From G.Dahmen@qmw.ac.uk Mon Apr 29 11:47:29 1996
Date: Mon, 29 Apr 1996 16:45:20 +0100
From: G.Dahmen@qmw.ac.uk (Gereon Dahmen)
To: gcnews@astro.umd.edu
Subject: submit C18O_TGC_Proc.tex to appear in the Proceedings of the 4th 
         ESO/CTIO Workshop on ``The Galactic Center''
Cc: huette@cfa.harvard.edu, G.Dahmen@qmw.ac.uk
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\markboth{G.\ Dahmen et al.}{The Molecular Gas in the Galactic Center 
Region based on C$^{18}$O Measurements}
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\begin{document}
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\title{The Molecular Gas in the Galactic Center Region based on 
C$^{18}$O Measurements \\[1mm] 
Presentation of a Large Scale $J$\,=\,1\,--\,0 Survey obtained 
with the 1.2m Southern Millimeter-Wave Telescope at CTIO}
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\author{G.~Dahmen$^{1,2}$, S.~H\"uttemeister$^{3,1}$, 
T.L.~Wilson$^{1}$, R.~Mauersberger$^{4,1}$, A.~Linhart$^{1}$, 
L.~Bronfman$^{5}$, A.R.~Tieftrunk$^{1}$, K.~Meyer$^{1}$, 
W.~Wieden- h\"over$^{1}$, T.M.~Dame$^{3}$, E.S.~Palmer$^{3}$, 
J.~May$^{5}$, J.~Aparici$^{5}$, F.~Mac- Auliffe$^{5}$}
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\affil{
$^1$ Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel 69, \\ 
~~53121 Bonn, Germany \\ 
$^2$ Physics Department, Queen Mary \& Westfield College, \\ 
~~University of London, Mile End Road, London E1 4NS, U.K. \\ 
$^3$ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, \\ 
~~Cambridge, MA 02138, U.S.A. \\ 
$^4$ Steward Observatory, The University of Arizona, Tucson, AZ 85716, \\ 
~~U.S.A. \\ 
$^5$ Departamento de Astronom\'\i{}a, Universidad de Chile, Casilla 36-D, \\ 
~~Santiago de Chile, Chile}
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\begin{abstract} 
A large scale C$^{18}$O($J=1-0$) survey of the central few hundred pc
($-1.05^{\circ} \leq l \leq +3.6^{\circ}$, $-0.9^{\circ} \leq b \leq
+0.75^{\circ}$) of the Galaxy is presented. These 9$^{\prime}$
resolution data were obtained with the 1.2\,m Southern Millimeter-Wave
Telescope (SMWT) at CTIO and compared to \mbox{$^{12}$CO(1--0)} data
also obtained with this telescope. In addition, \linebreak[4]
\mbox{HNCO(5$_{0,5}$--4$_{0,4}$)} line data included in the
spectrometer passband are also presented.

Although both $^{12}$CO and C$^{18}$O are thought to be tracers of the
molecular mass, their distribution and line shapes differ
significantly.  The \mbox{C$^{18}$O(1--0)} line is mucher weaker than
expected from the ``Standard $I_{\rm ^{12}CO(1-0)}/{\cal N}_{\rm H_2}$
Conversion Formula'' obtained by Strong et al.\ (1988). LVG
calculations suggest that on large scales the \mbox{$^{12}$CO(1--0)}
emission is only of intermediate ($\tau = 1 - 5$) or low optical depth
($\tau < 1$).  In this case, the ``Standard Conversion Formula''
overestimates ${\cal N}_{\rm H_2}$. Our \mbox{C$^{18}$O(1--0)} data
combined with other H$_2$ tracers indicate a total molecular mass of
$(3^{+2}_{-1}) \cdot 10^7\ {\rm M_{\odot}}$. The existence of a
widespread component of molecular gas with low density (thin gas) is
found to be very likely.
\end{abstract}

\keywords{Radiative transfer --- Surveys --- ISM: molecules, structure --- 
Galaxy: center --- Radio lines: ISM}

\section{The Instrumentation of the 1.2\,m SMWT} 

The primary antenna of the SMWT is a 1.2~meter parabolic aluminium
dish. The telescope has a 3~mm liquid nitrogen cooled superheterodyne
receiver and a  main-beam size of 8$.\mkern-4mu^\prime$8 at 115.3~GHz.
A detailed description of the telescope system can be found in Bronfman
et al.\ (1988, 1989).

For the \mbox{C$^{18}$O(1--0)} survey (line frequency 109.782160~GHz),
the telescope control computer system and software as well as the data
reduction facilities were upgraded (Dahmen 1995).  The
Max-Planck-Institut f\"ur Radioastronomie (MPIfR) in Bonn, Germany,
made available a broadband (795~MHz) AOS (Linhart 1994).

\section{Observations and Data Reduction} 

The observations were carried out between the beginning of August 1993
and the end of August 1994. A detailed description of the observing
procedure, the observations, and the data reduction is given in Dahmen
(1995).  The calibration stability was excellent over the course of the
survey.  The data were scaled to $T_{\rm MB}$ using comparison
measurements done with the 1.2\,m NMWT, where the scaling is known with
a high accuracy (Cohen et al.\ 1986).

\section{Results of the C$^{18}$O(1--0) Galactic Center Survey} 

\begin{figure}
\psfig{figure=c18o_-225_225_lbcont+grey.ps,bbllx=450pt,bblly=0pt,bburx=125pt,bbury=737pt,angle=-90,height=4.5cm}
\caption{The integrated intensity of the Galactic Center region in
\mbox{C$^{18}$O(1--0)}. The velocity over which the intensity is
integrated ranges from $-$225.0 to +225.0~km\,s$^{-1}$. The solid
contour levels range from 3.9 to 28.05 in steps of 3.45~K\,km\,s$^{-1}$
where the lowest level is the 3$\sigma$-value. The dashed contour is at
2.6~K\,km\,s$^{-1}$ which is the 2$\sigma$-value. The circle in the
lower left corner of the plot indicates the beam size of
9$.\mkern-4mu^\prime$2.} \label{C18OContAll}
\end{figure} 

The survey presented here covers the area of $-1.05^{\circ} \leq l \leq
+3.6^{\circ}$ and $-0.9^{\circ} \leq b \leq +0.75^{\circ}$. In
Fig.~\ref{C18OContAll}, we show a contour map of the integrated
intensity of the \mbox{C$^{18}$O(1--0) line}, covering the complete
emission range of the Galactic center region from $-$225.0 to
+225.0~km\,s$^{-1}$. The main C$^{18}$O emission regions coincide with
the known continuum and CO peaks Sgr\,A (with the extension to
Sgr\,B1), Sgr\,B2, Sgr\,C and Sgr\,D. In addition, Clump~2 is weak but
visible. In the middle panel of Fig.~\ref{VerglChan50}, a channel map
of 50~km\,s$^{-1}$ width centered at +50~km\,s$^{-1}$ is shown.  A
detailed discussion of the data can be found in Dahmen (1995) and will
be published soon (Dahmen et al.\ 1996).

\section{The HNCO(5$_{0,5}$--4$_{0,4}$) Line in the Survey} 

Because of the large bandwidth of the AOS the emission of the
\mbox{5$_{0,5}$--4$_{0,4}$} transition of HNCO at 109.905573~GHz fell
mostly (depending on $v_{\rm LSR}$) into the range of the
spectrometer.  In Fig.~\ref{HNCOContAll}, the integrated intensity is
plotted as a contour map, covering the velocity range from $-$37.5 to
+137.5~km\,s$^{-1}$.  This is the complete emission range of the
\mbox{HNCO(5$_{0,5}$--4$_{0,4}$)} line which is covered by the
spectra.  Most notably the \mbox{HNCO(5$_{0,5}$--4$_{0,4}$)} emission
is much more restricted to the Galactic plane than the
\mbox{C$^{18}$O(1--0)} emission.

\begin{figure}
\psfig{figure=hnco_-37.5_137.5_lbcont+grey.ps,bbllx=450pt,bblly=0pt,bburx=125pt,bbury=737pt,angle=-90,height=4.5cm}
\caption{The integrated intensity of the Galactic Center region in
\mbox{HNCO(5$_{0,5}$--4$_{0,4}$)}. The velocity over which the
intensity is integrated ranges from $-$37.5 to +137.5~km\,s$^{-1}$. The
solid contour levels are 2.4, 5.0, 7.5, and from 10.0 to 42.0 in steps
of 4.0~K\,km\,s$^{-1}$ where the lowest level is the 3$\sigma$-value.
The dashed contour is at 1.6~K\,km\,s$^{-1}$ which is the
2$\sigma$-value.  The circle in the lower left corner of the plot
indicates the beam size of 9$.\mkern-4mu^\prime$2.} \label{HNCOContAll}
\end{figure}

\section{$^{12}$CO(1--0) Measurements}

To determine the comparability of our C$^{18}$O data we have also taken
some \mbox{$^{12}$CO(1--0)} data (using the same system) in March 1994
and August 1994. Our $^{12}$CO map covers the inner region of the
C$^{18}$O map (see Fig.~\ref{VerglChan50}). As in the case of
C$^{18}$O, the data were scaled to $T_{\rm MB}$.  In the top panel of
Fig.~\ref{VerglChan50}, a channel map of 50~km\,s$^{-1}$ width centered
at +50~km\,s$^{-1}$ is exemplarily shown. A detailed discussion of the
\mbox{$^{12}$CO(1--0)} data can be found in Dahmen (1995).  As also
shown there, our $^{12}$CO data are in an excellent agreement with the
\mbox{$^{12}$CO(1--0)} survey obtained by Bitran (1987) in 1984 and
with the \mbox{$^{12}$CO(1--0)} data being obtained with the 7\,m
Bell-Labs telescope since 1986.

\begin{figure}
\psfig{figure=vergl_25_75_lbcont+grey.ps,height=12cm}
\caption{The integrated intensity of the Galactic Center region of
\mbox{$^{12}$CO(1--0)}, \mbox{C$^{18}$O(1--0)}, and their ratio in the
velocity interval from +25 to +75.0~km\,s$^{-1}$ (50~km\,s$^{-1}$
width). The circle in the lower left corner of the plots indicates the
beam size of 9\arcmin.  The ratio was calculated with an
1-$\sigma$-threshold, thus, if the content of a channel either in
$^{12}$CO or in C$^{18}$O was below 1$\sigma$ r.m.s.\ the 1$\sigma$
value was taken instead for the calculation of the ratio.}
\label{VerglChan50}
\end{figure}

\section{C$^{18}$O and $^{12}$CO in Comparison}

The global differences between the C$^{18}$O data and the $^{12}$CO data 
are:
\begin{enumerate}
\item The $^{12}$CO emission at Sgr\,B2 is not as strikingly strong 
      compared to the other emission maxima. 
\item The $^{12}$CO emission is much more widespread than the C$^{18}$O 
      emission. In fact there is no position inside the map where no 
      $^{12}$CO emission is visible. However, the smaller latitude extent 
      of the C$^{18}$O emission might be influenced by the detection limit 
      of the rather weak \mbox{C$^{18}$O(1--0)} line. 
\item The $^{12}$CO emission from Clump~2 is much stronger compared to the 
      other features than in C$^{18}$O. 
\end{enumerate}

A comparison of the line shapes of C$^{18}$O and $^{12}$CO toward
selected positions shows that they often differ significantly.  A
detailed analysis (see Dahmen~1995) shows that the standard conversion
formula for the determination of the $^{12}$CO column density does not
work in the Galactic center region and that the assumption of high
optical depth for the $^{12}$CO emission is not generally valid there.

\section{Integrated Intensity Ratios} 

An analysis of the integrated intensity ratio (see, e.g., the bottom
panel of Fig.~\ref{VerglChan50}) shows that the $^{12}$CO/C$^{18}$O
ratio in the Galactic Center region is generally higher than the value
of about 15 which is expected from the compilation of the ``standard''
conversion factors. Wherever C$^{18}$O is above the detection limit
this ratio is at least of the order 40, mostly of the order of 60 to
80, in several areas of the order 90 to 120, and toward a few
positions even as high as 190.

From LVG calculations (see Dahmen 1995), it was confirmed that
the large scale $^{12}$CO emission in the Galactic Center region is
dominated by emission with intermediate ($\tau = 1 - 5$) or low optical
depths ($\tau < 1$). High optical depth emission ($\tau \ge 10$) is
restricted to very limited areas such as Sgr\,B2.  For the 4 intensity
ratio ranges, the following conditions were found:
\begin{enumerate}
\item For low intensity ratios of about 40: $n_{\rm H_2} \sim 
      10^{3.5}$~cm$^{-3}$, $T_{\rm kin} \sim 50$~K, and $\tau \sim 3.0$. 
\item For intermediate ratios of 60 to 80 which are the most common: 
      $n_{\rm H_2} \sim 10^{3.0}$~cm$^{-3}$, $T_{\rm kin} \sim 50$~K, and 
      $\tau < 2.0$. 
\item For high ratios of 90 to 120 as found in several areas, in 
      particular in the Sgr\,D region and in Clump~2: $n_{\rm H_2} \sim 
      10^{3.0}$~cm$^{-3}$, $T_{\rm kin} \sim 100$~K, and $\tau < 1.0$. 
\item For very high ratios up to 190 which are present toward a few 
      positions: $n_{\rm H_2} \sim 10^{2.0}$~cm$^{-3}$, $T_{\rm kin} \sim 
      150$~K, and $\tau \sim 2.0$. 
\end{enumerate}

\section{The Molecular Mass in the Galactic Bulge} 

\begin{table}[b]
\caption{The gas mass in the central 600~pc of the Galactic Center from 
different tracers}
\begin{tabular}{lrl}
{\bf Tracer} & \multicolumn{1}{c}{$\boldmath {\cal M}_{\bf mol}$}
 & {\bf Reference} \\[1mm] 
\hline & & \\[-3mm] 
$^{12}$CO(1--0)            &          $2.8 \cdot 10^8 \, {\rm M_{\odot}}$
 & Dahmen (1995)\,/\,Bitran (1987) \\ 
C$^{18}$O(1--0)            &          $1.7 \cdot 10^7 \, {\rm M_{\odot}}$
 & Dahmen (1995) \\ 
$^{12}$CO(1--0) (thin gas) &          $0.7 \cdot 10^7 \, {\rm M_{\odot}}$
 & Dahmen (1995) \\ 
Dust\,/\,IRAS              &          $3.6 \cdot 10^7 \, {\rm M_{\odot}}$
 & Cox \& Laureijs (1989) \\ 
Dust 800\,$\mu$m           &        $> 0.4 \cdot 10^7 \, {\rm M_{\odot}}$
 & Lis \& Carlstrom (1994) \\ 
Dust\,/\,COBE              & 3.1\,--\,$7.0 \cdot 10^7 \, {\rm M_{\odot}}$
 & Sodroski et al.\ (1994)\,/ \\ 
 & & ~~~data of Bitran (1987) \\ 
0.1--1.0 GeV $\gamma$-rays &        $< 5.8 \cdot 10^7 \, {\rm M_{\odot}}$
 & Blitz et al.\ (1985) \\ 
\end{tabular}
\end{table}

Using the standard conversion formula (Strong et al.\ 1988), the total
molecular mass is found to be $2.8 \cdot 10^{8} \, {\rm M_{\odot}}$
from the \mbox{$^{12}$CO(1--0)} emissivity found by Bitran (1987). On
the contrary, from the emissivity of \mbox{C$^{18}$O(1--0)}, the total
molecular mass is found to be $1.7 \cdot 10^7 \, {\rm M_{\odot}}$,
taking the average excitation conditions into account (see Dahmen
1995). Because $^{12}$CO emission of intermediate and low optical depth
is dominant in the Galactic center region the existence of a widespread
component of molecular gas with low density (thin gas) is found to be
very likely.  Invisible in C$^{18}$O due to subthermal excitation
conditions, its additional mass contribution is estimated to be about
$0.7 \cdot 10^7 \, {\rm M_{\odot}}$. Comparing this to other tracers of
molecular mass (see Table~1 and Dahmen 1995), we obtain a weighted best
estimate of ${\cal M}_{\rm mol} = (3^{+2}_{-1}) \cdot 10^7 \,
{\rm M_{\odot}}$ by ignoring the result from the standard conversion
formula for $^{12}$CO.

Probably, the high $^{12}$CO emissivity is caused by the large scale
emission being dominated by a rather small fraction of gas at moderate
or low $\tau$ and the non-virialisation of a considerable fraction of
the molecular gas in the gravitational potential of the Galactic bulge.
This results in an overestimate of the molecular gas mass when applying
the standard conversion factor.  The main cause of the difference in
mass estimates from the two CO isotopes is, therefore, not the emission
from the peaks but the extended emission from $^{12}$CO of rather low
optical depth.

\begin{references}
\reference Bitran, M.E.\ 1987, Ph.D.\ Thesis, University of Florida
\reference Blitz, L., Bloemen, J., Hermsen, W., Bania, T.M.\ 1985, A\&A 
           143, 267
\reference Bronfman, L., Cohen, R.S., Alvarez, H., May, J., Thaddeus, 
           P.\ 1988, ApJ 324, 248
\reference Bronfman, L., Alvarez, H., Cohen, R.S., Thaddeus, P.\ 1989, 
           ApJS 71, 481
\reference Cohen, R.S., Dame, T.M., Thaddeus, P.\ 1986, ApJS 60, 695
\reference Cox, P., Laureijs, R.\ 1989, {\em IRAS Observations of the 
           Galactic Center\/}. In M.\ Morris (ed.), {\em The Center of 
           the Galaxy\/}, IAU Symp.\ 136, 121
\reference Dahmen, G.\ 1995, Ph.D.\ Thesis, Universit\"at Bonn
\reference Dahmen, G., H\"uttemeister, S., Wilson, T.L., Mauersberger, 
           R., Linhart, A., Bronfman, L., Tieftrunk, A.R., Meyer, K., 
           Wiedenh\"over, W., Dame, T.M., Palmer, E.S., May, J., Aparici, 
           J., Mac-Auliffe, F., to be submitted to A\&AS 
\reference Linhart, A.\ 1994, Diploma Thesis, Universit\"at Bonn
\reference Lis, D.C., Carlstrom, J.E.\ 1994, ApJ 424, 189
\reference Sodroski, T.J., Bennett, C., Boggess, N., Dwek, E., Franz, 
           B.A., Hauser, M.G., Kelsall, T., Moseley, S.H., Odegard, N., 
           Silverberg, R.V., Weiland, J.L.\ 1994, ApJ 428, 638
\reference Strong, A.W., Bloemen, J.B.G.M., Dame, T.M., Grenier, I.A., 
           Hermsen, W., Lebrun, F., Nyman, L.-\AA., Pollock, A.M.T., 
           Thaddeus, P.\ 1988, A\&A 207, 1
\end{references} 

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