The minimum mass for star formation by dynamical fragmentation: dependence on epoch, dust abundance, and environment

Abstract

ABSTRACT We estimate the minimum mass of a star formed by dynamical collapse and fragmentation, as a function of epoch, dust abundance, and environment. Epoch is parametrized by redshift, zred, through the variation in the temperature of the cosmic microwave background. The dust abundance is parametrized by the mass-fraction in dust, ZD, with the additional simplifying assumption that the intrinsic properties of dust do not change with ZD, only the amount of dust. Environment is parametrized by the energy-density of the ambient suprathermal radiation fields through a dilution factor ω⋆ (applied to a blackbody radiation field at $T_{\star }=10^4\, {\rm K}$). The critical condition is that a spherical proto-fragment should be able to cool, and therefore contract, fast enough to detach from neighbouring proto-fragments. The minimum mass increases with increasing redshift, increasing dust abundance, and increasing suprathermal background. Values in the range from $M_{{\rm MIN}}\sim 0.002\, {\rm M}_{\odot }$ to $M_{{\rm MIN}}\sim 0.2\, {\rm M}_{\odot }$ are obtained at the extremes of the parameter ranges we have considered (0 ≤ zred ≤ 8, 0.00016 < ZD < 0.04, and 10−15 ≤ ω⋆ ≤ 10−8). Our results agree quite well with the predictions of detailed numerical simulations invoking similar redshifts and dust abundances, but our estimates are somewhat lower; we attribute this difference to resolution issues and the small-number statistics from the simulations. The increased minimum masses predicted at high redshift and/or high suprathermal background result in significantly bottom-light initial mass functions, and therefore low mass-to-light ratios, provided that the dust abundance is not too low. The changes due to high suprathermal background may be particularly important for star formation in galactic nuclei and at high redshift.