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 T _vir ≳ 2 × 10⁴ K (M _DM ≳ 2 × 10⁸ M _⊙), 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 SFRs 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.