The Next Generation Virgo Cluster Survey (NGVS) XXXI. The kinematics of
  intra-cluster globular clusters in the core of the Virgo cluster
  Intra-cluster (IC) populations are expected to be a natural result of the
hierarchical assembly of clusters, yet their low space densities make them
difficult to detect and study. We present the first definitive kinematic
detection of an IC population of globular clusters (GCs) in the Virgo cluster,
around the central galaxy, M87. This study focuses on the Virgo core for which
the combination of NGVS photometry and follow-up spectroscopy allows us to
reject foreground star contamination and explore GC kinematics over the full
Virgo dynamical range. The GC kinematics changes gradually with galactocentric
distance, decreasing in mean velocity and increasing in velocity dispersion,
eventually becoming indistinguishable from the kinematics of Virgo dwarf
galaxies at $\mathrm{R>320\, kpc}$. By kinematically tagging M87 halo and
intra-cluster GCs we find that 1) the M87 halo has a smaller fraction
($52\pm3\%$) of blue clusters with respect to the IC counterpart ($77\pm10\%$),
2) the $(g'-r')_{0}$ vs $(i'-z')_{0}$ color-color diagrams reveal a galaxy
population that is redder than the IC population that may be due to a different
composition in chemical abundance and progenitor mass, and 3) the ICGC
distribution is shallower and more extended than the M87 GCs, yet still
centrally concentrated. The ICGC specific frequency,
$S_{N,\mathrm{ICL}}=10.2\pm4.8$, is consistent with what is observed for the
population of quenched, low-mass galaxies within 1~Mpc from the cluster's
center. The IC population at Virgo's center is thus consistent with being an
accreted component from low-mass galaxies tidally stripped or disrupted through
interactions, with a total mass of
$\mathrm{M_{ICL,tot}=10.8\pm0.1\times10^{11}M_{\odot}}$.
