The Faint End of the Cluster Galaxy Luminosity Function at High Redshift
  We measure the faint end slope of the galaxy luminosity function (LF) for
cluster galaxies at 1<z<1.5 using Spitzer IRAC data. We investigate whether
this slope, alpha, differs from that of the field LF at these redshifts, and
with the cluster LF at low redshifts. The latter is of particular interest as
low-luminosity galaxies are expected to undergo significant evolution. We use
seven high-redshift spectroscopically confirmed galaxy clusters drawn from the
IRAC Shallow Cluster Survey to measure the cluster galaxy LF down to depths of
M* + 3 (3.6 microns) and M* + 2.5 (4.5 microns). The summed LF at our median
cluster redshift (z=1.35) is well fit by a Schechter distribution with
alpha[3.6] = -0.97 +/- 0.14 and alpha[4.5] = -0.91 +/- 0.28, consistent with a
flat faint end slope and is in agreement with measurements of the field LF in
similar bands at these redshifts. A comparison to alpha in low-redshift
clusters finds no statistically significant evidence of evolution. Combined
with past studies which show that M* is passively evolving out to z~1.3, this
means that the shape of the cluster LF is largely in place by z~1.3. This
suggests that the processes that govern the build up of the mass of low-mass
cluster galaxies have no net effect on the faint end slope of the cluster LF at
z<1.3.
