It is notoriously difficult to localize short \gamma -ray bursts ( sGRBs ) and their hosts to measure their redshifts .
These measurements , however , are critical to constrain the nature of sGRB progenitors , their redshift distribution and the r -process element enrichment history of the universe .
Here , we present spectroscopy of the host galaxy of GRB 111117A and measure its redshift to be z = 2.211 .
This makes GRB 111117A the most distant high-confidence short duration GRB detected to date .
Our spectroscopic redshift supersedes a lower , previously estimated photometric redshift value for this burst .

We use the spectroscopic redshift , as well as new imaging data to constrain the nature of the host galaxy and the physical parameters of the GRB .
The rest-frame X-ray derived hydrogen column density , for example , is the highest compared to a complete sample of sGRBs and seems to follow the evolution with redshift as traced by the hosts of long GRBs ( lGRBs ) .

The host lies in the brighter end of the expected sGRB host brightness distribution at z = 2.211 , and is actively forming stars .
Using the host as a benchmark for redshift determination , we find that between 43 and 71 per cent of all sGRB redshifts should be missed due to host faintness for hosts at z \sim 2 .
The high redshift of GRB 111117A is evidence against a lognormal delay-time model for sGRBs through the predicted redshift distribution of sGRBs , which is very sensitive to high- z sGRBs .

From the age of the universe at the time of GRB explosion , an initial neutron star ( NS ) separation of a _ { 0 } < 3.2 ~ { } R _ { \odot } is required in the case where the progenitor system is a circular pair of inspiralling NSs .
This constraint excludes some of the longest sGRB formation channels for this burst .