We report the discovery of 854 ultra diffuse galaxies (UDGs) in the Coma cluster using deep R band images, with partial B, i, and Halpha band coverage, obtained with the Subaru telescope. Many of them (332) are Milky Way-sized with very large effective radii of r_e>1.5kpc. This study was motivated by the recent discovery of 47 UDGs by van-Dokkum et al. (2015); our discovery suggests >1,000 UDGs after accounting for the smaller Subaru field. The new UDGs show a distribution concentrated around the cluster center, strongly suggesting that the great majority are (likely longtime) cluster members. They are a passively evolving population, lying along the red sequence in the CM diagram with no Halpha signature. Star formation was, therefore, quenched in the past. They have exponential light profiles, effective radii re ~ 800 pc- 5 kpc, effective surface brightnesses mu_e(R)=25-28 mag arcsec-2, and stellar masses ~1x10^7 - 5x10^8Msun. There is also a population of nucleated UDGs. Some MW-sized UDGs appear closer to the cluster center than previously reported; their survival in the strong tidal field, despite their large sizes, possibly indicates a large dark matter fraction protecting the diffuse stellar component. The indicated baryon fraction ~<1% is less than the cosmic average, and thus the gas must have been removed from the possibly massive dark halo. The UDG population appears to be elevated in the Coma cluster compared to the field, indicating that the gas removal mechanism is related primarily to the cluster environment.
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