Effects of physical conditions on the stellar initial mass function: The low-metallicity star-forming region Sh 2-209

Recent work suggested that the variation of the initial mass function (IMF) of stars depends on the physical conditions, notably, the metallicity and gas density. We investigated the properties of two clusters, namely the main cluster (MC) and the subcluster (SC), in the low-metallicity HII region Sh 2-209 (S209) based on recently derived IMFs. We tested three previously published correlations using previous observations: the top-heaviness of the IMF in dependence on metallicity, the half-mass radius, and the most massive star in dependence on the stellar mass of the embedded clusters. For this region, two different galactocentric distances, namely 10.5 kpc and 18 kpc, were considered, where an age-distance-degeneracy was found for the previously determined IMF to be consistent with other formulated metallicity and density dependent IMFs. The determined half-mass radius r(h) approximate to (0.080 +/- 0.005) pc and the embedded cluster density rho(ecl) approximate to (0.2 +/- 0.1)x10(6) M-circle dot pc(-3) for the MC with an age of 0.5 Myr in S209 assuming a galactocentric distance of 18 kpc support the assumption that a low-metallicity environment results in a denser cluster, which leads to a top-heavy IMF. Thus, all three tests are consistent with the previously published correlations. The results for S209 are placed in the context with the IMF determination within the metal-poor cluster in the star-forming region NGC 346 in the Small Magellanic Cloud.