L. Peralta de Arriba, M. Balcells, J. Falcón-Barroso, I. Trujillo
Several studies published recently in the literature have found the unphysical result that the stellar mass (M_star) of many massive compact galaxies is larger than their dynamical mass (M_dyn). To address this issue we have studied the ratio between the stellar and dynamical masses for massive early-type galaxies (M_star > 10^11 M_sun) over the redshift range z ~ 0.2 to z ~ 1.1. We have split our sample according to their redshift, size and stellar mass. For each set we have built a stacked spectrum, obtained its velocity dispersion, and inferred the dynamical mass using the virial relation M_dyn = K \sigma_e^2 r_e / G with the virial coefficient K = 5.0; this assumes homology with nearby massive ellipticals. Our sample is completed using literature data, including individual galaxies up to z ~ 2.5. We find that the discrepancy between M_star and M_dyn grows as galaxies depart from the present-day relation between the stellar mass and the size: the more compact a galaxy, the larger its M_star / M_dyn. For some, very compact galaxies, M_star / M_dyn can be as high as ~30. Current uncertainties of stellar masses cannot solve this problem. Our results suggest that the homology hypothesis contained in the M_dyn formula above breaks down for compact galaxies. We provide an approximation to the virial coefficient K ~ 6.0 [r_e / (3.185 kpc)]^-0.81 [M_star / (10^11 M_sun)]^0.45, which solves the mass discrepancy problem. Such approximation implies non-homology. A rough approximation to the dynamical mass is given by M_dyn ~ [\sigma_e / (200 km s^-1)]^3.6 [r_e / (3 kpc)]^0.35 2.1 10^11 M_sun.
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http://arxiv.org/abs/1307.4376
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