The resolved star-formation relation in nearby active galactic nuclei

Aims. We present an analysis of the relation between the star formation rate (SFR) surface density (ΣSFR) and mass surface density of molecular gas (ΣH2), commonly referred to as the Kennicutt-Schmidt (K-S) relation, on its intrinsic spatial scale, i.e. the size of giant molecular clouds (~10−150 pc), 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 ΣH2, and tests its validity in the high-density central regions of spiral galaxies. Methods. We used interferometric IRAM 12CO(1−0) and 12CO(2−1) and SMA 12CO(3−2) emission line maps to derive ΣH2 and HST–Hα images to estimate ΣSFR. Results. Each galaxy is characterized by a distinct molecular SF relation on spatial scales between 20 to 200 pc. 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 >100 pc and sublinear on smaller scales. Depletion times range from ~1 and 2 Gyr, 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 ΣH2. 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 (