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