A new way to measure the distance to NGC1052-DF2

We employ a new way to measure the distance to NGC1052-DF2 via internal stellar velocity dispersions ($\sigma$) of its globular clusters (GCs). We obtained deep (15.1h), R=18,200, Ca Triplet integrated-light spectra for 10 GCs in NGC1052-DF2 using FLAMES GIRAFFE on VLT. For five GCs we measure $\sigma$, along with precision velocities for the whole sample. We also present a new photometric analysis based on 40 orbits of archival Hubble Space Telescope imaging for 16 spectroscopically confirmed GCs. Assuming that the NGC1052-DF2 GCs obey the $M_V$ -- log($\sigma$) relation followed by the Milky Way and M31 GCs, the NGC1052-DF2 GCs give a distance, $d=16.2\pm1.3$ (stat.) $\pm1.7$ (sys.) Mpc. By contrast, using a literature distance of $d=21.7$ Mpc from forward modelling of the TRGB, the GCs lie above the Milky Way + M31 relation by $\sim0.6$ magnitudes. For a shorter literature distance of 13 Mpc, the GCs fall below the relation by $\sim0.4$ mag. At $d = 16.2$ Mpc, we obtain mean dynamical $M/L_V = 1.61\pm0.44 M_\odot/L_\odot$, and median half-light radii, $r_h =3.0\pm0.5$ pc. This is entirely consistent with Milky Way GCs, with mean $M/L_V = 1.77\pm0.10 M_\odot/L_\odot$, median $r_h =3.2\pm0.6$ pc. For the further distance of 21.7 Mpc, we obtain low $M/L_V$ ratios ($M/L_V = 1.19\pm0.33 M_\odot/L_\odot$) which could suggest ages of $\sim6$ Gyr.. Such young ages are inconsistent with our MUSE stellar population (companion paper, Fahrion et al.) analysis of the NGC1052-DF2 GCs which indicates they are $\sim10$ Gyr old. For $d = 16.2$ Mpc, coupled with our new photometry, we find that the properties of the GCs in NGC1052-DF2 appear entirely consistent with those in the Milky Way and other Local Group galaxies. In order to reconcile the further distance with our results, a mass function more dwarf-depleted than the Milky Way GCs must be invoked for the GCs of NGC1052-DF2.