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

Abstract

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 ${M}_{\mathrm{vir}}=K\sigma {{\prime} }_{\star ,\mathrm{int}}^{2}R$ , with K a scaling factor, $\sigma {{\prime} }_{\star ,\mathrm{int}}$ the spatially integrated stellar velocity second moment from the LEGA-C survey, and R the effective radius measured from a Sérsic profile fit to Hubble Space Telescope imaging. The sample is representative for M _⋆ > 3 × 10¹⁰ M _⊙ and includes all types of galaxies, irrespective of morphology and color. We demonstrate that using R = R _sma (the semimajor axis length of the ellipse that encloses 50% of the light) in combination with an inclination correction on $\sigma {{\prime} }_{\star ,\mathrm{int}}$ produces an unbiased M _vir. We confirm the importance of projection effects on $\sigma {{\prime} }_{\star ,\mathrm{int}}$ by showing the existence of a similar residual trend between virial mass estimates and inclination for the nearby early-type galaxies in the ATLAS^3D survey. Also, as previously shown, when using a Sérsic profile-based R estimate, a Sérsic index-dependent correction to account for nonhomology in the radial profiles is required. With respect to analogous dynamical models for low-redshift galaxies from the ATLAS^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.