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We present the properties of NGC 4993, the host galaxy of GW170817, the firstgravitational wave (GW) event from the merger of a binary neutron star (BNS)system and the first with an electromagnetic (EM) counterpart. We use botharchival photometry and new optical/near-IR imaging and spectroscopy, togetherwith stellar population synthesis models to infer the global properties of thehost galaxy. We infer a star formation history peaked at $\gtrsim 10$ Gyr ago,with subsequent exponential decline leading to a low current star formationrate of 0.01 M$_{\odot}$ yr$^{-1}$, which we convert into a binary mergertimescale probability distribution. We find a median merger timescale of$11.2^{+0.7}_{-1.4}$ Gyr, with a 90% confidence range of $6.8-13.6$ Gyr. Thisin turn indicates an initial binary separation of $\approx 4.5$ R$_{\odot}$,comparable to the inferred values for Galactic BNS systems. We also use new andarchival $Hubble$ $Space$ $Telescope$ images to measure a projected offset ofthe optical counterpart of $2.1$ kpc (0.64$r_{e}$) from the center of NGC 4993and to place a limit of $M_{r} \gtrsim -7.2$ mag on any pre-existing emission,which rules out the brighter half of the globular cluster luminosity function.Finally, the age and offset of the system indicates it experienced a modestnatal kick with an upper limit of $\sim 200$ km s$^{-1}$. Future GW$-$EMobservations of BNS mergers will enable measurement of their population delaytime distribution, which will directly inform their viability as the dominantsource of $r$-process enrichment in the Universe.

the astrophysical journal. letters

The Electromagnetic Counterpart of the Binary Neutron Star Merger  LIGO/VIRGO GW170817. VII. Properties of the Host Galaxy and Constraints on  the Merger Timescale