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

In this paper, we measure the optical-to-virial velocity ratios V-opt/V-200c of disc galaxies in the Sloan Digital Sky Survey (SDSS) at a mean redshift of < z > = 0.07 and with stellar masses 10(9) < M-* < 10(11) M-circle dot. V-opt/V-200c, the ratio of the circular velocity measured at the optical radius of the disc (similar to 10 kpc) to that at the virial radius of the dark matter halo (similar to 150 kpc), is a powerful observational constraint on disc galaxy formation. It links galaxies to their dark matter haloes dynamically and constrains the total mass profile of disc galaxies over an order of magnitude in length scale. For this measurement, we combine V-opt derived from the Tully-Fisher relation (TFR) from Reyes et al. with V-200c derived from halo masses measured with galaxy-galaxy lensing. In anticipation of this combination, we use similarly selected galaxy samples for both the TFR and lensing analysis. For three M-* bins with lensing-weighted mean stellar masses of 0.6, 2.7 and 6.5 x 10(10) M-circle dot, we find halo-to-stellar mass ratios M-200c/M-* = 41, 23 and 26, with 1 sigma statistical uncertainties of around 0.1 dex, and V-opt/V-200c = 1.27 +/- 0.08, 1.39 +/- 0.06 and 1.27 +/- 0.08 (1 sigma), respectively. 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 disc 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 Data Release 7 footprint.