Cloud fragmentation and stellar masses

Theoretical arguments and numerical simulations both suggest that a star-forming cloud generally collapses to a flattened or filamentary configuration before fragmenting, and that fragmentation occurs as a result of the gravitational instability of the resulting layer or filament. A number of existing and new results for the stability of polytropic sheets, discs, and filaments are collected in this paper, and critical lengths and masses are derived for a variety of values of the polytropic exponent. The critical mass varies as T2/µ where T is the temperature and µ the surface density of the fragmenting cloud; the numerical coefficient is approximately the same for both sheets and filaments. Rotation and magnetic fields tend to inhibit fragmentation, but they do not fundamentally change the characteristic length and mass scales involved. The predictions of these stability analyses agree satisfactorily with the results of numerical simulations of the fragmentation of discs and filaments. The predicted critical masses in some well-studied regions of star formation also agree with the typical masses of the observed dense cloud clumps, and, in order of magnitude, with the masses of the young stars present. Differences in the observed fragment masses in different regions can be understood as due primarily to differences in the gas temperature, which is the dominant parameter controlling the mass scale for fragmentation. Fragmentation to smaller masses is likely to continue during the early stages of cloud evolution when the temperature decreases with increasing density, but it becomes less likely and may stop altogether when the temperature reaches its minimum value; this may produce a peak in the stellar initial mass function at the corresponding mass. The typical stellar mass should then increase strongly with increasing minimum cloud temperature.