Title: Fires in the deep: The luminosity distribution of early-time gamma-ray-burst afterglows in light of the Gamow Explorer sensitivity requirements

Abstract: Gamma-ray bursts (GRBs) are ideal probes of the Universe at high redshift (z > 5), pinpointing the locations of the earliest star-forming galaxies and providing bright backlights that can be used to spectrally fingerprint the intergalactic medium and host galaxy during the period of reionization. Future missions such as Gamow Explorer are being proposed to unlock this potential by increasing the rate of identification of high-z GRBs to rapidly trigger observations from 6-10 m ground telescopes, JWST, and the Extremely Large Telescopes. Gamow was proposed to the NASA 2021 Medium-Class Explorer (MIDEX) program as a fast-slewing satellite featuring a wide-field lobster-eye X-ray telescope (LEXT) to detect and localize GRBs, and a 30 cm narrow-field multi-channel photo-z infrared telescope (PIRT) to measure their photometric redshifts using the Lyman-alpha dropout technique. To derive the PIRT sensitivity requirement we compiled a complete sample of GRB optical-near-infrared afterglows from 2008 to 2021, adding a total of 66 new afterglows to our earlier sample, including all known high-z GRB afterglows. We performed full light-curve and spectral-energy-distribution analyses of these afterglows to derive their true luminosity at very early times. For all the light curves, where possible, we determined the brightness at the time of the initial finding chart of Gamow, at different high redshifts and in different NIR bands. We then followed the evolution of the luminosity to predict requirements for ground and space-based follow-up. We find that a PIRT sensitivity of 15 micro-Jy (21 mag AB) in a 500 s exposure simultaneously in five NIR bands within 1000s of the GRB trigger will meet the Gamow mission requirement to recover > 80% of all redshifts at z > 5.