The Morphology of the Galactic Dark Matter Synchrotron Emission with Self-Consistent Cosmic Ray Diffusion Models

The probability of two dark matter particles (χ) pair-annihilating into observable standard model particles is proportional to the thermally averaged pair-annihilation cross section times the relative particle velocity, σv , multiplied by the local particle dark matter number density squared, n 2 χ . The first quantity, σv , can be inferred from the requirement of having a relic abundance Ω χ ∼ 1/ σv on the same order as the universal dark matter density, i.e. Ω DM ∼ 0.24 [10]. The latter quantity is given by n 2 χ = (ρ DM /m χ ) 2 , where m χ indicates the mass of the dark matter particle χ. Most dark matter annihilation processes are therefore predicted to occur in regions with a large dark matter density. Both intuition and detailed results from N-body simulations (see e.g. [11][12][13]) indicate that the center of the Milky Way galaxy is likely the brightest local dark matter annihilation site (barring the possibility of highly concentrated local dark matter clumps [14]). Among the possible signatures of dark matter annihilation, extensive studies have focused on gamma rays (see e.g. [15,16] and references therein) and neutrinos (for a recent study see [17]), particle species which have the benefit of carrying directional and spectral information.

Other stable standard model particles produced in the pair annihilation of dark matter include charged cosmic rays such as electrons and positrons (e ± ) as well as (anti-)protons and (anti-)deuterons. These charged species scatter off of magnetic field irregularities in the Galaxy, losing energy and diffusing before reaching the Earth. The random-walk propagation of charged cosmic rays in the Galaxy is usually described with a diffusion-loss equation and solved numerically [18] or semi-analytically [19,20]. A pedagogical review of cosmic-ray propagation and interactions in the Galaxy is given in Ref. [21].

The possibility of detecting an anomalous spectral feature in the flux of leptons, which could be traced back to the pair-annihilation of particle dark matter, has been long discussed (for early studies see e.g. Ref. [22][23][24][25]). This scenario has recently gained great momentum after results from the Pamela space-based antimatter detector reported an excess of high-energy (10-100 GeV) positrons over the assumed background of secondary positron production by inelastic cosmic-ray interactions [26]. Tantalizingly, an excess (namely an anomalous “bump”) in the flux of electrons plus positrons was also recently reported by the balloon-borne experiments ATIC [27] and PPB-BETS [28] at energies in the range of several hundred GeV. This excess was subsequently not confirmed by data from the Fermi Large Area Telescope (LAT), which, however, did indicate a much harder spectrum for the e ± flux at high energy than previously assumed [29,30]. This implies that the positron deficit reported by Pamela is at an even greater contrast with the standard expectation from cosmic ray models. The Fermi results agree with the low-energy range of other determinations of the e ± flux [31].

Although astrophysical sources such as pulsars [30,[32][33][34][35][36] and supernova remnants [37,38] have been shown to provide a possible explanation for the positron fraction anomaly, dark matter models have been formulated which can fit both cosmic ray data and account for the positron excess (for a list of references see e.g. [34]). In general, dark matter models that account for the Pamela anomaly need to have a large pair-annihilation cross section compared to the estimates from the standard thermal-relic calculation. Furthermore, a mechanism or conservation law must be invoked to ensure that excess antiprotons are not produced at a detectable level, as the Pamela data place stringent constraints on any antiproton excess [39]. Dark matter models which

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