Star formation rates from young-star counts and the structure of the ISM across the NGC 346/N66 complex in the SMC

The rate at which interstellar gas is converted into stars, and its dependence on environment, is one of the pillars on which our understanding of the visible Universe is build. We present a comparison of the surface density of young stars (Sigma(star)) and dust surface density (Sigma(dust)) across NGC 346 (N66) in 115 independent pixels of 6 x 6 pc(2). We find a correlation between Sigma(star) and Sigma(dust) with a considerable scatter. A power-law fit to the data yields a steep relation with an exponent of 2.6 +/- 0.2. We convert Sigma(dust) to gas surface density (Sigma(gas)) and Sigma(star) to star formation rate (SFR) surface densities (Sigma(SFR)), using simple assumptions for the gas-to-dust mass ratio and the duration of star formation. The derived total SFR (4 +/- 1x10(-3) M-circle dot yr(-1)) is consistent with SFR estimated from the Ha emission integrated over the Ha nebula. On small scales the Sigma(SFR) derived using H alpha systematically underestimates the count-based Sigma(SFR), by up to a factor of 10. This is due to ionizing photons escaping the area, where the stars are counted. We find that individual 36 pc(2) pixels fall systematically above integrated disc galaxies in the Schmidt-Kennicutt diagram by on average a factor of similar to 7. The NGC 346 average SFR over a larger area (90 pc radius) lies closer to the relation but remains high by a factor of similar to 3. The fraction of the total mass (gas plus young stars) locked in young stars is systematically high (similar to 10 per cent) within the central 15 pc and systematically lower outside (2 per cent), which we interpret as variations in star formation efficiency. The inner 15 pc is dominated by young stars belonging to a centrally condensed cluster, while the outer parts are dominated by a dispersed population. Therefore, the observed trend could reflect a change of star formation efficiency between clustered and non-clustered star formation.