The Levy Function: a statistically valid model for the Initial Mass Function.
The search for a Universal Stellar Initial Mass Function (IMF) over more than 50 years has resulted in a broad consensus on a power law above 0.5−2 M¤, with a log normal form for lower masses. Here we show that many natural processes reveal similar statistical distributions. The Pareto Levy family of distributions, which include the Gaussian, Levy and Cauchy distributions, are statistically 'stationary' and therefore obey the central limit theorem. This makes them valid models for distributions resulting from the sums of many independent variables. Here we show that the Levy distribution provides a good fit to the observed IMF, and can be used to predict the number of unobserved, low mass stars and brown dwarfs.