2000ApJ...530L.119M

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 τ_grow and mean duration τ_stop, the stellar mass m has a probability density per logarithmic mass interval of ∼ m^–x, where x≡τ_grow/τ_stop. This power-law relation matches the IMF when τ_grow~τ_stop, 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 τ_grow greater than the free-fall time of the condensation by a factor of ∼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 ∼100 IMF-following stars with a mass range of 1-25 M_☉ in 1.4 Myr, in accord with the masses and ages of embedded clusters.