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