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\newcommand \htwo  {$\mbox{H}_2$}
%\newcommand \arcmin {\mbox{$^\prime$}}
%\newcommand \ie {{\em i.e.}}
\newcommand \eg {{\em e.g.}}
\newcommand \degree {\mbox{$^\circ$}}
%\newcommand \arcsec {\mbox{$^{\prime\prime}$}}
\newcommand \msun {\mbox{$\mathcal{M}_{\odot}$}}
\newcommand \co  {\mbox{$^{12}\mbox{CO(1-0)}$}}
\newcommand \kms {\mbox{km.s$^{-1}$}}
\newcommand \micron  {\mbox{$\mu$m}}
\newcommand \jyperbeam {\mbox{Jy.beam$^{-1}$}}
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%
\begin{document}
%
   \title{Molecular outflow in the Seyfert galaxy NGC 6764}

%   \subtitle{I. Overviewing the $\kappa$-mechanism}

   \author{S. Leon,
          \inst{1}
           A. Eckart, \inst{1}
           E. Schinnerer, \inst{2}
           J.  Scharw\"achter, \inst{1}
           J. Moultaka, \inst{1}
           M. Krips, \inst{1}
           S. Laine, \inst{3}
                     }

   \offprints{S. Leon}

   \institute{University of Cologne, I. Physikalische Institute, Cologne, Germany\\
              \email{sleon@ph1.uni-koeln.de}
              }

   \date{Received XX}


   \abstract{
  
   \keywords{Galaxy  -- ISM -- Individual: NGC 6764
               }
   }
 \titlerunning{Molecular outflow in NGC~6764}
 \authorrunning{Leon et al.}
   \maketitle
%
%________________________________________________________________

\section{Introduction}
NGC~6764 is a barred spiral classified as a low-ionization nuclear emission-line
region (LINER) from optical spectroscopy (Osterbrock \& Cohen 1982). This nearby
active galaxy (D=32 Mpc for $H_0 = 75 \kms$; 1\arcsec = 160 pc) is as well interesting
for its nuclear starburst which is very young as shown by its Wolf-Rayet (W-R) feature
at 0.47 \micron (HeII) as described in Schinnerer et al. (2000).



\begin{table}
\begin{tabular}{ll}
\hline
Parameter  & Value \\
\hline
\hline
$\alpha_{2000}$   & 19:08:16.494 \\ 
$\delta_{2000}$   & 50:55:59.46  \\
Type$^a$  & SB(s)bc  \\
Distance$^b$ (Mpc)  &  32  \\
m$_B^a$   & 12.6  \\
L$_{B}$ (10$^{10}$ L$_\odot$) &  1.5 \\
Inclination$^c$  & 61.5\degree \\
Major Axis PA$^c$   & 62\degree \\
Bar PA$^c$  & 74.6\degree \\
S$_{12\micron}$ (Jy) &  0.36 \\
S$_{25\micron}$ (Jy) &  1.29 \\
S$_{60\micron}$ (Jy) &  6.33 \\
S$_{100\micron}$ (Jy) & 11.56 \\
L$_{\mbox{FIR}}$ (10$^{10})$L$_\odot$) & 1.1  \\
L$_{\mbox{H$\alpha$}}$ (10$^{40}$ erg.s$^{-1}$)  & 23 \\
M$_{\mbox{HI}}$ (10$^9$\msun)  & 7. \\
S$_{326}^d$ (mJy)   & 309 \\
S$_{365}^a$ (mJy) &  244 \\
S$_{1400}^a$ (mJy) &  133 \\
S$_{4850}^a$ (mJy) &  34 \\ 
S$_{8460}^e$ (mJy) &  44 \\
\hline
\end{tabular}
\begin{tabular}{l}
$^a$ From NED (frequencies in MHz)\\
$^b$ Assuming H$_0=75$ \kms Mpc$^{-1}$.  \\
$^c$ From LEDA.\\
$^d$ From WENSS. \\
\end{tabular}
\caption{NGC~6764 global parameters.}
\label{tab_glob_param}
\end{table}


%__________________________________________________________________

\section{Observations and data reduction}
\subsection{CO data}
The CO(1--0) and CO(2--1) lines have been observed with the IRAM interferometer 
located on the Plateau de Bure (France) in 199X.
 We calibrated the visibilites using the
 1823+568 and 1828+487 as amplitude and phase references. The PdBI was phase-centered
at the position $\alpha_{2000}=19:08:16.370$ and $\delta_{2000}=50:55:59.58$. The 
velocity resolution was set to 10 \kms for the two CO transitions and the CLEANed maps
have been restored with a synthetised beam of $2.0\arcsec\times 1.6\arcsec$ 
(PA=7\degree ) for the CO(1--0) data and $1.25\arcsec\times 1.25\arcsec$ (PA=0\degree)
for the CO(2--1) data. The rms noise for the CO(1--0) channel maps is 2 mJy.beam$^{-1}$
(58 mK) for the CO(1--0) data and 5.5 mJy.beam$^{-1}$ (82.5 mK) for the CO(2--1)
data. Hereafter the velocity reference is fixed to be 2400 \kms, 114348.900 MHz rest
frequency for the CO(1--0) observation. The CO(2--1) observation heve been made at the
same rest velocity.\\
The total integrated CO(1--0) flux was measured by Sanders \& Mirabel (1985)
to be 225 Jy.km/s in the 55\arcsec beam of the NRAO-12m telescope.
 Our PdBI CO(1--0) observation detect a flux of 159 Jy.km/s, i.e filtering out
about 30 \% of the total flux, assuming all the flux is concentrated in the 
45\arcsec primary beam of the PdBI. The integrated intensity map for the CO(1--0) and
CO(2--1) are shown in Fig. \ref{fig_ico_pdbi}. The position of the CO emission
peak has been estimated using the higher spatial resolution of the CO(2--1) transition
and the procedure is the same as used for  the optical center (see hereafter). 
The CO(2--1) peak position is at $\alpha_{CO}(2000)=19:08:16.402$, 
$\delta_{CO}(2000)=50:56:0.29$.
Assuming that the spiral arms are trailing and with  the receding velocities being 
on the eastern side of the galaxy, the northern side is closer to us.


\begin{table}
\begin{tabular}{l|ll}
Parameter  &  CO(1-0) & CO(2-1) \\
\hline
\hline
Field of View (FWHM)   &  45\arcsec (6.9 kpc)   & 22\arcsec  (3.4 kpc)\\
Bandwidth	       &  270 MHz  		& 473 MHz   \\
Velocity resolution	& 10 \kms		& 10 \kms  \\
Visibility Calibrator  & \multicolumn{2}{c}{1823+568 and  3C380}		\\
Synthetised beam  &	$2\arcsec \times 1.6\arcsec$,7\degree &  $1.25\arcsec \times 1.25\arcsec$ \\
Equivalent $T_b$ for 1 \jyperbeam  & 29 K	& 15 K   \\
rms noise (per channel)     & 2 \mjyperbeam  & 6 \mjyperbeam \\
\hline
\end{tabular}
\caption{PdBI observations}
\end{table}



\begin{figure*}
\resizebox{!}{!}{\includegraphics{./figure/n6764_ico_10_21.eps}}
\caption{Integrated intensity for the CO(1--0) transition (a) and for the CO(2--1)
transition (b). The contours for (a) are 1,3,..,27 \jyperbeam .\kms and for
(b)  3,6,..,54 \jyperbeam .\kms}
\label{fig_ico_pdbi}
\end{figure*}


\subsection{Optical center}
From the new POSS-II digitalization (REFERENCE), the optical center has been 
estimated on the central part of the red image. 
To determine the center, we have filtered out, using the wavelet transform (e.g
Leon et al. 2000), the large scale emission of the central part. On the peak emission
a Gaussian fit has been performed to measure the position with a sub-pixel precision.
The optical center is found to be $\alpha_{opt}(2000)=19:08:16.494$, 
$\delta_{opt}(2000)=50:55:59.46$. The astrometry precision given by the plate is
better than 0.5\arcsec (McLean 2001).


\subsection{ISO data}
The Mid-Infrared observations have been performed   by the Infrared Space 
Observatory (ISO)  in december 1997 (P.I. H. Wozniak). The data have been retrieved 
from the ISO archives. The observations have been made with  the ISOCAM camera 
(Cesarsky et al. 1996). The smallest available pixel field of view (PFOV) is used, 
i.e., $1.5\arcsec px^{-1}$ is used, which gives a $45 \times  45$ field of view.
We show here the broad band filter LW2 ($\lambda_c=6.7 \micron$, $R=\lambda_c/\Delta
\lambda =2.0$). The PSF of the LW2 observation is 3\arcsec. 
As indicated by the ISO report of Cesarsky and Blommaert (2000), the 
astrometry of the ISO pointing is accurate at about 1.5\arcsec due to some play 
in the alignment of the optical axis with the detector. The position of the 
ISO map has been offset by one pixel (1.5 \arcsec) to match the CO peak (see 
discussion).  The flux calibration can be estimated to be accurate within 30 \%
(e.g. Wozniak et al. 1998).
(To Be removed maybe.)

\subsection{Radio continuum}
%The radio continuum observations have been kindly provided by L. Seppo, previously to
%publication. 
The data were obtained with the Very Large Array (VLA) at both 3.5 and 20 
cm in, respectively, the configurations C and A (see Fig. \ref{fig_vla20}. 
The different configurations allow
to have similar spatial resolutions at the two frequencies: $1.39\arcsec\times 
1.26\arcsec$ (PA=-45\degree ) at 20cm and $2.50\arcsec\times 2.0\arcsec$ 
(PA=15.5\degree). The peak position of the 20cm emission has been computed in
a similar way that the optical center. It is located at $\alpha_{20cm}(2000)=
19:08:16.316$, $\delta_{20cm}(2000)=50:55:59.37$. The accuracy is better than 
0.1\arcsec.

\begin{figure}
\resizebox{8.5cm}{8.5cm}{\includegraphics{./figure/n6764_vla20.eps}}
\caption{Radiocontinuum at 20 cm (VLA) with a synthesized beam of 
$2.50\arcsec\times 2.0\arcsec$. The contour levels are 0.1,0.35,..,3.85,4,5,..,14 
mJy.beam$^{-1}$ for a rms noise of 70 $\mu$Jy.beam$^{-1}$.}
\label{fig_vla20}
\end{figure}

The 20cm flux from the VLA observations is 128 mJy, which is only slightly resolved
out compared to the single dish measurement of 133 mJy. The 3.5cm flux is
 44 mJy, which indicated an inverted spectra between 6cm and 3.5cm (see Fig. 
\ref{fig_radioSED_flux}). The thermal contribution  at high frequency is more important
(REFERENCE).


\begin{figure}
\resizebox{8.5cm}{8.cm}{\includegraphics{./figure/n6764_radioSED.eps}}
\caption{Radiocontinuum flux at different wavelength from single-dish or low
spatial resolution measurements, except for the 8.4 GHz data (this work).}
\label{fig_radioSED}
\end{figure}



\section{The molecular gas}
\subsection{Distribution}
Adopting a conversion factor of X$_{\mbox{CO}} = 3\times10^{20}$cm$^{-2}$
(K.km.s$^{-1}$)$^{-1}$ (e.g. Scoville et al. 1987), the mass of molecular hydrogen
is:

\begin{equation}
M_{H_2} = 1.2\times 10^4 S_{CO} D^2
\end{equation}

where $S_{CO}$ is the CO flux density in Jy.\kms and D the distance in Mpc. The total
flux of our integrated CO(1--0) map gives a total molecular hydrogen mass of 2.9 
10$^9$ \msun. The surface mass density is computed by assuming an inclination of the 
nuclear disk similar to the outer disk of 61.5\degree (Eckart et al. 1991). 
%This 
%hypothesis is confirmed  by a gaussian fit of the CO(1--0) distribution in the
%nucleus which gives a ratio 2:1 for the ellipsoide, i.e an inclination of 60\degree.
On Fig. \ref{fig_h2dens} the molecular hydrogen surface mass density is shown, 
without including the minor components (mainly He) which would lead to 1.36 times 
the molecular hydrogen surface mass density. It reaches a mass density of up to 2650
\msun .pc$^{-2}$ at a projected distance of 1.25\arcsec ($\sim$ 190 pc) from the 
radiocontinuum peak which will be assumed to be the nucleus of the galaxy (see hereafter).
More than 98 \% of the total molecular gas mass measured by the PdBI is concentred
within the inner 800 pc, and as shown on the Fig. \ref{fig_h2cumu}, as much as  20 \% of
the total mass ($\sim 6 \times 10^8$ \msun) is concentrated in one beamsize 
($\sim$ 310 pc) around the CO(1--0) peak. Assuming a z-height of 100 pc, typical height
scale for molecular gas disk in galaxies (REFERENCE), it leads to a lower-limit
of 75 \msun .pc$^3$ for the molecular mass gas density in this region.


\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_h2dens.eps}}
\caption{Molecular hydrogen  surface mass density in the center of NGC~6764 
(i=61.5\degree)
in \msun pc${-2}$. The contours levels are starting at 2-$\sigma$ level (100 \msun 
pc$^{-2}$) up to the maximum of 2600 \msun pc$^{-2}$.}
\label{fig_h2dens}
\end{figure}

\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_gasmass_cumu.eps}}
\caption{Cumulative distribution of the molecular gas mass on the position
centered on the CO(1--0) peak.}
\label{fig_h2cumu}
\end{figure}

{\bf molecular outflow, central outflow (?), mass in the molecular outflows}


\subsection{Kinematics}
The channel maps shown on Fig. \ref{fig_co10_chanmap}, resp. Fig. 
\ref{fig_co21_chanmap}, for the CO(1--0) emission, resp. CO(2--1) emission, reveal 


{\bf m=1 mode, PV diagram, molecular outflow PV-features; streaming motions; connection
with the primary bar.}
 
\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_vla20_co10mom1.eps}}
\caption{Isovelocity field contours overlaying the 20cm radiocontinuum emission.
Thick lines are negative velocities by 10 \kms step. The reference velocity is 
2400 \kms 
(Heliocentric).}
\label{fig_h2dens}
\end{figure}


\begin{figure*}
\resizebox{17.5cm}{15cm}{\includegraphics{./figure/n6764_co10_channelmapR.eps}}
\caption{Channel maps for the CO(1--0) emission. The rms noise corresponds to 
2 mJy.beam$^{-1}$. The contours are -20,-10,..,130 mJy.beam$^{-1}$. The 
synthesized beam is $2\arcsec\times 1.6\arcsec$. The rest velocity is 2400 \kms.
The cross is located at the phase center, i.e. $\alpha_{2000}=$19:08:16.370  
and $\delta_{2000}$=50:55:59.58.}
\label{fig_co10_chanmap}
\end{figure*}


\begin{figure*}
\resizebox{17.5cm}{15cm}{\includegraphics{./figure/n6764_co21_channelmapR.eps}}
\caption{Channel maps for the CO(1--0) emission. The rms noise corresponds to 
2 mJy.beam$^{-1}$. The contours are -20,0,..,320 mJy.beam$^{-1}$. The 
synthesized beam is $1.25\arcsec\times 1.25\arcsec$. The rest velocity is 2400 \kms.}
\label{fig_co21_chanmap}
\end{figure*}



PV diagrams: 
(see Fig. \ref{fig_co_pvdiag})

\begin{figure*}
\begin{center}
\resizebox{14cm}{18cm}{\includegraphics{./figure/n6764_co_PV.eps}}
\caption{Position-velocity diagram of the CO(1--0) (left) and CO(2--1) (right)
emission in the center of NGC~6764. The offset 0 is taken at the CO peak.
The major axis PA is 62\degree, and the PA of 90\degree has been added to compare
with Fig. 1 of Eckart et al. (1996). The units are in \jyperbeam}
\label{fig_co_pvdiag}
\end{center}
\end{figure*}


\subsection{CO line ratio}
The line ratio for the integrated intensity between the CO(2--1) and CO(1--0)
transitions,  
$\Re = \frac{I_{CO(1--0)}}{I_{CO(2--1)}}$, is computed by convolving
the CO(2--1) integrated map to the spatial resolution of the CO(1--0) data and is 
shown on  the Fig.  \ref{fig_co_line_ratio}. The maximum $\Re$ is found to be 
0.84 combining all the channels. This ratio is in aggreement with the estimation
made by Eckart et al. (1991) from single dish observations. The
global line ratio measured there is interpreted as arising from moderately  warm,
dense and optically thick gas. Their conclusion remain globally  valid in the 
light of our new observations. Nevertheless new informations brought by the 
high spatial resolution have to be emphasized.


\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_coratio_total_grey.eps}}
\caption{CO(2--1) to CO(1--0) line ratio integrated on the whole range of
channels.}
\label{fig_co_line_ratio}
\end{figure}

\begin{figure*}
\resizebox{16cm}{20cm}{\includegraphics{./figure/n6764_coratio_chan.eps}}
\caption{CO(2--1) to CO(1--0) line ratio for different velocities, indicated on each panel, 
with a channel width of 10 \kms. The first contour is for 0.2 and by step of 
0.1.[{\bf Will be better the plot, if we keep it...}]}
\label{fig_co_line_ratio_chan}
\end{figure*}

Indeed, the ratio $\Re$ is clearly bimodal between the bluest 
 side associated with the starburst and 
the redest with the nucleus, as shown on the  Fig. \ref{fig_coratiomax_vel} where the
maximum ratio $\Re$ on the map is computed  for each CO(1--0) channel 
(10 \kms width).

\begin{figure}
\resizebox{8cm}{8cm}{\includegraphics{./figure/n6764_coratioMax_vel.eps}}
\caption{CO(2--1) to CO(1--0) maximum line ratio $\Re_{max}$ 
computed in the center of NGC~6764 for each CO(1--0) channel (10 \kms width).}
\label{fig_coratiomax_vel}
\end{figure}

To discriminate the localisation of the high-$\Re$ values, we have computed the
CO line ratio $\Re$ in the velocity range -170 to -130 \kms. The Fig. 
\ref{fig_coratio_lowvel} show clearly that the high CO line ratios ($\Re > 1.0$) 
are concentrated around the radiocontinuum peak in the center. It can be pointed
out. nevertheless, that the maximum of the CO line ratio ($\Re \sim 1.47$) 
is located 2\arcsec\ to the north of the radiocontinuum peak, when the  
local maximum at  the radiocontinuum peak is about $\Re \sim 1.16$. The 
difference 
between the maximum $\Re$ for each single channel (Fig. \ref{fig_coratiomax_vel}) and 
integrated over few adjacent channels is due to the higher noise in the CO(2--1) 
data  than in the CO(1--0) data. 
For the redshifted velocities towards the SE direction, the line ratio for the
channels comprising 140 to 190 \kms is about 0.85 at the CO(1--0) peak. It reaches
its maximum of $\sim 1.2$ about 2\arcsec SE from the maximum CO emission.






\begin{figure*}
\resizebox{8cm}{8cm}{\includegraphics{./figure/n6764_vla20_coratio_lowvel.eps}}
\resizebox{8cm}{8cm}{\includegraphics{./figure/n6764_vla20_coratio_highvel.eps}}
\caption{(Left panel) Radiocontinuum at 20 cm overlaid by the CO(2--1) to CO(1--0) 
line ratio $\Re$ 
computed for the velocities ranging from -170 up to -130 \kms. The contours
are drawn from 0.9 to 1.4 by step 0f 0.025. (Right panel) Radiocontinuum at 20 cm 
overlaid by the CO(2--1) to CO(1--0) line ratio $\Re$ 
computed for the velocities ranging from 140 up to 190 \kms. The contours
are drawn from 0.8 to 1.2 by step 0f 0.025 (right) }
\label{fig_coratio_lowvel}
\end{figure*}


% Ask Kotaro Kohno for the HCN/CO ratio they computed (Kohno et al. 2001). They
% refer to NGC~6764 as a composite galaxy with AGN/starburst composite
% 


\begin{table*}
\begin{tabular}{lllllll}
\hline
  Region  &  $\frac{CO(2-1)}{CO(1-0)}_{\mbox{Tot$^a$}}$ & 
$\frac{CO(2-1)}{CO(1-0)}_{\mbox{Low$^a$}}$ &
$\frac{CO(2-1)}{CO(1-0)}_{\mbox{High$^a$}}$  &  $\sigma_{Max}$  
& $\sigma_{V_{1-0}}$  & $\sigma_{V_{2-1}}$ \\
& &  & &  (\msun .pc$^{-2}$)  & (\kms) & (\kms) \\
\hline
\hline
CO(1--0) peak          &  0.82 &  0.93  & 0.85   & 2655        & 190  & 184  \\
Nucleus$^b$            &  0.76 &  1.12  &  0.63  & 1500        & 185  & 164 \\
Nucleus 2\arcsec N     &  0.72 &  1.47   &  -  & 960            & 150  & 220 \\
Outflow$^c$ 4\arcsec N &   -   & $\sim$ 0.25   &  -  & $\sim$ 200  & 220  & -   \\
Arm/bar 10\arcsec W    &   $\sim$ 0.25  & -   &  -  & $\sim$ 300  & 48   & -   \\
\hline
%\multicolumn{4}{1}{$^a$ CO(1--0) kinematics.}
\multicolumn{7}{l}{$^a$ CO line ratio relative to the total, low and high velocity channel
map, see text.} \\
\multicolumn{7}{l}{$^b$ Radiocontinuum peak (20cm), see text.} \\
\multicolumn{7}{l}{$^c$ Offset position relative to CO(1--0) peak.}\\
\end{tabular}
\end{table*}

\section{Nuclear Features}

\subsection{Star Formation}
From the 60 and 100 \micron IRAS flux, the total FIR luminosity can be estimated. 
Following Condon (1992), star formation rate for the massive star can be computed with
$SFR(M>\msun) = 9.1 10^{-11}(L_{FIR}/L_\odot)$, which gives a SFR of 1 \msun/yr. 
According to Xu et al. (1998) the IRAS S$_{25\micron}$ flux is entirely due to the AGN, when
40 \% of the  S$_{12\micron}$ flux is due to the NSB. Indeed, according the classification
made by Xu et al. (2001) from the IRAS flux, NGC 6764 is classified as an AGN and marginally
as a starburst. 
The H$\alpha$ line is mainly emitted in the HII regions where the new-born massive stars are
ionizing the gas. The total H$\alpha$ flux can be used as a tracer of the star formation
as computed by Kennicutt (1988) where: \\
\begin{equation}
\mbox{L(H}\alpha) = \frac{1.26\times10^{41}}{\mbox{erg/s}} \frac{\mbox{SFR}}{\mbox{\msun/yr}}
\end{equation}
For the NSB, the H$\alpha$ flux is estimated to be 1.3 10$^{41}$ erg/s (see Table 
\ref{tab_fluxes hereafter}, which gives a SFR of 1 \msun/yr, consistent with the FIR.
luminosity.
These two derivations of the SFR are concerning the massive stars only, taking into account
all the stellar range and given the optical extinction, Eckart et al. (1991) derived a value 
of 4 \msun/yr for the NSB. They found a supernova rate of $1.2 10^{-2}$/yr. The  supernovae
of type II
produce a radio continuum non-thermal emission L$_{NT}$, which can be estimated  
(Condon \& Yin 1990, Hill et al. 2001):
\begin{equation}
L_{NT} =  1.3\times 10^{23} \nu^{-\alpha}N_{SN}    
\end{equation}
where $L_{NT}$ is the non-thermal radio luminosity  in $W.Hz^{-1}$ at the frequency $\nu$, 
in GHz, for the non-thermal spectral index $\alpha$, with a production rate of $N_{SN}$ per 
year. For the NSB, the drawback is the determination of the spectral index from the 
non-thermal contribution. Since it  should rapidly steepens (Colina et al.XXX??), the 
mean spectral index in the NSB is likely to give an upper limit for the non-thermal 
contribution. The mean value in the inner 6\arcsec is $-0.51\pm0.22$, which leads to the 
following range for the non-thermal radio fluxes (see Fig. \ref{fig_nonthermalflux}): 
14 to 16 mJy at 20 cm for a spectral index between -0.3 and -0.7, 21 to 39 mJy at 6 cm and 
24 to 56 mJy at 3.5 cm. The uncertainty increase with the frequency, but it appears that the 
main contribution of the non-thermal flux for the SNII is at 3.5 cm. The total flux measured 
at this frequency is 44 mJy, with an apparent inverted spectra for the global radio 
flux distribution (Fig. \ref{fig_radioSED}). When the flux at low frequency is mainly produced 
by the AGN, the 3.5 cm contribution from the NSB is more important and is creating this inverted
spectra.

\begin{figure}
\resizebox{8cm}{7cm}{\includegraphics{./figure/n6764_radio_nothermal_snr.eps}}
\caption{Non-thermal flux, in mJy,  at 3 different frequencies for a range of non-thermal 
spectral  index between -1 and 0. The flux is computed for a supernovae  production rate of
$1.2\times10^{-2}$ per year (Eckart et al. 1991) in the center of NGC~6764.}
\label{fig_h2cumu}
\end{figure}




\subsection{The shell}
In the Table \ref{tab_shell} we indicate the basic parameters for the shell from the 
radiocontinuum  20cm observation.


\begin{table}
\begin{tabular}{l|ll}
 Parameter &  Observation & Physical Unit \\
\hline
h	&  7\arcsec  & 1080 pc \\
R$_{base}$ & 3.5\arcsec & 540 pc \\
\end{tabular}
\label{tab_shell}
\caption{Morphological parameters for the bubble derived from the 20cm radiocontiuum map.}
\end{table}



{\bf Energy buget (kinematic+gravitational] from the outflow components: 
molecular outflow, hot gas. Energy released by the SB.}


\section{Other tracers}
\subsection{Radiocontinuum}
The radiocontinuum is tracing thermal and non-thermal emission (synchrotron).

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\begin{figure}
\resizebox{8.5cm}{8cm}{\includegraphics{./figure/n6764_indexspec_color.eps}}
\caption{Spectra index $\alpha$ (S$_\nu \propto \nu^\alpha$) derived from the 20
and 3.5cm radiocontinuum.}
\label{fig_indexspec}
\end{figure}


\subsection{H$\alpha$ emission}
H$\alpha$ emission has been observed in NGC~6764 and provided to us kindly by 
D. Frayer.
Figure \ref{fig_halpha} shows the uncalibrated H$\alpha$ flux in the center of 
the galaxy.

\begin{figure}
\resizebox{8.5cm}{8.5cm}{\includegraphics{./figure/n6764_dss2_halpha_insert.eps}}
\caption{B image (DSS2) of NGC~6764 overlaid by the H$\alpha$ uncalibrated flux in 
the center of NGC~6764, the contours are spaced by 0.15dex step starting at 
0.5 $\sigma$ level.}
\label{fig_halpha}
\end{figure}

\begin{figure}
\resizebox{8.5cm}{8.5cm}{\includegraphics{./figure/n6764_halpha_Ico21.eps}}
\caption{H$\alpha$ emission overlaid by the CO(2--1) emission.}
\label{fig_halpha}
\end{figure}

\begin{figure}
\resizebox{9cm}{8.5cm}{\includegraphics{./figure/n6764_Index_halpha.eps}}
\caption{Spectral index $\alpha$ between the 20cm and 3.5cm radiocontinuum emission 
overlaid with the H$\alpha$ emission.}
\label{fig_halpha}
\end{figure}



\section{Discussion}
\subsection{The nuclear starburst}

NGC~6764 is harboring a nuclear starburst (NSB): Schinnerer et al. (2000) present
a detailed study of the starburst properties. It is actually shown that the 
galaxy has experienced 2 recent starbursts 15-30 and 3-5 Myr ago. The presence of 
bubles seen in radiocontinuum and H$\alpha$ is the indication of a very recent
starburst indeed. Registering the molecular gas distribution relative
to the other tracers (see Table \ref{tab_astrom_peak}) show that the bulk of the
molecular gas content is offset by 1--1.5\arcsec from the radiocontinuum peak but
is correlated with the $H\alpha$ peak. Moreover the bubble morphology is centred
on the CO(1--0) peak rather than on the radiocontinuum peak (see Figures XXXX).
The recent starburst associated should originate from the high-density molecular
gas concentration when the radiocontinuum peak traces the galaxy's nucleus.
The NSB is then located 185 pc away from the nucleus. NGC~6764 is disclosing a very
similar NSB to NGC~2782: as discussed by Jogee et al. (1998, 1999) in the latter
case, the morphology of the bubble is associated to the very recent SB.\\
\\

{\bf Thermal contribution in the radiocontinuum, see 
Lee et al. (2002); Star formation efficiency, scaling the ISO flux in the Starburst
to the total Lfir. Discuss the Xco conversion factor for SB. Discuss the high CO ratio
line with the Halpha feature in the SE direction of the SB.}

\begin{figure}
\resizebox{8.5cm}{8.5cm}{\includegraphics{./figure/n6764_vla20_ico_bar.eps}}
\caption{VLA 20cm emission overlaid by CO(1-0) emission with contour levels from
1 to 27 \jyperbeam\kms by step of 1 \jyperbeam\kms. The position of the major
axis and the bar are shown respectively by the solid and dashed lines.}
\label{fig_vla_ico_bar}
\end{figure}



%
%NSB properties:

\begin{table}
\begin{tabular}{lllll}
\hline
  & H$\alpha$ &  20cm & 3.5cm & M(H$_2$) \\
   & (10$^{39}$ erg.s$^{-1}$) &  (mJy) & (mJy) & (\msun)\\
\hline
\hline
  NSB  &     $\sim 130^a$ &  &   & $6.2\times10^8$ \\
  Nucleus &   & $90^b$  & $28^b$ & \\
  Outflow &   $\sim 45$   &  45 &  12  & $2.5\times10^7$\\
\hline
\multicolumn{5}{l}{$^a$ Includes as well the Nucleus contribution.}\\
\multicolumn{5}{l}{$^b$ Includes as well the NSB contribution.}
\end{tabular}
\caption{Bubble/Nucleus contributions for H$\alpha$ and 20cm radiocontinuum by
fitting a 2D gaussian on the central contribution. The molecular gas mass for the
NSB is the mass emcompassed by one CO(1-0) beam at the maximum (310$\times$250 pc).}
\label{tab_fluxes}
\end{table}

\begin{table}
\begin{tabular}{llll}
\hline
Tracer &  $\alpha_{2000}$ & $\delta_{2000}$  & D$_{20}$ \\
&    &    &   (\arcsec)  \\
\hline
\hline
20cm    & 19:08:16.316 & 50:55:59.37 &  \\
CO(1--0)$_{dyn}$ & 19:08:16.351 &  50:55:59.74  & 0.5   \\
CO(2--1) & 19:08:16.402 & 50:56:0.29  & 1.2  \\
H$\alpha$   & 19:08:16.440   &   50:55:59.87 &    1.3    \\
H$\alpha_{off}$ & 19:08:16.362 &  50:55:59.68  &  0.5     \\
Nucleus B-band &  19:08 :16.379 & 50:55:59.82 &	  0.6	  \\
Nucleus i-band &  19:08:16.374 &  50:55:59.69  &  0.6	  \\
\hline
\end{tabular}
\caption{Position (J2000.0)  of the peak emission in radiocontinuum
(20cm), CO emission and H$\alpha$ emission (off-filter and emission line). The
distance to the radiocontinuum peak is given in arcsec.}
\label{tab_astrom_peak}
\end{table}

% The typical error measure doing the astrometry on optical image from two DSS2 images 
% (Red and Blue) give about 1''. 

What is the tidal heating of molecular clouds due to a central mass concentration ?
The GMCs (few 10$^6$ \msun) are the location of massive star formation, like in 
NGC~6764. The tidal heating will increase the internal velocity $\sigma_{GMC}$ and
speed-up the destruction of the such GMCs, inhibitating the star formation. Let
us consider a central mass concentration M$_{\otimes}$, we call  hereafter SMBH,
 and a GMC of mass M$_{GMC}$ located at a distance R from this SMBH:
The tidal energy U$_t$ felt by the GMCs is then:

\begin{equation}
U_t(r) \approx  - \frac{GM_{\otimes}}{4R^3}r^2
\end{equation}

where r is the radius inside the GMC. The angular dependency of the tidal energy
in $\cos 2\theta$ is not taken into account. Taking a mass density 
profile $\rho(r) \propto r^{-2}$ for the GMCs (e.g. Williams et al. 1995), 
the total tidal energy U$_t$ of the GMC is given by :

\begin{equation}
U_t = - K \int_0^{r_t} 4 \pi U_t(r) \rho (r) r^2 dr \\
K=\frac{M_{GMC}}{4\pi r_t}
\end{equation}

where $r_t$ is the cutoff radius of the GMC. So the total tidal energy can be 
approximated to :
\begin{equation}
U_t = - \frac{G M_\otimes M_{GMC}}{12 R^3}r_t^2
\label{equa_energy_tidal}
\end{equation}

The internal energy of the GMC in virial equilibrium can be written as:

\begin{equation}
U_{GMC} \approx -\frac{1}{2}M_{GMC} \sigma^2
\label{equa_energy_gmc}
\end{equation}

From the equation \ref{equa_energy_tidal} and \ref{equa_energy_gmc}, the distance R
to the nucleus/SMBH where the tidal energy is comparable to the internal energy can
be approximated to :

\begin{equation}
U_{GMC} \approx U_t \Rightarrow R = \left ( \frac{GM_\otimes r_t^2}{6 \sigma^2} 
\right )^\frac{1}{3}
\end{equation}

For a  massive GMC of 60 pc of diameter and 10$^6$ \msun, the velocity 
dispersion is about 11 \kms (Sanders et al. 1985). Taking a $10^9$ \msun for 
the central SMBH, when Eckart et al. (1990) give an upper limit of $\sim 3\times
10^9$ \msun for the central mass in NGC~6764 within 5\arcsec, leads to the 
following radius tidal-dependency estimation for R:

\begin{equation}
R = 175 \mbox{pc} \left (\frac{M_\otimes}{10^9\msun} \right )^{\frac{1}{3}} \left ( \frac{r_t}{
\mbox{30 pc}}\right)^\frac{2}{3} \left ( \frac{\sigma}{\mbox{11 \kms}} 
 \right )^{-\frac{2}{3}} 
\end{equation}

The computation gives a value of about 200 pc for a central mass of 3
\begin{figure}
\resizebox{9cm}{8.5cm}{\includegraphics{./figure/tidal_trunc_gmc_bis.eps}}
\caption{Distance R (pc) to the nucleus of  mass M (\msun) where the tidal energy
of a GMC, of cutoff radius r$_t$ (pc),  is comparable to its internal 
energy (see text). The velocity dispersion is estimated from Sanders et al.
(1985) to be $\sigma = 1.35 r_t^{0.62} \kms$.}
\label{fig_tidal_trunc}
\end{figure}

See Taniguchi \& Wada (1996) for discussion. They have the opposite view...but not Kenney et al.
(1992). 

{\bf Shear effects close to the center; Safronov-Toomre Q value in the center: instabilities tracer ?;
m=1 mode efficient way to to initiate the strong starburst. Compare the molecular
gas density and SF with other SB/AGN (M82, N7419, N3079(Sofue et al. 2000: UHD,
ultra-high-density molecular disk in this gal., 10E5 Msun/pc2!!)) \\}

Timescale for a cloud to be torn off by the Coriolis force and differential 
rotation is $\tau_D \sim dV/dR-\omega \approx 10^6$ yrs (To be confirmed). To compare
with the Jeans instability timescale (see Sofue et al. 2000 as well).


\subsection{The central molecular outflow}
{\bf This has to be confirmed yet !}

\section{Conclusions}

{\bf Offset molecular gas concentration; high density H2; molecular gas outflow;
(central outflow??); Energy budget; Radiocontinuum morphology; thermal/non thermal
contribution; SFE; Bar connection; m=1 mode-SB interplay; etc}


\begin{acknowledgements}
This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG)
via grant SFB 494, by special funding from the Science Ministry of the Land
Nordrhein-Westfalen.
\end{acknowledgements}

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