Virial masses of galactic haloes from galaxy-galaxy lensing: theoretical modelling and application to Sloan Digital Sky Survey data

We present a theoretical analysis of galaxy-galaxy lensing in the context of halo models with cold dark matter motivated dark matter profiles. The model enables us to distinguish between the central galactic and non-central group/cluster contributions. We apply the model to the recent Sloan Digital Sky Survey (SDSS) measurements with known redshifts and luminosities of the lenses. This allows one to model accurately the mass distribution of a local galaxy population around and above L (*). We find that the virial mass of an L (*) galaxy is M (200) = (5 - 10) x 10 (11) h (-1) M-circle dot depending on the colour of the galaxy. This value varies significantly with galaxy morphology, with M-* for late types being lower by a factor of 10 in u', a factor of 7 in g' and a factor of 2.5-3 in r', i' and z ' relative to early types. The fraction of non-central galaxies in groups and clusters is estimated to be below 10 per cent for late types and around 30 per cent for early types. Using the luminosity dependence of the signal, we find that for early types the virial halo mass M scales with luminosity as M proportional toL (1.4+/-0.2) in red bands above L-*. This shows that the virial mass-to-light ratio (M/L) is increasing with luminosity for galaxies above L (*), as predicted by theoretical models. The virial mass-to-light ratio in the i' band is 17 (45) h M-circle dot /L-circle dot at L-* for late (early) types. Combining this result with cosmological baryon fraction, one finds that 70 (25) per cent h (-1) Y-i Omega(m)/12Omega(b) of baryons within r(200) are converted to stars at L (*), where Y (i) is the stellar mass-to-light ratio in the i' band. This indicates that for both early- and late-type galaxies around L (*) a significant fraction of all the baryons in the halo is transformed into stars.