Growth of an Initial Mass Function Cluster in a Turbulent Dense Core

A simple model of condensation growth and collapse in a turbulent dense core yields a distribution of stellar masses that matches the main features of the stellar initial mass function (IMF). In this model, stars in the "flat" and "power-law" parts of the IMF come from condensations with negligible and substantial growth, respectively. The mass accretion rate of a condensation is proportional to its mass, and the probability of stopping accretion is equal in every time interval, so the growth is exponential and its duration follows a Poisson distribution. For mass growth e-folding time taugrow and mean duration taustop, the stellar mass m has a probability density per logarithmic mass interval of approximately m-x, where x identical withtaugrow&solm0;taustop. This power-law relation matches the IMF when taugrow approximately taustop, as is expected if each of these times is set by the same properties of the surrounding core gas. We specify exponential growth arising from Bondi accretion onto a stationary Bonnor-Ebert sphere, in a core heated and stirred by associated stars. This growth is exponential, unlike the Bondi accretion onto a star, but "slow," with taugrow greater than the free-fall time of the condensation by a factor of approximately 4. We specify random stopping as due to sudden turbulent compression, which causes the condensation to collapse and stop accreting. For these mechanisms, a core with a density of 104 cm-3 grows a cluster of approximately 100 IMF-following stars with a mass range of 1-25 M middle dot in circle in 1.4 Myr, in accord with the masses and ages of embedded clusters.