Proper motion and physical parameters of the two open clusters NGC 1907 and NGC 1912

Ultra-diffuse galaxies (UDGs) are an unusual galaxy population. They are ghostlike galaxies with fainter surface brightness than normal dwarf galaxies, but they are as large as MW-like galaxies. The key question on UDGs is whether they are 'failed' giant galaxies or 'extended' dwarf galaxies. To answer this question, we study UDGs in massive galaxy clusters. We find an amount of UDGs in deep HST images of three Hubble Frontier Fields clusters, Abell 2744 (z=0.308), Abell S1063 (z=0.347), and Abell 370 (z=0.374). These clusters are the farthest and most massive galaxy clusters in which UDGs have been discovered until now. The color-magnitude relations show that most UDGs have old stellar population with red colors, while a few of them show bluer colors implying the existence of young stars. The stellar masses of UDGs show that they have less massive stellar components than the bright red sequence galaxies. The radial number density profiles of UDGs exhibit a drop in the central region of clusters, suggesting some of them were disrupted by strong gravitational potential. Their spatial distributions are not homogeneous, which implies UDGs are not virialized enough in the clusters. With virial masses of UDGs estimated from the fundamental manifold, most UDGs have M_200 = 10^10 - 10^11 M_Sun indicating that they are dwarf galaxies. However, a few of UDGs more massive than 10^11 M_Sun indicate that they are close to failed giant galaxies.