We present Magellan observations of the Swift short-duration gamma-ray burst ( GRB ) 161104A and its host galaxy at z = 0.793 \pm 0.003 .
We model the multi-band photometry and spectroscopy with the stellar population inference code Prospector , and explore the posterior using nested sampling .
We find a mass-weighted age of t _ { m } = 2.12 ^ { +0.23 } _ { -0.21 } Gyr , stellar mass of \log { ( M / M _ { \odot } ) } = 10.21 \pm 0.04 , metallicity of \log { ( Z / Z _ { \odot } ) } = 0.08 ^ { +0.05 } _ { -0.06 } , dust extinction of A _ { V } = 0.08 ^ { +0.08 } _ { -0.05 } , and a low star formation rate of \text { SFR } = 7 \times 10 ^ { -2 } M _ { \odot } yr ^ { -1 } .
These properties , along with a prominent 4000 Å break and optical absorption lines classify this host as an early-type , quiescent galaxy .
Using Dark Energy Survey galaxy catalogues , we demonstrate that the host of GRB 161104A resides on the outskirts of a galaxy cluster at z \approx 0.8 , situated \approx 1 Mpc from the likely Brightest Cluster Galaxy ( BCG ) .
We also present new modeling for 20 additional short GRB hosts ( \approx 33 \% of which are early-type galaxies ) , finding population medians of \log ( M / M _ { \odot } ) = 9.94 ^ { +0.88 } _ { -0.98 } and t _ { m } = 1.07 ^ { +1.98 } _ { -0.67 } Gyr ( 68 \% confidence ) .
We further find that the host of GRB 161104A is more distant , less massive and younger than the four other short GRB hosts known to be associated with galaxy clusters .
Cluster short GRBs have faint afterglows , in the lower \approx 11 \% ( \approx 30 \% ) of observed X-ray ( optical ) luminosities .
We place a lower limit on the fraction of short GRBs in galaxy clusters versus those in the field of \approx 5 - 13 \% , consistent with the fraction of stellar mass \approx 10 - 20 \% in galaxy clusters at redshifts 0.1 \leq z \leq 0.8 .
Future studies which take advantage of wider-field and deeper cluster surveys are needed to understand the true rate of short GRBs in clusters and their effect on heavy element enrichment in the intracluster medium .