  We develop a radiation pressure-balanced model for the interstellar medium of
high-redshift galaxies that describes many facets of galaxy formation at z>~6,
including star formation rates and distributions and gas accretion onto central
black holes. We first show that the vertical gravitational force in the disk of
such a model is dominated by the disk self-gravity supported by the radiation
pressure of ionizing starlight on gas. Constraining our model to reproduce the
UV luminosity function of Lyman-break galaxies (LBGs), we limit the available
parameter-space to wind mass-loading factors 1--4 times the canonical value for
momentum-driven winds. We then focus our study by exploring the effects of
different angular momentum transport mechanisms in the galactic disk and find
that accretion driven by gravitational torques, such as from linear spiral
waves or non-linear orbit crossings, can build up black hole masses by z=6
consistent with the canonical M-sigma relation with a duty cycle of unity,
while accretion mediated by a local viscosity such as in an alpha-disk results
in negligible BH accretion. Both gravitational torque models produce X-ray
emission from active galactic nuclei (AGN) in high-redshift LBGs in excess of
the estimated contribution from high-mass X-ray binaries. Using a recent
analysis of deep Chandra observations by Cowie et al., we can already begin to
rule out the most extreme regions of our parameter-space: the inflow velocity
of gas through the disk must either be less than one percent of the disk
circular velocity or the X-ray luminosity of the AGN must be substantially
obscured. Moderately deeper future observations or larger sample sizes will be
able to probe the more reasonable range of angular momentum transport models
and obscuring geometries.
