Adiabatic compression and indirect detection of supersymmetric dark matter

32 pages, 11 figures, final version to appear in JCAPInternational audienceRecent developments in the modelling of the dark matter distribution in our Galaxy point out the necessity to consider some physical processes to satisfy observational data. In particular, models with adiabatic compression, which include the effect of the baryonic gas in the halo, increase significantly the dark matter density in the central region of the Milky Way. On the other hand, the non-universality in scalar and gaugino sectors of supergravity models can also increase significantly the neutralino annihilation cross section. We show that the combination of both effects gives rise to a gamma-ray flux arising from the Galactic Center largely reachable by future experiments like GLAST. We also analyse in this framework the EGRET excess data above 1 GeV, as well as the recent data from CANGAROO and HESS. The analysis has been carried out imposing the most recent experimental constraints, such as the lower bound on the Higgs mass, the \bsg branching ratio, and the muon $g-2$. In addition, the recently improved upper bound on $B(B_s \to \mu^+ \mu^-)$ has also been taken into account. The astrophysical (WMAP) bounds on the dark matter density have also been imposed on the theoretical computation of the relic neutralino density through thermal production