A Minimum Hypothesis Explanation for an Imf with a Lognormal Body and Power Law Tail

We present a minimum hypothesis model for an IMF that resembles a lognormal distribution at low masses but has a distinct power-law tail. Even if the central limit theorem ensures a lognormal distribution of condensation masses at birth, a power-law tail in the distribution arises due to accretion from the ambient cloud, coupled with a non-uniform (exponential) distribution of accretion times. 1. A Model for the Initial Mass Function Observations of the field star IMF have long established the existence of a power-law tail in the intermediate and high mass regime (Salpeter 1955). Recent observations of stars within young embedded clusters (e.g., Muench et al. 2002), have also established the existence of a low mass peak in the stellar mass distribution. Submillimeter observations of dense protostellar condensations (e.g., Motte, André, & Neri 1998) also imply a power-law tail in the intermediate and high mass regime. Given the evidence for a peaked distribution, a natural explanation is to invoke the central limit theorem of statistics and argue that the IMF should be characterized by the lognormal probability density function (pdf) f(m) = 1 √ 2πσm exp [