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 10⁹ < M* < 10^ (11) M_⊙. V_ (opt) /V_ (200c), the ratio of the circular velocity measured at the optical radius of the disc (∼10 kpc) to that at the virial radius of the dark matter halo (∼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 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 TFR and lensing analysis. For three M* bins with lensing-weighted mean stellar masses of 0. 6, 2. 7 and 6. 5 × 10^ (10) M_⊙, we find halo-to-stellar mass ratios M_ (200c) /M_* = 41, 23 and 26, with 1σ 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 (1σ), 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.