Discovery of the optical afterglow and host galaxy of short GRB181123B at $z =1.754$: Implications for Delay Time Distributions.

We present the discovery of the optical afterglow and host galaxy of the {\it Swift} short-duration gamma-ray burst, GRB\,181123B. Observations with Gemini-North starting at $\approx 9.1$~hr after the burst reveal a faint optical afterglow with $i\approx25.1$~mag, at an angular offset of 0.59 $\pm$ 0.16$''$ from its host galaxy. Using $grizYJHK$ observations, we measure a photometric redshift of the host galaxy of $z = 1.77^{+0.30}_{-0.17}$. From a combination of Gemini and Keck spectroscopy of the host galaxy spanning 4500-18000~\AA , we detect a single emission line at 13390~\AA, inferred as H$\beta$ at $z = 1.754 \pm 0.001$ and corroborating the photometric redshift. The host galaxy properties of GRB\,181123B are typical to those of other SGRB hosts, with an inferred stellar mass of $\approx 1.7 \times 10^{10}\,M_{\odot}$, mass-weighted age of $\approx 0.9$~Gyr and optical luminosity of $\approx 0.9L^{*}$. 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 {\it Swift} sample on delay time distribution models. We find that log-normal models with mean delay times of $\approx 4-6$~Gyr are consistent with the observed distribution, but can be ruled out to $95\%$ confidence with an additional $\approx1-5$~{\it Swift} SGRBs recovered at $z>1.5$. In contrast, power-law models with $\propto$ $t^{-1}$ are consistent with the redshift distribution and can accommodate up to $\approx30$ SGRBs at these redshifts. Under this model, we predict that $\approx 1/3$ of the current {\it 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 delay time distributions, and thus their formation channels.