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 ( $10~M_{\odot}$) stars, where the necessarily high temperatures of 10⁸ K are found), whereas $^{17}{\rm O}$ (the result of hydrogen burning, 10⁸ K) originates in intermediate mass ( $10~M_{\odot}$) 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 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.