2014MNRAS.440.1634P

For many massive compact galaxies, their dynamical masses (Mdyn ∝ σ2re) are lower than their stellar masses (M{sstarf}). We analyse the unphysical mass discrepancy M{sstarf}/Mdyn > 1 on a stellar-mass-selected sample of early-type galaxies (M{sstarf} ≳ 10¹¹M_☉) at redshifts z ∼ 0.2 to z ∼ 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_dyn≡K σ_e^2 r_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 ∼ 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{sstarf} and Mdyn grows as galaxies depart from the present-day relation between stellar mass and size: the more compact a galaxy, the larger its M{sstarf}/Mdyn. Current uncertainties in stellar masses cannot account for values of M{sstarf}/Mdyn above 1. Our results suggest that the homology hypothesis contained in the Mdyn formula above breaks down for compact galaxies. We provide an approximation to the virial coefficient K ∼ 6.0[re/(3.185kpc)]-0.81[M{sstarf}/(1011M_☉)]0.45, which solves the mass discrepancy problem. A rough approximation to the dynamical mass is given by Mdyn ∼ [σe/(200 km/s)]3.6[re/(3kpc)]0.352.1x10¹¹M_☉.