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. (author)