On the function describing the stellar initial mass function

Abstract

We propose a functional form for the initial mass function (IMF), the L3 IMF, which is a natural heavy-tailed approximation to the log-normal distribution. It is composed of a low-mass power law and a high-mass power law which are smoothly joined together. Three parameters are needed to achieve this. The standard IMFs of Kroupa (2001, 2002) and Chabrier (2003a) (single stars or systems) are essentially indistinguishable from this form. Compared to other three-parameter functions of the IMF, the L3 IMF has the advantage that the cumulative distribution function and many other characteristic quantities have a closed form, the mass generating function, for example, can be written down explicitly. © 2012 The Author. Published by Oxford University Press on behalf of the Royal Astronomical Society.