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

We present the properties of NGC 4993, the host galaxy of GW170817, the first gravitational wave (GW) event from the merger of a binary neutron star (BNS) system and the first with an electromagnetic (EM) counterpart. We use both archival photometry and new optical/near-IR imaging and spectroscopy, together with stellar population synthesis models to infer the global properties of the host galaxy. We infer a star formation history peaked at $\gtrsim 10$ Gyr ago, with subsequent exponential decline leading to a low current star formation rate of 0.01 M$_{\odot}$ yr$^{-1}$, which we convert into a binary merger timescale 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. This in 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 and archival $Hubble$ $Space$ $Telescope$ images to measure a projected offset of the optical counterpart of $2.1$ kpc (0.64$r_{e}$) from the center of NGC 4993 and 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 modest natal kick with an upper limit of $\sim 200$ km s$^{-1}$. Future GW$-$EM observations of BNS mergers will enable measurement of their population delay time distribution, which will directly inform their viability as the dominant source of $r$-process enrichment in the Universe.