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.
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