Constraints on leptonically annihilating Dark Matter from reionization and extragalactic gamma background

TL;DR

The paper investigates whether leptonic dark matter (DM) annihilation can explain the PAMELA/Fermi/HESS (PFH) anomalies and derives constraints from two extragalactic observables: the diffuse extragalactic $\gamma$-ray background and the Thomson optical depth of the CMB. By using PYTHIA to generate final-state spectra and solving a radiative transfer equation that includes both prompt and inverse-Compton photons, the authors quantify energy deposition into the IGM via $\epsilon(z)$ and the consequent ionization history. They find that optical-depth constraints robustly exclude the PFH region for the $\tau^{-}+\tau^{+}$ channel and largely for $\mu^{-}+\mu^{+}$, while gamma-ray-background constraints (especially under a power-law $c(M)$) rule out the PFH region for all leptonic channels; fully low-redshift reionization models are disfavored due to excessive high-$z$ ionization and cross sections larger than PFH suggests. The results highlight the importance of halo concentration modeling for gamma-ray bounds and suggest that upcoming Fermi data will further tighten the allowed parameter space.

Abstract

The PAMELA, Fermi and HESS experiments (PFH) have shown anomalous excesses in the cosmic positron and electron fluxes. A very exciting possibility is that those excesses are due to annihilating dark matter (DM). In this paper we calculate constraints on leptonically annihilating DM using observational data on diffuse extragalactic gamma-ray background and measurements of the optical depth to the last-scattering surface, and compare those with the PFH favored region in the m_{DM} - <σ_A v> plane. Having specified the detailed form of the energy input with PYTHIA Monte Carlo tools we solve the radiative transfer equation which allows us to determine the amount of energy being absorbed by the cosmic medium and also the amount left over for the diffuse gamma background. We find that the constraints from the optical depth measurements are able to rule out the PFH favored region fully for the τ^{-}+τ^{+} annihilation channel and almost fully for the μ^{-}+μ^{+} annihilation channel. It turns out that those constraints are quite robust with almost no dependence on low redshift clustering boost. The constraints from the gamma-ray background are sensitive to the assumed halo concentration model and, for the power law model, rule out the PFH favored region for all leptonic annihilation channels. We also find that it is possible to have models that fully ionize the Universe at low redshifts. However, those models produce too large free electron fractions at z > ~100 and are in conflict with the optical depth measurements. Also, the magnitude of the annihilation cross-section in those cases is larger than suggested by the PFH data.

Figures (6)

• Figure 1: The final state distributions of electrons/positrons, photons, and neutrinos/antineutrinos for the annihilating DM with $m_{DM}=1$ TeV.
• Figure 2: (Upper panel) Boost factors $B(z)$ as defined in Eq. (\ref{['eq02']})) for various concentration models. (Lower panel) $f$-parameter as given by Eq. (\ref{['eq10']}), i.e. the ratio of the total energy deposition and local "smooth" energy injection rates for two different concentration models and two leptonic annihilation channels, assuming the annihilating DM particle with mass $m_{DM}=1$TeV. The short dashed lines show the ratio $\bar{\epsilon}/(4\pi \bar{\jmath})$ where for calculating $\bar{\epsilon}$ one takes $B=1$ in Eq. (\ref{['eq06']}). The results for the annihilation channel $DM+DM\rightarrow \tau^{-}+\tau^{+}$ are very similar to the $\mu^{-}+\mu^{+}$ case and for clarity are not shown here.
• Figure 3: The redshift $z^{'}$ where the optical depth for photons reaches unity (i.e., $\tau_{\nu}(z,z^{'})=1$ in Eq.(\ref{['eq07']})) for several "observer's redshifts": $z=0,10,100,500,1000$. Here the energy plotted is the photon energy at redshift $z$.
• Figure 4: Example $\gamma$-ray spectra at redshift $z=0$ assuming the annihilating DM particle with mass $m_{DM}=1$TeV. Here the two most extreme concentration models of Fig. \ref{['fig2']} have been used and the results are given for all three leptonic annihilation channels. The thermally averaged annihilation cross-section has been set to $25$ times its standard value of $\sim 3\times10^{-26}{\rm cm}^2$. The points with errorbars correspond to the EGRET measurements of the extragalactic gamma background as given in 1998ApJ...494..523S. The solid horizontal line, which is used in the following as an upper bound for the level of diffuse $\gamma$-ray background, represents the EGRET measurements reduced by a factor of three.
• Figure 5: The evolution of the ionization fraction (upper panel) and matter temperature (lower panel) for the model with the annihilating DM particle with mass $m_{DM}=1$TeV and with a thermally averaged cross-section $\langle\sigma_A\upsilon\rangle=3\times10^{-24}{\rm cm}^2$. The two most extreme concentration models of Fig. \ref{['fig2']} have been used and for clarity only the results for the $e^{-}+e^{+}$ channel are shown. The lowest solid line plots the case where the structure boost has been neglected, i.e. $B(z)=1$ and the dashed line corresponds to the standard "concordance" cosmology without an annihilating DM. In the lower panel the dotted line shows the evolution of the CMB temperature.