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تسجيل مستخدم جديدThe discrepancy between dynamical and stellar masses in massive compact galaxies traces non-homology
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For many massive compact galaxies, their dynamical masses ($M_mathrm{dyn} propto sigma^2 r_mathrm{e}$) are lower than their stellar masses ($M_star$). We analyse the unphysical mass discrepancy $M_star / M_mathrm{dyn} > 1$ on a stellar-mass-selected sample of early-type galaxies ($M_star gtrsim 10^{11} mathrm{M_odot}$) at redshifts $z sim 0.2$ to $z sim 1.1$. We build stacked spectra for bins of redshift, size and stellar mass, obtain velocity dispersions, and infer dynamical masses using the virial relation $M_mathrm{dyn} equiv K sigma_mathrm{e}^2 r_mathrm{e} / G$ with $K = 5.0$; this assumes homology between our galaxies and nearby massive ellipticals. Our sample is completed using literature data, including individual objects up to $z sim 2.5$ and a large local reference sample from the Sloan Digital Sky Survey (SDSS). We find that, at all redshifts, the discrepancy between $M_star$ and $M_mathrm{dyn}$ grows as galaxies depart from the present-day relation between stellar mass and size: the more compact a galaxy, the larger its $M_star / M_mathrm{dyn}$. Current uncertainties in stellar masses cannot account for values of $M_star / M_mathrm{dyn}$ above 1. Our results suggest that the homology hypothesis contained in the $M_mathrm{dyn}$ formula above breaks down for compact galaxies. We provide an approximation to the virial coefficient $K sim 6.0 left[ r_mathrm{e} / (3.185 mathrm{kpc}) right]^{-0.81} left[ M_star / (10^{11} mathrm{M_odot}) right]^{0.45}$, which solves the mass discrepancy problem. A rough approximation to the dynamical mass is given by $M_mathrm{dyn} sim left[ sigma_mathrm{e} / (200 mathrm{km s^{-1}}) right]^{3.6} left[ r_mathrm{e} / (3 mathrm{kpc}) right]^{0.35} 2.1 times 10^{11} mathrm{M_odot}$.
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