With Sloan Digital Sky Survey galaxy data and halo data from up-to-date N-body simulations within the \Lambda CDM framework we construct a semi-empirical catalog ( SEC ) of early-type galaxy-halo systems by making a self-consistent bivariate statistical match of stellar mass ( M _ { \star } ) and velocity dispersion ( \sigma ) with halo virial mass ( M _ { vir } ) as demonstrated here for the first time .
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 Navarro-Frenk-White 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 dissipationless N-body simulations for M _ { vir } \lesssim 10 ^ { 13.5 - 14.5 } { M } _ { \odot } .
These dark matter profiles imply that dark matter density is , on average , enhanced significantly in the inner region of halos with M _ { vir } \lesssim 10 ^ { 13.5 - 14.5 } { M } _ { \odot } 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 \approx 3 - 4 at M _ { vir } = 10 ^ { 12 } { M } _ { \odot } , and ( 2 ) the inner density slope has a mean of \langle \alpha \rangle \approx 1.3 with \rho _ { dm } ( r ) \propto r ^ { - \alpha } and a halo-to-halo rms scatter of { rms } ( \alpha ) \sim 0.4 - 0.5 for 10 ^ { 12 } { M } _ { \odot } \lesssim M _ { vir } \lesssim 10 ^ { 13 - 14 } { M } _ { \odot } 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 .