Powering reionization: assessing the galaxy ionizing photon budget at $z
  < 10$
  We present a new analysis of the ionizing emissivity ($\dot{N}_{\rm{ion}}$,
s$^{-1}$ Mpc$^{-3}$) for galaxies during the epoch of reionization and their
potential for completing and maintaining reionization. We use extensive SED
modelling -- incorporating two plausible mechanisms for the escape of Lyman
continuum photon -- to explore the range and evolution of ionizing efficiencies
consistent with new results on galaxy colours ($\beta$) during this epoch. We
estimate $\dot{N}_{\rm{ion}}$ for the latest observations of the luminosity and
star-formation rate density at $z<10$, outlining the range of emissivity
histories consistent with our new model. Given the growing observational
evidence for a UV colour-magnitude relation in high-redshift galaxies, we find
that for any plausible evolution in galaxy properties, red (brighter) galaxies
are less efficient at producing ionizing photons than their blue (fainter)
counterparts. The assumption of a redshift and luminosity evolution in $\beta$
leads to two important conclusions. Firstly, the ionizing efficiency of
galaxies naturally increases with redshift. Secondly, for a luminosity
dependent ionizing efficiency, we find that galaxies down to a rest-frame
magnitude of $M_{\rm{UV}} \approx -15$ alone can potentially produce sufficient
numbers of ionizing photons to maintain reionization as early as $z\sim8$ for a
clumping factor of $C_{\rm{H {\small II}}} \leq 3$.
