2 Results

   
2.1 HCN and CO  $\mathsfsl{1}\rightarrow\mathsfsl{0}$ distribution in the near-by sample

In this section we refer to the spectral maps shown in Figs. 1 to 6 of Paper I, which we show, as well as the CO  $2\rightarrow 1$ maps, here as contour plots (Figs. 1 to 17). We also describe the gas distribution in individual sources and then we summarise the gas distribution trends.

   
2.1.1 NGC 1068

Although fairly confined ( $\Theta_{\rm CO~1\rightarrow0}\approx$HPBW), there is still significant amounts of CO emission at map positions adjacent to the central position, although most of the CO emission is within one 44'' beam from the centre ( $\pm3$ kpc). The HCN shows a similar distribution although the emission in the adjacent positions is more marginal.

Even though it is faint (Paper I), CO is still detected out to $\approx$15 kpc from the nucleus thus extending much farther than the HCN (Fig. 21).

Figure 1: Contour map of CO  $1\rightarrow 0$ in NGC 1068. The levels are up to 75 K km s-1 in steps of 15 K km s-1. Here and in all the contour maps the integrated intensities are uncorrected for beam efficiencies and the observed grid points are shown.

Figure 2: Contour map of CO  $2\rightarrow 1$ in NGC 1068. The levels are up to 66 K km s-1 in steps of $\approx$13 K km s-1.

Figure 3: Contour map of HCN  $1\rightarrow 0$ in NGC 1068. The levels are up to 7 K km s-1 in steps of $\approx$1.2 K km s-1.

2.1.2 NGC 1365

Like NGC 1068, we find $\approx$80%-90% of the CO emission to be confined within one 34'' beam from the centre, i.e. $\approx$$\pm3$ kpc (Sandqvist et al. 1995), probably in the molecular ring (Sandqvist 1999).

Figure 4: Contour map of CO  $1\rightarrow 0$ in NGC 1365. The levels are up to 66 K km s-1 in steps of 11 K km s-1.

Figure 5: Contour map of CO  $2\rightarrow 1$ in NGC 1365. The levels are up to 72 K km s-1 in steps of $\approx$14 K km s-1.

Figure 6: Contour map of HCN  $1\rightarrow 0$ in NGC 1365. The levels are up to 4 K km s-1 in steps of $\approx$0.7 K km s-1.

The HCN results are very interesting in that, despite the fact that this molecule is expected to be confined to within $\approx$1 kpc (Sect. 1), we detected it out to map position (34'',68''), i.e. at $\approx$5 kpc, Fig. 7, and obtain a source size of $\approx$$\pm2$ kpc (Table 1).

Figure 7: HCN $1\rightarrow 0$ at (34'',68'') in NGC 1365. The velocity resolution is 80 km s-1 and the moment and baseline boxes used to determine the main-beam integrated intensity of $2.7\pm 0.7$ K km s-1 are shown. Note that no other HCN was detected at these distances (we mapped to $128''\times 128''$).

This map position is actually located very close to the major axis of the radio and molecular rings, i.e. at $30^{\circ}$ (Sandqvist et al. 1995; Sandqvist 1999). It should be noted that no detection was made towards the corresponding position in the SW ( $210^{\circ}$), and the CO and radio emission does appear to be stronger towards the NE (Sandquvist et al. 1995, Paper I)

Our result implies that there is a significant disk contribution to both the CO and the HCN luminosity, but the CO disk is much more extended.

2.1.3 NGC 2273

We find the CO emission to be fairly confined; $\approx$60% of the emission lies within the central beam ($\pm4$ kpc), which is not surprising as this is the most distant galaxy of the near-by sample.

Figure 8: Contour map of CO  $1\rightarrow 0$ in NGC 2273. The levels are up to 2.3 K km s-1 in steps of $\approx$0.4 K km s-1.

Our results imply that there is some disk contribution to the CO luminosity and so we expect the global HCN to CO line ratio to be affected by disk contamination.

   
2.1.4 NGC 4945

The CO and HCN may (see Sect. 2.1.8) have similar, and relatively small, source sizes (consistent with the results of Sandqvist Henkel et al. 1994), probably corresponding to the $r\approx300$ pc ring of Bergman et al. 1992 (1992; Dahlem et al. 1993.

Figure 9: Contour map of CO  $2\rightarrow 1$ in NGC 4945. The levels are up to 370 K km s-1 in steps of $\approx$62 K km s-1. Because of the added position angle to the CO  $1\rightarrow 0$ data of Dahlem et al. (1993) it was impossible for us to plot this as a contour plot, which can, however, be seen in their article.

Figure 10: Contour map of HCN  $1\rightarrow 0$ in NGC 4945. The levels are up to 18 K km s-1 in steps of 3.6 K km s-1.

There is a large-scale CO disk in this galaxy (Dahlem et al. 1993) which will also significantly affect the global CO/HCN luminosity ratio.

2.1.5 NGC 5033

In the nearest galaxy of the original sample (Heckman et al. 1989; 2000), the CO appears to be quite extended and only about 10% of the emission is in the central beam (Paper I). The optical disk of the galaxy is very extended and it is possible that the structure seen in our CO map (Fig. 11) is due to spiral arms or other features. Approximately $50\%$ of the HCN emission is confined within the central beam and its structure is dramatically distinct from any other galaxy in our sample; it appears that the HCN is located in a bar (Fig. 12).

Figure 11: Contour map of CO  $1\rightarrow 0$ in NGC 5033. The levels are up to 20 K km s-1 in steps of 5 K km s-1.

Figure 12: Contour map of HCN  $1\rightarrow 0$ in NGC 5033. The levels are up to 1.3 K km s-1 in steps of $\approx$0.1 K km s-1.

NGC 5033 is a likely example where the disk contribution could dramatically affect the global HCN/CO luminosity ratio.

2.1.6 Circinus

As in the case of NGC 4945, the CO and HCN may (see Sect. 2.1.8) share similar source sizes ([ $r\approx300$ pc, corresponding to the molecular ring of Curran et al. 1998).

Figure 13: Contour map of CO  $1\rightarrow 0$ in Circinus. The levels are up to 80 K km s-1 in steps of $\approx$13 K km s-1. Note the extension of the emission towards the SW in this and Fig. 14, where this portion of the molecular ring (Curran et al. 1998) is $\approx$1.4 times more luminous than the NE portion (Curran 1998) corresponding to enhanced star formation (Marconi et al. 1994; Marconi et al. Curran 2000).

Figure 14: Contour map of CO  $2\rightarrow 1$ in Circinus. The levels are up to 78 K km s-1 in steps of 13 K km s-1.

Figure 15: Contour map of HCN  $1\rightarrow 0$ in Circinus. The levels are up to 5.5 K km s-1 in steps of 1.1 K km s-1. Like Figs. 13 and 14 this also shows an extension of emission towards the SW.

The contour maps show that there is significant disk contribution to the CO luminosity which will cause the HCN to CO luminosity ratio to decrease with increasing radius.

   
2.1.7 NGC 6814

While there are significant amounts of CO located away from the central beam, most of the emission is confined within the adjacent map positions. Only $\approx$30% of the HCN is located within the central beam, and in fact there could be significant emission at 6 kpc (to the east) from the centre. Due to the incomplete map (Paper I) we were unable to produce a contour plot for this molecule.

Figure 16: Contour map of CO  $1\rightarrow 0$ in NGC 6814. The levels are up to 4.7 K km s-1 in steps of $\approx$0.9 K km s-1.

Figure 17: Contour map of CO  $2\rightarrow 1$ in NGC 6814. The levels are up to 2.3 K km s-1 in steps of $\approx 0.4$ K km s-1.

   
2.1.8 Source size fittings

The source sizes were measured assuming that the source distribution on the sky is Gaussian and deconvolving the telescope response (HPBW) from the full-width half-maximum (FWHM) diameter (see Paper I). It should be noted that the source size concept could be misleading here: The source sizes may seem similar because all galaxies have bright CO emission coming from their centres, thus causing the source size fits to look the same for HCN and CO $1\rightarrow 0$. Additionally, for many galaxies (like NGCs 4945 and 5033) there is low level disk emission (which is sub-thermally excited) which will contribute significantly to the luminosity, but only little to the source size fit. We show the fitted source sizes for the different transitions in Table 1.

 

 

Table 1: Source sizes of the various transitions in the sample expressed as diameters [kpc]. ^*All the values for NGCs 2273 (uncertainty $\sim$100% in CO; HCN was not detected, Paper I), 5033 and 6814 are estimated from the total cf. the average luminosities, as is the HCN value in Circinus (Paper I). Because of the relatively dense map spacing we can include values for CO  $2\rightarrow 1$ in NGC 4945 and Circinus although again these may be misleading (expected to be larger than HCN $1\rightarrow 0$) due to the CO $2\rightarrow 1$ beam being that much smaller.

Galaxy	$\Theta_{\rm HCN}$	$\Theta_{\rm CO~1\rightarrow0}$	$\Theta_{\rm CO~2\rightarrow1}$
NGC 1068	$\approx$2-4	3.0	-
NGC 1365	$\approx$4	4.5	-
NGC 2273	?	$\sim$7*	-
NGC 4945	0.5	0.5	0.4
NGC 5033	$\sim$2*	$\sim$2*	-
Circinus	$\approx$0.8*	0.8	0.6
NGC 6814	$\approx$3.5*	$\approx$4*	-

   
2.1.9 Summary

In general we see that the HCN is rarely confined to 1 kpc in the FIR weak (near-by) galaxies (Paper I and Table 1) although it does appear to be more concentrated towards the nucleus than the CO (Table 2), thus indicating significant CO contamination in the galactic disk.

 

 

Table 2: The approximate CO/HCN luminosity ratios for the near-by sample over the telescope beam (i.e. as in Curran et al. 2000), over the HCN map and over the full CO mapped region.

Galaxy	$L_{\rm CO}/L_{\rm HCN}$
	Beam	HCN Map	CO Map
NGC 1068	8	9	20
NGC 1365	11	11	19
NGC 2273	5	-	-
NGC 4945	13	20	35
NGC 5033	7	12	27
Circinus	15	33	45
NGC 6814	9	12	12
Average	9	16	26

Returning to Section 1, we can rule out the first option, i.e. that we had previously sampled most of the CO in the near-by sample, and attribute our previous results to points 2 and 3 (addressed in Sect. 2.2).

   
2.2 Luminosity ratios

In order to simultaneously analyse the two samples, in the following we use the full map (global) values (last column Table 2) for the near-by sample and the central beam values, which are analogous to these, for the distant galaxies.

Figure 18: $\log L_{{\rm CO}}$ versus $\log L_{\rm HCN}$ (units as in Fig. 5 of Curran et al. 2000 i.e. $\times 10^{3}$ K km s-1 kpc2) for all the detections. From these we obtain a mean fitted ratio of $L_{\rm CO}/L_{\rm HCN}=10^{+9}_{-10}$and using only sources with  km s-1, we obtain a ratio of $L_{\rm CO}/L_{\rm HCN}=20^{+40}_{-10}$.

As in Curran et al. (2000), in Figs. 18 and 19 we plot $\log L_{{\rm CO}}$ and $\log L_{{\rm FIR}}$ against $\log L_{\rm HCN}$for all of the sample. Unlike previously, where we obtained $L_{\rm CO}/L_{\rm HCN}\approx6$ for all of the detections and using only sources with  km s^-1, we find a definite difference between the distant and near-by samples, i.e. $L_{\rm CO}/L_{\rm HCN}=6\pm2$ (distant) and $L_{\rm CO}/L_{\rm HCN}=22\pm4$(from Paper I and Table 2). In fact all of the  km s^-1 sources lie to the left, above the fitted mean ratio line and, with the exceptions of NGCs 5135 (v=4112 km s^-1) and 7130 (v=4842 km s^-1), the  km s^-1 sources lie to the right, below the line, Fig. 18.

Figure 19: $\log L_{{\rm FIR}}$ [ ${L}_{\odot }$] versus $\log L_{\rm HCN}$ [K km s-1 pc2] for all the detections.

Again (Curran et al. 2000), in order to determine the far infrared/HCN luminosity correlation, i.e. compare our results with those of Solomon et al. (1992), we plotted $\log L_{{\rm FIR}}$ against $\log L_{\rm HCN}$, for all of the sources, Fig. 19. Once again we see that we obtain a fairly linear (on a log-log plot) relationship between the FIR and the HCN luminosities and from this we determine $L_{\rm FIR}\approx500\tiny\begin{array}{c}{+400}\\ {-200}\end{array}\normalsize L_{\rm HCN}~{L}_{\odot}({\rm K ~km~s}^{-1}~{\rm pc}^2)^{-1}$(cf. $\approx600\tiny\begin{array}{c}{+600}\\ {-300}\end{array}\normalsize L_{\rm HCN}~{L}_{\odot}~({\rm K ~km~s}^{-1}~{\rm pc}^2)^{-1}$previously). For the near-by and distant sources we obtain $L_{\rm FIR}\approx350~L_{\rm HCN}~{L}_{\odot}$ and $L_{\rm FIR}\approx600L_{\rm HCN}~{L}_{\odot}~({\rm K ~km~s}^{-1}~{\rm pc}^2)^{-1}$, respectively, suggesting additional FIR flux over and above that associated with the denser molecular gas in the distant sample. All of the near-by sources except NGC 1068 and Circinus lie below the line, i.e. like the distant sample, these two galaxies exhibit an excess in FIR compared to HCN. This also holds when, in order to account for the distances and the extents in our sample Solomon et al. (1992; Curran et al. 2000), we plot $L_{\rm FIR}/L_{\rm CO}$ against $L_{\rm HCN}/L_{\rm CO}$, Fig. 20.

Figure 20: $\log L_{{\rm FIR}}$ [ ${L}_{\odot}({\rm K~km~s}^{-1} {\rm pc}^2)^{-1}$] versus $\log L_{\rm HCN}$ normalised by the CO luminosity for all the detections [no units]. From this fit we also find $L_{\rm FIR}\approx500 L_{\rm HCN}~{L}_{\odot}({\rm K ~km~s}^{-1} {\rm pc}^2)^{-1}$.

From this, however, we see a large change in the position of NGC 4945 relative to Circinus in the figure. As suggested by Forbes & Norris (1998), this may indicate that not all of the FIR in NGC 4945 was sampled by Rice et al. (1988), although the shift in position for this galaxy does not appear to cause an abnormal deviation from the fit defined by the other Seyferts. We discuss the various luminosity relationships further in Sect. 3.2.

   
2.3 CO  $\mathsfsl{2}\rightarrow\mathsfsl{1}$/CO  $\mathsfsl{1}\rightarrow0$

In Table 3 we present the CO $2\rightarrow 1/1\rightarrow 0$luminosity ratio for the Southern sources in which we could

 

 

Table 3: The global CO $2\rightarrow 1/1\rightarrow 0$ luminosity/integrated intensity ratios (^*and those estimated from the radio continuum) compared with the integrated intensity ratios of Papadopoulos & Seaquist (1998) (PS98). The final column refers to the radius of the projected CO $1\rightarrow 0$ SEST beam.

Galaxy	Ratio	cf. PS98	R [kpc]
NGC 0034	0.45*	$0.8\pm0.1$	8.6
NGC 1068	$0.7\pm0.1$	$1.1\pm0.2$	1.6
NGC 1365	$\approx$1.1/0.8*	$0.55\pm0.09$	2.4
NGC 4945	$\approx$0.4	-	0.8
NGC 4593	0.6*	-	3.9
NGC 5135	0.7*	$0.85\pm0.15$	6.0
NGC 5548	0.73-2.9*	-	7.5
Circinus	$\approx$1.3	-	0.9
NGC 6814	$0.45\pm0.1/0.54^*$	$0.6\pm0.1$	2.3
NGC 7130	0.6*	$0.5\pm0.1$	7.0
NGC 7172	0.8*	-	3.8

simultaneously observe the CO $2\rightarrow 1$ and $1\rightarrow 0$lines. For the distant sources (NGCs 0034, 4593, 5135, 5548, 7130 and 7469) we could not map the CO $2\rightarrow 1$ emission, and therefore have no direct information on the CO source sizes. To estimate the line ratios we have therefore used the suggested correlation between the (low frequency) radio continuum and molecular gas distribution (e.g. Allen 1992; Bajaja et al. 1995). We found radio continuum images for 7 of the sample galaxies and used these to make estimates of the CO source sizes (see Appendix A of Curran et al. 2000b for details).

On the whole, our results seem consistent with those of Papadopoulos & Seaquist (1998), except in the cases of NGCs 0034 and 1365. In the former galaxy, when we look at the main beam brightness temperatures of Papadopoulos & Seaquist (1998), we see that they obtain $\approx$10 mK for CO $1\rightarrow 0$ in a 55'' beam and $\approx$7 mK in a 9 point grid map which convolves the 32'' $2\rightarrow 1$ beam to the $1\rightarrow 0$ beam size. At the distance of NGC 0034 these beam sizes correspond to diameters of 21 kpc and 12 kpc for the $1\rightarrow 0$and $2\rightarrow 1$ transitions, respectively. At these linear scales we would be surprised if the molecular gas filled the central beam in this, one of our distant (v=5931 km s^-1) sample galaxies. For a point source the intensity ratio should be divided by a factor of $\left(\frac{230~{\rm GHz}}{115~{\rm GHz}}\right)^{2}=4$ and where the beam is filled no correction is required. So we feel that the Papadopoulos & Seaquist (1998) ratio would be better quoted as 0.2-0.7 (i.e. somewhere between these two cases). The upper value is still consistent with their stated result and it should be remembered that our ratio is merely an estimate from the radio continuum, although it does lie in the range we obtain for the Papadopoulos & Seaquist (1998) result and in the two cases where we do have both CO and radio continuum maps (NGCs 1365 and 6814, Table 3), we find fair agreement in the values. In the case of NGC 1365, we believe that the opposite effect may be the cause of the discrepancy between our ratio and that of Papadopoulos & Seaquist (1998), i.e. that their $\approx$$\pm30''$ beam is insufficient to map all of the CO, which is seen out to (Fig. 2 of Paper I), in this near-by galaxy. Referring to Table 3 of Paper I, we note a CO  $2\rightarrow 1$/ $1\rightarrow 0$luminosity ratio of $0.38\pm0.08$ over the central beam. This is more consistent with Papadopoulos & Seaquist (1998) and (unlike NGC 4945) the increasing CO $2\rightarrow 1$/ $1\rightarrow 0$ratio with galactocentric radius perhaps suggests more vigorous star formation at larger radii (next paragraph).

Note that our two closest examples (which also share similar intrinsic properties, see Curran et al. 2001a), NGC 4945 and Circinus, have the most extreme values (one at either end of the range, Table 3) of global CO  $2\rightarrow 1/1\rightarrow 0$. The $\frac{{\rm CO}~1\rightarrow0}{{\rm HCN}~1\rightarrow0}$ ratio is also significantly higher in Circinus. Comparing the results with those of Curran et al. (2001a) who suggest that star formation may be more dominant in this galaxy, implies that the CO may be excited by large-scale star-burst activity for which the HCN does not necessarily provide a good tracer (Curran et al. 2001a and Sect. 3.2).