{The MERLIN data has been
obtained from the public archive ({\tt http://www.merlin.ac.uk}). The experiment
was planned and scheduled by A. Pedlar. The map shown in contours in Figure 
\ref{fig3} was produced applying standard methods using the program
{\sc difmap}.}.
This is the first direct detection of the X-ray jet of NGC\,1052.
\\
Close to the nucleus a tentative correlation between radio
and X-ray emission can be found while the synchrotron emission in the
radio lobes tends to anti-correlate with the X-ray intensity distribution.
East and west of the core, there are two X-ray emitting regions, coinciding
with enhanced brightness regions in the radio regime, which can
also be seen in an optical image, taken by the Hubble Space Telescope
(Pogge et al. 2000). The X-rays from these knots might be produced in a
very different physical process than the more diffuse, extended emission.
Synchrotron or
inverse Compton radiation could be responsible for their brightness over this
large frequency range but the poor photon statistics prevented
the derivation of spectra of either knot to test this hypothesis.\\
To constrain the emission process of the X-ray jet, we 
selected an annulus which excludes the 
nucleus itself but includes the whole area of the X-ray jet 
and fitted two 
different models to the jet--spectrum (see Figure \ref{fig4}): a Raymond and Smith 
plasma (Raymond \& Smith 1977) and a simple power--law.
We consider the power--law fit result of the X-ray jet as highly implausible,
because of the extraordinary steep photon index of $\Gamma\,\geq\,7$.\\
Because the radio as well as the X-ray jet are considered to be located deep 
inside the galaxy NGC\,1052 itself, we have to determine the amount of 
photoelectric absorption distributed along the line of sight.
Using the thermal source model, we find an attenuating column 
density of $N_{\rm HI}\,\simeq 3.5\times 10^{21}\,{\rm cm^{-2}}$. 
This value is about an order of magnitude higher than the galactic 
foreground column density belonging to the Milky Way of $N_{\rm HI} = 2\times10^{20}\,{\rm cm^{-2}}$ (Hartmann \& Burton 1997).
We attribute this additional X-ray attenuation to weakly ionized gas located 
inside the galaxy itself.
We derive a plasma temperature of
$kT = (0.5\pm0.2)$\,keV for the diffuse X-ray jet emission.
%__________________________________________________________________

\section{The X-ray spectrum of the nucleus}
\begin{figure*}
   \centering
   \includegraphics[clip,width=\textwidth]{kadler_fig4}
      \caption{X-ray spectrum of the jet (left panel) and core (right panel) of NGC\,1052. The solid line indicates
the best-fit model.
              }
         \label{fig4}
   \end{figure*}
The nuclear X-ray spectrum was extracted up to a diameter of 2\,arcsec.
Comparing both X-ray spectra in Figure \ref{fig4}   
reveals the much softer X-ray emission 
of the jet. The bulk of the X-ray jet emission originates below $E\,<\,2$\,keV 
while the X-ray spectrum of the nucleus has additional hard X-ray emission.
ASCA as well as the ROSAT PSPC could not separate between the nucleus and the
jet spatially but the soft X-ray emission of the jet was already detectable in terms
of a soft excess of the X-ray spectrum in the PSPC data.\\
The soft X-ray emission below $E\,<\,2$\,keV in the nuclear spectrum
is at a comparable intensity level as the X-ray emission of the jet.
Assuming that a fraction of the diffuse X-ray emission of the jet
originates also in the extraction region of the nucleus, 
we used a hybrid model for the X-ray spectral approximation of the nuclear spectrum
for the observed intensity distribution
\begin{equation}
I_{\rm obs} = (I_{\rm jet} + I_{\rm nucleus}\times e^{-\sigma\times N_H({\rm torus})})\times e^{-\sigma\times N_H({\rm gal.})}
\label{eq:i_obs}
\end{equation}
where $I_{\rm jet}$ is 
the X-ray spectrum of the jet and $I_{\rm nucleus}$ is the spectrum of the 
nucleus.
The photoelectric absorption produced by the torus is represented in Eq. (\ref{eq:i_obs}) 
by $e^{-\sigma\times N_H({\rm torus})}$ while the X-ray absorption produced by the
interstellar medium of the galaxy is $e^{-\sigma\times N_H({\rm gal.})}$.
We assumed a power--law type X-ray spectrum of the central X-ray source
and fixed the plasma temperature of the X-ray jet contribution as well as the
foreground X-ray absorbing column densities to the values derived in section 3.
The best fit values are: $N_{\rm H}({\rm torus}) = 0.8^{+1.5}_{-0.60}\times 10^{23}\,{\rm cm^{-2}}$ and $\Gamma = 0.38^{0.31}_{-0.21}$. The absorbed X-ray flux is
$F_{\rm X}({\rm 0.3\,-\,8.0\,keV}) = (4.3\,\pm\,1.4)\times10^{-12}\,{\rm erg\,s^{-1}\,cm^{-2}}$.\\
The derived $N_{\rm H}({\rm torus})$ is rather low. Data of other X-ray 
observatories imply much higher values for both, the $N_{\rm H}({\rm torus})$ as
well as $\Gamma$ (\cite{Wea99}, \cite{Gua99}, \cite{Gua00}) but
these high torus column densities are not supported by the CHANDRA data.
We assume that the apparent discrepancy between the CHANDRA data and previous
X-ray observations concerning the photon index is due to the pile--up
degradation ($\sim 30$\,\%) of the CHANDRA data.
The nuclear X-ray spectrum might appear
flatter than expected, because of the artificial hardening of the X-ray spectrum introduced
by the pile--up effect.
Taking this into consideration, our results are consistent with the 
analysis of Weaver et al. (1999) who fitted the combined ROSAT and ASCA data -- both are not affected by the pile--up
-- and derived in general steeper X-ray photon indices using a variety of models.
The determined absorbing column density, however, is not so sensitive to the pile--up
effect.\\  
We tried to substitute $I_{\rm nucleus}$ from a power--law to a thermal
bremsstrahlung model.
No approximation was feasible. In all cases the temperature
values exceed the upper temperature boundary of 1\,MeV.\\

%______________________________________________________________

\section{Summary}
The CHANDRA data provide for the first time direct evidence for
an X-ray jet in NGC\,1052 perfectly correlated in extent with the well studied radio jet.
The X-ray jet can be approximated best with thermal X-ray emission of a plasma
with k$T = 0.5$\,keV. This temperature is consistent with the thermal
component found earlier by Weaver et al. (1999) using ASCA and ROSAT data.
Its unabsorbed flux is $F_{\rm X-ray \,jet}({\rm 0.3\,-\,8.0\,keV}) =
(1.7\,\pm\,0.8)\times10^{-13}\,{\rm erg\,s^{-1}\,cm^{-2}}$, only 2\% of the
X-ray emission of the nucleus. Because of the strong pile--up degradation of
the CHANDRA data, no firm conclusions on the X-ray spectrum of the nucleus can
be deduced.\\
The absorbing column density of ionized material towards the approaching  
VLBI--jet derived from the brightness temperature distribution 
is of the order of $\sim 6 \cdot 10^{22}$\,cm$^{-2}$. This is in a good
agreement with the absorbing column density of neutral hydrogen 
($0.8^{+1.5}_{-0.60} \cdot 10^{22}$\,cm$^{-2}$)
derived from X-ray spectroscopy of the compact X-ray
core of NGC\,1052. 

\begin{acknowledgements}
MERLIN is a National Facility operated by the University of Manchester at 
Jodrell Bank Observatory on behalf of PPARC. 
The VLBA is operated by the National Radio Astronomy Observatory (NRAO),
a facility of the National Science Foundation operated under cooperative agreement
by Associated Universities, Inc.
The CHANDRA Data Archive (CDA) is part of the CHANDRA X-Ray Observatory Science Center 
(CXC) which is operated for NASA by the Smithsonian Astrophysical Observatory.

\end{acknowledgements}

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\end{document}