English

On the function describing the stellar initial mass function

Astrophysics of Galaxies 2015-06-12 v1

Abstract

We propose a functional form for the IMF, the L_3 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-2001a, Kroupa-2002a and Chabrier-2003b (single stars or systems) are essentially indistinguishable from this form. Compared to other 3-parameter functions of the IMF, the L_3 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.

Keywords

Cite

@article{arxiv.1212.0939,
  title  = {On the function describing the stellar initial mass function},
  author = {Thomas Maschberger},
  journal= {arXiv preprint arXiv:1212.0939},
  year   = {2015}
}

Comments

8 pages, 9 figures; MNRAS accepted

R2 v1 2026-06-21T22:48:55.432Z