Optical-to-virial velocity ratios of local disk galaxies from combined kinematics and galaxy-galaxy lensing

Abstract: In this paper, we measure the optical-to-virial velocity ratios Vopt/V200c of disk galaxies in the Sloan Digital Sky Survey (SDSS) at a mean redshift of <z> = 0.07 and with stellar masses 10^9 M_sun < M_* < 10^11 M_sun. Vopt/V200c, the ratio of the circular velocity measured at the virial radius of the dark matter halo (\sim150 kpc) to that at the optical radius of the disk (\sim10 kpc), is a powerful observational constraint on disk galaxy formation. It links galaxies to their dark matter haloes dynamically and constrains the total mass profile of disk galaxies over an order of magnitude in length scale. For this measurement, we combine Vopt derived from the Tully-Fisher relation (TFR) from Reyes et al. with V200c derived from halo masses measured with galaxy-galaxy lensing. In anticipation of this combination, we use similarly-selected galaxy samples for both the lensing and TFR analysis. For three M_* bins with lensing-weighted mean stellar masses of 0.6, 2.7, and 6.5 x 10^10 M_sun, we find halo-to-stellar mass ratios M_vir/M_* = 41, 23, and 26, with 1-sigma statistical uncertainties of around 0.1 dex, and Vopt/V200c = 1.27\pm0.08, 1.39\pm0.06, 1.27\pm0.08 (1{\sigma}). Our results suggest that the dark matter and baryonic contributions to the mass within the optical radius are comparable, if the dark matter halo profile has not been significantly modified by baryons. The results obtained in this work will serve as inputs to and constraints on disk galaxy formation models, which will be explored in future work. Finally, we note that this paper presents a new and improved galaxy shape catalogue for weak lensing that covers the full SDSS DR7 footprint.