2015A&A...577A.135C

We present an analysis of the relation between the star formation rate (SFR) surface density (Σ_SFR) and mass surface density of molecular gas (Σ_H2), commonly referred to as the Kennicutt-Schmidt (K-S) relation, on its intrinsic spatial scale, i.e. the size of giant molecular clouds (∼10-150pc), in the central, high-density regions of four nearby low-luminosity active galactic nuclei (AGN). These are AGN extracted from the NUclei of GAlaxies (NUGA) survey. This study investigates the correlations and slopes of the K-S relation, as a function of spatial resolution and of the different ¹²CO emission lines used to trace Σ_H2, and tests its validity in the high-density central regions of spiral galaxies. We used interferometric IRAM ¹²CO(1-0) and ¹²CO(2-1) and SMA ¹²CO(3-2) emission line maps to derive Σ_H2 and HST-Hα images to estimate Σ_SFR. Each galaxy is characterized by a distinct molecular SF relation on spatial scales between 20 to 200pc. The K-S relations can be sublinear, but also superlinear, with slopes ranging from ∼0.5 to ∼1.3; slopes are generally superlinear on spatial scales >100pc and sublinear on smaller scales. Depletion times range from ∼1 and 2Gyr, which is compatible with results for nearby normal galaxies. These findings are valid independently of which transition - ¹²CO(1-0), ¹²CO(2-1), or ¹²CO(3-2) - is used to derive Σ_H2. Because of either star-formation feedback, the lifetime of clouds, turbulent cascade, or magnetic fields, the K-S relation might be expected to degrade on small spatial scales (<100pc). However, we find no clear evidence of this, even on scales as small as ∼20pc, and this might be because of the higher density of GMCs in galaxy centers that have to resist higher shear forces. The proportionality between Σ_H2 and Σ_SFR found between 10 and 100M_☉/pc² is valid even at high densities, ∼10³M_☉/pc². However, by adopting a common CO-to-H₂ conversion factor (α_CO), the central regions of the NUGA galaxies have higher Σ_SFR for a given gas column than those expected from the models, with a behavior that lies between the mergers or high-redshift starburst systems and the more quiescent star-forming galaxies, assuming that the first ones require a lower value of α_CO.