Recent observations of the Lyman-break galaxy ( LBG ) luminosity function ( LF ) from z \approx 6 – 10 show a steep decline in abundance with increasing redshift .
However , the LF is a convolution of the mass function of dark matter halos ( HMF ) –which also declines sharply over this redshift range–and the galaxy-formation physics that maps halo mass to galaxy luminosity .
We consider the strong observed evolution in the LF from z \approx 6 – 10 in this context and determine whether it can be explained solely by the behavior of the HMF .
From z \approx 6 – 8 , we find a residual change in the physics of galaxy formation corresponding to a \sim 0.5 dex increase in the average luminosity of a halo of fixed mass .
On the other hand , our analysis of recent LF measurements at z \approx 10 shows that the paucity of detected galaxies is consistent with almost no change in the average luminosity at fixed halo mass from z \approx 8 .
The LF slope also constrains the variation about this mean such that the luminosity of galaxies hosted by halos of the same mass are all within about an order-of-magnitude of each other .
We show that these results are well-described by a simple model of galaxy formation in which cold-flow accretion is balanced by star formation and momentum-driven outflows .
If galaxy formation proceeds in halos with masses down to 10 ^ { 8 } M _ { \odot } , then such a model predicts that LBGs at z \approx 10 should be able to maintain an ionized intergalactic medium as long as the ratio of the clumping factor to the ionizing escape fraction is C / f _ { esc } \lesssim 10 .