Gamma rays from annihilations at the galactic center in a physical dark matter distribution

Abstract

We discuss the γ-ray signal to be expected from dark matter (DM) annihilations at the Galactic center. We describe the DM distribution in the Galactic halo, based on the Jeans equation for self-gravitating, anisotropic equilibria. In solving the Jeans equation, we adopted the specific correlation between the density ρ(r) and the velocity dispersion σ 2 r (r) expressed by the powerlaw behavior of the DM "entropy" K ≡ σ 2 r /ρ 2/3 ∝ r α with α ≈ 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 it yields a main-body profile consistent with the classic self-similar development of DM halos. In addition, we required the Jeans solutions to satisfy regular boundary conditions both at the center (finite pressure, round gravitational potential) and on the outskirts (finite overall mass). With these building blocks, we derived physical solutions, dubbed "α-profiles". We find the one with α = 1.25, suitable for the Galaxy halo, to be intrinsically flatter at the center than the empirical NFW formula, yet steeper than the empirical Einasto profile. 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 α-profile in relieving the astrophysical uncertainties related to the macroscopic DM distribution, and discuss its expected performance as a tool instrumental in interpreting the upcoming γ-ray data in terms of DM annihilation.

Dark Matter Halos: The Dynamical Basis of Effective Empirical Models

“…We stress that the handy SE representation is convenient in analyzing data in several contexts, including: the DM particle annihilation signal expected from the Galactic Center (see Lapi et al 2010a); rotation curves of dwarf and normal spiral galaxies (see Salucci et al 2007); individual and statistical properties of elliptical and spiral galaxies (see Cook et al 2009); strong and weak gravitational lensing (see Lapi et al 2009b), currently observed in clusters (e.g., Zitrin et al 2010) and soon in massive elliptical galaxies (see discussion by Bradač et al 2009); X-ray emission from the intracluster plasma (see Cavaliere et al 2009;Fusco-Femiano et al 2009, Lapi et al 2010b.…”

Fitting functions for dark matter density profiles

“…Whilst the finite angular resolution indicates that the observed signal should be finite (unless the density cusp is steeper than r −3/2 ), the signal from the r −1 cusp of an NFW halo should be significantly stronger than that from a cored halo provided that both are normalized locally in the Solar neighbourhood. For example, Lapi et al (2010) find that the NFW halo produces one to two orders of magnitude stronger annihilation signal towards the Galactic centre than the Einasto model with the resolution ranging from ≈ 3 deg 2 to ≈ 100 arcmin 2 .…”

“…In the following (Sect. 4.3), we shall briefly analyze the behaviour of the so-called astrophysical term J(φ) (e.g., Lapi et al 2010) in the CDM annihilation signal for the dark halo density profile given by our model family. We find that if the dark halo density profile diverges faster than r −1/2 as r → 0, the astrophysical term also formally diverges as φ → 0 -in particular, the r −α cusp (α > 1 2 ) results in J ∈ Θ(φ −(2α−1) ).…”