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

NGC 1052-DF2 and NGC 1052-DF4 are ultradiffuse galaxies that have extremely low velocity dispersions, indicating that they have little or no dark matter. Both galaxies host anomalously luminous globular clusters (GCs), with a peak magnitude of their GC luminosity function (GCLF) that is ∼1.5 mag brighter than the near-universal value of M_V ≈ -7.5. Here we present an analysis of the joint GCLF of the two galaxies, making use of new Hubble Space Telescope photometry and Keck spectroscopy and a recently improved distance measurement. We apply a homogeneous photometric selection method to the combined GC sample of DF2 and DF4. The new analysis shows that the peak of the combined GCLF remains at M_V ≈ -9 mag. In addition, we find a subpopulation of less luminous GCs at M_V ≈ -7.5 mag, where the near-universal GCLF peak is located. The number of GCs in the magnitude range of -5 to -8 is ${7}_{-4}^{+7}$ <!-- --> in DF2 and ${9}_{-5}^{+8}$ <!-- --> in DF4, similar to that expected from other galaxies of the same luminosity. The total GC number between M_V of -5 and -11 is ${19}_{-4}^{+9}$ <!-- --> for DF2 and ${19}_{-5}^{+9}$ <!-- --> for DF4, calculated from the background-subtracted GCLF. The data are consistent with both galaxies having two GC populations: the one expected for their luminosity, and a very luminous population composing ∼90% of the total cluster mass. The number of GCs does not scale with the halo mass in either DF2 or DF4, suggesting that N_GC is not directly determined by the merging of halos.