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We have used the  X  CO  conversion factor, local thermodynamic equilibrium and large velocity gradient approximation to parametrize the cold and warm phases of the interstellar medium from five different low transitions of the CO molecule in the central 21 arcsec (kpc) region of NGC 1097. We have applied a one‐component model and derived a typical kinetic temperature of about 33 K, a molecular hydrogen density of  4.9 × 10 3  M ⊙  pc −3   and a CO column density of  1.2 × 10 −2  M ⊙  pc −2  . A two‐component model results in 85 per cent cold‐to‐total gas fraction in the presence of a 90 K warm counterpart. Furthermore, we ‘resolve’ the spatially unresolved single‐dish observations by selecting velocity channels that in an interferometric velocity map correspond to specific regions. We have selected five such regions and found that the physical properties in these regions are comparable to those derived from the full line profile. This implies that the central kpc of NGC 1097 is rather homogeneous in nature and, although the regions are not uniquely located within the ring, the star formation along the ring is homogeneously distributed (in agreement with recent  Herschel  observations). We have further revised the mass‐inflow rate on to the supermassive black hole in this prototype low‐ionization nuclear emission‐line region/Seyfert 1 galaxy and found that accounting for the total interstellar medium and applying a careful contribution of the disc thickness and corresponding stability criterion increases the previous estimations by a factor of 10. Finally, we have calculated the  X  CO  conversion factor for the centre of NGC 1097 using an independent estimation of the surface density to the CO emission and obtained  at a radius 10.5 arcsec and  at a radius 7.5 arcsec. With the approach and analysis described in this paper, we have demonstrated that important physical properties can be derived to a resolution beyond the single‐dish resolution element; however, caution is necessary while interpreting the results.

Physical condition of the molecular gas at the centre of NGC 1097