A Tip of the Red Giant Branch Distance of $22.1 pm 1.2$ Mpc to the Dark Matter Deficient Galaxy NGC1052-DF2 from 40 Orbits of Hubble Space Telescope Imaging

The large and diffuse galaxies NGC1052-DF2 and NGC1052-DF4 have been found to have very low dark matter content and a population of luminous globular clusters. Accurate distance measurements are key to interpreting these observations. Recently, the distance to NGC1052-DF4 was found to be $20.0pm 1.6$ Mpc by identifying the tip of the red giant branch (TRGB) in 12 orbits of Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging. Here we present 40 orbits of HST ACS data for NGC1052-DF2 and use these data to measure its TRGB. The TRGB is readily apparent in the color-magnitude diagram. Using a forward model that incorporates photometric uncertainties, we find a TRGB magnitude of $m_{rm F814W, TRGB} = 27.67 pm 0.10$ mag. The inferred distance is $D_{rm TRGB} = 22.1 pm 1.2$ Mpc, consistent with the previous surface brightness fluctuation distances to the bright elliptical galaxy NGC1052. The new HST distance rules out the idea that some of NGC1052-DF2s unusual properties can be explained if it were at $sim 13$ Mpc; instead, it implies that the galaxys globular clusters are even more luminous than had been derived using the previous distance of 20 Mpc. The distance from NGC1052-DF2 to NGC1052-DF4 is well-determined at $2.1pm 0.5$ Mpc, significantly larger than the virial diameter of NGC1052. We discuss the implications for formation scenarios of the galaxies and for the external field effect, which has been invoked to explain the intrinsic dynamics of these objects in the context of modified Newtonian dynamics.