A&A 367, 457-469 (2001)
DOI: 10.1051/0004-6361:20000462

Molecular gas conditions in NGC 4945 and the Circinus galaxy[*]

S. J. Curran1,2 - L. E. B. Johansson1 - P. Bergman1 - A. Heikkilä1,3 - S. Aalto1


1 - Onsala Space Observatory, Chalmers University of Technology, 439 92 Onsala, Sweden
2 - European Southern Observatory, Casilla 19001, Santiago 19, Chile
3 - Observatory, PO Box 14, 00014 University of Helsinki, Finland

Received 11 July 2000 / Accepted 5 December 2000

Abstract
We present results of a multi-transition study of the dense molecular gas in the central part of the hybrid star-burst/Seyfert galaxies NGC 4945 and the Circinus galaxy. From the results of radiative transfer calculations, we estimate in NGC 4945 $n_{{\rm H}_2}=3~10^3{-}10^4$ cm-3 and $T_{\rm kin}\approx100$ K and in Circinus $n_{{\rm H}_2}=2~10^3{-}10^5$ cm-3 and $T_{\rm kin}\approx50{-}80$ K for the molecular hydrogen density and kinetic temperature, respectively. As well as density/temperature tracing molecules, we have observed C17O and C18O in each galaxy and the value of C18O/C $^{17}{\rm O}\approx6$ for the isotopic column density ratio suggests that both have relatively high populations of massive stars. Finally, although star formation is present, the radiative transfer results combined with the high HCN/CO and (possibly) HCN/FIR, radio/FIR ratios may suggest that, in comparison with Circinus, a higher proportion of the dense gas emission in NGC 4945 may be located in the hypothesised central nuclear disk as opposed to dense star forming cloud cores. Contrary to the literature, which assumes that all of the far-infrared emission arises from star formation, our results suggest that in NGC 4945 some of this emission could arise from an additional source, and so we believe that a revision of the star formation rate estimates may be required for these two galaxies.

Key words: galaxies: abundances - galaxies: individual: NGC 4945, Circinus - galaxies: nuclei - galaxies: Seyfert - galaxies: star-burst


1 Introduction

Seyfert galaxies account for $\sim $10% of all galaxies (Maiolino & Rieke 1995; Ho et al. 1997) and along with LINERs[*] and radio quiet quasars constitute one of the three main classes of active galactic nuclei (AGNs); the other classes being the more luminous FRI radio galaxies/BL Lac objects and the most luminous FRII radio galaxies/quasars. Although sometimes associated with enhanced star-burst activity (e.g. Whittle 1992; Gu et al. 1997; Roy et al. 1998; Gu et al. 1999), a Seyfert nucleus exhibits the tell-tale signs of an AGN via a non-stellar nuclear source (Rigopoulou et al. 1997) and unlike star-burst galaxies, the nuclei are often associated with radio or optical jets (Hummel et al. 1983; de Grijp et al. 1985; Cecil et al. 1992)[*]. Recently, Curran et al. (2000) have shown, from a sample of 20 Seyfert galaxies, that the HCN/CO luminosity ratio is similar to that of ultra-luminous infrared galaxies (ULIRGs), while being significantly higher than that of normal spiral galaxies; $\frac{L_{\rm HCN}}{L_{\rm CO}}\approx1/6$ for the distant sources ( $L_{\rm FIR}\approx30~10^{10}~{L}_{\odot}$) and $\frac{L_{\rm HCN}}{L_{\rm CO}}\approx1/17$ for the near-by sources ( $L_{\rm FIR}\approx2~10^{10}~{L}_{\odot}$) (Curran et al. 2000), cf. $\frac{L_{\rm HCN}}{L_{\rm CO}}\approx1/80$ for normal spirals (Solomon et al. 1992). The fraction of the HCN brightness which arises from the AGN (via the water maser disks[*]) or from star forming cores is still, however, uncertain (e.g. Kohno et al. 1999).

NGC 4945 has its visual appearance dominated by strong and patchy extinction in the disk, which hides any distinct visible nucleus, although a relatively strong and compact (30'') non-thermal radio source, which is coincident with the peak of red and infra-red emission (Moorwood & Glass 1984), is visible in the central region. Also, wide absorption lines (OH, CH, H2CO) are found towards the radio-continuum nucleus (Whiteoak & Gardner 1975; Whiteoak & Gardner 1985; Ables et al. 1987; Whiteoak & Wilson 1990). Towards this position a very powerful H2O maser has been detected (dos Santos & Lépine 1979; Batchelor et al. 1982; Greenhill et al. 1997). The nucleus exhibits star-burst as well as Seyfert characteristics and has properties similar to that of Circinus although for some species the molecular line characteristics differ.

The Circinus galaxy also has ${\rm H_{2}O}$ maser activity (Gardner & Whiteoak 1982; Greenhill et al. 1995; Greenhill et al. 1997; Greenhill 2000) the high luminosity of which suggests the presence of an active galactic nucleus (AGN). Again, this galaxy is host to nuclear star-burst activity (Harnett et al. 1990; Moorwood et al. 1996a) and the presence of visible and near infra-red coronal lines (Oliva et al. 1994), an X-ray reflection dominated spectrum (Matt et al. 1996) and broad polarised H$\alpha$ (Oliva et al. 1998) suggest the presence of a hidden Seyfert nucleus.

These almost edge-on near-by Southern galaxies (Freeman et al. 1977; de Vaucouleurs et al. 1981; Ables et al. 1987) are similar, in that:

1.
Both possess molecular rings with very similar properties, which are associated with the star-burst activity (Bergman et al. 1992; Dahlem et al. 1993; Marconi et al. 1994; Curran et al. 1998);
2.
Both galaxies have a dynamical mass of $3~10^9~{M}_{\odot}$ within the central 600 pc (Mauersberger et al. 1996; Curran et al. 1998);
3.
They also share similar X-ray properties (see Spoon et al. 2000).
Because of the large variety of molecules (at least in NGC 4945, Whiteoak et al. 1990; Henkel et al. 1994) and the proximity of the galaxies, extraordinarily strong emission lines from a number of molecules may be observed. Thus a relatively detailed observational study of the chemical and physical properties of the molecular gas in the central parts of these galaxies is possible, even with the sensitivity and the angular resolution of the present day single dish millimetre-wave telescopes. We have observed spectral line emission from a number of molecules (some in several transitions) and extend the previous studies of Whiteoak et al. (1990); Bergman et al. (1992); Henkel et al. (1994) and present our results in this paper.

2 Observations and results


 

 
Table 1: The integrated line intensities observed towards the centre of NGC 4945; the detections are shown in Fig. 1. Here and in Table 2, the uncertainties are due to $1\sigma $ rms noise fluctuations and the $\approx \pm 5\%$ accuracy of $\eta _{\rm mb}$. The upper limits where obtained by assuming the same velocity range as for the CO (and other molecules), i.e. $\approx $300 km s-1 to $\approx $800 km s-1. The H2CO $J_{\rm K_a, K_c}=2_{0,2}\rightarrow 1_{0,1}$ line is a blend with HC3N $J=16\rightarrow 15$

Molecule		 Transition $I_{\rm mb}$ [K km s-1]

12CO		 $1\rightarrow 0$ $510\pm30$
  $2\rightarrow 1$ $740\pm40$
  $3\rightarrow 2$ $760\pm50$
13CO $1\rightarrow 0$ $30\pm2$
  $2\rightarrow 1$ $86\pm5$
C18O $1\rightarrow 0$ $8.4\pm0.8$
  $2\rightarrow 1$ $29\pm2$
C17O $1\rightarrow 0$ $1.8\pm0.4$
  $2\rightarrow 1$ $5\pm1$
CS $2\rightarrow 1$ $9.3\pm0.8$
  $3\rightarrow 2$ $11\pm1$
13CS $2\rightarrow 1$ <2
SO $3_2\rightarrow 2_1$ $1.2\pm0.3$
  $4_3\rightarrow 3_2$ $1.4\pm0.2$
HCN $1\rightarrow 0$ $24\pm2$
  $3\rightarrow 2$ $45\pm4$
H13CN $1\rightarrow 0$ $1.1\pm0.4$
HCO+ $1\rightarrow 0$ $21\pm1$
  $3\rightarrow 2$ $37\pm3$
H13CO+ $1\rightarrow 0$ $2.3\pm0.5$
  $3\rightarrow 2$ <4
H2CO $2_{1,2}\rightarrow 1_{1,1}$ $6.5\pm0.7$
  $2_{0,2}\rightarrow1_{0,1}$ $5.4\pm0.5$
  $2_{1,1}\rightarrow 1_{1,0}$ $5.9\pm0.6$
  $3_{0,3}\rightarrow2_{0,2}$ <3
  $3_{2,2}\rightarrow2_{2,1} $ <3
  $3_{1,2}\rightarrow2_{1,1} $ <3
CH3C2H $6\rightarrow5$ <2



 

 
Table 2: The integrated line intensities observed towards the centre of Circinus; the detections are shown in Fig. 2. The CO data are taken from Curran et al. (1998). As in the case of NGC 4945 (Table 1), the integrated intensities were estimated by assuming the same velocity range as for the CO i.e. $\approx $200 km s-1 to $\approx $650 km s-1

Molecule		 Transition $I_{\rm mb}$ [K km s-1]

12CO		 $1\rightarrow 0$ $180\pm10$
  $2\rightarrow 1$ $220\pm20$
  $3\rightarrow 2$ $230\pm20$
13CO $1\rightarrow 0$ $12\pm1$
  $2\rightarrow 1$ $24\pm4$
C18O $1\rightarrow 0$ $4.3\pm0.4$
C17O $1\rightarrow 0$ $0.9\pm0.1$
CS $2\rightarrow 1$ $3.2\pm0.3$
  $3\rightarrow 2$ $3.0\pm0.3$
  $5\rightarrow 4$ $1.1\pm0.3$
SO $3_2\rightarrow 2_1$ $0.8\pm0.2$
HCN $1\rightarrow 0$ $5.2\pm0.8$
HNC $1\rightarrow 0$ $3\pm1$
HCO+ $1\rightarrow 0$ $7\pm1$
H2CO $2_{1,2}\rightarrow 1_{1,1}$ $0.8\pm0.2$


The observations were carried out in June 1989, February 1993, June 1995, June 1998, December 1998, December 1999 and April 2000 with the Swedish-ESO Sub-millimetre Telescope (SEST)[*] at La Silla, Chile. The receiver system consisted of a 3 mm Schottky mixer and cryogenic 1.3 mm, 2 mm and 3 mm SIS mixers. The mixers were tuned to single sideband mode (resulting system temperatures, corrected for the atmosphere, were typically $T_{\rm A}^{*}\approx200{-}550$ K), and connected to low resolution acousto-optical spectrometers (1440 channels, total bandwidth of 1 GHz). Dual beam-switching, with a beam-throw of $\approx $12$^\prime$ in azimuth, was used as observing mode. The intensity calibration was done with the chopper-wheel method. Pointing and focus checks were made towards stellar SiO masers as well as the continuum source in Centaurus A. The pointing offsets were typically 3'' rms in each coordinate. Calibration uncertainties are estimated to be $\pm10, 15 ~{\rm and}~ 20\%$ in the 3, 2 and 1.3 mm bands, respectively.

2.1 Observational results

Figures 1 and 2 show the observed spectra. The observational results are summarised in Tables 1 and 2, where main-beam integrated intensities are given[*]. The total uncertainty in the observed intensities is obtained by adding quadratically the contribution of noise in the spectra to the calibration and pointing uncertainties.

In NGC 4945 most of the molecules have stronger emission in the blue-shifted than in the red-shifted part of the line. An exception to this is CS, whose emission is more evenly distributed over the full spectral profile (this has previously been noted by Henkel et al. 1990). This asymmetry[*] in the spectra may indicate that the chemistries differ in the two regions or that the excitation is varying, e.g. due to differences in the gas density/temperature, electron density or the background infrared radiation. Henkel et al. (1994) have suggested that the differing emission strengths may be due to differences in the exposure to the far-infrared (FIR) radiation. Yet another possible explanation is self-absorption, i.e. some locations suffering a greater degree of saturation (Henkel et al. 1990), perhaps due to a temperature gradient across the molecular ring where the inner edge is expected to be hotter than the outer.

Unlike those of NGC 4945 the profiles in Circinus are fairly symmetric. Again checking against previous observations, the lines are similar to those which have been previously observed i.e. 12CO $1\rightarrow 0$(Johansson et al. 1991; Israel 1992; Elmouttie et al. 1997; Elmouttie et al. 1998), 13CO $1\rightarrow 0$, 12CO $2\rightarrow 1$, 13CO $2\rightarrow 1$ (Johansson et al. 1991) and HCO+, HCN and HNC, in the $1\rightarrow 0$ transition (Israel 1992).


  \begin{figure} \par\includegraphics[angle=-90,width=5.6cm,clip]{10096a.ps}\hspac... ...hspace*{3mm} \includegraphics[angle=-90,width=5.6cm,clip]{10096o.ps}\end{figure} Figure 1: The observed spectra in NGC 4945. Apart from H2CO $2_{1,1}\rightarrow 1_{1,0}$, which required the removal of a higher order baseline, a constant or first order baseline has been subtracted from each spectra. The spectra have been smoothed to a channel width corresponding to 10 km s-1 (except C17O $2\rightarrow 1$, SO $3_2\rightarrow 2_1$ and SO $4_3\rightarrow 3_2$ to 20 km s-1). The intensity scale is $T_{\rm A}^*$ and the velocity scale is relative to the local standard of rest (l.s.r.)
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 \begin{figure}\vspace{8.5cm} \setlength{\unitlength}{1in} \special{psfile=10096... ...ffset=130 hscale=25 vscale=25 angle=-90} \addtocounter{figure}{-1}\end{figure} Figure 1: continued. The H13CN and H13CO+ $1\rightarrow 0$ transitions lie in the same band, centred on 86.55 GHz, at 86.34 GHz (1280 km s-1) and 86.75 GHz (-140 km s-1), respectively. These spectra are shown with a resolution corresponding to 50 km s-1 (the remainder of the spectra being shown smoothed to 10 km s-1). The weak detections (here and in Fig. 2), are shown with the baseline and moment boxes used to determine their integrated intensities, given in Table 1
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  \begin{figure} \par\includegraphics[angle=-90,width=5.6cm,clip]{10096v.ps}\hspac... ...space*{3mm} \includegraphics[angle=-90,width=5.6cm,clip]{10096kk.ps}\end{figure} Figure 2: The observed spectra in Circinus. A constant or first order baseline has been subtracted from each spectra. The spectra have been smoothed to a channel width corresponding to 10 km s-1(except C17O $1\rightarrow 0$, CS $5\rightarrow 4$, HNC $1\rightarrow 0$ and H2CO ( $2_{1,2}\rightarrow 1_{1,1}$) to 20 km s-1) and SO $3_2\rightarrow 2_1$ to 40 km s-1. The intensity scale is $T_{\rm A}^*$ and the velocity scale is relative to the local standard of rest (l.s.r.)
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2.2 Excitation and radiative transfer analysis

In the analysis we use velocity integrated line intensities, $I=\int{T {\rm d}v}$, which have been corrected for beam-dilution due to finite source and beam sizes. This is carried out by assuming that the source distribution on the sky is Gaussian and applying the full-width half-maximum (FWHM) diameter ( $\Theta _{\rm source}$) of the corresponding 12CO transition to the various CO isotopomers. The other molecules have transitions of higher excitation requirements and in those cases the CO $2\rightarrow 1$ value of $\Theta _{\rm source}$is applied (Table 3). The resulting corrected intensity ratios are shown in Table 4.


 

 
Table 3: The beam widths, $\Theta _{\rm mb}$, at SEST and source sizes, $\Theta _{\rm source}$, of the various CO transitions. In the case of NGC 4945 the $1\rightarrow 0$ value is from Dahlem et al. (1993); Mauersberger et al. (1996), the $2\rightarrow 1$ value from Dahlem et al. (1993); Mauersberger et al. (1996); Curran (2000) and the $3\rightarrow 2$ value from Mauersberger et al. (1996); Curran (2000). For Circinus all the values are obtained from the maps of Curran et al. (1998). Applying the FWHMs listed to the relation $I=I_{\rm mb}/\eta _{\rm bf}$ (where $\eta _{\rm bf}=\Theta _{\rm source}^{2}/(\Theta _{\rm mb}^{2}+\Theta _{\rm source}^{2}$)), in order to correct for the Gaussian beam-filling factor, we obtain the corrected intensity ratios listed in Table 4

CO $1\rightarrow 0$ CO $2\rightarrow 1$ CO $3\rightarrow 2$

SEST beam		 45'' 22'' 15''
NGC 4945 29'' 20'' 15''
Circinus 42'' 31'' 21''



 

 
Table 4: Integrated line intensity ratios. For the values listed in Table 3 the uncertainties in $\Theta _{\rm source}$ (typically 10%) lead to uncertainties of $\approx $10% in the values of $\eta _{\rm bf}$ $\left(\frac{\Delta\eta}{\eta}=2(1-\eta)\frac{\Delta\Theta}{\Theta}\right)$, or $\sim $20% for ratios involving different source sizes

Molecule(s)		 Transitions I ratio
    NGC 4945 Circinus

12CO		 $2\rightarrow 1/1\rightarrow 0$ $1.0\pm0.2$ $1.0\pm0.2$
  $3\rightarrow2/1\rightarrow0$ $0.9\pm0.2$ $0.9\pm0.2$
13CO $2\rightarrow 1/1\rightarrow 0$ $1.9\pm0.4$ $1.5\pm0.5$
12CO/13CO $1\rightarrow0/1\rightarrow0$ $17\pm2$ $14\pm2$
  $2\rightarrow1/2\rightarrow1$ $8.3\pm0.8$ $10\pm3$
C18O $2\rightarrow 1/1\rightarrow 0$ $2.4\pm0.6$ -
12CO/C18O $1\rightarrow0/1\rightarrow0$ $59\pm9$ $41\pm7$
  $2\rightarrow1/2\rightarrow1$ $25\pm4$ -
C17O $2\rightarrow 1/1\rightarrow 0$ $1.7\pm0.9$ -
12CO/C17O $1\rightarrow0/1\rightarrow0$ $300\pm80$ $230\pm50$
  $2\rightarrow1/2\rightarrow1$ $170\pm50$ -
C18O/C17O $1\rightarrow0/1\rightarrow0$ $5\pm2$ $6\pm2$
  $2\rightarrow1/2\rightarrow1$ $7\pm2$ -
CS $2\rightarrow1/3\rightarrow2$ $1.7\pm0.3$ $1.8\pm0.6$
  $2\rightarrow1/5\rightarrow4$ - $7\pm3$
CS/13CS $2\rightarrow1/2\rightarrow1$ >4 -
SO $3_2\rightarrow2_1/4_3\rightarrow3_2$ $1.4\pm0.9$ -
CS/SO $2\rightarrow1/3_2\rightarrow2_1$ $8\pm3$ $3\pm1$
  $3\rightarrow2/4_3\rightarrow3_2$ $7\pm3$ -
HCN $1\rightarrow0/3\rightarrow2$ $2.6\pm0.4$ -
HCN/H13CN $1\rightarrow0/1\rightarrow0$ $20\pm10$ -
HCN/HNC $1\rightarrow0/1\rightarrow0$ - $1.7\pm0.8$
HCO+ $1\rightarrow0/3\rightarrow2$ $2.7\pm0.4$ -
12CO/CS $2\rightarrow1/2\rightarrow1$ $23\pm5$ $31\pm6$
  $3\rightarrow2/3\rightarrow2$ $36\pm5$ $52\pm10$
12CO/HCN $1\rightarrow0/1\rightarrow0$ $7.5\pm0.9$ $17\pm4$
  $3\rightarrow2/3\rightarrow2$ $18\pm3$ -
12CO/HCO+ $1\rightarrow0/1\rightarrow0$ $8\pm1$ $13\pm4$
  $3\rightarrow2/3\rightarrow2$ $20\pm3$ -
HCN/HCO+ $1\rightarrow0/1\rightarrow0$ $1.2\pm0.2$ $0.7\pm0.2$
  $3\rightarrow2/3\rightarrow2$ $1.2\pm0.2$ -
HCO+/H13CO+ $1\rightarrow0/1\rightarrow0$ $9\pm3$ -
HCO+/13CO $1\rightarrow0/1\rightarrow0$ $2.0\pm0.2$ $1.2\pm0.3$
HCO+/CS $3\rightarrow2/3\rightarrow2$ $1.7\pm0.3$ -
H13CN $1\rightarrow0/3\rightarrow2$ >3 -
H2CO $\frac{2_{1,2}\rightarrow1_{1,1}+2_{1,1}\rightarrow1_{1,0}}{2_{0,2}\rightarrow1_{0,1}}$ $2.3\pm0.7$ -
H2CO $2_{1,2}\rightarrow1_{1,1}/2_{1,1}\rightarrow1_{1,0}$ $1.2\pm0.2$ -
H2CO $2_{1,2}\rightarrow1_{1,1}/2_{0,2}\rightarrow1_{0,1}$ $1.3\pm0.2$ -


For both galaxies we find a 12CO $2\rightarrow 1/1\rightarrow 0$intensity ratio of $\approx $1 which is typical for star-burst/Seyfert galaxies (Aalto et al. 1991; Dahlem et al. 1993)[*]. Also, the CO $1\rightarrow 0$/HCN $1\rightarrow 0$ intensity ratios are similar to those found in (other) Seyfert galaxies; with NGC 4945 showing the same ratio as for the more distant Seyferts and Circinus showing a similar ratio to the near-by sample (see Sect. 1). In NGC 4945 our 12CO and 13CO $2\rightarrow 1/1\rightarrow 0$ ratio agrees with that previously determined (e.g. Dahlem et al. 1993; Henkel et al. 1994).

In order to estimate the prevailing physical conditions and column densities in the molecular gas, we have performed radiative transfer calculations. In order to complement this, in temperature and column density estimates we have also applied local thermodynamic equilibrium (LTE) calculations. The presented column density estimates are peak values in the sense that the intensities have been corrected for finite source and beam size. However, small-scale (i.e. structures smaller than the assumed source size) beam-filling has not been taken into account. Conversion to beam-averaged quantities is obtained by multiplication by $\eta _{\rm bf}$ (see Table 3 for the definition of this).

2.2.1 The radiative transfer results

The code used here is described in Jansen (1995): The excitation problem involves statistical equilibrium of a multi-level system (incorporating typically 12 rotational levels in the lowest vibrational state of the molecule in question). The radiative transfer is treated in the mean-escape probability (MEP) approximation: like the large velocity gradient (LVG) method (e.g. Leung & Liszt 1976), this uses a local source function in which the optical depth in each transition determines the mean escape probability (Osterbrock 1989) of a photon from a typical location within a cloud. The model gas cloud has a spherical shape and a uniform density and kinetic temperature. The gas density and the temperature are estimated by fitting the observed line ratios of different transitions of CO, CS, HCN and HCO+ to the excitation and radiative transfer model. The intensity ratios for each species were constrained by a routine which tested the goodness-of-fit by calculating the $\chi ^2$error of the MEP integrated intensity ratios for each of the observed values. The 12CO and C18O intensity ratios gave limits for the column density whereas 13CO was quite specific (e.g. using $2\rightarrow1/1\rightarrow0=1.9$ in NGC 4945). Examining the results we selected, for example, the 12CO column density which gave the observed 12CO $1\rightarrow 0$ to 13CO $1\rightarrow 0$ intensity ratio. This process was repeated for each transition of each isotopomer.

For NGC 4945 this gave $N(^{12}{\rm CO})/N(^{13}{\rm CO})\approx50$ for the relative column densities and solutions could only be found for $T_{\rm kin}\approx100$ K and $n_{{\rm H}_2}\approx3~10^3$ cm-3, i.e. as Henkel et al. (1994). Constraining the HCN solutions using the $1\rightarrow0/3\rightarrow2$ and the CO/HCN $1\rightarrow0/1\rightarrow0$ and $3\rightarrow2/3\rightarrow2$ line ratios, we could obtain a solution for $n_{{\rm H}_2}\approx10^4-10^5$ cm-3, regardless of kinetic temperature. For CS at the kinetic temperature defined by the CO, the $2\rightarrow1/3\rightarrow2$ line ratios only permit a value of $n_{{\rm H}_2}\approx10^4$ cm-3. Note that solutions at this molecular hydrogen density can be found over a range of kinetic temperatures (e.g. $T_{\rm kin}=10$ K, $N_{\rm CS}/\Delta v\approx6~10^{14}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$ and $T_{\rm kin}=150$ K, $N_{\rm CS}/\Delta v\approx5~10^{13}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$), but for densities higher than this ( $n_{{\rm H}_2}=10^5$ cm-3), solutions can only be found for $T_{\rm kin}\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\disp... ...{\offinterlineskip\halign{\hfil$\scriptscriptstyle ... K (for $n_{{\rm H}_2}=10^6$ cm-3 there are no solutions). It is important to note that these results apply to the observed intensity ratios (within errors) only[*], and so still hold if the CS traces a different gas component to the CO. The upper limit for the $1\rightarrow0/3\rightarrow2$ transitions of H13CN together with the HCN/H13CN $1\rightarrow0/1\rightarrow0$ ratio gives the range of column densities shown in Table 5, where the MEP results are summarised. Note that, as for the CO isotopomers, we obtain a HCN/H13CN column density ratio of $\approx $50-200.


 

 
Table 5: The MEP solutions for NGC 4945 for $T_{\rm kin}=100$ K. The column density is derived for a cloud velocity width of $30{\rm ~km~s}^{-1}$, Eq. (1). These solutions satisfy both the observed line ratios for each isotopomer and the line ratios between isotopomers (within uncertainties)

Molecule		 $n_{{\rm H}_2}$ [cm-3] N [cm-2]

12CO		 3 103 $\approx $6 1018
13CO 3 103 1.2-1.5 1017
C18O 3 103 $\approx $3 1016
HCN 104 1.5-2.4 1016
  105 $\approx $3 1015
CS 104 1.5-2.4 1015
HCO+ 104 1.5-2.1 1015
H13CN 104 1-3 1014



  \begin{figure} \vspace{6cm} \setlength{\unitlength}{1in} \special{psfile=10096ll.eps hoffset=40 voffset=-10 hscale=90 vscale=90 angle=0} \end{figure} Figure 3: MEP solutions for the CO isotopomers per velocity interval at $T_{\rm kin}=100$ K, $n_{{\rm H}_2}=3~10^3$ cm-3 (i.e. for NGC 4945). The plots show the $2\rightarrow 1/1\rightarrow 0$ intensity ratio against the column density per unit line width [cm $^{-2}~({\rm km~s}^{-1})^{-1}$] for each isotopomer, and give N(12CO $)/\Delta v \gtrsim 3~10^{16}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$, $(N^{13}{\rm CO})/\Delta v\sim 10^{16}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$ and $N({\rm C}^{18}O)/\Delta v\lesssim 10^{16}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$. In this and Fig. 4, the circles indicate the nominal observed values with the associated uncertainties shown as bars. Note that these are only the solutions for each isotopomer and are therefore valid over the range of column densities constrained by the error bars. In the case of the final solutions (Tables 5 and 6), however, we also take into account the ratios between different isotopomers
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For the CO values in Circinus, solutions could only be found for $T_{\rm kin}\approx50{-}80$ K and $n_{{\rm H}_2}=2~10^3$ cm-3, i.e. as the warm gas solution of Curran et al. (1998), where we obtained solutions of the CO isotopomers convolved to the 12CO $1\rightarrow 0$ beam. The column densities give $N(^{12}{\rm CO})/N(^{13}{\rm CO})=60{-}80$. Since we have only the $1\rightarrow 0$transition available in this galaxy, models for HCN and HCO+ are not so easy to constrain. Assuming, however, a similar kinetic temperature between the various tracers and using the 12CO/HCN $1\rightarrow0/1\rightarrow0$ and 12CO/HCO+ $1\rightarrow0/1\rightarrow0$ ratios (i.e. the HCN and CO trace similar regions), solutions may be found for $n_{{\rm H}_2}\sim10^4{-}10^6$ cm-3. From the $2\rightarrow1/3\rightarrow2$and $2\rightarrow1/5\rightarrow4$ ratios of CS, we could only find a solution at a molecular hydrogen density of $n_{{\rm H}_2}\sim10^5$ cm-3. Note that solutions using this molecule could only be obtained over a similar temperature range as for the CO. No solutions which satisfy the observed CO/CS ratios at $n_{{\rm H}_2}\approx10^4$ or 106 cm-3 could be found, regardless of kinetic temperature[*]. The results are summarised in Table 6.


 

 
Table 6: The MEP solutions for Circinus for $T_{\rm kin}=50{-}80$ K. The column density is derived for a cloud velocity width of $10{\rm ~km~s}^{-1}$, Eq. (1). These solutions satisfy both the observed line ratios for each isotopomer and the line ratios between isotopomers (within uncertainties)

Molecule		 $n_{{\rm H}_2}$ [cm-3] N [cm-2]

12CO		 2 103 $\approx $2 1018
13CO 2 103 2.5-3 1016
HCN 104 $\approx $1 1015
  105 $\approx $1 1014
  106 <1 1014
CS 105 $\approx $5 1013
HCO+ 105 $\approx $3 1013



  \begin{figure} \vspace{6cm} \setlength{\unitlength}{1in} \special{psfile=10096mm.eps hoffset=40 voffset=-10 hscale=90 vscale=90 angle=0} \end{figure} Figure 4: MEP solutions for the CO isotopomers per velocity interval at $T_{\rm kin}=50$ K, $n_{{\rm H}_2}=2~10^3$cm-3 (i.e. for Circinus). The plots show the $2\rightarrow 1/1\rightarrow 0$ intensity ratio against the column density per unit line width [cm $^{-2}~({\rm km~s}^{-1})^{-1}$] for each isotopomer, and give $N(^{12}{\rm CO})/\Delta v\gtrsim 10^{15}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$ and $N(^{13}{\rm CO})/\Delta v\lesssim 10^{16}$ cm $^{-2}~({\rm km~s}^{-1})^{-1}$
Open with DEXTER

Using the total observed line emission to estimate an individual cloud velocity width (neglecting effects due to cloud-cloud shielding) from

 \begin{displaymath}\Delta v = \left(1+\frac{\Theta_{\rm mb}^2}{\Theta_{\rm source}^2}\right) \sqrt{4\ln2 /\pi} \frac{I_{\rm mb}}{T_{\rm MEP}}, \end{displaymath} (1)

where $I_{\rm mb}$ is the total velocity integrated intensity (Tables 1 and 2) and $T_{\rm MEP}$ is the antenna temperature obtained from the MEP analysis[*], we find velocity widths of $\approx $ $30{\rm ~km~s}^{-1}$ and $\approx $ $10{\rm ~km~s}^{-1}$ for NGC 4945 and Circinus, respectively. These values are applied to the derived column densities per unit line width to give the values shown in Tables 5 and 6.

2.2.2 The LTE results

In order to complement the MEP results, we applied the LTE model to the observed data. Since this method[*] depends only upon the excitation temperature ( $T_{\rm ex}$) and the column density, it is the simplest way to analyse the observed line ratios. Here we have assumed that the excitation temperature is the same for both 12CO and 13CO.


 

 
Table 7: The minimum $\chi ^2$ LTE solutions. Note that, unlike previously, these are beam averaged column densities (based upon the velocity integrated intensities)

Galaxy		 $T_{\rm ex}$ [K] $N(^{12}{\rm CO})$ [cm-2] $N(^{12}{\rm CO})/N(^{13}{\rm CO})$

NGC 4945		 20 2 1019 40
Circinus 14 2 1018 25


From the solutions (Table 7) we see that the LTE results differ significantly from the solutions obtained from the radiative transfer calculations, although the derived column densities are reasonable, cf. $\approx $8 1019 cm-2 for the peak column densities in NGC 4945, obtained by multiplying the 12CO column density per unit line width ($\approx $2 1017 cm $^{-2}~({\rm km~s}^{-1})^{-1}$) over the full line width (Fig. 1). For Circinus the value obtained is closer to that for an individual cloud (see Table 6). Applying the temperatures and column densities from the LTE solutions to the MEP code we can satisfy the observed intensity ratios for $N(^{12}{\rm CO})>6~10^{19}$ cm-2 and >5 1019 cm-2 in NGC 4945 and Circinus, respectively. We cannot, however, reproduce the observed 13CO ratios: 13CO $2\rightarrow1/1\rightarrow0<1.1$ for NGC 4945 and <0.87 (or $\approx $0.9 for $N(^{13}{\rm CO})>2~10^{18}$ cm-2) for Circinus using the molecular hydrogen densities obtained from the MEP solutions.

3 Discussion

From the MEP analysis it appears that the molecular gas in the two galaxies arises from a relatively dense phase, i.e. $n_{{\rm H}_2}=3~10^3{-}10^4$ cm-3 in NGC 4945 and $n_{{\rm H}_2}=2~10^3{-}10^5$ cm-3 in Circinus[*]. The observed line ratios may be solved for a constant kinetic temperature in each galaxy, i.e. $T_{\rm kin}=100$ K and $T_{\rm kin}=50{-}80$ K in NGC 4945 and Circinus, respectively. Our results for NGC 4945 compare well with those of the LVG model of Henkel et al. (1994), i.e. $T_{\rm kin}=100$ K, $n_{{\rm H}_2}=3~10^3$ cm-3 and $^{12}{\rm C}/^{13}{\rm C}\sim50$ for the CO cloud component. Like Henkel et al. (1994), we find the model of Bergman et al. (1992) insufficient in density, due to an underestimate of the 12CO $2\rightarrow 1/1\rightarrow 0$ ratio (obtained from Whiteoak et al. 1990), in order to reproduce our value for this intensity ratio (which is similar to that previously obtained by Dahlem et al. 1993; Henkel et al. 1994). In the remainder of this section we will discuss the MEP results.

In NGC 4945 the star-burst is believed to have reached an advanced stage of evolution (Koornneef 1993; Henkel et al. 1994) and the presence of strong far-infrared and continuum radiation sources, as well as the water masers, indicate current vigorous star-formation activity (Moorwood & Glass 1984; Moorwood & Oliva 1994; Nakai et al. 1995; Moorwood et al. 1996b). Recent enrichment of the interstellar medium by massive stars is possibly indicated by a high $^{18}{\rm O}/^{17}{\rm O}$ abundance ratio. $^{18}{\rm O}$ is believed to be produced by helium burning (i.e. in massive ( $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displaystyle ... $10~M_{\odot}$) stars, where the necessarily high temperatures of $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displaystyle ...108 K are found), whereas $^{17}{\rm O}$ (the result of hydrogen burning, $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displaystyle ...108 K) originates in intermediate mass ( $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displaystyle ... $10~M_{\odot}$) stars. Accordingly the $^{18}{\rm O}/^{17}{\rm O}$abundance ratio may yield information on the relative abundances of these stars[*]. Estimating this from the C18O/C17O intensity ratio, we obtain a value of $\approx $6 in both NGC 4945 and Circinus. This compares well with the previously obtained value of Henkel et al. (1994); $8\pm2$. Also we obtain $\approx $30-60 for the C16O/C18O intensity ratio in NGC 4945 (cf. the value of $\approx $40, Henkel et al. 1994) and the MEP analysis supports a column density ratio of $\approx $200 (cf. $\approx $150, Henkel et al. 1994). For Circinus the intensity ratio is $\approx $40.

Looking at the CO/HCN ratios, we see that 12CO $1\rightarrow 0$/HCN $1\rightarrow0\approx8$ and $\approx $17 for NGC 4945 and Circinus, respectively. Whereas the value for Circinus is similar to that expected from $L_{\rm FIR}\sim10^{10}~L_{\odot}$Seyfert galaxies, the value for NGC 4945 is closer to that expected from $L_{\rm FIR}\sim10^{11}~L_{\odot}$ Seyferts (Curran et al. 2000). Naturally, since these two galaxies are somewhat closer than those of Curran et al. (2000), due to CO contamination from the disk, we would expect a lower CO/HCN ratio provided that the HCN is more concentrated towards the nucleus than the CO. The fact remains, however, that the CO/HCN ratio in NGC 4945 is about half that in Circinus. If the CO traces the dynamical mass, and since both galaxies have a dynamical mass of $3~10^9~{M}_{\odot}$ within the central 600 pc (Mauersberger et al. 1996; Curran et al. 1998), this suggests that there is twice as much HCN in the nuclear region of NGC 4945[*].

Examining the HCN/FIR luminosity ratios, we find that for NGC 4945, $L_{\rm HCN}=19\pm1~{\rm K ~km~s}^{-1}~{\rm kpc}^2$ and $L_{\rm FIR}=9.1~10^{9}~L_{\odot}$ and that for Circinus $L_{\rm HCN}=4.9\pm0.7~{\rm K ~km~s}^{-1}~{\rm kpc}^2$ (the HCN in both galaxies within the HPBW of 57'') and $L_{\rm FIR}=6.2~10^{9}~L_{\odot}$ (calculated from Lonsdale et al. 1985[*]). These values give $\frac{L_{\rm HCN}}{L_{\rm FIR}}~({\rm NGC~4945})\approx2.5\frac{L_{\rm HCN}}{L_{\rm FIR}}~({\rm Circinus})$[*], and this strongly suggests that the HCN luminosity in NGC 4945 arises from an additional component to the star forming cores, e.g. the dense gas component of the inner circumnuclear disk (Kohno et al. 1999; Curran et al. 2000): although the maser emission occurs on very small (pc) scales, the inner molecular gas structure[*] which has an elevated (cf. the ring) HCN to CO intensity ratio[*] is still extended enough to be perfectly detectable with beams of $\approx $2'' in near-by AGNs (Sternberg et al. 1994; Helfer & Blitz 1995; Tacconi et al. 1998). Note also that from mid-IR spectroscopy of NGC 4945, Spoon et al. (2000) postulate that compared to Circinus the narrow line region and/or UV radiation from the AGN may be severly obscured. This could perhaps be due to the central accumulation of dense gas and this hypothesis may be further supported by:

1.
The results of Forbes & Norris (1998) who find that the radio/FIR ratio is higher for NGC 4945 (in the radio-loud AGN regime) than for the rest of their Seyfert sample (including Circinus), which share similar ratios to star-burst galaxies. They do, however, attribute this to an underestimate of the total FIR flux due to the source not being wholly sampled (Rice et al. 1988). This would lower the HCN/FIR luminosity ratio in NGC 4945 by a factor of 6. It should be noted that Circinus and NGC 4945 (e.g. Forbes & Norris 1998) are by far the two closest Seyferts, and due to its large extent (Freeman et al. 1977; Jones et al. 1999) a correction should also be required for Circinus, but this galaxy has not been included in the sample of Rice et al. (1988). This may have the effect of maintaining a similar radio/FIR relation between the two galaxies.
2.
Although fairly dense at 104 cm-3, the higher density tracers are still an order of magnitude more diffuse than in Circinus (based on the more definite CS value). Densities of 105 cm-3 are typical of star-forming cloud cores (Solomon et al. 1990). Note also, from near-IR spectroscopy, Storchi-Bergmann et al. (1999) find that the nuclear excitation in Circinus is dominated by the star-burst activity.
The latter result contradicts the inferred star formation rates of $7.8~M_{\odot}~{\rm yr}^{-1}$ for NGC 4945 (Dahlem et al. 1993)[*] and $2.5~M_{\odot}~{\rm yr}^{-1}$ for Circinus (Elmouttie et al. 1998), but these estimates are based upon the total FIR luminosity which could be misleading if some of this radiation originates from the AGN.

In support of our excitation analysis, in Circinus we find ${\rm HNC}(1\rightarrow0)/{\rm HCN}(1\rightarrow0)=0.6\pm0.3$, which is typical of galaxies with $L_{\rm IR}\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displ... ...skip\halign{\hfil$\scriptscriptstyle ... and suggests the presence of warm gas (Hüttemeister et al. 1995). In NGC 4945, assuming optically thin lines, we calculate a formaldehyde ortho/para ratio of H2CO $\left(\frac{2_{1,2}\rightarrow1_{1,1}+2_{1,1}\rightarrow1_{1,0}}{2_{0,2}\rightarrow1_{0,1}}\right)\approx2.3$; or probably even slightly higher than this since the $2_{0,2}\rightarrow1_{0,1}$ line is blended with the HC3N $16\rightarrow15$ line[*], Table 1.

From HCN observations of the star-burst galaxies M 82 and NGC 253, which like NGC 4945 and Circinus share similar CO and FIR properties, Jackson et al. (1995) find that the $4\rightarrow3/1\rightarrow0$ intensity ratio gives molecular hydrogen and column densities per unit line width:

1.
In M 82 the values are $\sim $104 cm-3 and $\sim $1014 cm $^{-2}~({\rm km~s}^{-1})^{-1}$, respectively, i.e. similar to what we find in NGC 4945;
2.
In NGC 253 the values are $\sim $105 cm-3 and $\sim $1013 cm $^{-2}~({\rm km~s}^{-1})^{-1}$, respectively, i.e. similar to what we find in Circinus.
That is, gas densities of an order of magnitude greater, within 300 pc[*] (where the gas is densest), in NGC 253 than in M 82. Although both are classed as star-burst galaxies, from the literature M 82 appears to be fairly typical with a 100-pc scale star-burst ring (e.g. Young & Scoville 1982; Nakai et al. 1987; Curran et al. 1998), but possibly harbouring a weak AGN (Wills et al. 1999), while the centre of NGC 253 appears to be completely dominated by star forming activity, i.e. a large number of individual radio and X-ray sources due to the presence of stars (i.e. formation, supernova remnants and X-ray binaries) located within the innermost $\sim $20 pc of the nucleus (Ulvestad & Antonucci 1997; Vogler & Pietsch 1999). And so the conditions in M 82 and NGC 253, may be likened to those in NGC 4945 and Circinus, respectively, may possibly reflect the presence/significant contribution of an AGN, i.e. the higher density gas in Circinus and NGC 253 being due to a larger fraction of the radiation arising from star formation cf. NGC 4945 and M 82[*]. For these two galaxies there also exist observations of the CS $2\rightarrow 1$ and SO $3_2\rightarrow 2_1$transitions. These are excited collisionally under similar conditions[*] (e.g. Petuchowski & Bennett 1992) and so prove useful in probing the conditions of the molecular gas. For the CS $2\rightarrow 1$ to SO $3_2\rightarrow 2_1$ intensity ratio we obtain a value of $8\pm3$ in NGC 4945 and $3\pm1$ in Circinus; the former value agreeing with those of both M 82 and NGC 253, i.e. $\approx $8 and $\approx $7, respectively[*] (Sage et al. 1990; Petuchowski & Bennett 1992). Also, Galactic GMC data (Nilsson et al. 2000) show CS $2\rightarrow 1$/SO $3_2\rightarrow 2_1$ intensity ratios in the range 0.3-11, and typical[*] values are in the range 2-5, i.e. as for Circinus ( $N({\rm SO})\approx N({\rm CS})$)[*], while SO seems to be a factor of 2-3 less abundant than CS in NGC 4945.

4 Summary

We have observed a number of molecules, in several transitions in the central positions of NGC 4945 and the Circinus galaxy. From a mean-escape probability analysis of the data we conclude the following:

1.
In NGC 4945 the CO traces molecular hydrogen densities of $n_{{\rm H}_2}\approx3~10^3$ cm-3 and HCN, CS and HCO+ trace densities of $\sim $104 cm-3;
2.
In Circinus these values are $\approx $2 103 cm-3 and $\sim $105 cm-3.
This result implies that the molecular gas in Circinus may be found in denser cores than in NGC 4945. In conjunction with the (relatively) high HCN/CO (and possibly HCN/FIR and radio/FIR) ratio(s) in NGC 4945, this result suggests that much of the HCN and FIR radiation may arise from the AGN rather than the star-burst[*] (up to 50% of the bolometric luminosity in NGC 4945 may be due to the AGN, Spoon et al. 2000). If this is to be believed, then previous calculations of the star formation rate in this galaxy may be significant overestimates.

We also find that the kinetic temperature of the gas to be $T_{\rm kin}=100$ K and $T_{\rm kin}=50{-}80$ K in NGC 4945 and Circinus, respectively (from H2 lines, Spoon et al. 2000 also find warm gas, $T_{\rm ex}=160$ K, in NGC 4945). Could the higher temperature in NGC 4945 be related to the asymmetric shapes of (the temperature tracing) molecular profiles? A temperature gradient across the observed region could cause the possible self-absorption: Molecular rings (which have been insinuated in both these galaxies) are expected to have higher temperatures in their inner radius due to heating from the AGN and star formation, and so we may expect such asymmetric profiles in both cases. The fact that this is not seen in the Circinus spectra may simply imply a smaller gradient in accordance with the lower temperature derived. We hope that future interferometric (ALMA) studies of these galaxies will answer this through detailed mapping of temperature tracing molecules.

We find column densities (per unit line-width) of $\approx $2 1017 cm $^{-2}~({\rm km~s}^{-1})^{-1}$ for 12CO in both galaxies. Combined with the 13CO results, these values suggest a 12C/13C ratio of $\approx $50 for NGC 4945 and $\approx $60-80 for Circinus. These values are typical of Galactic clouds ($\approx $40-90, Goldsmith 1987), but higher than in the Galactic centre.

We also report the first detection of SO in these galaxies, thus increasing the number of extragalactic SO detections to six (Petuchowski & Bennett 1992; Johansson et al. 1994; Takano et al. 1995; Chin et al. 1998; Heikkilä et al. 1999).

Finally, worth noting is the fact that both the MEP and LTE methods suggest that the gas in NGC 4945 is warmer than in Circinus (by roughly the same factor), and so perhaps LTE methods could provide a useful simple means of determining the relative gas temperatures in a larger sample of Seyfert galaxies.

Acknowledgements
We wish to thank the referee Christian Henkel for his helpful comments, Francisco Azagra at SEST for locating some of the older data for us and the operators in general for their help with the observations. Thanks also to Michael Olberg, John Black and Silvana Nikolic at Onsala for their help with RADEX. Also at Onsala, Antonis Polatidis who made modifications (not possible from SEST) to Figs. 3 and 4. AH acknowledges financial support from the Academy of Finland through grant No. 1011055.

References

 

Copyright ESO 2001