2009 Fermi Symposium, Washington, D.C., Nov. 2-5 2 energy range: where the integral is over the whole line of sight, r is the comoving distance and E$_{γ,}$$_{0}$ is the energy mea- sured by the observer at z = 0. The gamma ray emis- sivity ϵ$_{γ}$ (energy emitted per unit energy range, unit volume and unit time) associated with dark matter annihilation is given by: where d N$_{γ}$/ d E$_{γ}$ is the total differential photon spec- trum summed over all channels of annihilation, m$_{χ}$ and ρ$_{χ}$ are the mass and density of neutralinos, and 〈 σv 〉 is the thermally averaged product of the annihi- lation cross section and the Møller velocity. Note that ϵ$_{γ,}$$_{0}$ is evaluated at the blueshifted energy (1 + z ) E$_{γ,}$$_{0}$ along the line-of-sight to compensate for the cosmo- logical redshifting. Of all the quantities in Eq. (2), only ρ$_{χ}$ depends on the spatial distribution of neutralinos, the rest is related to its intrinsic properties, which we can con- veniently analyze separately by defining the so called SUSY factor: dark matter Ω$_{DM}$. This condition reduces the allowed regions in the parameter space considerably. The different regions in the mSUGRA parameter space that satisfy these constraints have been studied often in the past and have received generic names: (B) bulk region (low values of m$_{0}$ and m$_{1}$$_{/}$$_{2}$ ), (FP) focus point region (large values of m$_{0}$ ), (CA) co-annihilation region (low m$_{0}$ and m$_{χ}$ < ∼ m$_{˜}$ τ $_{1}$, where ˜ τ$_{1}$ is the lightest slepton) and (RAF) rapid annihilation funnel region (for large values of tan β and a specific condition for m$_{χ}$ $^{1}$). Instead of making a full scan of the allowed pa- rameter space, we define several “benchmarks points” which fulfill all the experimental constraints discussed above and which can be taken as representative of the different regions that we just described. The benchmark points were selected following the analy- sis of Battaglia et al. [2004] and Gondolo et al. [2004]. We use the numerical code DarkSUSY Gondolo et al. [2004, 2005] to analyze these benchmark points. Fig. 1 shows the energy spectrum of f$_{SUSY}$ com- puted for four of the benchmark points analyzed, which are representatives of the different regions: CA (black), FP (red), RAF (green ) and B (blue). The main features of Fig. 1 are determined by the photon spectrum d N$_{γ}$/ d E$_{γ}$ which receives contribu- tions from three mechanisms of photon production Bringmann et al. [2008]: (i) gamma-ray continuum emission following the decay of neutral pions produced In the present section we describe the particular SUSY model that we used to compute the gamma-ray emis- sivity produced by dark matter annihilation. We restrict our analysis to the framework of the minimal supergravity model (mSUGRA), which is popular, among other reasons, due to its relative sim- plicity. The large number of free parameters in general SUSY is reduced to effectively four free parameters in mSUGRA: m$_{1}$$_{/}$$_{2}$ , m$_{0}$ , A$_{0}$ , which are the values of the gaugino and scalar masses and the trilinear coupling, all specified at the GUT scale, tan β which is the ratio of the expectation values in the vacuum of the two neutral SUSY Higgs, and finally, the sign of µ , the Higgsino mass parameter. The general 5-dimensional parameter space of the mSUGRA model is significantly constrained by var- ious requirements: consistency with radiative elec- troweak symmetry breaking (EWSB) and experimen- tal constraints on the low energy region. It is also nor- mally assumed that if the major component of dark matter is the lightest neutralino, then its relic den- sity Ω$_{χ}$ should be equal to the observed abundance of $^{1}$The relation which should hold is: 2 m$_{χ}$ $_{≈}$m$_{A}$ , where A is the CP-odd Higgs boson; see for example Feng [2005] for details. eConf C091122 f$_{SUSY}$ = d N$_{γ}$ d E$_{γ}$ 〈 σv 〉 m 2 χ . (3) ϵ$_{γ}$ = E$_{γ}$ d N$_{γ}$ d E$_{γ}$ 〈 σv 〉 2 [ ρ$_{χ}$ m$_{χ}$ ] 2 , (2) 2. Dark matter annihilation and the SUSY factor I$_{γ,}$$_{0}$ = 1 4 π ∫ ϵ$_{γ,}$$_{0}$ ( E$_{γ,}$$_{0}$ (1 + z ) , z ) d r (1 + z ) $_{4}$, (1) Figure 1: SUSY factor as a function of γ -ray emission energy for a selection of benchmark points representatives of the allowed regions in the mSUGRA parameter space: CA (black), FP (red), RAF (green ) and B (blue).