The Brightest Galaxies at Cosmic Dawn from Scatter in the Galaxy
  Luminosity versus Halo Mass Relation
  The Ultraviolet Luminosity Function (UVLF) is a key observable for
understanding galaxy formation from cosmic dawn. There has been considerable
debate on whether Schechter-like LFs (characterized by an exponential drop-off
at the bright end) that well describe the LF in our local Universe are also a
sufficient description of the LF at high redshifts ($z>6$). We model the UVLF
over cosmic history with a semi-empirical framework and include a log-normal
scatter, $\Sigma$, in galaxy luminosities with a conditional luminosity
function approach. We show that stochasticity induces a flattening or a
feedback scale in the median galaxy luminosity versus halo mass relation,
$L_{c}(M_{h})$ to account for the increase of bright objects placed in lower
mass halos. We observe a natural broadening in the bright-end exponential
segment of the UVLF for $z>6$ if processes that regulate star-formation acts on
the same mass scale as at $z\sim5$, where the degree of broadening is enhanced
for larger $\Sigma$. Alternatively, if the bright-end feedback is triggered at
a near-constant luminosity threshold, the feedback threshold occurs at
progressively lower halo masses with increasing redshift, due to galaxies being
more luminous on average at a fixed halo mass from rapid halo assembly. Such
feedback results in a LF shape with a bright-end closer to that of a Schechter
function. We include predictions for the $z>8$ UVLFs from future all-sky
surveys such as WFIRST which has the potential to both quantify the scatter and
type of feedback, and provide insight behind the mechanisms that drive star
formation in the early Universe.
