An overmassive Dark Halo around an Ultra-diffuse Galaxy in the Virgo
  Cluster
  Ultra diffuse galaxies (UDGs) have the sizes of giant galaxies but the
luminosities of dwarfs. A key to understanding their origins comes from their
total masses, but their low surface brightnesses ($\mu(V) \geq$ 25.0) generally
prohibit dynamical studies. Here we report the first such measurements for a
UDG (VCC~1287 in the Virgo cluster), based on its globular cluster system
dynamics and size. From 7 GCs we measure a mean systemic velocity $v_{\rm sys}$
= 1071$^{+14}_{-15}$ km/s, thereby confirming a Virgo-cluster association. We
measure a velocity dispersion of 33$^{+16}_{-10}$ km/s within 8.1 kpc,
corresponding to an enclosed mass of $(4.5 \pm 2.8)\times10^{9}$ $M_{\odot}$
and a $g$-band mass-to-light ratio of $(M/L)_g = 106^{+126}_{-54}$. From the
cumulative mass curve, along with the GC numbers, we estimate a virial mass of
$\sim8\times10^{10}$ $M_{\odot}$, yielding a dark-to-stellar mass fraction of
$\sim3000$. We show that this UDG is an outlier in $M_{\rm star} - M_{\rm
halo}$ relations, suggesting extreme stochasticity in relatively massive
star-forming halos in clusters. Finally, we discuss how counting GCs offers an
efficient route to determining virial masses for UDGs.
