  We investigate the physical and chemical conditions necessary for low-mass
star formation in extragalactic environments by calculating various
characteristic timescales associated with star formation for a range of initial
conditions. The balance of these timescales indicates whether low-mass star
formation is enhanced or inhibited under certain physical conditions. In this
study, we consider timescales for free-fall, cooling, freeze-out, desorption,
chemistry and ambipolar diffusion and their variations with changes in the gas
density, metallicity, cosmic ray ionisation rate and FUV radiation field
strength. We find that extragalactic systems with high FUV radiation field
strengths and high cosmic ray fluxes considered at a range of metallicities,
are likely to have enhanced low-mass star formation unless the magnetic
pressure is sufficient to halt collapse. Our results indicate that this is only
likely to be the case for high-redshift galaxies approaching solar
metallicities. Unless this is true for all high-redshift sources, this study
finds little evidence for a high-mass biased IMF at high redshifts.
