2009MNRAS.397.1435R

We study the relationship between the gas column density (Σ_gas) and the star formation rate (SFR) surface density (Σ_SFR) for a sample of 23 extremely faint dwarf irregular galaxies drawn from the Faint Irregular Galaxy GMRT (Giant Metrewave Radio Telescope) Survey (FIGGS). Our sample galaxies have a median Hi mass of 2.8x10⁷M_☉ and a median blue magnitude M_B∼ -13.2. Σ_SFR is derived from Galaxy Evolution Explorer (GALEX) data, while Σ_gas is derived from the GMRT-based FIGGS Hi 21-cm survey data. We find that Σ_gas averaged over the star-forming region of the disc lies below most estimates of the `threshold density' for star formation, and that the average Σ<sub>SFR</sub> is also lower than would be expected from the `Kennicutt-Schmidt' law. This deviation is indicative of an environmental dependence of star formation efficiencies, since the Kennicutt relation was derived from data on the central regions of large spiral and starburst galaxies. The star formation efficiency in small galaxies may be more relevant to modelling of star formation in gas-rich, low-metallicity systems in the early universe. We also use our data to look for small-scale (400 and 200pc) correlations between Σ_SFR and Σ_gas. For 18 of our 23 galaxies, we find that Σ_SFR can be parametrized as having a power-law dependence on Σ_gas. The power-law relation holds until one reaches the sensitivity limit of the GALEX data, i.e. we find no evidence for a `threshold density' below which star formation is completely cut off. The power-law slopes and coefficients however vary substantially from galaxy to galaxy, and are in general steeper than the value of ∼1.4 derived for large galaxies by Kennicutt. Further, as for the globally averaged quantities, the Σ_SFR at 400pc resolution is in general lower than that predicted by the Kennicutt relation, with the deviation decreasing with increasing Σ_gas. Our computation of Σ_SFR uses a calibration that assumes solar metallicity and a standard Salpeter initial mass function (IMF), similarly, the Σ_gas we use is not corrected for the molecular gas density. Incorporating corrections for molecular gas and low metallicity will increase the deviation from the Kennicutt relation. Conversely, truncating the IMF at the high-mass end would decrease the deviation from the Kennicutt relation. For the five galaxies for which a power law does not provide a good parametrization of the (Σ_SFR,Σ_gas) relation, there are substantial offsets between the ultraviolet (UV) bright regions and the Hi high column density maps. Four of these five galaxies have Hi masses near the lower end of our sample distribution, while the remaining galaxy has a large central Hi hole. We have 200pc resolution images for 10 of our galaxies. At this resolution, the offsets between the peaks in the Hi and UV images are more pronounced, and a power-law parametrization is possible for only five of the 10 galaxies.