The Mass Scale of High-Redshift Galaxies: Virial Mass Estimates Calibrated with Stellar Dynamical Models from LEGA-C

Dynamical models for $673$ galaxies at $z=0.6-1.0$ with spatially resolved (long-slit) stellar kinematic data from LEGA-C are used to calibrate virial mass estimates defined as $M_{\rm{vir}}=K \sigma'^2_{\star,\rm{int}} R$, with $K$ a scaling factor, $\sigma'_{\star,\rm{int}}$ the spatially-integrated stellar velocity second moment from the LEGA-C survey and $R$ the effective radius measured from a S\'ersic profile fit to HST imaging. The sample is representative for $M_{\star}>3\times10^{10}~M_{\odot}$ and includes all types of galaxies, irrespective of morphology and color. We demonstrate that using $R=R_{\rm{sma}}$~(the semi-major axis length of the ellipse that encloses 50\% of the light) in combination with an inclination correction on $\sigma'_{\star,\rm{int}}$~produces an unbiased $M_{\rm{vir}}$. We confirm the importance of projection effects on $\sigma'_{\star,\rm{int}}$ by showing the existence of a similar residual trend between virial mass estimates and inclination for the nearby early-type galaxies in the ATLAS$^{\rm{3D}}$~survey. Also, as previously shown, when using a S\'ersic profile-based $R$ estimate, then a S\'{e}rsic index-dependent correction to account for non-homology in the radial profiles is required. With respect to analogous dynamical models for low-redshift galaxies from the ATLAS$^{\rm{3D}}$~survey we find a systematic offset of 0.1 dex in the calibrated virial constant for LEGA-C, which may be due to physical differences between the galaxy samples or an unknown systematic error. Either way, with our work we establish a common mass scale for galaxies across 8 Gyr of cosmic time with a systematic uncertainty of at most 0.1 dex.