Conservative Constraints on Dark Matter Annihilation into Gamma Rays

TL;DR

This work derives conservative upper limits on the dark matter annihilation cross section into gamma rays across a broad mass range by integrating Galactic, Andromeda, and cosmic-diffuse gamma-ray data, and translates these into total cross-section limits using a conservative branching ratio to gamma rays, Br$(\gamma\gamma) \ge 10^{-4}$. The methodology combines DM halo modeling (favoring a Kravtsov profile), line-of-sight integrals, and cosmological diffusion with observational data from COMPTEL, EGRET, H.E.S.S., INTEGRAL, and Andromeda, while explicitly accounting for astrophysical uncertainties and background subtractions. Neutrino-based bounds are found to be very competitive, often stronger than gamma-ray limits at high masses, whereas gamma-ray data provide the strongest limits at intermediate and low masses; altogether, the results significantly constrain large DM annihilation signals and outline clear paths for improvement with future gamma-ray observatories such as GLAST. The paper emphasizes that, although the current limits are well above the canonical thermal relic cross section, they establish a robust, conservative baseline that can be substantially tightened with better background modeling and higher-resolution measurements.

Abstract

Using gamma-ray data from observations of the Milky Way, Andromeda (M31), and the cosmic background, we calculate conservative upper limits on the dark matter self-annihilation cross section to monoenergetic gamma rays, <sigma_A v>_{gamma gamma}, over a wide range of dark matter masses. (In fact, over most of this range, our results are unchanged if one considers just the branching ratio to gamma rays with energies within a factor of a few of the endpoint at the dark matter mass.) If the final-state branching ratio to gamma rays, Br(gamma gamma), were known, then <sigma_A v>_{gamma gamma} / Br(gamma gamma) would define an upper limit on the total cross section; we conservatively assume Br(gamma gamma) > 10^{-4}. An upper limit on the total cross section can also be derived by considering the appearance rates of any Standard Model particles; in practice, this limit is defined by neutrinos, which are the least detectable. For intermediate dark matter masses, gamma-ray-based and neutrino-based upper limits on the total cross section are comparable, while the gamma-ray limit is stronger for small masses and the neutrino limit is stronger for large masses. We comment on how these results depend on the assumptions about astrophysical inputs and annihilation final states, and how GLAST and other gamma-ray experiments can improve upon them.

Figures (3)

• Figure 1: Example dark matter annihilation signals, shown superimposed on the Galactic and extragalactic gamma-ray spectra measured by COMPTEL and EGRET. In each case, the cross section is chosen so that the signals are normalized according to our conservative detection criteria, namely, that the signal be 100% of the size of the background when integrated in the energy range chosen (0.4 in $\log_{10}E$, shown by horizontal arrows). The narrow signal on the right is the Galactic Center flux due to annihilation into monoenergetic gamma rays, for $m_\chi = 1$ GeV; the signal is smeared as appropriate for a detection with finite energy resolution. The broad feature on the left is the cosmic diffuse signal for annihilation into monoenergetic gamma rays at $m_\chi = 0.1$ GeV, smeared by redshift.
• Figure 2: The limits on the partial cross section, $\langle \sigma_A v \rangle_{\gamma\gamma}$, derived from the various gamma-ray data. Our overall limit is shown as the dark shaded exclusion region. For comparison, the light-shaded region shows the corresponding limits for the NFW (rather than the Kravtsov) profile.
• Figure 3: The gamma-ray and neutrino limits on the total annihilation cross section, selecting $Br(\gamma\gamma) = 10^{-4}$ as a conservative value. The unitarity and KKT bounds are also shown. The overall bound on the total cross section at a given mass is determined by the strongest of the various upper limits.