Anisotropy of the cosmic gamma-ray background from dark matter annihilation

TL;DR

This paper develops a halo-model framework to predict the angular power spectrum of the cosmic gamma-ray background arising from dark matter annihilation, focusing on the density-squared emissivity and its 3D fluctuations. The authors derive how the angular power spectrum $C_l$ is connected to the 3D power spectrum $P_f(k)$ of $f=\delta^2-\langle\delta^2\rangle$, showing that the four-point (1-halo and 2-halo) contributions dominate over the two-point term, with the 1-halo term governing small scales. They apply the formalism to GeV-scale neutralinos and MeV-scale DM, finding that future detectors like GLAST (GeV) and ACT (MeV) should detect the predicted anisotropy, and that the shape of $C_l$ depends on the minimum halo mass $M_{\min}$, enabling a diagnostic of micro-halo survival and substructure. The work argues that the angular power spectrum provides a robust, smoking-gun signature to distinguish DM annihilation from astrophysical backgrounds and offers a quantitative tool to probe halo substructure and DM particle properties.

Abstract

High-energy photons from dark matter annihilation contribute to the cosmic gamma-ray background (CGB). Since dark matter particles are weakly interacting, annihilation can happen only in high density regions such as dark matter halos. The precise shape of the energy spectrum of CGB depends on the nature of dark matter particles, as well as the cosmological evolution of dark matter halos. In order to discriminate between the signals from dark matter annihilation and other astrophysical sources, however, the information from the energy spectrum may not be sufficient. We show that dark matter annihilation also produces a characteristic anisotropy of the CGB, which provides a powerful tool for testing the origin. We develop the formalism based on a halo model approach to calculate the three-dimensional power spectrum of dark matter clumping, which determines the power spectrum of annihilation signals. We show that the sensitivity of future gamma-ray detectors such as GLAST should allow us to measure the angular power spectrum of CGB anisotropy, if dark matter particles are supersymmetric neutralinos and they account for most of the observed mean intensity of CGB in GeV region. On the other hand, if dark matter has a relatively small mass, and accounts for most of the CGB in MeV region, then the future Advanced Compton Telescope should be able to measure the anisotropy in MeV region. As the intensity of photons from annihilation is proportional to the density squared, we show that the predicted shape of the angular power spectrum of gamma rays from dark matter annihilation is different from that due to other astrophysical sources such as blazars. Therefore, the angular power spectrum of the CGB provides a smoking-gun signature of dark matter annihilation.

Figures (12)

• Figure 1: Average intensity of the CGB from dark matter annihilation compared with the COMPTEL and EGRET data. The curve in GeV region is the predicted intensity for neutralinos with $m_\chi = 100$ GeV, while that in MeV region is the prediction for MeV dark matter particles with $m_\chi = 20$ MeV. As for the normalization, we have used $\langle \sigma v \rangle = 3 \times 10^{-26}$ cm$^3$ s$^{-1}$, and extra "boost" factors have been multiplied to match the observational data. For details of the boost factors, see the last paragraph of Sec. II.
• Figure 2: Dimensionless power spectrum of $f=\delta^2 - \langle \delta^2 \rangle$, $\Delta_{f,2}^2(k)$ [Eq. (\ref{['eq:dimpow']})], from the two-point correlation term [Eq. (\ref{['eq:P_f,2']})], evaluated at $z=0$ for $M_{\rm min} = 10^6 M_\odot$.
• Figure 3: The function that determines the four-point contribution to the power spectrum of CGB anisotropy, $v(k|M)$ [see Eqs. (\ref{['eq:PS 1-halo\n term']}) and (\ref{['eq:PS 2-halo term']})], as a function of $k$ evaluated at $z=0$ for various values of $M$. The value of $M$ labeling each curve is spaced by one order of magnitude, with the largest and smallest values as indicated.
• Figure 4: Dimensionless power spectrum of $f=\delta^2-\langle\delta^2\rangle$ from the four-point contribution, $\Delta_{f,4}^2(k)$ [Eq. (\ref{['eq:dimpow']})], by the 1-halo (dotted) and 2-halo (dashed) terms [Eqs. (\ref{['eq:PS 1-halo term']}) and (\ref{['eq:PS\n 2-halo term']})]. Both are evaluated at $z=0$ for $M_{\rm min} = 10^6 M_\odot$.
• Figure 5: The same as Fig. \ref{['fig:Delta']} but for the smaller minimum mass, $M_{\rm min} = 10^{-6} M_\odot$. Contributions from halos of various mass ranges are also shown.