Constraints on the z ∼ 5 Star-forming Galaxy Luminosity Function From Hubble Space Telescope Imaging of an Unbiased and Complete Sample of Long Gamma-Ray Burst Host Galaxies

We present rest-frame UV Hubble Space Telescope imaging of the largest and most complete sample of 23 long-duration gamma-ray burst (GRB) host galaxies between redshifts 4 and 6. Of these 23, we present new WFC3/F110W imaging for 19 of the hosts, which we combine with archival WFC3/F110W and WFC3/F140W imaging for the remaining four. We use the photometry of the host galaxies from this sample to characterize both the rest-frame UV luminosity function (LF) and the size–luminosity relation of the sample. We find that when assuming the standard Schechter-function parameterization for the UV LF, the GRB host sample is best fit with $\alpha =-{1.30}_{-0.25}^{+0.30}$ and ${M}_{* }=-{20.33}_{-0.54}^{+0.44}$ mag, which are consistent with results based on z ∼ 5 Lyman-break galaxies. We find that ∼68% of our size–luminosity measurements fall within or below the same relation for Lyman-break galaxies at z ∼ 4. This study observationally confirms expectations that at z ∼ 5 Lyman-break and GRB host galaxies should trace the same population and demonstrates the utility of GRBs as probes of hidden star formation in the high-redshift Universe. Under the assumption that GRBs unbiasedly trace star formation at this redshift, our nondetection fraction of 7/23 is consistent at the 95% confidence level with 13%–53% of star formation at redshift z ∼ 5 occurring in galaxies fainter than our detection limit of M _1600Å ≈ −18.3 mag.