  The origin of supermassive black holes (SMBHs) in galactic nuclei is one of
the major unsolved problems in astrophysics. One hypothesis is that they grew
from >10^5 M_sun black holes that formed in the `direct collapse' of massive
gas clouds that have low concentrations of both metals and molecular hydrogen
(H_2). Such clouds could form in the early (z>10) Universe if pre-galactic gas
is irradiated by H_2-photodissociating, far-ultraviolet (FUV) light from a
nearby star-forming galaxy. In this work, we re-examine the critical FUV flux
J_crit that is required to keep H_2 photodissociated and lead to direct
collapse. We submit that the same galaxies that putatively supply the
extraordinary FUV fluxes required for direct collapse should also produce
copious amounts of soft X-rays, which work to offset H_2 photodissociation by
increasing the ionization fraction and promoting H_2 formation. Accounting for
this effect increases the value of J_crit by a factor of at least 3-10,
depending on the brightness temperature of FUV radiation. This enhancement of
J_crit suppresses the abundance of potential direct collapse sites at z>10 by
several orders of magnitude. Recent studies---without accounting for the soft
X-rays from the FUV source galaxies---had already arrived at large values of
J_crit that implied that direct collapse may occur too rarely to account for
the observed abundance of high-redshift quasars. Our results suggest that
J_crit should be even higher than previously estimated, and pose an additional
challenge for the direct collapse scenario via strong FUV radiation to explain
the high-redshift quasar population.
