  We present new results on the relationship between central galaxies and dark
matter haloes inferred from observations of satellite kinematics in the Sloan
Digital Sky Survey (SDSS) DR7. We employ an updated analysis framework that
includes detailed mock catalogues to model observational effects in SDSS. Our
results constrain the colour-dependent conditional luminosity function (CLF) of
dark matter haloes, as well as the radial profile of satellite galaxies.
Confirming previous results, we find that red central galaxies live in more
massive haloes than blue galaxies at fixed luminosity. Additionally, our
results suggest that satellite galaxies have a radial profile less centrally
concentrated than dark matter but not as cored as resolved subhaloes in dark
matter-only simulations. Compared to previous works using satellite kinematics
by More et al., we find much more competitive constraints on the galaxy-halo
connection, on par with those derived from a combination of galaxy clustering
and galaxy-galaxy lensing. We compare our results on the galaxy-halo connection
to other studies using galaxy clustering and group catalogues, showing very
good agreement between these different techniques. We discuss future
applications of satellite kinematics in the context of constraining cosmology
and the relationship between galaxies and dark matter haloes.
