Discovery of the Optical Afterglow and Host Galaxy of Short GRB 181123B at z=1.754: Implications for Delay Time Distributions

We present the discovery of the optical afterglow and host galaxy of the Swift short-duration gamma-ray burst (SGRB) GRB 181123B. Observations with Gemini-North starting approximate to 9.1 hr after the burst reveal a faint optical afterglow with i approximate to 25.1 mag at an angular offset of 0.'' 59 +/- 0.'' 16 from its host galaxy. Using grizYJHK observations, we measure a photometric redshift of the host galaxy of z = 1.77(-0.17)(+0.30). From a combination of Gemini and Keck spectroscopy of the host galaxy spanning 4500-18000 angstrom, we detect a single emission line at 13390 A, inferred as H beta at z = 1.754 +/- 0.001 and corroborating the photometric redshift. The host galaxy properties of GRB 181123B are typical of those of other SGRB hosts, with an inferred stellar mass of approximate to 9.1 x 10(9)M(circle dot), a mass-weighted age of approximate to 0.9 Gyr, and an optical luminosity of approximate to 0.9L*. At z = 1.754, GRB 181123B is the most distant secure SGRB with an optical afterglow detection and one of only three at z > 1.5. Motivated by a growing number of high-z SGRBs, we explore the effects of a missing z > 1.5 SGRB population among the current Swift sample on delay time distribution (DTD) models. We find that lognormal models with mean delay times of approximate to 4-6 Gyr are consistent with the observed distribution but can be ruled out to 95% confidence, with an additional one to five Swift SGRBs recovered at z > 1.5. In contrast, power-law models with proportional to t(-1) are consistent with the redshift distribution and can accommodate up to approximate to 30 SGRBs at these redshifts. Under this model, we predict that approximate to 1/3 of the current Swift population of SGRBs is at z > 1. The future discovery or recovery of existing high-z SGRBs will provide significant discriminating power on their DTDs and thus their formation channels.