Dark Matter Interpretations of the Electron/Positron Excesses after FERMI

TL;DR

This paper analyzes whether the PAMELA positron excess and the FERMI/HESS $e^+ + e^-$ measurements can be explained by dark matter annihilation or decay into leptons. It systematically maps DM model space into leptophilic final states, including scenarios with hidden-sector showers and long-lived mediators, and examines how the indirect signals—especially diffuse gamma rays from inverse Compton scattering—depend on DM mass, density profile, and propagation. The authors find that DM masses of order TeV are favored and that leptonic channels such as $4e$, $4\mu$, and $4\tau$ can fit the data, while lighter DM or purely $e^+e^-$ channels are disfavored unless new spectral smearing mechanisms are invoked. A robust, testable prediction is a gamma-ray excess from ICS in FERMI data if the $e^{\pm}$ excess originates throughout the DM halo; gamma and neutrino bounds further constrain the viable channels, but mechanisms like hidden-sector showers or quasi-constant density profiles can reconcile some tensions. Overall, the work provides a framework for interpreting the $e^{\pm}$ anomalies within DM scenarios and outlines concrete observational tests to confirm or refute the DM origin.

Abstract

The cosmic-ray excess observed by PAMELA in the positron fraction and by FERMI and HESS in the electron + positron flux can be interpreted in terms of DM annihilations or decays into leptonic final states. Final states into tau's or 4mu give the best fit to the excess. However, in the annihilation scenario, they are incompatible with photon and neutrino constraints, unless DM has a quasi-constant density profile. Final states involving electrons are less constrained but poorly fit the excess, unless hidden sector radiation makes their energy spectrum smoother, allowing a fit to all the data with a combination of leptonic modes. In general, DM lighter than about a TeV cannot fit the excesses, so PAMELA should find a greater positron fraction at higher energies. The DM interpretation can be tested by FERMI gamma observations above 10 GeV: if the electronic excess is everywhere in the DM halo, inverse Compton scattering on ambient light produces a well-predicted gamma excess that FERMI should soon detect.

Figures (13)

• Figure 1: Sample DM fits. In the upper (lower) row we consider DM annihilations into $\mu^+\mu^-\mu^+\mu^-$ ($\tau^+\tau^-$) with MED diffusion minmedmax and the NFW (isothermal) DM profile: all good fits are very similar. Left: the positron fraction compared with the PAMELA excess. Middle: the $e^++e^-$ flux compared with the FERMI and HESS data. Right: the DM contribution to the diffuse photon energy spectra produced by bremsstrahlung (dashed red curve) and IC (black thick line); we also separately show the 3 IC components from star-light (red), CMB (green), dust (blue).
• Figure 2: Left: Energy spectra of the 3 galactic light components isrf, normalized to unity. Right: The functions $R_i(E_e)$ which encode the relativistic corrections to the ICS energy loss. The black think line shows the function $R(E_e)$ defined below Eq. (\ref{['eq: JG']}).
• Figure 3: Slices of the energy density profiles $u(r,z)$ of star-light (red upper curve) re-scattered by dust (blue), CMB (green horizontal line), and of the presumed galactic magnetic fields (dashed). Left: Profiles as a function of the radius $r$, for a fixed $z=1$ kpc. Right: Profiles as a function of the height, $z$, for a fixed $r=0$. The values corresponding to $B=1$ and $10\mu{\rm G}$ are indicated in the right plot.
• Figure 4: Inverse Compton: exact vs approximated. We compare our full calculation for ICS (solid curves) with the diffusion-less $I=1$ approximation of eq. (\ref{['eq:ICapprox']}) (dashed curves) for the '$10^\circ\div 20^\circ$' region and DM annihilating into $\mu^+\mu^-$ with $\sigma v=10^{-22} cm^3/s$ and NFW with MED propagation. Additionally we plot the individual contributions to ICS from CMB (blue), dust (green) and starlight (red), while the total contribution is in black. The ICS approximation is good within a factor of two.
• Figure 5: Global fit to PAMELA, FERMI and HESS data. The labels on each curve indicate the primary DM annihilation (left) or decay (right) channel. In the left panel a hypothetical flux from a pulsar is also plotted, with an assumption that the flux is given by $\Phi=E^{-p} e^{-E/M}$. In the left panel all final states for DM annihilation do not include hidden sector FSR, except for the curve labelled $4\mu-sh$. This curve demonstrates that by including the hidden sector shower the $\chi^2$ is significantly improved and is as good of fit as any other hypothesis.