A Complex Luminosity Function for the Anomalous Globular Clusters in NGC 1052-DF2 and NGC 1052-DF4

NGC1052-DF2 and NGC1052-DF4 are ultra-diffuse galaxies (UDGs) that were found to have extremely low velocity dispersions, indicating they little or no dark matter. Both host anomalously luminous globular cluster (GC) systems, with a peak magnitude of their GC luminosity function (GCLF) is $\sim1.5$ magnitudes brighter than the near-universal value $M_V \approx -7.5$. Here we present an analysis joint GCLF two galaxies, making use new HST photometry Keck spectroscopy, recently improved distance measurement. We apply homogeneous photometric selection method combined sample DF2 DF4. The shows remains at -9$ mag. In addition, find subpopulation less GCs -7.5$ mag, where located. number in range $-5$ $-8$ $7.1_{-4.34}^{+7.33}$ $8.6_{-4.83}^{+7.74}$ DF4, similar expected from other same luminosity. total between $M_V$ $-11$ $18.5_{-4.42}^{+8.99}$ for $18.6_{-4.92}^{+9.37}$ calculated background-subtracted GCLF. updated both $37^{+11.08}_{-6.54}$. do not scale halo mass either suggesting $N_{GC}$ directly determined by merging halos.