CMB constraints on WIMP annihilation: Energy absorption during the recombination epoch

We compute in detail the rate at which energy injected by dark matter (DM) annihilation heats and ionizes the photon-baryon plasma at $z\sim 1000$, 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.

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 $\mathrm{H}/\mathrm{He}$ gas, photon-photon scattering, and pair production on the CMB. All the curves assume a $\mathrm{He}$ mass fraction of $1/4$, with a density of $2.57\times {10}^{-7}\mathrm{amu}/{\mathrm{cm}}^3$ 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 5, which had an error leading to cooling times approximately a factor of 3 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 $2.57\times {10}^{-7}\mathrm{amu}/{\mathrm{cm}}^3$ 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 38: 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 $M_{\mathrm{DM}}=1000\mathrm{GeV}$ (top) and $M_{\mathrm{DM}}=10\mathrm{GeV}$ (bottom), for $\chi \chi \to \varphi \varphi$ followed by $\varphi \to e^{+}{e}^{-}$, with $m_{\varphi }=1\mathrm{GeV}$.

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 and (anti)protons. Upper left panel: direct annihilation to SM leptons. Upper right panel: direct annihilation to nonleptonic 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 $\mathtt{R}\mathtt{E}\mathtt{C}\mathtt{F}\mathtt{A}\mathtt{S}\mathtt{T}$ 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 ${\sigma }_8$ [5].

Figure 6

Constraints on the annihilation cross-section $⟨{\sigma }_{A}v⟩$ the efficiency factor $f$. The dark blue area is excluded by WMAP5 data at 95% confidence, whereas the lighter blue area shows the region of parameter space that will be probed by Planck. The cyan area is the zone that can ultimately be explored by a cosmic variance limited experiment with angular resolution comparable to Planck. Constraints are taken from 43 (Fig. 4). The data points indicate the positions of models which fit the observed cosmic-ray excesses, as fitted in 21, 56. Squares: PAMELA only. Diamonds: PAMELA and Fermi. Crosses: PAMELA and ATIC. Error bars indicate the factor-of-4 uncertainty in the required boost factor due to uncertainties in the local dark matter density (any substructure contributions are not taken into account). For models labeled by XDM followed by a ratio, the annihilation is through an XDM intermediate light state to electrons, muons and pions in the given ratio (e.g. “XDM $4:4:1$” corresponds to $4:4:1$ annihilation to $e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$ and ${\pi }^{+}{\pi }^{-}$).