A Complex Luminosity Function for the Anomalous Globular Clusters in
  NGC1052-DF2 and NGC1052-DF4
  NGC1052-DF2 and NGC1052-DF4 are ultra-diffuse galaxies (UDGs) that were found
to have extremely low velocity dispersions, indicating that they have little or
no 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 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 GC luminosity function remains at $M_V \approx -9$ mag. In
addition, 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 the
magnitude 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 of
the 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, calculated
from the background-subtracted GCLF. The updated total number of GCs in both
galaxies is $37^{+11.08}_{-6.54}$. The number of GCs do not scale with the halo
mass in either DF2 or DF4, suggesting that $N_{GC}$ is not directly determined
by the merging of halos.
