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In this work we examine the physical conditions of the global molecular gas reservoir in the host galaxies of Seyfert nuclei. The prime motivation is to examine if there are any large scale differences among the two types of Seyferts and whether the observed larger star formation rate in the host galaxies of type 2 Seyferts is also accompanied by a systematically larger molecular gas reservoir. Since starburst activity is expected to influence the state of the molecular gas and hence have an effect on outcome of the different methods used to derive its mass, we also conducted a multi-transition study of the inner starburst region of the archetypal Seyfert 2 galaxy NGC 1068.

For the statistical part of our study we acquired sensitive 12CO, 13CO, J=1--0, J=2--1 observations and collected available data from the literature for a sample of 27 Seyfert galaxies. We find that Seyferts have average 12CO/13CO J=1--0 and J=2--1 line ratios of R_{10}=12 and R_{21}=13 respectively, with no discernible dependence on the Seyfert type.

The r_{21}=(2--1)/(1--0) line ratio for 12CO does not reveal any significant difference between the two types but Seyferts as a class seem to have systematically lower values of r_{21}(=0.5-0.7) than average spirals and starbursts. Moreover for all the galaxies examined, but especially for Seyferts and starbursts, we find that r_{21} is likely to be smaller as the area of the galaxy sampled by the telescope beam becomes larger. This is interpreted as the consequence of a global gas excitation gradient in galaxies where warm (T_{kin}>= 20K) gas lies confined in their central regions (<=1 kpc) while a colder (T_{kin}<= 10 K), and/or sub-thermally excited gas phase dominates the more extended CO emission in the disk. For Seyferts and starbursts we find that this gas excitation gradient may be quite similar.

We also present fully sampled 12CO, 13CO J=2--1, 3--2 maps of the inner 1' x 1' region of NGC 1068 and combine these measurements with an interferometric map of 12CO J=1--0 that includes single dish data and hence recovers all the flux present. This allows a reliable estimate of the 12CO (J=3--2)/(J=1--0) ratio at the highest angular resolution currently possible and the use of this sensitive line ratio to probe the physical condition of the molecular gas. We also obtained interferometric maps of the 13CO, C18O J=1--0 and two single-dish measurements of the C18O J=2--1~transitions.

The observed line ratios suggest a two-component gas phase being present in the starburst region of NGC 1068. The one component is diffuse, warm (T_{kin} > 35 K) and not virialized, with moderate 12CO J=1--0 optical depths (tau = 1-2) and dominates the 12CO emission. The other component is more spatially concentrated and dense, contains the bulk of the molecular gas mass, and is very likely virialized. In this phase the rarer isotopes 13CO, C18O have significant optical depths (tau > 1).

The usual way of estimating molecular gas mass is from the 12CO J=1--0 luminosity and a standard galactic conversion factor. This may overestimate the gas mass present if the gas phase dominating the emission of 12CO is not virialized. Hence, earlier suggestions that the larger 12CO J=1--0 luminosity of Seyfert 2 with respect to Seyfert~1 galaxies means a correspondingly larger molecular gas mass must be viewed with caution. Indeed the reported differences in the CO luminosity between the two Seyfert types can be readily attributed to the presence of warmer and possibly non-virialized gas in type 2 more often than in type 1 rather than to a difference in total molecular gas mass.

On the other hand deducing molecular gas mass from 13CO under the assumption that this isotope has small/moderate optical depth may significantly underestimate the gas mass present since much of this gas mass may be contained in the dense gas phase where 13CO can have substantial optical depth.