The joint detection of gravitational waves and electromagnetic radiation from the binary neutron star (BNS) merger GW170817 has provided unprecedented insight into a wide range of physical processes: heavy element synthesis via the $r$-process; the production of relativistic ejecta; the equation of state of neutron stars and the nature of the merger remnant; the binary coalescence timescale; and a measurement of the Hubble constant via the standard siren technique. In detail, all of these results depend on the distance to the host galaxy of the merger event, NGC4993. In this paper we measure the surface brightness fluctuation (SBF) distance to NGC4993 in the F110W and F160W passbands of the Wide Field Camera 3 Infrared Channel on the Hubble Space Telescope (HST). For the preferred F110W passband we derive a distance modulus of $m{-}M=33.05pm0.08pm0.10$ mag, or a linear distance $d=40.7pm1.4pm1.9$ Mpc (random and systematic errors, respectively); a virtually identical result is obtained from the F160W data. This is the most precise distance to NGC4993 available to date. Combining our distance measurement with the corrected recession velocity of NGC4993 implies a Hubble constant $H_0=71.9pm 7.1~km~s^{-1}~Mpc^{-1}$. A comparison of our result to the GW-inferred value of $H_0$ indicates a binary orbital inclination of $i,{gtrsim},137~deg$. The SBF technique can be applied to early-type host galaxies of BNS mergers to ${sim,}100$ Mpc with HST and possibly as far as ${sim,}300$ Mpc with the James Webb Space Telescope, thereby helping to break the inherent distance-inclination degeneracy of the GW signals at distances where many future BNS mergers are likely to be detected.
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