CMB Constraints on WIMP Annihilation: Energy Absorption During the Recombination Epoch

TL;DR

The paper develops a detailed framework to quantify how energy from dark matter annihilation deposits into the photon–baryon plasma near recombination, altering the ionization history and CMB power spectra. By solving the coupled evolution of electron and photon spectra and moving beyond the on-the-spot approximation, it derives redshift-dependent deposition efficiencies $f(z)$ for a wide range of channels and masses, and translates these into CMB constraints on the annihilation cross section, including Sommerfeld-enhanced scenarios. The results show that models proposed to explain cosmic-ray electron/positron excesses are largely in tension with WMAP5, especially when Sommerfeld enhancement is unsaturated, and Planck is expected to decisively test many of these scenarios. The work provides accurate fits for $f(z)$ and a practical framework for applying CMB constraints to specific DM models, with significant implications for the viability of non-thermal production and light-force-carrier theories.

Abstract

We compute in detail the rate at which energy injected by dark matter annihilation heats and ionizes the photon-baryon plasma at z ~ 1000, and provide accurate fitting functions over the relevant redshift range for a broad array of annihilation channels and DM masses. The resulting perturbations to the ionization history can be constrained by measurements of the CMB temperature and polarization angular power spectra. We show that models which fit recently measured excesses in 10-1000 GeV electron and positron cosmic rays are already close to the 95% confidence limits from WMAP. The recently launched Planck satellite will be capable of ruling out a wide range of DM explanations for these excesses. In models of dark matter with Sommerfeld-enhanced annihilation, where sigma v rises with decreasing WIMP velocity until some saturation point, the WMAP5 constraints imply that the enhancement must be close to saturation in the neighborhood of the Earth.

Figures (6)

• Figure 1: A comparison of the photon cooling time to the Hubble time at $z=1000$, for different photon energies. The dominant processes (in order of increasing energy) are ionization, Compton scattering, pair production on the H/He gas, photon-photon scattering, and pair production on the CMB. All the curves assume a He mass fraction of 1/4, with a density of $2.57 \times 10^{-7}$ amu / cm$^{3}$ today. The dotted curve shows pair production on a neutral IGM, the dashed curve shows pair production on a fully ionized IGM, and the dashed-dotted curve represents pair production on the CMB. This figure updates Fig. 1 in Padmanabhan:2005es, which had an error leading to cooling times approximately a factor of three longer.
• Figure 2: A comparison of the photon cooling time (from all processes) to the Hubble time over the entire redshift range of interest. The plot assumes a He mass fraction of 1/4, with a baryon density of $2.57 \times 10^{-7}$ amu / cm$^{3}$ today, and the standard ionization history and fiducial cosmology. The dashed line corresponds to $t_\mathrm{cool} = t_H$. There is a discrepancy between this figure and Fig. 2 in the originally published version of Chen:2003gz: the authors of that paper have advised us that upon revising their calculation, their results now agree with ours.
• Figure 3: The photon spectrum as a function of energy at several redshifts for $M_\mathrm{DM} = 1000$ GeV (top) and $M_\mathrm{DM} = 10$ GeV (bottom), for $\chi \chi \rightarrow \phi \phi$ followed by $\phi \rightarrow e^+ e^-$, with $m_\phi = 1$ GeV.
• Figure 4: The "deposited power fraction" $f(z)$ is the ratio of the power deposited in the gas (in the form of ionizations, excitations, and heating) to the mass energy liberated by WIMP annihilations. For electron channels, $f(z) \sim 1$ at high $z$, but other channels lose some fraction of their power to neutrinos, protons and neutrons. Upper left panel: direct annihilation to SM leptons. Upper right panel: direct annihilation to non-leptonic SM states ("light quarks" corresponds to 50 $\%$ annihilation to u quarks, 50 $\%$ to d quarks). Lower left panel: XDM-type models with annihilation through an intermediate 1 GeV state to electrons and muons. Lower right panel: XDM-type models with annihilation through an intermediate 1 GeV state to charged pions, and through an intermediate 4 GeV state to taus. The legend indicates the annihilation channel and the WIMP mass. The kink around $z=1700$ is an artifact of an approximation made in RECFAST and has no impact on our results.
• Figure 5: CMB power spectra for three different DM annihilation models, with power injection normalized to that of a 1 GeV WIMP with thermal relic cross section and $f=1$, compared to a baseline model with no DM annihilation. The models give similar results for the TT (left), TE (middle), and EE (right) power spectra. This suggests that the CMB is sensitive to only one parameter, the average power injected around recombination. All curves employ the WMAP5 fiducial cosmology: the effects of DM annihilation can be compensated to a large degree by adjusting $n_s$ and $\sigma_8$Padmanabhan:2005es.