Dimensional argument for the impact of turbulent support on the stellar initial mass function

¹ CRAL (UMR CNRS 5574), École Normale Supérieure de Lyon, 69364 Lyon Cedex, France
e-mail: gilles.chabrier@ens-lyon.fr
² School of Physics, University of Exeter, Exeter, EX4 4QL, UK
³ LERMA (UMR CNRS 8112), École Normale Supérieure, 75231 Paris Cedex, France

Received: 18 May 2011
Accepted: 2 August 2011

Abstract

We present a simple dimensional argument to illustrate the impact of nonthermal support from turbulent velocity dispersion on the shape of the prestellar core mass function (CMF), precursor of the stellar initial mass function (IMF). The argument demonstrates the need to invoke such support to recover the Salpeter slope in the high-mass part of the CMF/IMF, whereas pure thermal support leads to a much steeper slope. This simple dimensional argument clearly highlights the results obtained in the complete Hennebelle-Chabrier theory of the IMF.