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\usepackage{graphicx}

\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{$^{12}\mbox{CO}$}}
\newcommand \kms {\mbox{km.s$^{-1}$}}
\newcommand \kmskpc {\mbox{km.s$^{-1}$.kpc$^{-1}$}}
\newcommand \micron  {\mbox{$\mu$m}}
\newcommand \jyperbeam {\mbox{Jy.beam$^{-1}$}}
\newcommand \mjyperbeam {\mbox{mJy.beam$^{-1}$}}
\newcommand \twelvecoonezero {\mbox{$^{12}$CO(1--0) }}
\newcommand \twelvecotwoone  {\mbox{$^{12}$CO(2--1) }}

%
\begin{document}
%
   \title{Molecular outflow in the composite galaxy NGC 6764 }

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

   \author{S. Leon,
          \inst{1,2}
           A. Eckart, \inst{2}
           E. Schinnerer, \inst{3}
           S.-W. Lee \inst{4}
	   M. Krips, \inst{3}
           S. Laine, \inst{5}
	   J. Scharwächter, \inst{3}
                     }

   \offprints{S. Leon, stephane@iaa.es}

   \institute{$^1$ Instituto de Astrof\'{\i}sica de Andaluc\'{\i}a, Granada, Spain \\
	      $^2$ University of Cologne, I. Physikalische Institute, Cologne, Germany\\
              $^3$ Caltech, Los Angeles, USA \\
	      $^4$ University of Toronto, Astronomy Department, Toronto, Canada \\
	      $^5$ Space Telescope Insitute, Baltimore, USA
              }

   \date{Received XX}


   \abstract{
NGC~6764 is a composite galaxy exhibiting central activity (LINER) and recent
massive star formation (Wolf-Rayet galaxies). We present new high-resolution interferometric data 
of the  \twelvecoonezero and \twelvecotwoone emission in the central part of the galaxies together 
with high resolution VLA data of the radiocontinuum emission at 20 and 3.5 cm. The nucleus shows 
a carateristic bubble-like radiocontinuum emission centered on the CO and H$\alpha$ emission and 
slightly offset from the radiocontinuum peak at the center, identified as the AGN. 
The total molecular gas in the center is found to be about 7 $10^8$ \msun, with a CO-to-H$_2$ 
conversion 3 times lower than the standard one. A \twelvecoonezero emission is found to correlate
with the edge of the radiocontinuum emission in the outflow with a projected expansion velocity  
up to 50 \kms relative to the systemic velocity of the galaxy. About $10^7$ \msun of molecular
gas is detected in the outflows, likely ejected by the the stellar winds from the recent starburst.
The resonances inferred from the rotation curve indicate the possible presence of Inner Lindlbad 
Resonances
in the center ($\sim$ 1 kpc) when the star formation and the molecular gas is peaking at 400 pc from
the radio continuum peak, identified as the kinematical center.



   \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). The inital studies of Rubin
et al. (1975) showed evidence for streaming motions in the nucleus. The recent studies of Eckart et al.
(1991, 1996) and Schinnerer (2000) have analyzed in great details the central starburst, traced by the 
W-R emission. Their  millimetric observations have shown a central concentration  of molecular gas together
with near-infrared emission line. The 2.12 \micron\ H$_2$ line exhibits extensions in agreement with the
VLA maps available. The population synthesis model made on NIR spectral lines suggests that NGC~6764 
has undergone two recent starburst: one occured 3-5 Myr ago (W.-R. features) and another older occured
15-50 Myr ago. The {\it ROSAT} data traces mainly the central AGN with a variation of a factor 2 over a 
time scale  of 7 days (Schinnerer et al. 2000). NGC~6764 is a typical  composite galaxy exhibiting 
central AGN together with a starburst. Recently with a study of the HCN and CO emission in the center 
of NGC~6764, Kohno et al. (2001) have classified this galaxy as a composite based on the high HCN/CO line
ratio ($\sim 0.7$) in the center which makes them suggest of an ``AGN-starburst cohabitation'' in the very 
center. The interplay between AGN and starburst is a longstanding problem and still matter to a lot of 
debate. \\
Since activity and star formation are taking place in the center of NGC~6764, it is another case for the 
study of the fueling of the two  gas consumption process.  The onset/shutdown of the starburst
is driving by the local properties of the molecular gas, density, velocity dispersion, gravitational 
instabilities(Combes 2001) and  the destruction processes at play, like the local tidal field 
(Launhardt, Zylka \& Mezger 2002), starburst feedback (Dopita 1985, Scalo \& Chapell 1999), 
gas consumption (Franceschini et al. 1998), tidal shearing (Kenney, Jeffrey, Carlstrom \& Young 1993).
A key problem is to bring the molecular gas in the inner part of the galaxy (few hundreds of pc)
where both activity are located: since a large reservoire of molecular gas is usually available in spiral 
galaxies at large radius (Young et al. 1995), angular momentum must be removed of the gas to fall indwards 
the center. Asymmetric perturbations, bars (Athanassoula 1992), tidal 
interaction with a companion (Mihos \& Hernquist 1994), mergers (Barnes \& Hernquist 1996)  are shown 
to be an efficient way to such angular momentum removal. According to the resonances at play in the center
of the galaxies (Combes \& Gerin 1985) or specific orbits, like the $x_2$ orbits in barred galaxies 
(Contopoulos \& Papayannopoulos 1980), the gas can be trapped in circumnuclear rings around 
the center or flow towards the center,
even if it is not yet clear what can take over the large scale asymetries in the very center down to few
to tens of pc (Combes 2002). Nested bars inside 1 kpc have been proposed as possible mechanism (Shlosman, 
Frank \& Begelman 1989), but recent survey (Martini et al. 2002)  do not find evidence for difference in the 
dust morphology in the central part of galaxies between active and non-active galaxies.
X-rays emission (HRI {\it ROSAT} instrument)  in NGC~6764 shows extended emission up to 15 \arcsec 
(Schinnerer
et al. 2000) roughly along the minor axis. This result together with the previous radio continuum VLA map 
(Ulvestad, Wilson \& Sramek 1981) suggest the presence of pressure-driven outflow from the AGN and/or 
the starburst. The formation of powerful outflow in the center of spiral galaxies is crucial  for the 
enrichment of the galaxy halo (Kunth et al. 2002). Several mechanisms have been proposed to 
explain these outflows:
thermal wind from a (circum)nuclear starburst (Colina, Arribas \& Borne 1999), a thermal wind from the 
AGN (Krolik \& Bergelman 1986) or ram-pressure along the radio jet (Taylor, Dyson \& Axon 1992). 
Outflows are well detected in the X-rays, radio continuum  or ionized gas: recent results by {\it CHANDRA}
show spectacular outflows from AGN/Starburst galaxies where, as in M51 (Terashima \& Wilson 2001), 
the spectra and the morphology sugges that the clouds are shock-heated by the bipolar outflow from the Seyfert
nucleus where the emission of the extranuclear clouds are powered by the jets. In the starburst galaxy Circinus
there is also large-scale X-ray emission both along and perpendicular to the galaxy disk, up to 600 pc 
above the
disk (Smith \& Wilson 2001) which is likely associated with the circumnuclear starburst. For more than
two decades large scale radio halo outside the disk have been observed in radio continuum 
(Hummel, van Gorkom \&  Kotanyi 1983, Hummel, Beck \& Dettmar 1991). 
The starburst leads to the formation of OB associations or  super star-clusters (SSCs) 
where the massive stars, through  strong supersonic stellar winds, inject both energy and mass 
into the interstellar medium. After a period of about 3.5 Myr these stars form supernov\ae, which 
add to both the energy and mass loss from the starburst. 
The effect of these winds and 
supernov\ae is to sweep up the ISM and produce shock-heating of both ISM and wind material, with the formation
 of an expanding superbubble of hot gas ($10^6-10^7$ K) contained within a shell of cool ISM material 
($10^4$ K). 
The formation of such a structure will be accompanied by extended X-ray emission from the hot gas
and optical H alpha line emission from the cooler shell. The superbubble with a larger internal ISM pressure
expands in the low-pressure halo ISM until the onset of Rayleigh-Taylor instabilities which disrupts
the superbubble and allow the hot gas to escape in the form of a galactic wind, like in M82 (Strickland, 
Ponman \& Stevens 1997). The cold molecular gas is expecting to wrap that superbubble in an expanding cocoon.
Few galaxies up to date have detection of outflowing molecular gas: M82 has a molecular gas mass 
of $\sim 10^6$ \msun\  detected  in a 45 \kms expanding bubble (Wei\ss et al. 1999), NGC~2782 harbors
a molecular outflow of $\sim 2\times 10^7$ (Jogee et al. 1998) which appears to be in 
the early stage ($\sim 4\times 10^6$ yrs) before the onset of the Rayleigh-Taylor instabilities, in NGC~3079
four  expanding CO shells have been identified (Irwin \& Sofue 1996) which appear 
to have arisen in a single starburst few $10^6$ yrs ago. The behavior of the molecular gas in such energetic
outflows is still poorly known. Since it is the fuel for star formation, its fall-back on the disk galaxy
can induce new star formation episods (Norman \& Ikeuchi 1989), moreover its kinetic and potential energy 
is subtracted to the
energy released by the outflow and the global energy budget, constraining the origin of the outflows, 
can be strongly dependent on the molecular gas phase, like in NGC~2782 (Jogee et al. 1998) or the off-center
outflow in NGC~5775 (Lee et al. 2001). \\

In this paper, we present new observations of the CO(1--0) and CO(2--1) lines made with the IRAM 
Plateau de Bure  
Interferometer (PdBI\footnote{Based on
observations carried with the IRAM Plateau de Bure Interferometer. IRAM is operated by INSU/CNRS (France),
MPG (Germany) and IGN (Spain)}) 
at high resolution (1.3--2 \arcsec). We also present new high-resolution VLA\footnote{The VLA is a research 
facility of the National Radio Astronomy Observatory (NRAO), which is operated by Associated Universities Inc.,
under contract with the National Science Fondation.}
maps 
of the radio continuum at 1.4 GHz and 8.4 GHz. We describe our new observations in \S 2, in \S 3 we 
describe the molecular gas content in the center of NGC~6764 (R $<$ 3 kpc). In the \S 4 and \S 5 we describe
the star formation and the central outflows, and we discuss these results in \S 6.


\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) &  31 \\
\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 \twelvecoonezero and \twelvecotwoone lines have been observed with the IRAM interferometer 
located on the Plateau de Bure (France) in 1998.
 We calibrated the visibilites using the
radio galaxies  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 for the deconvolution 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 \twelvecoonezero data and $1.25\arcsec\times 1.25\arcsec$ (PA=0\degree)
for the \twelvecotwoone data. The rms noise for the  channel maps is 2 mJy.beam$^{-1}$
(58 mK) for the \twelvecoonezero data and 5.5 mJy.beam$^{-1}$ (82.5 mK) for the \twelvecotwoone
data. Hereafter the velocity reference is fixed to be 2400 \kms, giving a redshifted frequency of
114348.900 MHz  for the \twelvecoonezero observations and 228693.200 MHZ for the \twelvecotwoone 
observations.
The total integrated \twelvecoonezero 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 \twelvecoonezero observation detect a flux of 112 Jy.km/s, i.e filtering out
about 50 \% of the total flux, assuming all the emission is concentrated in the 
45\arcsec\ primary beam of the PdBI. It indicates that a large fraction of the molecular 
gas must be present in a diffuse component.
The integrated intensity map for the \twelvecoonezero and
\twelvecotwoone 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 \twelvecotwoone transition
and the procedure is the same as used for  the optical center (see hereafter). 
The \twelvecotwoone 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 \twelvecoonezero transition (a) and for the \twelvecotwoone
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{Radio continuum}

The data were obtained with the Very Large Array (VLA) at both 3.5 and 20cm 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) at 3.5cm. The peak position of the 20cm emission has been computed  
by filtering out 
the large spatial scales, using the wavelet transform (e.g. Leon et al. 2000), 
and fitting a Gaussian 
on the
small scale planes to measure the central peak with a sub-pixel precision. 
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 90 mJy, which is slightly resolved
out compared to the single dish measurement of 133 mJy (White \& Becker 1992), i.e 68 \% of the
total flux is recovered by the VLA observations. The 3.5cm flux is
 31 mJy, which indicates a flattening spectra between 6cm and 3.5cm (see Fig. 
\ref{fig_radioSED}), with a spectral index of $\alpha^{3.5}_{6}=$-0.17. The best power-law fit 
($\chi^2$ fitness)  for the measurement  between 325 MHz and 8.4 GHz is found with a 
spectral index of $\alpha=-0.46$.



\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 (He included):

\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 \twelvecoonezero map gives a total molecular hydrogen mass of 2.0 
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 \twelvecoonezero 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. 
The molecular gas surface density reaches a maximum of  1850
\msun .pc$^{-2}$ at a projected distance of 1.25\arcsec ($\sim$ 190 pc) from the 
radiocontinuum peak which is 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 ($\sim 4 \times 10^8$ \msun) is concentrated in one beamsize 
($\sim$ 310 pc) around the \twelvecoonezero peak. Assuming a z-height of 50 pc, typical height
scale for molecular gas disk in our Galaxy (Malhotra 1994), it leads to a lower-limit
of 106 \msun .pc$^{-3}$ (n(H$_2)\sim 2.2 10^3 \mbox{cm}^{-3}$) for the average molecular  
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{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}



\begin{figure}
\resizebox{8.5cm}{8.5cm}{\includegraphics{./figure/n6764_halfaLog_co10_color.eps}}
\caption{H$\alpha$ emission in NGC6764 (Log scale) overlaid by the integrated intensity of the
CO(1-0) emission (contour levels 1,3,..,30 \jyperbeam).}
\label{fig_halpha_co10}
\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 \twelvecoonezero peak.}
\label{fig_h2cumu}
\end{figure}


Apart from the central concentration, the CO distribution (see Fig. \ref{fig_ico_pdbi}) shows an
extension towards the western side  and a spur roughly 
perpendicular to the major axis. Comparing the CO distribution with the bar orientation 
(see Fig. \ref{fig_vla_ico_bar}) reveals that the western feature extending up to 10\arcsec\
from the center is aligned with the primary bar. 
It is commonly accepted that the gas is 
inflowing
along the leading edge of the bars towards the center since the seminal paper of Athanassoula 
(1992). 
Numerical simulations (Athanassoula 1992) have shown that the gas is inflowing towards the center along
the  bar, with the shock loci on the leading edge.
When the molecular gas distribution  is compared to the H$\alpha$ emission in this 
region, it appears to be associated with two star forming regions 
($5\times 10^{39}$ and $3\times 10^{39}$ erg/s [H$\alpha$+NII] flux  respectively) which are  among the
 brightest
of the galaxy, excluding the strong H$\alpha$ emission at the tip of the bar (Rozas et al. 1996).
Since the galaxy is very inclined, the location of these regions and the molecular gas associated
 with is more ambiguous. Comparing with hydrodynamical simulations of gas in barred (Piner et al.
1995) the location of these star forming region is consistent with an inner ring, which may corresponds
with an inner Lindblad resonance (Combes \& Gerin 1985): in this picture the western feature of 
the molecular gas
is associated with the inflowing gas connecting to the inner ring where star forming regions are
present. The location of the ILRs are discussed hereafter. Different authors have attributed 
the molecular gas concentration in the center of bar galaxies
to the crowding of the $x_2/x_1$ orbits (Kenney et al. 1992, Kohno et al. 1997). \\
The CO-spur visible on the north is likely  associated with the radio continuum superbubble 
observed at 20cm (see Fig \ref{fig_vla20} \& \ref{fig_vla_ico_bar}). The \twelvecoonezero  emission is 
correlated
with the norh-eastern  edge of the 20cm radiocontinuum bubble. The CO emission is detected  up 
to 8\arcsec\ above the disk plane; correcting for the disk inclination (i=61\degree) 
it is found
that the molecular gas reaches 1.5 kpc above the plane. Since there is no clear  kinematic 
signature of the outflowing molecular gas, the mass-load by the outflow is estimated from the
CO spatial distribution only: cutting at one beamsize above the CO-peak and integrating to the 
northern feature gives a molecular gas mass in the out-of-plane outflow of 1.7 10$^7$\msun.


\subsection{$^{12}$CO  as molecular gas mass tracer ?}


To estimate the molecular gas mass, we have used the ``standard'' CO-to-H$_2$ conversion factor,
$X^{std}_{CO}= 3 10^{20} cm^{-2}K^{-1} km^{-1}s$ estimated
in the Milky Way galactical disk from the comparison between the $\gamma$ ray emission and the
\twelvecoonezero integrated line intensity (Strong et al. 1988). This conversion factor takes into 
account the 
Helium content. In the galactical disk this empirical value is found to match quite well the
theoritical one (Radford et al. 1991). Nevertheless there are growing evidences that this
conversion factor is overestimated by a factor 3-10 in the central part of galaxies, especially
in starbursts. The physical reasons for this discrepancy have been discussed by various authors
already: metallicity gradient (Dahmen et al.1998), broadening of the CO line by bulge  
potential (Stacy et al. 1989, Mauersberger et al. 1996), physical condition of the gas (optical 
depth, temperature, density).
In NGC 253, a nearby starburst, Mauersberger et al. (1996) found a conversion factor $\sim 7$ times
lower than $X^{std}_{CO}$ in the central part of the galaxy, where they argue that the 
central potential well is broadening the CO lines and its emission could be partially optically
thin. This conversion factor has been found to be 3 to 10 times lower in the galactic bulge than in
the disk (Sodroski et al. 1995). Based on line transfer models, measurements of the cold 
dust emission and comparison with the optical extinction A$_v$, this factor is about 3-4 lower in 
M51, NGC891 and NGC3593 (Adler et al. 1992, Garc\'{\i}a-Burillo et al. 1992, Garc\'{\i}a-Burillo 
et al. 2000).
In a sample of ultraluminous infrared galaxies (ULIRGs), Solomon et al. (1997) found that in these
CO-bright objects the conversion factor $X^{std}_{CO}$ overestimates by a factor 4 the molecular
gas mass. In the  ULIRG Arp 220, Downes  \& Solomon (1998) found that the ratio is 6 times
lower compared to the Milky Way derivation, and their whole sample gives a mean value of $\sim 5$ 
times lower.\\
The optical extinction A$_V$ can be estimated from the gas column density (Bohlin et al. 1978)
using:
\begin{equation}
\frac{(N_{HI}+2N_{H_2})}{A_V} = 1.87\times 10^{21} \mbox{cm$^{-2}$.mag$^{-1}$}
\end{equation}
Applying this to the molecular gas density computed with $X^{std}_{CO}$ and neglecting the 
HI contribution in the center (Wilcots et al. 2001), the peak A$_V$ is found to be $\sim$ 125 mag
and extinction of A$_V \sim 20$ mag extending up to 900 pc eastern  from the CO peak.  
This extinction is clearly overestimated through the high column density computed with the standard
conversion factor. Eckart et al. (1991) estimate an extinction A$_V$=3--4 towards the nucleus, which
is not compatible with the exctintion derived from the molecular gas column density, even when the
CO peak is offset from the very center. 
The IRAS FIR flux at 100 \micron\ can be used to give a lower limit of the extinction A$_B$ (Laureijs
et al. 1987) by:
\begin{equation}
\frac{IRAS(100\micron)}{A_B}=6.3 MJy.sr^{-1}.mag^{-1}
\end{equation}

The optical extinction A$_B$  is then found to be about 5.5 mag. This is a lower limit 
assuming that the 100 \micron\ flux is spread over the whole beam of IRAS (4\arcmin).
Taking a typical ratio of $A_B/A_V$=1.3, obtained by modelling the dust and stellar content
in spiral galaxies (Xilouris et al. 1999), then we get $A_V > 4$ mag in NGC6764.
The dust mass computed from
the IRAS fluxes at 60 and 100 \micron\ gives a total mass of M$_d$=$1.4\times10^6\msun$ with a mean 
temperature of 36.5 K. It is known from FIR observations with ISO that the IRAS data are missing
a cold component, T$_d < 20$ K,  from the dust emission (Alton et al. 1998, Trewhella et al. 2000) 
emitting beyond 150 \micron. This component can be 2-10 times more massive than 
the warm dust mass M$_d$. A similar result has been found in elliptical galaxies, observing
the $\lambda$1250 \micron\ bolometric emission (wiklind \& Henkel 1995).
In the outer Galaxy, Sodroski et al (1994) find a gas-to-dust ratio about 200, using the 
COBE data reaching larger wavelength than IRAS.
In NGC~6764
the gas-to-mass ratio, using the standard CO-to-H$_2$ conversion factor leads to $M_{gas}/M_{dust} 
\sim 1400$. This factor is by far larger than the typical galactical value, indicating an 
overestimation of the molecular gas mass obtained from the \twelvecoonezero luminosity and the standard
conversion factor.\\
In order to have a visual extinction  A$_V$ in accordance with the previous modelling 
(Eckart et al.  1991, Schinnerer et al. 2000), and to get a more realistic gas-to-dust ratio, we
 take a conversion factor X$\sim X^{std}_{CO}/3$.  This  scaling match the one 
found in previous study for the center of (starburst) galaxies and  has been chosen to fit
  the gas-to-dust mass modeled by Xilouris et al. (1999).
Hereafter the molecular gas mass will be given with this conversion factor, but the reader should 
keep in mind that this calibration is likely correct in a range of a factor 2. 

\subsection{Kinematics}

%{\bf m=1 mode, PV diagram, molecular outflow PV-features; streaming motions; connection
%with the primary bar.}
 
The Figure \ref{fig_co_mom1} shows the beam-smeared map of the intensity-weighted \twelvecoonezero 
velocity field, derived from the first moment of the \twelvecoonezero data cube overlaying the 20cm
radiocontinuum emission. The observations
are consistent with the  global rotation of the disk, dynamically centered on the 20cm peak, 
combined with streaming motions/warping disk:  the strongest deviation  from the rotation pattern,
the ``spider diagram'', on the eastern side is along the molecular outflow
originating from the \twelvecoonezero peak, at 2--3\arcsec\ to the NE direction of the radio continuum
peak. The noise on the velocity field is important since the CO emission is centrally concentrated 
with a lower intensity beyond the peak.
The \twelvecoonezero integrated intensity peak does
not correlate with the dynamical center, indicating a possible m=1  mode  in the  center.
The position angle (PA) inferred by symmetrizing the velocity field is found to be 70\degree$\pm 5$, which is
slightly larger than the isophotal one (61.5\degree). From the HI data of Wilcots et al. (2001), it is visible
a shift between the outer disk ($\sim 58\degree$) and the inner disk PA ($\sim 76 \degree$): the difference
can be attributed to an external warp and/or to the streaming motion in the center caused by the bar, 
as confirmed by the disturbed CO velocity field. 

The Figure \ref{fig_co_mom2} shows the beam-smeared map of the intensity-weighted \twelvecoonezero 
velocity dispersion  in the center, derived from the second moment  of the \twelvecoonezero data 
cube overlaid by the \twelvecoonezero integrated intensity. In the center, the velocity dispersion
$\sigma_V$ reaches value up to 200 \kms. Such high velocity dispersion is not  internal
to the molecular gas concentrations (the velocity dispersion in GMCs are few tens of \kms) 
but is nearly completely formed by the beam-smeared
velocity gradient along the rotation curve. The maximum velocity dispersion is located slightly 
offset from the
the dynamical center, which corresponds to the 20 cm peaks at the coordinates $\alpha_{20cm}$(J2000)
= 19:08:16.316  and $\delta_{20cm}$(J2000)= 50:55:59.37. Thus the maximum velocity dispesion is located
0.5--1\arcsec between the radio continuum peak and the molecular gas peak. Since this offset is smaller
than the CO(1-0) spatial resolution, it is likely due to beam-smeared contributions of the central part
together with the intrinsic velocity dispersion created by the starburst. This gives us an indication of the
location of the starburst closer to the center than the molecular gas peak. Schinnerer et al.
(2000) found in the NIR emission, an active/young starburst very close to the center and an older
with an extent of $\sim$200 pc.
 An high-velocity dispersion  is visible as well at the north of the \twelvecoonezero
peak, where the velocity dispersion $\sigma_V$ is about 150 \kms. 

\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.}
\label{fig_co_mom1}
\end{figure}

\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_co10disp_Ico10.eps}}
\caption{Velocity dispersion from the \twelvecoonezero observations overlaid by the
\twelvecoonezero integrated intensity with contours levels 2,4,..30 \jyperbeam\kms}
\label{fig_co_mom2}
\end{figure}

It is appealing to associate this
high velocity dispersion from the  stellar winds at the origin of the molecular
outflow. To estimate the amount of velocity dispersion created in the starburst region,  
we compute the odd-decomposition of $\sigma_v^2$ along a radial cut relative to the 20cm radiocontinuum 
peak, namely
\begin{equation}
\sigma_{V,odd}^{2}(\mbox{\bf x})=\frac{\sigma_V^2(\mbox{\bf x})-\sigma_V^2(\mbox{\bf -x})}{2}
\end{equation}

where $x$ is the position along the radial cut.
Then, the excess of $\sigma_V$ on one side relative to the other can be computed as $\sigma_V(+)=
\sqrt{2\times \sigma_{V,odd}^{2}}$ , which is shown for a cut along the major axis on the figure 
\ref{fig_co_disp_excess}. Two bumps marking a local excess of velocity dispersion are present: the
peak at 2\arcsec\ (84 \kms) is associated with the \twelvecoonezero integrated intensity connected to
the central starburst at about 100-300 pc from the nucleus; the peak at 4--6\arcsec\ (78 \kms), 
$\sim$ 800 pc from the nucleus, is likely connected to streaming motion (inflow, outflow) of
the gas along the bar, connecting to the central part  and, as well the smaller starforming region 
visible in H$\alpha$ (see figure \ref{fig_halpha_co10}). Since the rotation gradient is less 
pronounced at this 
radius, the actual value is more accurate regarding the beam-smearing. The contribution 
from  streaming motion in the center is difficult to estimate by lack of spatial resolution.

Using the corrected conversion factor for the molecular gas mass, the  
kinematic energy $E_{kin}^{SB}$ 
deposited by the starburst in the molecular gas can be estimated by $E_{kin}^{SB}=\frac{1}{2} M_{H_2}
<\sigma_V^2(+)>$, i.e. $3.7\times10^{54}$ ergs, with $<\sigma_V^2(+)>=(54 \kms)^2$ and $M_{H_2}=1.3
\times 10^8$\msun.
The molecular gas mass is estimated to be $\sim$ 20\% of the total molecular gas mass, see figure 
\ref{fig_h2cumu}, which encloses one \twelvecoonezero beam. Still the molecular gas mass of the region
perturbed by the starburst event is likely to be overestimated since of the offset between the 
\twelvecoonezero peak and the starburst region (see above). The velocity dispersion is estimated to
the average value of 54 \kms. For comparison in NGC~ 3504 which has a stronger starburst than NGC6764
(2.3 \msun/yr) and the same amount of molecular gas ($\sim 2\times 10^9$\msun, Young et al. 1984)
, Kenney et al. (1993) found an intrinsic CO velocity dispersion of 20-50 \kms in the inner 200 pc. 
It appears thus that the kinematic energy deposited in the molecular gas by the central starburst
is overestimated.\\
High velocity dispersion is found between the radius  4 to 7 \arcsec\ (640--1100 pc)  
with a peak of 80 \kms. It is spatially  correlated with the two western massive HII regions 
(see figure \ref{fig_halpha_co10}). The velocity field (figure \ref{fig_co_mom1}) shows streaming motions
located on the leading edge of the bar at these radii, where the gas is expected to inflow towards the center
(e.g. Athanassoula 1992).


\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_disp_oddpart.eps}}
\caption{The asymmetry of the \twelvecoonezero  velocity dispersion $\sigma_V(+)$ is 
computed along the major axis (see text for explanation). The two bumps are connected to the
starburst (84 \kms) and to the bar reconnection zone (78 \kms). These values are given
without  beam-smearing deconvolution.}
\label{fig_co_disp_excess}
\end{figure}

Figure \ref{fig_co10_chanmap} shows the \twelvecoonezero channel map at 10 \kms\ velocity resolution.
\twelvecoonezero emission is detected in the individual channels at 2.5$\sigma$ level from the 
velocity 2210 to 2600 \kms (LSR). Two \twelvecoonezero peaks are developping in the very center
at  negative and positive velocities. The second stronger peak is developping mainly at negative velocities
(-110--20 \kms) and is separated of the primary peak by $\sim$2\arcsec, which is not visible on the
integrated \twelvecoonezero map.
Extended weak feature are showing
up as well. One is visible from the \twelvecoonezero peak towards the north from the velocities 
-40 to 130 \kms, the other is more extended (see figure \ref{fig_Ico10_20_100}) from 
the velocities 10 to 100 \kms. The first feature  is associated with the molecular outflow, 
visible on the \twelvecoonezero  integrated
intensity, flaring up to 6\arcsec ($\sim$ 1 kpc)  (see figure \ref{fig_vla_ico_bar}). 
The redshifted velocities are compatible with the inclination of the galaxy and z-motion.
The faint and extended feature between 10--100 \kms is covering an area of about 1 kpc$^2$ between
5 and 10 \arcsec in radius ($\sim$800--1600 pc). At the velocity of 70 \kms, its extension is reaching a
maximum with a total extension of 12 \arcsec oriented North-South ($\sim$1.9 kpc). The velocity field
shows little sign of streaming motion in this region, indicating an in-plane motion of the molecular gas.
The western feature (W) has a large velocity extent from -80 \kms up to 10 \kms. Nevertheless it cannot 
account for the 80 \kms velocity dispertion, dubbed as bar reconnection on the figure \ref{fig_co_disp_excess}.



\begin{figure}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_20_100kms_Ico10.eps}}
\caption{Integra \twelvecoonezero (Jy.\kms) in the velocity range 20--100\kms.
The contours are from 0.05 to 1 Jy.\kms by step of 0.05 ($\sigma \sim 0.02$ Jy.\kms).}
\label{fig_Ico10_20_100}
\end{figure}



\begin{figure*}
\resizebox{17.5cm}{15cm}{\includegraphics{./figure/n6764_co10_chanmap_2.eps}}
\caption{Channel maps for the \twelvecoonezero emission. The rms noise corresponds to 
2 mJy.beam$^{-1}$. The contours are 5,15,25,..,95 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 \twelvecotwoone 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*}

The PV diagram of the \twelvecoonezero and \twelvecotwoone are shown on the figure \ref{fig_co_pvdiag}
along and perpendicular to the major axis (PA=62\degree) and at a PA=90\degree to compare with the
\twelvecoonezero observations of the Nobeyama Array (ckart et al. 1996). 


\begin{figure*}
\begin{center}
\resizebox{14cm}{18cm}{\includegraphics{./figure/n6764_co_PV.eps}}
\caption{Position-velocity diagram of the \twelvecoonezero (left) and \twelvecotwoone (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*}


From the CO(1-0) data and the HI data from Wilcots et al. (2001), the rotation curve has been 
computed, using the taks Inspector in {\tt Gipsy}. It flattens to a terminal velocity of 250 \kms at a 
radius of $\sim$ 12 kpc. The HI spatial resolution is poor compared to the CO observations  but
allow to get data at larger radius. From the rotation curve and in the epyciclic approximation, 
the azimutal frequency ($\Omega$) and radial frequency ($\kappa$) have been computed. The bar pattern speed is 
estimated from its corotation and the length of the bar semi major axis ($\sim$6.5 kpc). 
Several studies (Athanassoula 1992, Combes \& Elmegreen 1993, Sempere et al. 1995, ) have shown that 
the ratio of the 
corotation and the semi major axis of the bar can be placed in the range 1--1.5 . The determination 
is not strongly dependent of the exact value since the frequency $\Omega$ is flattening in that 
domain. The bar pattern speed $\Omega_{bar}$ is estimated to be 22 \kmskpc with a corotation (CR) at a radius
of 40\arcsec (6.5 kpc), taking a ratio of 1 between the CR and the bar semi major axis. 
The Inner Lindblad Resonances  (ILRs),when they exist,  are the loci where the bar pattern speed 
equals $\Omega-\kappa /2$. Figure 
\ref{fig_resonances} show these frequencies : an ILR is present in the center and tentitatively 
an inner and outer Lindblad Resonances (iILR and oILR) exist at a radius of 1 and 1.7 kpc 
(6 and 10\arcsec).
Four-fold resonances with $\Omega_{\mbox{bar}} = \Omega\pm\kappa/4$, or (inner/outer) Ultraharmonic Resonances 
(i/oUHR), are found at a radius of 3.9 kpc (24\arcsec, iUHR) and a radius of 16.5 kpc (100 \arcsec, oUHR). 
At these resonances the gas orbits can be 
periodic and form rings (Byrd et al. 1998). Contrary to the UHR location which is not very dependent 
of the bar pattern speed, the ILRs are very sensitive to it. The table \ref{tab_resonances} summarizes
the location of the resonances found in NGC~6764.\\
In a non dissipational case and infinite thin gaseous disk, the resonances can be associated with 
ring in the galaxies (Byrd et al. 1998). The 3D structure of the gas disk and the dissipation affects
such picture (Combes \& Gerin 1985; Regan \& Teuben 2003): a nuclear ring is located between the iILR and oILR,
but can move inwards or even disappears. An inner ring can be present as well at the iUHR. In NGC~6767,
given the uncertainty on the ILR location, the star forming region (W) and the molecular gas concentration
on the eastern part (see figure \ref{fig_Ico10_20_100} are  located about such ILRs. In the recent
simulations of regan \& Teuben (2003) such resonances are associated in some cases to the $x_2$ orbit family,
perpendicular to the main bar. The gas is trapped on close orbits in the center and form nuclear rings which
evolve in time and its radius is decreasing. In addition, the simulations show as well that gas is 
accumulating in the ring as time progresses because gas is flowing down the bar dust lanes. This has been
able to trigger star formation at the location W recently. It should be noticed that most of the molecular
gas is concentrated in the inner kpc.


\begin{table}
\begin{tabular}{l|lllll}
Resonance & iILR & oILR & iUHR & CR & oUHR \\
\hline
Radius & 6\arcsec & 10\arcsec   & 24\arcsec & 40\arcsec & 100\arcsec \\  
\end{tabular}
\label{tab_resonances}
\caption{Resonances  in NGC~6764 between the disk and the wave-based bar
feature ($\Omega_{\mbox{bar}}$=22 \kmskpc). (see text for description)}
\end{table}



\begin{figure}
\begin{center}
\resizebox{9cm}{8cm}{\includegraphics{./figure/n6764_resonances_fig.eps}}
\caption{Azimutal frequency $\Omega$ (stars) estimated from the rotation curve (HI+CO data). 
The third first data point are from CO(1-0) observations and the outer point from the HI 
observations (Wilcots et al. 2001). The UHR (diamond) and ILRs (cross) have estimated by setting
the bar corotation at the semi major axis of the bar ($\sim$ 40\arcsec). The bar pattern speed
is estimated to be 22\kmskpc.}
\label{fig_resonances}
\end{center}
\end{figure} 


\subsection{CO line ratio}
The line ratio for the integrated intensity between the \twelvecotwoone and \twelvecoonezero
transitions,  
$\Re = \frac{I(\twelvecoonezero)}{I(\twelvecotwoone)}$, is computed by convolving
the \twelvecotwoone integrated map to the spatial resolution of the \twelvecoonezero 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{\twelvecotwoone to \twelvecoonezero line ratio integrated on the whole range of
channels overlaid by the \twelvecoonezero contour levels (1,3,5,..,30 \jyperbeam\kms).}
\label{fig_co_line_ratio}
\end{figure}


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


The maximum line ratio $\Re_{max}$ for each \twelvecoonezero and \twelvecotwoone channel (10 \kms 
width)
is shown on the  Fig. \ref{fig_coratiomax_vel}. Clearly a bimodal feature is present with a peak
on the blue and red side. The blue side with a peak at -140 \kms is associated with the molecular
gas closer to the very center, as shown on the CO line ratio channel maps on the Fig. 
\ref{fig_co_line_ratio_chan}. The red side with a peak at 140 \kms reaches a value maximum of
about 1.2. This high  CO line ratio is associated with the bulk of the molecular gas as it
will be shown from the CO line ratio channel maps.\\



\begin{figure*}
\begin{center}
\resizebox{15cm}{20cm}{\includegraphics{./figure/n6764_coratio_chan.eps}}
\end{center}
\caption{\twelvecotwoone to \twelvecoonezero line ratio for different velocities, 
indicated on each panel, 
with a channel width of 10 \kms. The first contour is for 0.4 and by step of 
0.1. The radio continuum peak is shown by a cross.}
\label{fig_co_line_ratio_chan}
\end{figure*}


The \twelvecotwoone/\twelvecoonezero line ratio has been computed for each channel 
(10 \kms width). The lack  of the 
short spacing data for the two transitions can affect the true value by missing the extended 
molecular gas emission (Wei\ss et al. 2001). Nevertheless this line ratio is an indicator of the 
most extreme conditions of the moelcular gas (hot kinetic temperature, low density). The figure
\ref{fig_co_line_ratio_chan} shows this CO line ratio from the channel -180 \kms up to 200 \kms with
the central velocity being the systemic velocity of NGC~6764 (2400 \kms). From -180 to -40 \kms
the peak of the CO line ratio is correlated with the nucleus (the radiocontinuum peak is 
indicated by  a cross). 
The peak at -140 \kms seen in the figure \ref{n6764_coratioMax_vel.eps} is likely to be
the edge effect seen on the CO line ratio at this velocity. The ``true'' maximum is reached at 
-130 \kms with a value of 0.9. at the exact position of the radiocontinuum peak (within a pixel). 
The western feature of CO emission has a mean CO line ratio of 0.3, which is likely 
underestimated
because of the filtering-out of the extended emission.
These high CO line ratios for blueshifted gas in the nucleus have to be associated with outflows molecular gas 
powered by the AGN. The counterpart for redshifted gas in the nucleus are not detected with such high line ratio.
From -140 to the highest velocity  channels,
the peak of the CO line ratio appears to be slightly shifted relative the CO emission peak, both 
ingrated and channel by channel. There is an offset of $\sim 1--2$\arcsec to the south-eastern fo the CO
line ratio peak. 

%A pattern is present on the positive velocity channel with the isocontour of
%CO line ratio aligned along  a PA of 160\degree. 
The isocontours of the line ratio are oriented along a PA of 160\degree for the velocities 0 to 140 \kms
On the figure \ref{fig_coratio_halpha_120}, the CO
line ratio at the channel 120 \kms is overlaid by the H$\alpha$ emission. The H$\alpha$ emission
peaks with the starburst emission, which is slightly offset from the center (see below) and and 
extended plume is visible on the south-eastern part, extending down to connect with the external
superbubble. The extended H$alpha$ emission is created by superwinds from O new-born stars.
This high-velocity superwinds (1000--2000 \kms, Chevalier et al. 1985) will excite the 
low density molecular gas  on its path to give a higher CO line ratio. This anisotropy of the 
CO line ratio relative to the plane of the galaxy (about 2\arcsec$\sim$ 300 pc  below the plane)
together with the extended H$alpha$ emission may indicate that the star forming region is 
slightly offset towards the south and the lower z-column density of molecular gas to the south is
creating this anisotropy of the H$alpha$ emission, together with the CO line ratio. 
The radiocontinuum at 20 cm show as well this feature and present a total intensity stronger
in the southern part than in the norther part (21 vs. 37 mJy).
This particular orientation is clearly visible as well on the CO integrated line ratio on the
figure \ref{fig_co_line_ratio_chan}


\begin{figure}
\resizebox{8cm}{8cm}{\includegraphics{./figure/n6764_coratio_halpha_color.eps}}
\caption{\twelvecotwoone/\twelvecoonezero line ratio at the channel 120 \kms (10 \kms width) 
overlaid by the H$alpha$ isocontours.}
\label{fig_coratio_halpha_120}
\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
\twelvecoonezero peak          &  0.82 &  0.93  & 0.85   & 1860        & 190  & 184  \\
Nucleus$^b$            &  0.76 &  1.12  &  0.63  & 1000        & 185  & 164 \\
Nucleus 2\arcsec N     &  0.72 &  1.47   &  -  & 670            & 150  & 220 \\
Outflow$^c$ 4\arcsec N &   -   & $\sim$ 0.25   &  -  & $\sim$ 140  & 220  & -   \\
Arm/bar 10\arcsec W    &   $\sim$ 0.25  & -   &  -  & $\sim$ 210  & 48   & -   \\
\hline
%\multicolumn{4}{1}{$^a$ \twelvecoonezero 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 \twelvecoonezero peak.}\\
\end{tabular}
\end{table*}



\section{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 nearly 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  supernov\ae
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 31 mJy, with a spectra flattening at high frequency 
(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 
flattening spectra. By fitting the radiocontinuum between 326 MHz and 4.8 MHz where the 
non-thermal contribution is dominating, the spectral index is found to be $\alpha=-0.46$ and 
extrapolating the non-thermal contribution up to 8.5 GHz, we found a contribution of 6 mJy which 
is much below the measured value of 31 mJy, indicating a large contribution of the thermal gas
produced by the NSB. \\
The free-free contribution (``Bremsstrahlung'') can be estimated from the H$\alpha$ flux. The Balmer
lines provide an estimation of the ionizing photons present in the source. Combining with an estimate
of the extinction present, these data can be used to estimate the thermal radio continuum, using the
H$\alpha$ flux (Caplan \& Deharveng 1986).  Assuming an electron temperature of $10^4$ K with an
optical extinction of $A_V= 4.$ which compromises our estimate and the previous estimate of the 
extinction, the thermal radio continuum emission at 3.5cm is computed to be 14.8 mJy, integrating 
the H$\alpha$ luminosity in the outflow. 
The Halpha extinction is given using $A_\alpha = 0.605*A_V$. The Figure \ref{fig_ratio_radio_halpha}
shows the ratio between the radio flux (mJy) and the H$\alpha$ luminosity ($10^{40}$ erg/s) for
the free-free contribution. This ratio is found to be 75 \% at 8.4 GHz.  At maximum the thermal
contribution is thus about 23 mJy in NGC6764 (Zurita et al. 2000). This estimate from the H$\alpha$
flux is likely {\bf underestimating}the thermal contribution  because of the uncertainty on $A_\alpha$.
The table \ref{tab_radio_th-noth}
gives an estimate of the thermal and non-thermal radio continuum from the H$\alpha$ estimation.


\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 supernov\ae  production rate of
$1.2\times10^{-2}$ per year (Eckart et al. 1991) in the center of NGC~6764.}
\label{fig_radioflux_snr}
\end{figure}

\begin{table}
\begin{tabular}{llll}
\hline
Frequency  & Thermal  & Non-Thermal  & ratio $\frac{\mbox{Thermal}}{\mbox{Total}}$  \\
	   &  (mJy)	& (mJy)	    &  \\
\hline
\hline
1.4 GHz	   &  17.6    & 115.4	     &  13\% \\
4.8 GHz	   &  15.6    & 18.4	     &  46\% \\
8.4 GHz	   &  14.8    & 16.3	     &  48\%  \\
\hline
\end{tabular}
\label{tab_radio_th-noth}
\caption{Thermal  (free-free) and non-thermal (synchrotron) contribution to the radio continuum
emission in the center of NGC~6764. The thermal contribution is estimated from the H$\alpha$ flux (see
text).}
\end{table}

\begin{figure}
\resizebox{8cm}{7cm}{\includegraphics{./figure/radio_halpha_ratio.eps}}
\caption{Ratio of the thermal radio continuum emission (mJy) and H$\alpha$ luminosity 
($10^{40}$ erg/s)
at the distance
of NGC~6764, assuming an electron temperature of 10,000 K and an optical extinction $A_V= 4$.}
\label{fig_ratio_radio_halpha}
\end{figure}






\section{The outflow/shell}
In the Table \ref{tab_shell} we indicate the basic morphological 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. h is the
height and R$_{base}$ is the disk radius .}
\end{table}



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

The energy budget of the different gas phase in the outflow is an indicator of the physical processes
responsibles for such event. The kinetic energy of the cold molecular gas is estimated using an
observed expansion velocity of 40 \kms (see XX). Assuming that the bulk of the molecular gas is
perpendicular to the disk plane, the velocity escape V$_{esc}$ is 80 \kms.
Applying the correction to the CO-to-H$_2$ conversion factor of 1/3 (see \S XX) the molecular
gas mass in the outflow is $5.7\times 10^6$ \msun. Thus the molecular gas  kinetic energy E$_{kin}$ 
in the ouflow is $E_{kin}=\frac{1}{2} M_{gas} * V_{esc}=3.6\times 10^{53}$ ergs. The estimation of the 
potential energy is hampered by the necessity to have a mass distribution of the galaxy. Moreover the 
bar and the inclination make very uncertain the fitting of the different component. We choose to have
an order-of-magnitude for the potential energy by the following approach: the bulge and disk component
are modeled as described in (Combes, Leon \& Meylan 1999) by respectively a Plummer law ($\Phi_b$)and a  
Miyamoto-Nagai model ($\Phi_d$). These models are represented such as:

\begin{eqnarray}
\Phi_b & = &  -GM_b(r^2+a^{2}_{b})^{-1/2} \\
\Phi_d & = & -GM_d(r_{c}^{2}+(\sqrt{z^2+h^{2}_{d}}+a_{d})^2)^{-1/2}\\
\end{eqnarray}
 
Where $M_b$ and $M_d$ are the bulge and disk mass,$a_b$,$a_d$ the respective radial scale and $h_d$ the disk 
height scale. The bulge and disk masses are taken to $10^{10}$ and $7\times 10^{10}$ \msun, the radial scales
$a_d$ and $a_b$ and the height scale $h_d$ are respectively taken to 5,0.5 and 0.3 kpc. With the bulk of 
the molecular gas at $Z\sim 500$ pc, the potential energy is found to be $E_{pot} \sim 10^{55}$ ergs, which 
is far larger than the kinetic energy. Consequently we can predict that the molecular gas is close to its 
maximum height above the plane and will fall back towards the disk plane in the next few $10^6$ yrs, according to 
the age of  the recent starburst.
For a starburst with a SFR=1\msun$^{-1}$, different model have been computed (instantaneous or continuous),
and the total energy released by SNs and stellar wind at the age of the recent NGC~6764 starburst 
($\sim$ 5 Myr) is in the range  $10^{54}--10^{55}$ ergs which is compatible with the kinematical 
and potential energy of the molecular gas, without no need to invoke the  AGN or other mechanisms (hypernov\ae,
tidal interaction).
To complement the energy budget, we compute the total thermal energy $E_x$ involved by the hot X-ray gas. We make
use of the X-ray parameters derived by Eckart et al. (1996) from {\em ROSAT} observations in the band 0.1-2.4 kev.
They estimate the electron density $n_e \sim 0.2f_s^{-1/2} \mbox{cm}^{-3}$, the volume of the extended X-ray gas 
to $V\sim 7 10^{63} \mbox{cm}^{3}$ and the temperature $T\sim 4 10^6$ K. The total thermal energy is given 
then by $E_x \sim 3n_ekTVf_s$, with $f_s$ the volume factor filling factor, i.e. $E_x \sim 2.3 10^{54} f_s^{1/2}$
ergs. Without any estimation of $f_s$, we  use as lower limit for $f_s > 0.01$, as found in the 
starburst galaxy  NGC~3256 (Heckman et al. 1990,  Moran et al. 1999), which leads to $E_x > 2.3 10^{53}$ ergs.
The starburst in NGC~6764 appears still capable of releasing sufficient energy to form the X-ray hot gas bubble.


To estimate the distribution of the radiocontinuum emission at 20cm in the outflow/bubble, the 
central component has been subtracted by fitting a gaussian on the central flux above a threshold
of 4 \mjyperbeam. The 20cm-subtracted map is then rotated of 17\degree to put the outflow
principal axis  along the x,y axis. The total flux remaining on the center-subtracted map is 
63 mJy, about 60 \% of the VLA observation. In table \ref{tab_vla20_sub} the 20cm measurements
for the center-subtracter emission in the frame of the outflow are presented: there is an offset of the 
outflow flux relative to the central radiocontinuum and relative to the disk plane. Different reasons can 
explain this offset: 1) the SB is located on the Western part of center and slightly down the plane with a lower 
gas column density in the southern part. 2) there is a contribution of a radio jet in the southern part in
addition of the SB outflow.

\begin{table}
\begin{tabular}{l|ll}
Outflow  &  East    & West  \\
 \hline
North & 14 mJy   &  7 mJy  \\
South & 24 mJy  &  13 mJy  \\
\end{tabular}
\caption{The 20cm radiocontinuum emission in the outflow frame (rotation of 17 \degree) after
subtracting the central component associated with the AGN (63 mJy). The center is fixed to 
the central radiocontinuum and the flux is given in mJy.}
\label{tab_vla20_sub}
\end{table}



\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_dss} shows the H$\alpha$ emission 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_dss}
\end{figure}

\begin{figure}
\resizebox{8.5cm}{8.5cm}{\includegraphics{./figure/n6764_halpha_Ico21.eps}}
\caption{H$\alpha$ emission overlaid by the \twelvecotwoone emission.}
\label{fig_halpha_co21}
\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_vla35}
\end{figure}



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

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 centered
on the \twelvecoonezero 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.\\
\\

Without any high-resolution spectroscopy in the very center it
is very problematic to derive the mass of the SBH present to trigger the AGN. Nevertheless we 
can put some upper limit on its mass from the CO kinematics. The CO PV diagram (see Fig. 
\ref{fig_co_pvdiag}) along the minor axis shows mainly the unresolved rotational motion around the 
nucleus. In a beamsize of 2\arcsec (320 pc at the NGC6764 distance) the maximum unresolved 
rotational velocity $V^{unr}_{rot} $ corrected for the inclination can estimated to:

\begin{equation}
V^{unr}_{rot} = \frac{G M_{tot}}{R}
\end{equation}
where$ M_{tot}$ is the total enclosed mass in the radius R. In the unresolved beam size of the
PdBI, the total mass enclosed is in a radius of 150 pc is 1.5 $10^9 \msun$.


% {\bf 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.}


%
%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  &     $\sim 130^a$ &  &   & $4.3\times10^8$ \\
  Nucleus &   & $90^b$  & $28^b$ & \\
  Outflow &   $\sim 45$   &  45 &  12  & $1.7\times10^7$\\
\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 &  \\
\twelvecoonezero$_{dyn}$ & 19:08:16.351 &  50:55:59.74  & 0.5   \\
\twelvecotwoone & 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''. 


\subsection{GMC destruction in the center by a central mass}
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. 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}

The tidal compression is not the only destructive process on the GMCs. The differential
rotation can disrupt as well the GMCs. Using the formulation given by Kenney et al. (1992), the 
critical density of GMCs to bear that shearing is given from the rotation curve by
$\rho_{\mbox{shear}}=3V_{\mbox{rot} \frac{-d\Omega}{dR}/(2\pi G}$. since we are considering the GMCs
in the central kpc, the rotation curve can be split into the disk component from the rotation curve 
and the circular component from the central mass. In our approximation the central mass gathers the
putative SMBH and the bulge mass in the inner 200 pc leading to the very high velocity observed
and resolved in the very center. The figure \ref{fig_tidal_shearing} show the critical density
for different central component mass together with the disk component from the fitted rotation
curve: With a central mass greater than $10^8$ \msun, the tidal shearing is very effective in the 
inner kpc for GMCs greater than 5 pc.

\begin{figure}
\resizebox{9cm}{8.5cm}{\includegraphics{./figure/n6764_tidalshear.eps}}
\caption{Critical density of the molecular clouds through the differential tidal shearing
of the galaxy rotation. The solid line shows the critical density from the inner fitted
rotation curve. The dotted lines shows the critical density for different central mass (in \msun).
The dashed horizontal lines shows the means density of molecular clouds with differents 
diameter D from Sanders et al. (1985) with $<\rho> = 19.5 (D/\mbox{20 pc})^{-0.75}$ \msun.pc$^{-3}$}
\label{fig_tidal_shearing}
\end{figure}

The unresolved high velocity in the very center reach 200 \kms. It is an upper limit for the circular motion
of the molecular gas, given the streaming and winding motions. The SF is peaking in the central 400 pc, this 
location together with the ILRs about 0.5-1 kpc indicated a central mass lower than 10$^7$ \msun. To allow GMCs
with diameter $D< 15-25$ pc within the inner 400 pc, even a smaller central mass is required (M$\sim 1-5 
10^6\msun$. The shearing effect appears to be more effective than the tidal compression-stretching shown
on figure \ref{fig_fig_tidal_trunc}. However the tidal shearing due to differential rotation becomes 
ineffective at larger radius where the rotation curve is flattening. 






%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).




\section{Conclusions}
Here we summarize the results of our high-resolution mapping of the \twelvecoonezero and
\twelvecotwoone millimetric line and radiocontinuum at 20 and 3.5 cm in the center of
the composite galaxy NGC~6764. They can be summarized as following:

\begin{itemize}

\item The bulk of the $^{12}$CO emission lines  are concentrated in the very center of the galaxy and is
offset from the 20cm radiocontiuum peak by $\sim 1.2\arcsec$ measured with  the \twelvecoonezero peak. 
A more extended component is detected along the bar in the western side. 

\item Non-thermal radiocontinuum emission at 20 and 3.5 cm are detected outside of the disk plane 
caracteristic
of an outflow starbust-driven shape-like. The buuble-like outflow is detected up to z=1.3 kpc above
the plane (deprojected). \twelvecoonezero emission is detected on the NE edge of the outflow: about 
$1.7\times
10^7 \msun$ is driven by the ouflow out of the plane.

\item The total molecular gas mass (including He) is found to be $6.7\times10^8 \msun$ using a 
CO-to-H$_2$
conversion factor equal to 1/3 of the Galactical one. This value is motivated by the A$_V$ 
measurements (IRAS
and \htwo column density), dust-to-gas mass ratio and recent studuy of molecular gas in starburst 
galaxies.

\item The \twelvecotwoone / \twelvecoonezero line ratio is computed over each channel (10 \kms 
velocity width):
it reaches a maximum of 1 up to 2 for the nucleus associated with the AGN (20cm radiocontinuum peak). 
In the 
bulk of the molecular gas the maximum ratio is about 1.-1.3 compatible with a warm (T$_{kin} \ge 20 $K)
and dense gas ($n_{\htwo} > 2\times 10^4 \mbox{cm}^{-3}$) as found by Eckart et al. (1991). More 
likely in the nucleus the gas is colder and much less dense with an optical depth smaller than 1
(to be checked ?? and confirmed) where the peak \co line ratio reach a value of 2.


\item The kinematics of the \co lines indicate a disk/torus geometry in the center with the bulk 
of the molecular gas slightly offset from the kinematic center associated with the radiocontinuum peak.
Streaming motions are overlaying pure rotational pattern, especially on the western side where an 
extended
\co emission is found associated with the bar. The P-V diagram of these streaming motions are 
compatible
with gas trapped on $x_2$ orbits in the center of NGC~6764.

\item An important part of the radiocontinuum at 3.5 cm is thermal... The outflow geometry
indicates an age of $\sim$ 3-5 Myr for the recent starburst. (loose statement).


\item The H$\alpha$ emission together with the \co line ratio and the asymmetry of the radiocontinuum 
flux in the outflow lead to the conclusion of an z-offset nuclear starburst below the plane (southern).
(see sketch on Fig. \ref{fig_sketch}). A central massive concentration may prevent starburst to occur
in the very center by destroying GMC under because of the tidal forces.



\end{itemize}

The molecular gas in the composite galaxy NGC~6764 is sensitive both to the recent massive starburst
and the AGN in nucleus.  




\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 for one of us (S.L.).
\end{acknowledgements}

\begin{thebibliography}{}

\bibitem{} Adler, D. S., Lo, K. Y., Wright, M. C. H., Rydbeck, G., Plante, R. L., Allen, R. J. 1992, 
ApJ, 392, 497
\bibitem{} Alton, P. B., Bianchi, S., Rand, R. J., Xilouris, E. M., Davies, J. I., Trewhella, M. 
1998, ApJ, 507, 125
\bibitem{} Athanassoula, E. 1992, MNRAS, 259, 345
\bibitem{} Barnes, J., Hernquist, L. 1996, ApJ, 471, 115
\bibitem{} Bohlin, R. C., Savage, B. D., Drake, J. F. 1978, ApJ, 224, 132
\bibitem{} Byrd, G.G., Ousley, D., dalla Piazza, C. 1998, MNRAS, 298, 78
\bibitem{} Colina, L., Arribas, S., Borne, K.D. 1999, ApJ, 527, L13
\bibitem{} Combes, F. 2002, 'Active Galactic Nuclei: from Central Engine to Host Galaxy', Eds.: 
S. Collin, F. Combes and I. Shlosman., ASP, Conference Series, p. 54.
\bibitem{} Combes, F., Gerin, M.  1985, A\&A, 150, 327 
\bibitem{} Combes, F., Elmegreen, B.G. 1993, A\&A, 271, 391 
\bibitem{} Combes, F., Leon, S., Meylan, G. 1999, A\&A, 352, 149
\bibitem{} Combes, F. 2001, 'The Central Kiloparsec of Starbursts and AGN: The La Palma Connection', 
ASP Vol. 249. Eds  Knapen,J.H., Beckman, J.E., Shlosman,I, Mahoney, T.J, p. 475
\bibitem{} Condon, J. J., Yin, Q. F. 1990, ApJ, 357, 97 
\bibitem{} Contopoulos, G., Papayannopoulos, T. 1980, A\&A, 92, 33
\bibitem{} Dahmen, G., Huttemeister, S., Wilson, T. L., Mauersberger, R. 1998, A\&A, 31, 959
\bibitem{} Dopita, M.A. 1985, ApJ, 295, 5
\bibitem{} Downes, D., Solomon, P. M. 1998, ApJ, 507, 615
\bibitem{} Eckart, A.,  Cameron, M., Boller, Th., Krabbe, A., Blietz, M., Nakai, N., 
Wagner, S. J., Sternberg, A. 1996, ApJ, 472, 588
\bibitem{} Eckart, A., Cameron, M., Jackson, J. M., Genzel, R., Harris, A. I., Wild, W.,
 Zinnecker, H. 1991, ApJ, 372, 67
\bibitem{} Garc\'{\i}a-Burillo, S., Guelin, M., Cernicharo, J., Dahlem, M. 1992, A\&A, 266, 21
\bibitem{} Garc\'{\i}a-Burillo, S., Sempere, M. J., Combes, F., Hunt, L. K., Neri, R. 2000, A\&A, 
363, 869
\bibitem{} Kenney, J. D. P., Wilson, C. D., Scoville, N. Z., Devereux, N. A.; Young, J. S.  1992, 
ApJ, 395, 79
\bibitem{} Kohno, K., Kawabe, R., Vila-Vilar\'{o}, B. 1999, ApJ, 511, 157
\bibitem{} Kohno, K. et al. 2001, ``The Central Kiloparsec of Starbursts and AGN: The La Palma Connection'', 
ASP Conference Proceedings Vol. 249. Eds Knapen,J. H., J. E. Beckman, J.E.,  Shlosman, I. and Mahoney, T.J. 
San Francisco: Astronomical Society of the Pacific, 2001, p. 672.
\bibitem{} Kunth, D. Legrand, F. Tenorio-Tagle, G. Silich, S. Mas-Hesse, J. M. Cervi\~no, M. 2002, Ap\&SS, 
281, 261
\bibitem{}  Hill, T. L., Heisler, C. A., Norris, R. P., Reynolds, J. E.; Hunstead, R. W. 2001,
 AJ, 121, 128 
\bibitem{} Franceschini, A., Silva, L., Fasano, G., Granato, L., Bressan, A. Arnouts, S., Danese, L. 1998,
ApJ, 506, 600
\bibitem{} Heckman, T. M., Armus, L.,Miley, G. K. 1990, ApJS, 74, 833
\bibitem{} Hummel, E., van Gorkom, J. H., Kotanyi, C. G. 1983, ApJ, 267, 5
\bibitem{} Hummel, E., Beck, R, Dettmar, R.-J. 1991, A\&AS, 87, 309
%\bibitem{} Irwin, J. A., Seaquist, E. R. 1990, ApJ, 353, 469
\bibitem{} Irwin, J. A., Sofue, Y. 1996, ApJ, 464, 738
\bibitem{} Jogee, S. Kenney, J. D. P., Smith, B. J. 1998, 1998, ApJ, 494, 185
\bibitem{} Kenney, J. D. P., Carlstrom, J. E., Young, J. S. 1993, ApJ, 418, 687
\bibitem{} Krolik, J.H., Begelman, M.C. 1986, 308, L55
\bibitem{} Launhardt, R., Zylka, R., Mezger, P. G. 2002, A\&A, 384, 112
\bibitem{} Laureijs, R. J., Mattila, K., Schnur, G. 1987, A\&A, 184, 269
%\bibitem{} Lee, S.-W., Irwin, J. A., Dettmar, R.-J., Cunningham, C. T., Golla, G., Wang, Q. D. 2001, 
A\&A, 377, 759
\bibitem{} Lee, S.-W., Seaquist, E. R., Leon, S., García-Burillo, S., Irwin, J. A. 2002, ApJ, 573, 107
\bibitem{} Leon, S., Meylan, G., Combes, F. 2000, A\&A, 359, 907
\bibitem{} Malhotra, S. 1994, ApJ, 433,687
\bibitem{}  Mauersberger, R., Henkel, C., Wielebinski, R., Wiklind, T., Reuter, H.-P. 1996, A\&A, 
305,.421
\bibitem{}  McLean, B. 2001 in Virtual Observatories of the Future, ASP Conference Proceedings, 
Vol. 225. Eds.  R. J. Brunner, S. G. Djorgovski, and A. S. Szalay. San Francisco: Astronomical 
Society of the Pacific, p.103
\bibitem{} Mihos, J. Christopher, Hernquist, L. 1994, ApJ, 425, 13
\bibitem{} Moran, E. C., Lehnert, M. D.; Helfand, D. J. 1999ApJ, 526, 649
\bibitem{} Norman, C. A., Ikeuchi, S. 1989, ApJ, 345, 372
\bibitem{} Piner, B. G., Stone, J. M., Teuben, P. J. 1995, ApJ, 449, 508
\bibitem{} Radford, S. J. E., Downes, D., Solomon, P. M. 1991, ApJ, 368L, 15
\bibitem{} Regan, M.W., Teuben, P. 2003, ApJ, 582, 723
\bibitem{} Rozas, M.; Beckman, J. E.; Knapen, J. H. 1996, A\&A, 307, 735
\bibitem{} Sanders, D.B., Scoville, N.Z., Solomon, P.M. 1985, ApJ, 289, 373
%\bibitem{} Sanders, D. B., Mirabel, I. F. 1985, ApJ, 298, 31
\bibitem{} Scalo, J., Chappell, D. 1999, MNRAS, 310, 1
\bibitem{} Schinnerer, E.,  Eckart, A., Boller, Th.  2000, ApJ, 545, 205
\bibitem{} Sempere, M.J., Garcia-Burillo, S., Combes, F., Knapen, J. H. 1995, A\&A, 296, 45
\bibitem{} Smith, D. A., Wilson, A. S. 2001, ApJ, 557, 180
\bibitem{} Solomon, P. M., Downes, D., Radford, S. J. E., Barrett, J. W. 1997, ApJ, 478, 144
\bibitem{} Sodroski T.J. et al. 1994, ApJ, 428, 638
\bibitem{} Sodroski T.J. et al. 1995, ApJ, 452, 262
\bibitem{} Stacy, J. G., Bitran, M. E., Dame, T. M., Thaddeus, P. 1989 The Center of the Galaxy:
 Proceedings of the 136th Symposium of IAU, Los Angeles, U.S.A., Ed M. Morris, Kluwer 
Academic Publishers, Dordrecht, p.157
\bibitem{} Strong, A. W., Bloemen, J. B. G. M., Dame, T. M., Grenier, I. A., Hermsen, W., 
Lebrun, F., Nyman, L.-A., Pollock, A. M. T., Thaddeus, P. 1988, A\&A, 207, 1
\bibitem{} Taylor, D., Tyson, Axon, D.J. 1992, MNRAS, 255, 351
\bibitem{} Terashima, Y., Wilson, A.S. 2001, ApJ, 560, 139
\bibitem{} Trewhella, M., Davies, J. I., Alton, P. B.; Bianchi, S., Madore, B. F. 2000, 
ApJ, 543, 153
\bibitem{} Ulvestad, J.S., Wilson, A.S., Sramek, R.A. 1981, ApJ, 247, 419
\bibitem{} Wei\ss, A., Fabian, W. Neininger, N., Klein, U. 1999, A\&A, 345, 23
\bibitem{} Wei\ss , A., Neininger, N., Hüttemeister, S., Klein, U 2001, A\&A, 365, 571
\bibitem{} Wiklind, T., Henkel, C. 1995, A\&A, 297, 71
\bibitem{} Wilcots, Eric M., Turnbull, M. C.; Brinks, E. 2001, ApJ, 560, 110
\bibitem{} Xilouris, E. M., Byun, Y. I., Kylafis, N. D., Paleologou, E. V., Papamastorakis, J. 1999
A\&A, 344, 868
\bibitem{} Young, J. et al. 1995, ApJS, 98, 219
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