The dependence of the initial mass function on metallicity and the opacity limit for fragmentation

We investigate the dependence of stellar properties on the opacity limit for fragmentation that is set by the metallicity of a molecular cloud. We compare the results from two large-scale hydrodynamical simulations of star cluster formation, which resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical, but in the new simulation the onset of the opacity limit occurs at a lower gas density, and this is expected to increase the minimum mass of a brown dwarf by a factor of 3 [to approximate to 9 Jupiter masses (M-J)]. We find that the lowest mass object is a factor of 3 higher in the low-metallicity calculation, as expected. However, apart from this shift of the low-mass cut-off, the initial mass functions (IMFs) produced by the two calculations are indistinguishable. In particular, the median (characteristic) mass is unchanged. These results add support to the accretion-ejection model proposed by Bate & Bonnell for the origin of the initial mass function (IMF), which predicts that the characteristic mass should vary in proportion to the mean thermal Jeans mass in the cloud. They also indicate that the form of the IMF above the low-mass cut-off should not display a strong metallicity dependence, assuming that the cooling is dominated by dust and that the overall mean thermal Jeans mass of a molecular cloud does not depend on its metallicity. However, if the mean thermal Jeans mass of a molecular cloud is set by the thermal behaviour of gas during the formation of the cloud, this should lead to an indirect dependence of the characteristic mass of the IMF on metallicity because of the link between the characteristic mass and the mean thermal Jeans mass of the cloud.