The Next Generation Virgo Cluster Survey (NGVS). XIII. The Luminosity
  and Mass Function of Galaxies in the Core of the Virgo Cluster and the
  Contribution from Disrupted Satellites
  We present measurements of the galaxy luminosity and stellar mass function in
a 3.71 deg$^2$ (0.3 Mpc$^2$) area in the core of the Virgo cluster, based on
$ugriz$ data from the Next Generation Virgo Cluster Survey (NGVS). The galaxy
sample consists of 352 objects brighter than $M_g=-9.13$ mag, the 50%
completeness limit of the survey. Using a Bayesian analysis, we find a best-fit
faint end slope of $\alpha=-1.33 \pm 0.02$ for the g-band luminosity function;
consistent results are found for the stellar mass function as well as the
luminosity function in the other four NGVS bandpasses. We discuss the
implications for the faint-end slope of adding 92 ultra compact dwarfs galaxies
(UCDs) -- previously compiled by the NGVS in this region -- to the galaxy
sample, assuming that UCDs are the stripped remnants of nucleated dwarf
galaxies. Under this assumption, the slope of the luminosity function (down to
the UCD faint magnitude limit, $M_g = -9.6$ mag) increases dramatically, up to
$\alpha = -1.60 \pm 0.06$ when correcting for the expected number of disrupted
non-nucleated galaxies. We also calculate the total number of UCDs and globular
clusters that may have been deposited in the core of Virgo due to the
disruption of satellites, both nucleated and non-nucleated. We estimate that
~150 objects with $M_g\lesssim-9.6$ mag and that are currently classified as
globular clusters, might, in fact, be the nuclei of disrupted galaxies. We
further estimate that as many as 40% of the (mostly blue) globular clusters in
the core of Virgo might once have belonged to such satellites; these same
disrupted satellites might have contributed ~40% of the total luminosity in
galaxies observed in the core region today. Finally, we use an updated Local
Group galaxy catalog to provide a new measurement of the luminosity function of
Local Group satellites, $\alpha=-1.21\pm0.05$.
