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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.