GRAVITATIONAL FORMATION TIMES AND STELLAR MASS DISTRIBUTIONS FOR STARS OF MASS 0.3-30 M-CIRCLE-DOT

The width of the 1.3 cm line of NH3 in a dense core is related by simple power laws to the luminosity and mass of the most massive star associated with the core. These relations link the mass of the star to the initial conditions in the gas which formed the star. At the size scale approximately 0.1 pc of NH3 line observations, the effects of stellar winds on the core velocity dispersion are estimated from observations of cores with and without stars, and from the dependence of the wind momentum flux on stellar luminosity. The estimated wind contribution increases with stellar luminosity, but is generally comparable to or less than the nonstellar contribution to the nonthermal motions, which is probably of magnetic origin. The wind contribution is removed from the observed velocity dispersion to estimate the velocity dispersion in the prestellar core gas. This dispersion is used to estimate the time for a core associated with a star of mass 0.3-30 M. to form such a star. The infall model includes both thermal and nonthermal motions. The nonthermal part of the velocity dispersion in the region which contains one stellar mass of gas is assumed to be bounded by values (a) the same as observed at the radius r(obs), and (b) smaller than observed by a factor (r/r(obs))1/2. The predicted infall times for stars of mass 0.3, 3, and 30 M. are 1-2, 4-8, and 1-12 x 10(5) yr. The range of gravitational formation times is at most a factor of 10, significantly smaller than the factor of 100 in the range of stellar masses. A cloud forming a star cluster can produce a distribution of stellar masses which matches that of the IMF for stars more massive than 2-3 M., provided cores have pressure proportional to that of the underlying cluster cloud, and velocity dispersion related to stellar mass as indicated by NH3 line observations.