ATIC, PAMELA, HESS, Fermi and nearby Dark Matter subhalos

TL;DR

This work analyzes the local $e^+e^-$ flux from annihilating dark matter, showing a universal spectral slope $F_{e^eta}(E) \sim E^{-2}$ for $1\,\text{GeV} \ll E \ll E_*$, with the cutoff energy $E_*$ set by the underlying DM model. Using the diffusion-loss framework, the authors separate the source term into a density- and velocity-dependent luminosity and an injection spectrum, and explore how Sommerfeld enhancement and DM halo/profile affect the spectrum. They demonstrate that, in smooth halos, the slope is robust, but nearby DM clumps can produce detectable high-energy features and harden the spectrum, particularly under Sommerfeld boosts; Via Lactea II-based statistics suggest a non-negligible probability ($\sim4\%-15\%$) of such subhalo effects. The results have direct implications for interpreting ATIC, PAMELA, HESS, and Fermi data, indicating that low-energy observations favor a universal DM contribution while high-energy features could arise from a rare local clump, and that future measurements will further constrain the role of substructure in DM annihilation signals.

Abstract

We study the local flux of electrons and positrons from annihilating Dark Matter (DM), and investigate how its spectrum depends on the choice of DM model and inhomogeneities in the DM distribution. Below a cutoff energy, the flux is expected to have a universal power-law form with an index n ~ -2. The cutoff energy and the behavior of the flux near the cutoff is model dependent. The dependence on the DM host halo profile may be significant at energies E < 100 GeV and leads to softening of the flux, n < -2. There may be additional features at high energies due to the presence of local clumps of DM, especially for models in which the Sommerfeld effect boosts subhalo luminosities. In general, the flux from a nearby clump gives rise to a harder spectrum of electrons and positrons, with an index n > -2. Using the Via Lactea II simulation, we estimate the probability of such subhalo effects in a generic Sommerfeld-enhanced model to be at least 4%, and possibly as high as 15% if subhalos below the simulation's resolution limit are accounted for. We discuss the consequences of these results for the interpretation of the ATIC, PAMELA, HESS, and Fermi data, as well as for future experiments.

Figures (8)

• Figure 1: The $e^+e^-$ flux depending on the number of steps in the toy model DM annihilation (see text). In order to keep the maximum values of $E^3 F$ at $E_* = 600$ GeV, we choose the DM mass $M_{\rm DM} \sim e^{\frac{k - 1}{2}} E_*$. Apart from overall normalization, the spectra look similar to each other for $E \ll E_*$. Model dependence shows up for energies $E \gtrsim E_*$.
• Figure 2: The dependence of $e^+e^-$ flux on the DM halo profile. We use NFW Navarro:1996gj, Einasto ($\alpha = 0.17$) Navarro:2003ew, and Isothermal Bahcall:1980fbKamionkowski:1997xg profiles. The difference from the homogeneous distribution is proportional to ${x^2_{\rm diff}(E)} / { r_0^2 }$, where $r_0 = 8$ kpc is the distance from the center of the Galaxy. For small energies the characteristic diffusion distance increases and the corrections are more significant. Similar results were obtained in Hooper:2004bq for $M_{\rm DM} = 300$ GeV.
• Figure 3: Some properties of DM subhalos using results of Via Lactea II simulation Diemand:2008in. The upper plot shows the expected number of subhalos within a distance $r$ from the Earth. In the lower plot we show the ratio of luminosities of all subhalos within $r$ to the total luminosity of the host halo in the solid sphere of radius $r$ around the Earth. We plot the ratio of luminosities without Sommerfeld enhancement, with generic $S \sim 1 / v$ enhancement, and with resonant $S \sim 1 / v^2$ enhancement. These curves only account for subhalos resolved in the Via Lactea II simulation, $M_{\rm sub} \gtrsim 10^5 M_\odot$, and should be viewed as lower limits.
• Figure 4: The probability to observe an order one feature at high energies from a clump of dark matter versus the index $s$ of the luminosity function [Eq. (\ref{['lum_index']})]. The break at $s = 2$ corresponds to equipartition of DM luminosity. For $s < 2$ the luminosity is saturated by large clumps, for $s > 2$ the luminosity is saturated by small clumps. The overall normalization is model dependent.
• Figure 5: The luminosity function from VL2 subhalos, assuming NFW density and velocity dispersion profiles for the same three models as in Fig. \ref{['ViaLactea']}. Without Sommerfeld enhancement (circles) the luminosity function is equipartioned ($s=2$) down to the simulation's completeness limit, $L \sim 10^4 M_\odot^2$ pc$^{-3}$. For comparison we also show the distribution when the sample is restricted to subhalos with more than 250 particles ($M > 10^6 M_\odot$) [small circles]. In the $S \sim 1/v$ Sommerfeld case (squares), the luminosity function is steeper ($s=2.8$) above the saturation luminosity of $L_{\rm sat} \sim 2 \times 10^9 M_\odot^2$ pc$^{-3}$. Below saturation the distribution is expected to flatten to $s=2$ (dashed lines), and indeed this behavior is clearly seen for a model with a higher saturation luminosity of $L_{\rm sat} \sim 3 \times 10^{10} M_\odot^2$ pc$^{-3}$ corresponding to $m_\phi/M_{\rm DM} = 5 \times 10^{-5}$ (small squares). For $S \sim 1/v^2$ (triangles) the luminosity function above $L_{\rm sat}=10^{11} M_\odot^2$ pc$^{-3}$ is even steeper ($s=4.9$).