A Globular Cluster Luminosity Function Distance to NGC 4993 Hosting a Binary Neutron Star Merger GW170817/GRB 170817A

NGC 4993 hosts a binary neutron star merger emitting gravitational waves and electromagnetic waves, GW170817/GRB 170817A. The distance to this galaxy is not well established. We select the globular cluster candidates from the Hubble Space Telescope/ACS F606W images of NGC 4993 in the archive, using the structural parameters of the detected sources. The radial number density distribution of these candidates shows a significant central concentration around the galaxy center at the galactocentric distance $r<50''$, showing that they are mostly the members of NGC 4993. Also the luminosity function of these candidates is fit well by a Gaussian function. Therefore the selected candidates at $r<50''$ are mostly considered to be globular clusters in NGC 4993. We derive an extinction-corrected turnover Vega magnitude in the luminosity function of the globular clusters at $20''<r<50''$, F606W (max)$_0= 25.36\pm0.08$ ($V_0 =25.52\pm0.11$)} mag. Adopting the calibration of the turnover magnitudes of the globular clusters, $M_V({\rm max})=-7.58\pm0.11$, we derive a distance to NGC 4993, $d=41.65\pm3.00$ Mpc ($(m-M)_0=33.10\pm0.16$). The systematic error of this method can be as large as $\pm0.3$ mag. This value is consistent with the previous distance estimates based on the fundamental plane relation and the gravitational wave method in the literature. The distance in this study can be used to constrain the values of the parameters including the inclination angle of the binary system in the models of gravitational wave analysis.