  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=
\sigma_r^2/\rho^{2/3} ~ r^\alpha with \alpha ~ 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.
