PROTOSTAR MASS DUE TO INFALL AND DISPERSAL

The mass of a protostar is calculated from the infall and dispersal of an isothermal sphere in a uniform background. For high contrast between peak and background densities and for short dispersal time t(d), the accretion is self-limiting''; gas beyond the core is dispersed before it accretes, and the protostar mass approaches a time-independent value of low mass. For lower density contrast and longer dispersal time, the accretion runs away''; gas accretes from beyond the core, and the protostar mass approaches massive star values. The final protostar mass is approximately the initial gas mass whose free-fall time equals td. This mass matches the peak of the IMF for gas temperature 10 K, peak and background densities 10(6) and 10(3) cm(-3), respectively, and td comparable to the core free-fall time t(core). The accretion luminosity exceeds 1 L-circle dot for 0.1 Myr, as in the Class 0'' phase. For t(d)/t(core) 0: 4 0: 8 and temperature 7-50 K, self-limiting protostar masses are 0.08-5 M-circle dot. These protostar and core masses have ratio 0: 4 +/- 0: 2, as expected if the core mass distribution and the initial mass function have the same shape.