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Physical Condition of Molecular Gas at the Centre of NGC 1097

We have used the Xco conversion factor, Local Thermal Equilibrium and Large Velocity Gradient approximation to parametrize the cold and warm phase of the interstellar medium from five different low transitions of CO in the central 21"(kpc) of NGC 1097. We have applied a one-component model and derived a typical kinetic temperature of ~33K, and its molecular Hydrogen density and a CO column density. A two-component model results in 85% cold-to-total gas fraction with a 90K 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 onto the Supermassive Black Hole in this prototype LINER/Sy1 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 10. Finally we have calculated the Xco for the centre of NGC 1097 using an independent estimation of the surface density to the CO emission, and obtained Xco=(2.8+-0.5)x10^20 cm^-2(K km s^-1)^-1 at radius 10.5" and Xco=(5.0+-0.5)x10^20 cm^-2(K km s^-1)^-1 at 7.5". With the approach and analysis described, we have demonstrated that important physical properties can be derived to a resolution beyond the single dish resolution element, however, caution is necessary for interpreting the results.(Abriged)