Isothermal Fragmentation: Is there a low-mass cut-off?

TL;DR

This paper investigates the conditions under which isothermal gas clouds fragment during collapse, revealing that the infall Mach number determines collapse mode and that the low-mass cut-off is a numerical artifact, not set by initial conditions.

Contribution

It identifies the infall Mach number as the key parameter controlling collapse versus fragmentation and shows the low-mass cut-off is numerically determined, not physically.

Findings

Infall Mach number, not initial turbulence, governs collapse mode.

Fragmentation produces a power-law mass function with slope near -2.

Low-mass cut-off is a numerical artifact, independent of initial cloud properties.

Abstract

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.