Gamma-ray Constraints on Dark Matter Annihilation into Charged Particles

TL;DR

This work derives robust upper bounds on the DM annihilation cross section into $e^+e^-$ by exploiting the model-independent gamma-ray flux from internal bremsstrahlung near the endpoint $E_\gamma = m_\chi$. By coupling the IB spectrum $dN_\gamma/dE$ to the halo-averaged line-of-sight factor $\mathcal{J}_{\Delta\Omega}$ and confronting it with COMPTEL, EGRET, H.E.S.S., and M31 data, the authors obtain profile-dependent limits spanning $m_\chi \sim 10^{-3}-10^4$ GeV, with Kravtsov providing the most conservative bounds. The results show the IB bounds on $\langle \sigma_A v \rangle_{e^+e^-}$ are typically weaker than the $\gamma\gamma$ channel by a factor of about $10^2$, but can exceed neutrino-based total-cross-section limits, and are competitive with synchrotron-based constraints while being less sensitive to astrophysical uncertainties. This IB method offers a clean, near-ideal probe for leptonic DM channels and complements future gamma-ray observations to constrain DM models with enhanced leptonic final states.

Abstract

Dark matter annihilation into charged particles is necessarily accompanied by gamma rays, produced via radiative corrections. Internal bremsstrahlung from the final state particles can produce hard gamma rays up to the dark matter mass, with an approximately model-independent spectrum. Focusing on annihilation into electrons, we compute robust upper bounds on the dark matter self annihilation cross section $<σ_A v >_{e^+e^-}$ using gamma ray data from the Milky Way spanning a wide range of energies, $\sim10^{-3} - 10^4$ GeV. We also compute corresponding bounds for the other charged leptons. We make conservative assumptions about the astrophysical inputs, and demonstrate how our derived bounds would be strengthened if stronger assumptions about these inputs are adopted. The fraction of hard gamma rays near the endpoint accompanying annihilation to $e^+e^-$ is only a factor of $\alt 10^2$ lower than for annihilation directly to monoenergetic gamma rays. The bound on $<σ_A v >_{e^+e^-}$ is thus weaker than that for $<σ_A v >_{γγ}$ by this same factor. The upper bounds on the annihilation cross sections to charged leptons are compared with an upper bound on the {\it total} annihilation cross section defined by neutrinos.

Figures (4)

• Figure 1: Internal bremsstrahlung gamma-ray spectra per $\chi\chi\rightarrow e^+e^-$ annihilation, for $m_\chi=$ 100, 200, 500, and 1000 GeV.
• Figure 2: Number of gamma rays per DM annihilation ($\int_{E_{\rm min}}^{m_\chi}dE\,\, dN_\gamma/dE$) as a function of the lower limit of integration, for IB emission from $\chi\chi\rightarrow e^+e^-$ (solid line). A typical bin size used in the analysis is shown. The DM mass used is 1000 GeV; variation with $m_\chi$ is very small. Shown for comparison is the number of photons per annihilation for the process $\chi\chi\rightarrow\gamma\gamma$ (dashed line) in which the photons are always at the endpoint.
• Figure 3: Upper limit on $\langle \sigma v \rangle_{e^+e^-}$ as a function of DM mass for the Kravtsov (solid line), NFW (dashed line) and Moore (dotted-dashed line) profiles.
• Figure 4: Upper limits on the partial cross sections $Br(ii)\times\langle \sigma v \rangle_{total}$ for various final states $ii=e^+e^-$ (solid black line; labeled), $\mu^+\mu^-$ (thick dashed line; labeled), $\tau^+\tau^-$ (thick dashed line; labeled), $\gamma\gamma$ (red line; labeled), and $\bar{\nu}\nu$ (blue line; labeled), using the conservative Kravtsov profile. Each of these partial cross-section limits is independent, with no relationship assumed between the branching ratios to particular final states. Also shown are the KKT (thin dashed line) and unitarity (thin dotted-dashed line) limits on the total cross section described in the text, and the cross section for thermal relic DM (natural scale). The $\gamma\gamma$ and $\bar{\nu} \nu$ limits are taken from Ref. MJBBY and Ref. YHBA, respectively.