5 Conclusions

1.

Maps of the central arcmin of the starburst galaxies NGC 6946 and NGC 5236 (M 83) in various transitions of ¹²CO and ¹³CO, and in [CI] confirm the compact nature of the central molecular gas emission in both galaxies. Most of this gas is within a few hundred parsec from the nucleus. Major-axis position-velocity diagrams show that in both galaxies the circumnuclear molecular gas is in very rapid solid-body rotation. The steepness of the velocity gradient only becomes apparent at the higher spatial resolutions;

2.

Relative ¹²CO, ¹³CO and C^o line intensities observed in matched beams are virtually identical in NGC 6946 and M 83, although the [CII] line intensity in the literature is much stronger by a factor of 7 in M 83. Spatially integrated line intensity ratios do not differ much from those obtained in the central 21'' beam, except for [CI] which is either more strongly concentrated towards the nucleus than CO or insufficiently mapped;

3.

The velocity-integrated ¹²CO intensities in both galaxies decrease only slowly with increasing rotational level. The intensities in the J=1-0, J=2-1, J=3-2 and J=4-3 transitions are in the ratio of 1:1:0.65:0.45 respectively. Both galaxies have observed ¹²CO/¹³CO isotopic ratios of about 11, 9.5 and 12.5 in the first three transitions;

4.

The intensity of the neutral carbon line at 492 GHz relative to J=2-1 (and J=1-0) ¹²CO is about 0.2 in both galaxy centers. The relative intensity of the ionized carbon line is 0.08 for NGC 6946 and 0.55 for M 83;

5.

The resemblance of the relative CO line intensities suggests that the dense interstellar medium in both galaxies is very similar. However, the great difference in [CII] intensities shows that a reliable picture is only obtained by observing and modelling both atomic carbon and carbon monoxide lines;

6.

Modelling of the observed line ratios suggest a multi-component molecular medium in both galaxies. In NGC 6946, a dense component with $n(\h2) \approx$ 0.3-1.0  $10^{4} \,{\rm cm^{-3}}$ and $T_{\rm kin} \approx$30 K is present together with a significantly less dense $n(\h2) \approx$ 0.5-1.0  $10^{3} \,{\rm cm^{-3}}$ and hotter $T_{\rm kin} \approx 100$-150 K component. Atomic carbon column densities appear to be about 1.5 times the CO column density. The gas in M 83 may likewise be approximated by two similar components.The denser is both somewhat less dense ( $n(\h2) \approx 0.3 ~ 10^{4} \,{\rm cm^{-3}}$) and somewhat hotter ( $T_{\rm kin} = 60$ K) than its counterpart in NGC 6946. The more tenuous component is practically identical to its counterpart in NGC 6946. M 83 is more affected by CO dissociation, as its atomic carbon to CO ratio is about four. In both starburst centers, most of the molecular mass (about two thirds) is associated with the PDR hot, relatively tenuous phase. In M 83, a significant molecular gas volume must be associated with ionized carbon rather than CO;

7.

With an estimated gas-phase [C]/[H] abundance of 4 10^-4, the centers of NGC 6946 and M 83 contain almost identical total (atomic and molecular) gas masses of about 3 10⁷ $M_{\odot}$ within R = 0.3 kpc. Peak face-on gas mass densities are, however, rather different: typically 45 $M_{\odot}$ pc^-2 for NGC 6946 and almost three times higher, 115 $M_{\odot}$ pc^-2 for M 83. The central molecular concentration in M 83 is denser and hotter than the one in NGC 6946.

Acknowledgements

We are indebted to Ewine van Dishoeck and David Jansen for providing us with their detailed radiative transfer models and to Paul van der Werf for his willingness to reanalyse the ISO $\h2$ measurements within the context of our results. Fabienne Casoli kindly supplied us with an IRAM J=2-1 ¹²CO map for comparison with our data. We thank the JCMT personnel for their support and help in obtaining the observations discussed in this paper.