3 Discussion

3.1 Gas distributions

For all of our galaxies the HCN/CO luminosity ratio increases towards the nucleus (Table 2), and when we combine our results with those of previous interferometric observations for the much studied NGC 1068, Figs. 21 and 22,

Figure 21: The CO to HCN intensity/luminosity ratio variation with distance from the nucleus of NGC 1068. HB95 refers to data taken from Helfer & Blitz (1995), CAB00 from Curran et al. (2000) and HB93 from Helfer & Blitz (1993). The star-burst activity in this galaxy is associated with the CO ring of radius 0.9-2.4 kpc (Myers & Scoville 1987; Planeas et al. 1991). Around these radii it is seen that the ratio appears to follow an increasing trend (a detail is shown in Fig. 22) and although there is relatively little CO out in the galactic disk ($\approx$15 kpc, see Paper I), the ratio is very high due to near total lack of HCN.

Figure 22: Detail of Fig. 21 showing the CO to HCN intensity/luminosity within the galactic bulge of NGC 1068 (a second order polynomial fit is shown). It is seen here that the relative HCN abundance continues to increase within the inner radius ( 1 kpc) of the star forming ring, perhaps supporting the results of Curran et al. (2001a) who suggest that HCN abundances may not be the best tracer of star-burst activity.

we find that, while the HCN/CO ratio is high within the star-forming region, the ratio keeps increasing within this radius: In AGN the growth of the central super-massive black hole is regulated by the ongoing star-burst with which it competes for the in-flowing material. While the presence of a star-burst will restrict feeding to the black hole, there is expected to be an inner limit to the proximity of this star formation, since tidal effects will exert shear on the parent gas clouds, tearing them apart (e.g. the inner limit for a molecular cloud of density 10⁴  $\hbox{{\rm cm}}^{-3}$ approaching a $10^8~M_\odot$  black hole is 55 pc, Lang 1980; Maiolino & Rieke 1995). As well as this, ionising radiation from the black hole will hinder star formation in molecular clouds (Silk & Rees 1998). For example, in NGC 7214 the star formation rate is found to increase with distance from the nucleus (Radovich et al. 1998) and in Circinus the star-burst is seen to occur at $\sim$200 pc from the nucleus (e.g. Marconi et al. 1994), while in the star-burst galaxy NGC 253, the nucleus is apparently dominated by stars (Ulvestad & Antonucci 1997; Vogler & Pietsch 1999). In this, and all galaxies, a super-massive black hole may also exist, although the presence of stars close to this may still be permitted due to the low activity of the black hole (no mega-masers are observed, see Curran 2000b), which could be the consequence of a low feeding rate (Bryant & Hunstead 1999). For example, although such a black hole is believed to be present in the Galactic centre (e.g. Kormendy & Richstone 1995), young stars are observed very close to this (e.g. Okuda et al. 1990; Nagata et al. 1990; Nagata et al. 1995).

Finally, from Table 2 and Fig. 21, we see again that contamination by CO in the disk is indeed an issue, although from the average value of $L_{\rm CO}/L_{\rm HCN}$over the HCN map (Table 2) we can see that any such contamination which may exist in the distant sample is still not sufficient to bring a similar average luminosity ratio between the two samples.

3.2 Differences between the near-by and distant samples

Previously, we suggested this difference in the luminosities could be due to a selection effect, i.e. we only detect the FIR bright galaxies at these distances (corresponding to  km s^-1) and so the distant sample may be intrinsically different, not only in its FIR and molecular gas luminosities, but in gas distributions to the near-by sample. Now that we have complete CO luminosity values for the near-by sample, we can say that this certainly seems to be a possibility. That is, that in order to produce the high HCN/CO ratios in the distant sample we could have relatively little disk contamination, at least in relation to the HCN which seems to be considerably more extended than previously thought (Sect. 1).

Figure 23: $\log L_{\rm CO}/L_{{\rm FIR}}$ [ ${\rm K ~km~s}^{-1}~{\rm kpc}^2~{L}_{\odot}^{-1}$] versus $\log L_{{\rm FIR}}$ [ ${L}_{\odot }$].

Returning to the ratios, we see a decrease of relative CO luminosity with FIR luminosity (Fig. 23) which implies, not only that the distant sources are more FIR bright (Sect. 1), but that this is in excess relative to CO. This could arise either from young stars and/or the AGN, both of which we would expect to also be traced by the HCN (Curran et al. 2001a).

In the former situation we would expect the $L_{\rm FIR}/L_{\rm HCN}$ratio to be fairly independent of the FIR luminosity of the galaxy and in the latter we might expect this ratio to increase (see Curran et al. 2000), i.e. a further FIR contribution than that of the star formation. Plotting the $L_{\rm HCN}/L_{\rm FIR}$ ratio versus $L_{\rm FIR}$ (Fig. 24) we see that the HCN/FIR ratio may well decrease with the FIR luminosity, perhaps indicating that the latter scenario may be the case. Although, as well as the elevated FIR emission due to the accumulation of HCN towards the nucleus (as opposed to star forming regions), the HCN luminosity may also increase accordingly (Curran et al. 2001a and references therein), although Fig. 21 suggests that while the HCN/CO ratio is as high as that of ULIRGs over the region of enhanced star formation, there exists excess HCN at smaller radii, indicating correspondingly higher FIR luminosities at these radii. So rather than a matter of relative luminosities, the question becomes a matter of distribution: How much dense gas/FIR emission arises from the nucleus with respect to the 100 pc-scale star forming ring (Curran 2000b and references therein)?

From Figs. 19 and 20 there appears to be no FIR to HCN excess in comparison with normal spirals and ULIRGs (Solomon et al. 1992).

Figure 24: $\log L_{\rm HCN}/L_{{\rm FIR}}$ [ ${\rm K ~km~s}^{-1}~{\rm kpc}^2~{L}_{\odot}^{-1}$] versus $\log L_{{\rm FIR}}$ [ ${L}_{\odot }$]. As in Curran et al. (2000) the least squares linear fit is shown.

This may be caused by the possibility that both the FIR and HCN emission could come from stars and material surrounding the central engine. In an attempt to distinguish between these two sources of radiation, we note:

1.

From above, $\frac{L_{\rm FIR}}{L_{\rm HCN}}(\tiny {\rm distant}\normalsize )\approx2\frac{L_{\rm FIR}}{L_{\rm HCN}}(\tiny {\rm near-by}\normalsize )$, giving a FIR excess in the distant sample;

2.

From Fig. 23 we note an excess of FIR in comparison to CO emission in the distant sample. In order to approximately quantify this:

a.

From Fig. 18 and Paper I we find $\frac{L_{\rm HCN}}{L_{\rm CO}}(\tiny {\rm distant}\normalsize )\mathrel{\mathch... ...>\cr\sim\cr}}}}2\frac{L_{\rm HCN}}{L_{\rm CO}}(\tiny {\rm near-by}\normalsize )$ i.e. also an excess of HCN emission in the distant sample.

b.

Multiplying this with the previous equation gives $\frac{L_{\rm FIR}}{L_{\rm CO}}(\tiny {\rm distant}\normalsize )\mathrel{\mathch... ...>\cr\sim\cr}}}}4\frac{L_{\rm FIR}}{L_{\rm CO}}(\tiny {\rm near-by}\normalsize )$.

This is a very rough calculation which assumes an average distant source compared to an average near-by source and the value is probably considerably greater than 4 (i.e. $\approx$10, Tables 3 and 5 of Paper I). It does show, however, that both HCN and FIR are in excess in the distant sample but that the FIR increases more rapidly than the HCN luminosity with the FIR output of the galaxy. Why should this be if the HCN and FIR are signatures of both star and nuclear activity? One possible answer could be that while both the line and thermal emission arise from cloud cores and nuclear gas, the beam-filling in the latter would be considerably less than in the more widely distributed HCN associated with star formation (Helfer & Blitz 1993; Sternberg et al. 1994; Helfer & Blitz 1995; Tacconi et al. 1998). Since the FIR radiation actually originates from re-radiation by the dust grains (e.g. Rees et al. 1969; Rieke 1978; Lebofsky & Rieke 1980), we expect this to be a lot more isotropic and therefore not so seriously affected by the beam-filling.

3.

Applying this argument to the results of Curran et al. (2001a):

a.

Both NGC 4945 and Circinus are well known for their vigorous star-burst activity (e.g. Harnett et al. 1990; Dahlem et al. 1993; Moorwood et al. 1996; Siebenmorgen et al. 1997; Oliva et al. 1999; Viegas et al. 1999), and lie close to the other weaker (near-by) galaxies in Figs. 23 and 24, perhaps suggesting that such Seyfert/star-burst activity may be fairly typical for the near-by sources. However, while in the literature we can find a reference to star-burst activity in each near-by source, we can also find such references for the distant sample;

b.

Note that in Fig. 18 Circinus exhibits a definite HCN deficiency (compared to the rest of the sample) and that from Curran et al. (2001a), $\frac{L_{\rm FIR}}{L_{\rm HCN}}(\tiny {\rm NGC~4945}\normalsize )\approx0.4\frac{L_{\rm FIR}}{L_{\rm HCN}}(\tiny {\rm Circinus}\normalsize )$.

This apparently contradicts point 2 (above) since Curran et al. (2001a) believe that NGC 4945 has greater Seyfert activity and therefore should have more FIR in comparison to HCN emission. The discrepancy is perhaps due to the possibility that not all of the FIR radiation has been sampled in NGC 4945 (Forbes & Norris 1998) but also, with regard to point 2, that both the galaxies are considerably closer ( times) than the distant sample. That is, the central HCN does provide ample beam-filling, although this would be confused with HCN in the star forming rings (Bergman et al. 1992; Dahlem et al. 1993; Marconi et al. 1994; Curran et al. 1998).

Note that for Figs. 23 and 24, the errors (Paper I) as well as variance in the sample could produce an apparent correlation since we are plotting x/y versus x. This emphasises the uncertainties in these results making the above points highly speculative. The real solution to the question of relative star-burst/AGN contribution is discussed in Sect. 4.

3.3 Differences in the dense gas between type 1 and type 2 Seyferts

Previously (Curran 2000a), we found for the distant sample that both the main Seyfert classes had on average similar abundances of molecular gas, i.e.

$$\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}2)\approx\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}1)$$ (1)

$\sim$10 $^{-8}{\rm ~K~ km~s}^{-1}{\rm ~kpc}^2~{L}_{\odot}^{-1}$, for all of the sample. However, this result was not so certain with the possibility that

$$\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}2)>\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}1),$$ (2)

which supports the results of Heckman et al. (1989), who find a significant difference in molecular gas abundances between the two main Seyfert classes. However, note that Eq. (1) supports the results of Maiolino et al. (1997) and their sample corresponds to our distant galaxies (i.e. none with v<4000 km s^-1). When we re-examine our results by adding the global $L_{\rm CO}$values for the near-by sample, we find that

$$\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}2)\approx\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}1)$$ (3)

$\approx$ $3\times10^{-8}{\rm ~K~ km~s}^{-1}{\rm ~kpc}^2~{L}_{\odot}^{-1}$, i.e. there is no significant difference in molecular gas abundances between the two main Seyfert classes.

In order to ascertain the implications of this result, i.e. if the fluxes could be of different origins between the two classes, we looked at the HCN/FIR (as well as the CO/HCN) luminosity ratios between the classes. From this it became clear, however, that we would have to consider the distinction between the distant and near-by samples, e.g. obtaining an average of $L_{\rm CO}/L_{\rm HCN}$ for one of the Seyfert classes, irrespective of distance, would give a standard deviation which was nearly as large as the average value. Hence further statistics became meaningless, i.e. we have only 3 detections of HCN in Sy1s (Curran et al. 2000), one of which is in the near-by sample (NGC 6814). This analysis emphasised that although Eq. (3) is valid in that it still holds, there is little point in assigning an average value between the distant and near-by samples, which are evidently quite different. So all we are justified in stating is that

$$\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}2)\approx\frac{L_{\rm CO}}{L_{\rm FIR}}({\rm Sy}1)$$ (4)

$\approx$ $1.6\times10^{-8}{\rm ~K~ km~s}^{-1}{\rm ~kpc}^2~{L}_{\odot}^{-1}$ for v>4000 km s^-1, and that it is clear that statistics will have to be very much improved in order to determine if the relative HCN luminosities vary between the two main Seyfert classes. Note that, from the distribution of the number of sources binned according to the flux, Thean et al. (2001) find, on the whole, that Sy2s are marginally more likely to have stronger 60 $\mu$m infrared emission than Sy1s, perhaps suggesting a more dominant starburst contribution in the former.

3.4 Sub-thermally excited CO

Only for four of the galaxies (NGC 1365, NGC 5548, Circinus and NGC 7172) does the CO  $2\rightarrow 1/1\rightarrow 0$ ratio appear to be (Table 3). So for most of the sample the CO emission seems to be sub-thermally excited, indicating densities below cm^-3. This belies the bright HCN emission emerging from several of these objects, e.g. NGC 0034, which suggests gas densities cm^-3. This discrepancy could be resolved if the CO $1\rightarrow 0$ source size is larger than that of the CO $2\rightarrow 1$, so that regions of sub-thermally excited emission lie outside (at larger radii) those of bright HCN emission, leaving the CO $2\rightarrow 1$source size closer to that of the HCN  $1\rightarrow 0$, although we see from Table 1 that this doesn't appear to be the case. This would also mean that a pointing error would be more serious in the $2\rightarrow 1$ transition due to the smaller beam and (perhaps) source size. Another possibility is that there is perhaps a mixture of low and high density gas in the inner region, causing a large filling factor of diffuse, unbound low density gas embedding clumps of higher density gas. Models on the production of such a medium have been discussed by Jog & Das (1992). In order to check this, high resolution, multi-transitional observations of CO combined with further studies of the emission from high density tracer molecules are necessary, although cases of sub-thermally excited CO emission from luminous mergers have been discussed before (e.g. 1992; Aalto et al. 1995). For ULIRGs the situation is even less clear: Many seem to have very sub-thermal global CO  $2\rightarrow 1$/ $1\rightarrow 0$ line ratios although we believe that the CO emission is very concentrated (i.e. no extended disk distribution). For these the idea of a diffuse, low density inter-cloud medium will work very well, thus being both under high pressure and hot, the CO $2\rightarrow 1$/ $1\rightarrow 0$ line ratio will still be low due to low densities and large velocity gradients.