1 Introduction

Activity in galaxies spans from centrally located active galactic nuclei (AGN) to more extended but less powerful starbursts, although in some extreme ultra-luminous infrared galaxies (ULIRGs) the star-powered luminosity may rival that of a compact AGN. Both phenomena appear to be associated with significant amounts of circumnuclear gas and high resolution observations reveal that the HCN, which is much more centralised than the CO, tends to trace gas in the nuclear regions of Seyfert galaxies (e.g. Tacconi et al. 1996; Helfer & Blitz 1997).

Previously, we (Curran et al. 2000) found, from a survey of 20 Seyfert galaxies, an HCN/CO luminosity ratio of $\approx$1/6 for all 13 HCN detections, a ratio similar to that of ULIRGs. We were, however, surprised, to find that such a high HCN/CO luminosity ratio holds for both the "distant'' sources (of recessional velocity  km s^-1, where the beamwidth exceeds $\approx$10 kpc) and the "near-by'' sources (  km s^-1, beamwidth 10 kpc), since we expect a larger CO contribution from the galactic disk in the distant sources, which would result in a lower $L_{\rm HCN}$/ $L_{\rm CO}$ ratio compared to the near-by galaxies.

Since the results of Curran et al. (2000) were based on single-beam observation, at the centre of the source, these results suggested that either:

1.

For the near-by galaxies we have sampled most of the CO in our single beam observation;

2.

The HCN is more extended than the beam in the near-by sources;

3.

Or perhaps the most plausible explanation, simply that the mean luminosity ratio differs between the near-by and distant galaxies.

There may also exist different angular CO distributions between the near-by and distant galaxies, since for the latter sources the high HCN/CO luminosity ratio may suggest that the CO is highly centralised (as is believed to be the case for the HCN; within $\approx$1 kpc, Downes et al. 1992; Nguyen et al. 1992; Tacconi et al. 1996). Interestingly, the mean values of the far infrared luminosities are $L_{\rm FIR}\approx30\times10^{10}~{L}_{\odot}$ and $L_{\rm FIR}\approx2\times10^{10}~{L}_{\odot}$ for the full distant and near-by samples respectively (including the galaxies where Curran et al. 2000 did not detect HCN). In the case of ULIRGs, the higher FIR luminosity ( $L_{\rm FIR}\sim10^{12}~{L}_{\odot}$) is an indicator of a high central CO concentration (Bryant 1997), and the high values of $L_{\rm FIR}$ in our distant sample may also imply a selection effect, in which our distant sources comprise mainly of galaxies suffering from little CO contamination from the galactic disk. It is thus probable that in the distant galaxies we sample the whole CO and HCN. In the near-by sources, however, it is possible that the full distributions are not mapped. In order to account for the limitations of the sampling by our single beam of regions of different linear extent, in Paper I (Curran et al. 2001b) we mapped the distribution of CO and HCN in order to assess the contribution of the galactic disk and to take into account the total molecular gas content of each galaxy.

In this paper we shall use the results presented in Paper I to study the CO to HCN luminosity ratios and compare these with the FIR luminosities: In ULIRGs, the relatively high HCN luminosities are believed to be due to the presence of dense star forming cores (Solomon et al. 1992). However, in the case of Seyferts this excess of (denser) gas traced by the HCN (as well as the excess FIR) may also be due to the accumulation of gas around the active nucleus, terminating in the obscuration (Kohno et al. 1999; Curran et al. 2000), and a large fraction of the gas traced by the CO may act as a resevoir for star formation in Seyferts (Curran 2000a; Curran et al. 2001a). In this paper we shall also discuss the CO  $2\rightarrow 1$/CO  $1\rightarrow 0$ ratios for the Southern sources in which we could observe this higher CO transition with SEST.