On the Constancy of the Characteristic Mass of Young Stars

The characteristic mass Mc in the stellar initial mass function (IMF) is about constant for most star-forming regions. Numerical simulations consistently show a proportionality between Mc and the thermal Jeans mass MJ at the time of cloud fragmentation, but no models have explained how it can be the same in diverse conditions. Here we show that MJ depends weakly on density, temperature, metallicity, and radiation field in three environments: the dense cores where stars form, larger star-forming regions ranging from GMCs to galactic disks, and the interiors of H II regions and super star clusters. In dense cores, the quantity T3/2n−1/2 that appears in MJ scales with core density as n0.25 or with radiation density as U0.1 at the density where dust and gas come into thermal equilibrium. On larger scales, this quantity varies with ambient density as n−0.05 and ambient radiation field as U−0.033 when the Kennicutt-Schmidt law of star formation determines U(n) . In super star clusters with ionization and compression of prestellar globules, MJ varies as the 0.13 power of the cluster column density. These weak dependencies on n, U, and column density imply that most environmental variations affect the thermal Jeans mass by at most a factor of ~2. Cosmological increases in MJ, which have been suggested by observations, may be explained if the star formation efficiency is systematically higher at high redshift for a given density and pressure, if dust grains are smaller at lower metallicity, and so hotter for a given radiation field, or if small prestellar cores are more severely ionized in extreme starburst conditions.