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Ultra-diffuse galaxies (UDGs) are spatially extended low surface brightness stellar systemswith regular elliptical-like morphology. They are found in large numbers in galaxy clusters andgroups, but their formation and evolution remain poorly understood because their low surfacebrightnesses have made studies of their internal dynamics and dark matter content challeng-ing. Here we present spatially resolved velocity profiles, stellar velocity dispersions, ages andmetallicities of 8 UDGs in the Coma cluster and cluster membership confirmation for another10 UDGs. We use intermediate-resolution spectra obtained with Binospec, the MMT’s newhigh-throughput optical spectrograph and complement it with multi-wavelength photometricdata from GALEX, Spitzer, and Subaru. We derive dark matter fractions between 50% and90% within the half-light radius using Jeans dynamical models. Two galaxies exhibit majoraxis rotation, two others have highly anisotropic stellar orbits, and one shows signs of triax-iality. In the Faber–Jackson and mass–metallicity relations and on the Fundamental Plane,the 8 UDGs fill the gap between cluster dwarf elliptical (dE) and fainter dwarf spheroidal(dSph) galaxies. Overall, observed properties of all UDGs can be explained by a combinationof internal processes (supernovae feedback) and environmental effects (ram-pressure stripping,interaction with neighbors). These observations suggest that UDGs and dEs are members ofthe same galaxy population.