Gamma-Ray-Burst Host Galaxy Surveys at Redshift z>4: Probes of Star
  Formation Rate and Cosmic Reionization
  Measuring the star formation rate (SFR) at high redshift is crucial for
understanding cosmic reionization and galaxy formation. Two common
complementary approaches are Lyman-Break-Galaxy (LBG) surveys for large samples
and Gamma-Ray-Burst (GRB) observations for sensitivity to SFR in small
galaxies. The z>4 GRB-inferred SFR is higher than the LBG rate, but this
difference is difficult to understand, as both methods rely on several modeling
assumptions. Using a physically motivated galaxy luminosity function model,
with star formation in dark-matter halos with virial temperature Tvir>2e4 K
(M_DM>2e8 M_sun), we show that GRB and LBG-derived SFRs are consistent if GRBs
extend to faint galaxies (M_AB<-11). To test star formation below the detection
limit L_lim~0.05L^*_{z=3} of LBG surveys, we propose to measure the fraction
f_det(L>L_lim,z) of GRB hosts with L>L_lim. This fraction quantifies the
missing star formation fraction in LBG surveys, constraining the
mass-suppression scale for galaxy formation, with weak dependence on modeling
assumptions. Because f_det(L>L_lim,z) corresponds to the ratio of star
formation rates derived from LBG and GRB surveys, if these estimators are
unbiased, measuring f_det(L>L_lim,z) also constrains the redshift evolution of
the GRB production rate per unit mass of star formation. Our analysis predicts
significant success for GRB host detections at z~5 with f_det(L>L_lim,z)~0.4,
but rarer detections at z>6. By analyzing the upper limits on host-galaxy
luminosities of six z>5 GRBs from literature data, we infer that galaxies with
M_AB>-15 were present at z>5 at 95% confidence, demonstrating the key role
played by very faint galaxies during reionization.
