  Observations of galaxy-galaxy lensing from Sloan Digital Sky Survey (SDSS)
are combined with the Tully-Fisher and fundamental plane relations to derive
constraints on galactic halo profiles.We show that both for early and late type
galaxies around L* the rotation velocity drops significantly from its peak
value at the optical radius to the virial radius, v_opt/v_200 \sim 1.8 with
about 20% uncertainty. Such a drop is expected in models in which the halo
profile is very concentrated, so that it declines steeper than isothermal at
large radii. This large drop can be explained as a result of both a
concentrated dark matter profile and a significant stellar contribution to the
rotation velocity at the optical radii. We model the stellar component with a
thin rotationally supported disk or a Hernquist profile and use adiabatic dark
matter response model to place limits on the halo concentration as a function
of the stellar mass to light ratio. For reasonable values of the latter we find
concentrations consistent with CDM predictions, suggesting there is no evidence
for low concentrations for the majority of halos in the universe. We also
discuss the origin of Faber-Jackson relation L \propto sigma^4 in light of L
\propto v_200^2.5 relation found for early type galaxies from galaxy-galaxy
lensing. This leads to a decrease in v_opt/v_{200} with luminosity above L*, so
that at 7L_* the ratio is 1.4. This is expected from the fundamental plane
relation and implies that relations such as Tully-Fisher and Faber-Jackson are
not simply relations between the mass of dark matter halo and galaxy
luminosity, but are also significantly influenced by the baryonic effects on
the rotation velocity at optical radii.
