The stellar velocity dispersion of a compact massive galaxy at z=1.80 using X-Shooter: confirmation of the evolution in the mass-size and mass-dispersion relations

Recent photometric studies have shown that early-type galaxies at fixed stellar mass were smaller and denser at earlier times. In this paper we assess that finding by deriving the dynamical mass of such a compact quiescent galaxy at z=1.8. We have obtained a high-quality spectrum with full UV-NIR wavelength coverage of galaxy NMBS-C7447 using X-Shooter on the VLT. We determined a velocity dispersion of 294 +- 51 km/s. Given this velocity dispersion and the effective radius of 1.64 +- 0.15 kpc (as determined from HST-WFC3 F160W observations) we derive a dynamical mass of 1.7 +- 0.5 x 10^11 Msun. Comparison of the full spectrum with stellar population synthesis models indicates that NMBS-C774 has a relatively young stellar population (0.40 Gyr) with little or no star formation and a stellar mass of ~1.5 x 10^11 Msun. The dynamical and photometric stellar mass are in good agreement. Thus, our study supports the conclusion that the mass densities of quiescent galaxies were indeed higher at earlier times, and this earlier result is not caused by systematic measurement errors. By combining available spectroscopic measurements at different redshifts, we find that the velocity dispersion at fixed dynamical mass was a factor of ~1.8 higher at z=1.8 compared to z=0. Finally, we show that the apparent discrepancies between the few available velocity dispersion measurements at z>1.5 are consistent with the intrinsic scatter of the mass-size relation.