Authors: Shang et. al.
Link to the Paper: http://arxiv.org/abs/0906.4773
The paper presents the estimates of J(crit) values needed for a halo to undergo direct collapse. They perform 3-D hydrodynamical adaptive mesh refinement (AMR) simulations of gas collapse in three different protogalactic halos with Tvir >10e4 K, irradiated by a UV flux with various intensities and spectra.
They then determine the J(crit) required to suppress molecular (hydrogen) cooling in each of the three halos simulated above and find that;[i] for a hard spectrum (metal free stars):
J(crit) is between 10e4 to 10e5,[ii] for a softer spectrum (normal stellar population) J(crit) lies between 30 to 300.
The values are ~ 3 to 10 percent lower than previous estimates. They argue that this improved estimate resulted from a better hydrogen molecule-dissociational rate that they adopted. As seen in the Dijkstra paper (see previous post), the reduction in J(crit) exponentially increases the number of rare halos exposed critical radiation; there by preventing fragmentation and ensuing direct collapse. This might give rise to 10e5 solar mass objects at the centre of these haloes- progenitors for SMBH.