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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 HubbleFrontier 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 Abell370, $N(\rm UDG)=644\pm104$. Combining these results with those of Abell S1063($z=0.348$) and Abell 2744 ($z=0.308$) \citep{Lee17}, we derive a mean radialnumber density profile of UDGs in the three clusters. The number densityprofiles of UDGs and bright galaxies show a discrepancy in the central regionof the clusters: the profile of UDGs shows a flattening as clustercentricdistance decreases, while that of bright galaxies shows a continuous increase.This implies that UDGs are prone to disruption in the central region of theclusters. The relation between the abundance of UDGs and virial masses of theirhost systems is described by a power-law with an index nearly one: $N({\rmUDG})\propto M_{200}^{0.99\pm0.05}$ for $M_{200}>10^{13}~M_{\odot}$. Weestimate approximately dynamical masses of UDGs using the fundamental manifoldmethod, 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 smallnumber of them could be failed $L^{*}$ galaxies. These results suggest thatmultiple origins may contribute to the formation and evolution of UDGs inmassive galaxy clusters.

The Nature of Ultra-diffuse Galaxies in Distant Massive Galaxy Clusters: Abell 370 in the Hubble Frontier Fields