Conservative Constraints on Dark Matter from the Fermi-LAT Isotropic Diffuse Gamma-Ray Background Spectrum

TL;DR

This study uses the Fermi-LAT isotropic diffuse gamma-ray background to place conservative limits on WIMP dark matter annihilation across standard model final states, emphasizing final-state radiation and avoiding strong substructure boosts. By modeling both Galactic and extragalactic contributions within CDM halo frameworks (NFW and Einasto) and using conservative halo mass cutoffs, the authors derive 95% CL constraints that approach the thermal relic cross-section for low-mass, hadronic channels and reanalyze HESS Galactic Ridge results for robustness. Their analysis rules out dark matter interpretations of the PAMELA and Fermi e+/e- data for two-body leptonic final states, while four-lepton channels via light mediators remain only partially excluded, highlighting the continued viability of some DM scenarios. Overall, the work provides a rigorous and conservative gamma-ray constraint on DM annihilation that is competitive with dwarf-galaxy and Galactic-pole limits and will sharpen with future LAT data and halo-model refinements.

Abstract

We examine the constraints on final state radiation from Weakly Interacting Massive Particle (WIMP) dark matter candidates annihilating into various standard model final states, as imposed by the measurement of the isotropic diffuse gamma-ray background by the Large Area Telescope aboard the Fermi Gamma-Ray Space Telescope. The expected isotropic diffuse signal from dark matter annihilation has contributions from the local Milky Way (MW) as well as from extragalactic dark matter. The signal from the MW is very insensitive to the adopted dark matter profile of the halos, and dominates the signal from extragalactic halos, which is sensitive to the low mass cut-off of the halo mass function. We adopt a conservative model for both the low halo mass survival cut-off and the substructure boost factor of the Galactic and extragalactic components, and only consider the primary final state radiation. This provides robust constraints which reach the thermal production cross-section for low mass WIMPs annihilating into hadronic modes. We also reanalyze limits from HESS observations of the Galactic Ridge region using a conservative model for the dark matter halo profile. When combined with the HESS constraint, the isotropic diffuse spectrum rules out all interpretations of the PAMELA positron excess based on dark matter annihilation into two lepton final states. Annihilation into four leptons through new intermediate states, although constrained by the data, is not excluded.

Figures (5)

• Figure 1: Shown is the observed isotropic diffuse background spectrum observed by Fermi-LAT (points with errors), and representative models of the annihilation spectrum of the Galactic (upper) and extragalactic (lower) contributions from the channel $\chi\chi\rightarrow b\bar{b}$ for $m_\chi = 10\rm GeV$ (solid), and for $m_\chi = 100\rm\ GeV$ (dashed). Both cases have the annihilation cross section $\langle \sigma_{\rm A} v\rangle = 3\times 10^{-26}\ \rm cm^3\ s^{-1}$.
• Figure 2: Constraints on the partial cross section of annihilation of dark matter to quarks, leptons, gauge bosons and Higgs, for $m_h = 120\rm GeV$. The regions are labeled by their corresponding constraining observations as described in the text: "Fermi-LAT Diffuse" from the Fermi-LAT isotropic diffuse $\gamma$-ray background. The regions labeled "HESS GR" are for three different cases, solid cyan using the conservative Einasto profile as described in the text, hashed cyan from the most stringent case, a low mass high concentration NFW profile, and the canonical $\rho_\odot = 0.3{\rm\ GeV\ cm^{-3}}, R_\odot = 8.5\rm\ kpc$ NFW profile as a dotted line for reference. All constraints are at 95% CL.
• Figure 3: Shown is a comparison of our work to the Fermi-LAT collaboration, Abdo et al. Abdo:2010dk constraints from the extragalactic signal in the diffuse extragalactic background from dark matter annihilation into the $b\bar{b}$ final state. Our limits from the extragalactic background with not boost enhancement of annihilation are comparable to and consistent with that of the Abdo et al. "MS-II Res" model due to similar chosen halo mass cut-off values. Our total 95% CL limit shown here and used in Fig. \ref{['array_plot']} comes from Galactic and extragalactic contributions, with a conservative boost factor, as described in the text. Shown also is our 95% extragalactic limit alone, and the conservative model in Abdo et al. of "MS-II sub1."
• Figure 4: Shown are constraints on regions of parameter space in annihilating dark matter models consistent with interpretations of the PAMELA positron excess (light pink region in all panels), and feature in the Fermi-LAT $e^+/e^-$ spectrum (red region in $\mu^+\mu^-$ and $\tau^+\tau^-$ panels), from Ref. Meade:2009iu (all 99% CL). All MW constraints and signals are for Einasto profiles, and at 95% CL. Our analysis of the Fermi-LAT isotropic diffuse background is shown along with our reanalysis of constraints from HESS observations of the Galactic Ridge (labeled HESS GR). We show several other recent constraints for comparison: ICS radiation constrained by Fermi-LAT data from the $3^\circ\times 3^\circ$ Galactic center exclude the region within the triple-dot-dashed regions in all panels Cirelli:2009dv; Galactic radio synchrotron observations exclude the region within the dotted line, in all panels Meade:2009iu; in the central $\mu^+\mu^-$ panel, we show the exclusion regions final state radiation constraints in Fermi-LAT observations of Draco (dashed line), and ICS radiation constraints from Fermi-LAT observations of Ursa Minor (dot-dashed line) Abdo:2010ex. All PAMELA models with $m_\chi \lesssim 1\rm\ TeV$ are firmly excluded by the lack of a $\gtrsim 20\%$ drop in the Fermi $e^+/e^-$ spectrum below 1 TeV Meade:2009iu.
• Figure 5: Interpretations of PAMELA and Fermi $e^+/e^-$ with an intermediate dark force carrying particle $\phi$ allowing for dark matter annihilation into four lepton final states. The upper (lower) two panels are $4e$ ($4\mu$) final states with $m_\phi = 0.3\rm\ GeV$ and $m_\phi = 0.8\rm GeV$. Galactic radio synchrotron observations exclude the region within the dotted line, in all panels Meade:2009iu. All PAMELA models with $m_\chi \lesssim 1\rm TeV$ are firmly excluded by the lack of a $\gtrsim 20\%$ drop in the Fermi $e^+/e^-$ spectrum below 1 TeV Meade:2009iu.