  With SDSS galaxy data and halo data from up-to-date N-body simulations we
construct a semi-empirical catalog (SEC) of early-type systems by making a
self-consistent bivariate statistical match of stellar mass (M_star) and
velocity dispersion (sigma) with halo virial mass (M_vir). We then assign
stellar mass profile and velocity dispersion profile parameters to each system
in the SEC using their observed correlations with M_star and sigma.
Simultaneously, we solve for dark matter density profile of each halo using the
spherical Jeans equation. The resulting dark matter density profiles deviate in
general from the dissipationless profile of NFW or Einasto and their mean inner
density slope and concentration vary systematically with M_vir. Statistical
tests of the distribution of profiles at fixed M_vir rule out the null
hypothesis that it follows the distribution predicted by N-body simulations for
M_vir ~< 10^{13.5-14.5} M_solar. These dark matter profiles imply that dark
matter density is, on average, enhanced significantly in the inner region of
halos with M_vir ~< 10^{13.5-14.5} M_solar supporting halo contraction. The
main characteristics of halo contraction are: (1) the mean dark matter density
within the effective radius has increased by a factor varying systematically up
to ~ 3-4 at M_vir = 10^{12} M_solar, and (2) the inner density slope has a mean
of <alpha> ~ 1.3 with rho(r) ~ r^{-alpha} and a halo-to-halo rms scatter of
rms(alpha) ~ 0.4-0.5 for 10^{12} M_solar ~< M_vir ~< 10^{13-14} M_solar steeper
than the NFW profile (alpha=1). Based on our results we predict that halos of
nearby elliptical and lenticular galaxies can, in principle, be promising
targets for gamma-ray emission from dark matter annihilation.
