Virial masses of galactic halos from galaxy-galaxy lensing: theoretical modeling and application to SDSS

We present a theoretical analysis of galaxy-galaxy lensing in the context of halo models with CDM motivated dark matter profiles. The model enables us to separate between the central galactic and noncentral group/cluster contributions. We apply the model to the recent SDSS measurements with known redshifts and luminosities of the lenses. This allows one to accurately model the mass distribution of a local galaxy population around and above $L_{\star}$. We find that virial mass of L* galaxy is M*=(5-10)x10^{11}h^{-1}M_{\sun}, depending on the color of the galaxy. This value varies significantly with galaxy morphology with M* for late types being a factor of 10 lower in u', 7 in g' and a factor of 2.5-3 lower in r', i' and z' relative to early types. Fraction of noncentral galaxies in groups and clusters is estimated to be below 10% for late types and around 30% 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 \propto L^1.4 in red bands above L*. This shows that the virial mass to light ratio is increasing with luminosity for galaxies above L*, as predicted by theoretical models. The virial mass to light ratio in i' band is 17(45)hM_{\sun}/L_{\sun} at L* for late (early) types. Combining this result with cosmological baryon fraction one finds that 0.7(0.25)h^{-1}\Upsilon_i\Omega_m/12\Omega_b of baryons within the virial radius are converted to stars at L*, where \Upsilon_i is the stellar mass to light ratio in i' band. This indicates that both for early and late type galaxies around L* a significant fraction of all the baryons in the halo is transformed into stars.