The Nature of Ultra-diffuse Galaxies in Distant Massive Galaxy Clusters:
  Abell 370 in the Hubble Frontier Fields
  We report the discovery of ultra-diffuse galaxies (UDGs) in Abell 370
($z=0.375$). We find 46 UDGs in Abell 370 from the images of the Hubble
Frontier Fields (HFF). Most UDGs are low-luminosity red sequence galaxies,
while a few of them are blue UDGs. We estimate the abundance of UDGs in Abell
370, $N(\rm UDG)=644\pm104$. Combining these results with those of Abell S1063
($z=0.348$) and Abell 2744 ($z=0.308$) \citep{Lee17}, we derive a mean radial
number density profile of UDGs in the three clusters. The number density
profiles of UDGs and bright galaxies show a discrepancy in the central region
of the clusters: the profile of UDGs shows a flattening as clustercentric
distance decreases, while that of bright galaxies shows a continuous increase.
This implies that UDGs are prone to disruption in the central region of the
clusters. The relation between the abundance of UDGs and virial masses of their
host systems is described by a power-law with an index nearly one: $N({\rm
UDG})\propto M_{200}^{0.99\pm0.05}$ for $M_{200}>10^{13}~M_{\odot}$. We
estimate approximately dynamical masses of UDGs using the fundamental manifold
method, and find that most UDGs have dwarf-like masses $(M_{200}<10^{11}$
$M_{\odot})$. This implies that most UDGs have a dwarf-like origin and a small
number of them could be failed $L^{*}$ galaxies. These results suggest that
multiple origins may contribute to the formation and evolution of UDGs in
massive galaxy clusters.
