  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)
