6 [CI] and CO column densities

To further investigate the physical conditions characterizing the central gas clouds that give rise to the observed emission, we have plotted for our galaxy sample the [CI]/J=2- $1 {\rm ^{13}CO}$ line intensity ratio versus the [CI]/J=4- $3 {\rm ^{12}CO}$ line ratio. For comparison purposes, we have added points corresponding to a few Galactic starforming regions (White & Sandell 1995; Israel & Baas, unpublished), the N 159/N 160 starforming complex in the Large Magellanic Cloud (Bolatto et al. 2000), and the Milky Way Center (Fixsen et al. 1999). As the latter do not list  ${\rm ^{13}CO}$ intensities, we have assumed a J=2- $1 \, {\rm ^{12}CO}/{\rm ^{13}CO}$ intensity ratio of 8.5, which is the mean value we find for the galaxies observed by us (Israel & Baas 1999, 2001, as well as papers in preparation).

Figure 4: Observed line intensity ratios [CI]/ ${\rm ^{13}CO}$ versus [CI]/CO 4-3 compared to radiative-transfer model ratios at selected gas densities, for a range of temperatures and column densities. All model calculations assume an isotopic ratio $[{\rm ^{12}CO}]/[{\rm ^{13}CO}]$ = 40. Galaxy centers are marked by filled hexagons, LMC star formation regions N 159 and N 160 by open hexagons, Galactic star formation regions W 58 and ON-1 by open triangles and the Milky Way Center by a cross. Lines indicate families of column density ratios N[CI]/N(CO) = 0.1, 0.3, 1 and 3. Within each family, dotted line corresponds to N(CO)/d $V = 3 \times 10^{16} \,{\rm cm^{-2}}/\,{\rm {km\,s^{-1}}}$, solid line to N(CO)/d $V = 1 \times 10^{17} \,{\rm cm^{-2}}/\,{\rm {km\,s^{-1}}}$ and dashed line to N(CO)/d $V = 3 \times 10^{17} \,{\rm cm^{-2}}/\,{\rm {km\,s^{-1}}}$. Temperatures of (from left to right) 150, 100, 60, 30, 20 and 10 K are marked by small open circles on each curve.

To put the observed points in context, we have used the Leiden radiative transfer models to calculate the same line intensity ratio in a grid with gas densities in the range n = 500-10 000 $\,{\rm cm^{-3}}$, kinetic temperatures in the range $T_{\rm kin}$ = 10-150 K and CO column densities N(CO)/dV = 0.3, 1.0 and 3.0 $\times 10^{17}$ $\,{\rm cm^{-2}}/\,{\rm {km\,s^{-1}}}$ respectively. We considered N([CI])/N(CO) abundance ratios of 0.1, 0.3, 1.0 and 3.0 respectively. The results are shown in Fig. 4, always assuming an isotopic ratio $[{\rm ^{12}CO}]/[{\rm ^{13}CO}]$ = 40. Small variations in the assumed isotopic ratio lead to small shifts in the various curves depicted in Fig. 4, mostly along lines of constant temperature.

It is immediately clear from Fig. 4 that the predicted [CI]/ ${\rm ^{13}CO}$ intensity ratio is roughly proportional to the N([CI])/N(CO) abundance ratio at any given gas-density. Variation of the actual CO column density by over an order of magnitude or variation of the gas kinetic temperature has very little effect on the line intensity ratio except at the highest densities and column densities where saturation effects caused by high optical depths become dominant. At given column densities, however, the [CI]/ ${\rm ^{13}CO}$ intensity ratio does depend on the gas-density and is roughly inversely proportional to $\sqrt n$. The [CI]/J = 4- $3\,{\rm ^{12}CO}$ intensity ratio strongly varies as a function of gas kinetic temperature and density, as well as column density.

Further inspection of Fig. 4 shows that the starforming regions in the Milky Way and the LMC are found distributed along curves that mark neutral carbon versus CO abundances N(C$^{\circ}$)/NCO) $\approx$ 0.1-0.3. The galaxy center ratios, in contrast, mostly seem to imply significantly higher neutral carbon abundances. Only the point representing the quiescent bulge of NGC 7331 appears to be associated with an equally low carbon abundance. Depending on the assumed value of the total gas density, centers of quiescent galaxies are associated with carbon abundances N(C$^{\circ}$)/NCO) $\approx$ 0.3 ( $n = 500 \,{\rm cm^{-3}}$) to 1.0 ( $n = 10^{4} \,{\rm cm^{-3}}$). This is consistent with earlier determinations such as N(C$^{\circ}$)/NCO) $\approx$ 0.8 (-0.4, +0.7) for the Milky Way (Serabyn et al. 1994). In contrast, active galaxies have C$^{\circ}$ column densities well exceeding CO column densities independent of the gas parameters assumed. The diagonal distribution of galaxy points roughly follows lines of constant kinetic temperature. The corresponding temperature value varies as a function of density n and column density (N): $T_{\rm kin} > 150$ K for $n = 500 \,{\rm cm^{-3}}$, whereas $T_{\rm kin} = 30$-60 K for n = 0.3- $1.0 \times 10^{4} \,{\rm cm^{-3}}$, $N < 10^{17} \,{\rm cm^{-2}}/\,{\rm {km\,s^{-1}}}$. Only the high-density models imply a kinetic temperature range covering the fairly narrow dust temperature range 33 K $\leq T_{\rm d} \leq$ 52 K characterizing these galaxy centers (Smith & Harvey 1996). This can be taken as a suggestion that at least the molecular carbon monoxide emission from galaxy centers arises mostly from warm, dense gas as opposed to either hot, tenuous gas or cold, very dense gas. Possible exceptions to this are NGC 278 and in particular NGC 7331, M 51 and NGC 4826 which occupy positions in the diagrams of Fig. 4 suggesting low temperatures $T_{\rm kin} = 10$-20 K and consistent with the full density range including the highest densities.

For M 82, Stutzki et al. (1997) estimated from the directly observed $\,{\rm ^{3}P_{2}}$- ${\rm ^{3}P_{1}\,[CI]}/{\rm ^{3}P_{1}}{-}{\rm ^{3}P_{0}\,[CI]}$ line ratio a density $n \geq 10^{4} \,{\rm cm^{-3}}$ and a temperature T = 50-100 K. This is in very good agreement with our estimates. However, the I([CI])/ $I({\rm ^{13}CO})$ ratio of three suggests an abundance N[CI]/N(CO) = 2, i.e. four times higher than estimated by Stutzki et al. (1997), although not ruled out by their results - see also Schilke et al. (1993).