Annabel Cartwright

The Levy
Function: a statistically valid model for the Initial Mass Function.

Anthony Whitworth

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.