We discuss the \gamma -ray signal to be expected from dark matter ( DM ) annihilations at the Galactic Center .
To describe the DM distribution in the Galactic halo we base on the Jeans equation for self-gravitating , anisotropic equilibria .
In solving the Jeans equation , we adopt the specific correlation between the density \rho ( r ) and the velocity dispersion \sigma ^ { 2 } _ { r } ( r ) expressed by the powerlaw behavior of the DM ‘ entropy ’ K \equiv \sigma _ { r } ^ { 2 } / \rho ^ { 2 / 3 } \propto r ^ { \alpha } with \alpha \approx 1.25 - 1.3 .
Indicated ( among others ) by several recent N -body simulations , this correlation is privileged by the form of the radial pressure term in the Jeans equation , and yields a main body profile consistent with the classic self-similar development of DM halos .
In addition , we require the Jeans solutions to satisfy regular boundary conditions both at the center ( finite pressure , round gravitational potential ) and in the outskirts ( finite overall mass ) .
With these building blocks we derive physical solutions , dubbed ‘ \alpha -profiles ’ .
We find the one with \alpha = 1.25 , suitable for the Galaxy halo , to be intrinsically flatter at the center relative to the empirical NFW formula , yet steeper than the empirical Einasto profile .
So on scales of 10 ^ { -1 } deg it yields annihilation fluxes lower by a factor 5 than the former yet higher by a factor 10 than the latter ; such fluxes will eventually fall within the reach of the Fermi satellite .
We show the effectiveness of the \alpha -profile in relieving the astrophysical uncertainties related to the macroscopic DM distribution , and discuss its expected performance as a tool instrumental to interpret the upcoming \gamma -ray data in terms of DM annihilation .