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NGC1052-DF2 and NGC1052-DF4 are ultra-diffuse galaxies (UDGs) that were foundto have extremely low velocity dispersions, indicating that they have little orno dark matter. Both galaxies host anomalously luminous globular cluster (GC)systems, with a peak magnitude of their GC luminosity function (GCLF) that is$\sim1.5$ magnitudes brighter than the near-universal value of $M_V \approx-7.5$. Here we present an analysis of the joint GCLF of the two galaxies,making use of new HST photometry and Keck spectroscopy, and a recently improveddistance measurement. We apply a homogeneous photometric selection method tothe combined GC sample of DF2 and DF4. The new analysis shows that the peak ofthe combined GC luminosity function remains at $M_V \approx -9$ mag. Inaddition, we find a subpopulation of less luminous GCs at $M_V \approx -7.5$mag, where the near-universal GCLF peak is located. The number of GCs in themagnitude range of $-5$ to $-8$ is $7.1_{-4.34}^{+7.33}$ in DF2 and$8.6_{-4.83}^{+7.74}$ in DF4, similar to that expected from other galaxies ofthe same luminosity. The total GC number between $M_V$ of $-5$ to $-11$ is$18.5_{-4.42}^{+8.99}$ for DF2 and $18.6_{-4.92}^{+9.37}$ for DF4, calculatedfrom the background-subtracted GCLF. The updated total number of GCs in bothgalaxies is $37^{+11.08}_{-6.54}$. The number of GCs do not scale with the halomass in either DF2 or DF4, suggesting that $N_{GC}$ is not directly determinedby the merging of halos.

A Complex Luminosity Function for the Anomalous Globular Clusters in NGC1052-DF2 and NGC1052-DF4