Detecting dark matter annihilation with CMB polarization: Signatures and experimental prospects

Dark matter (DM) annihilation during hydrogen recombination ($z\sim 1000$) will alter the recombination history of the Universe, and affect the observed CMB temperature and polarization fluctuations. Unlike other astrophysical probes of DM, this is free of the significant uncertainties in modelling galactic physics, and provides a method to detect and constrain the cosmological abundances of these particles. We parametrize the effect of DM annihilation as an injection of ionizing energy at a rate ${ϵ}_{\mathrm{DM}}$, and argue that this simple “on the spot” modification is a good approximation to the complicated interaction of the annihilation products with the photon-electron plasma. Generic models of DM do not change the redshift of recombination, but change the residual ionization after recombination. This broadens the surface of last scattering, suppressing the temperature fluctuations and enhancing the polarization fluctuations. We use the temperature and polarization angular power spectra to measure these deviations from the standard recombination history, and therefore, indirectly probe DM annihilation. The modifications to the temperature power spectrum are nearly degenerate with the primordial scalar spectral index and amplitude; current CMB data are therefore unable to put any constraints on the annihilation power. This degeneracy is broken by polarization; Planck will have the sensitivity to measure annihilation power ${ϵ}_{\mathrm{DM}}(z=1000)>{10}^{-15}\mathrm{eV}/\mathrm{s}/\mathrm{\text{proton}}$, while high sensitivity experiments (e.g. NASA’s CMBpol) could improve that constraint to ${ϵ}_{\mathrm{DM}}(z=1000)>4\times {10}^{-16}\mathrm{eV}/\mathrm{s}/\mathrm{\text{proton}}$, assuming a fractional detector sensitivity of $\Delta T/T\sim 1\mu \mathrm{K}$ and a beam of $3^{\prime }$. These limits translate into a lower bound on the mass of the DM particle, $M_{\mathrm{DM}}>10-100\mathrm{GeV}$, assuming a single species with a cross section of $⟨{\sigma }_{A}v⟩\sim 2\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$, and a fraction $f\sim 0.1-1$ of the rest mass energy used for ionization. The bounds for the Wilkinson microwave anisotropy probe (WMAP) 4y data are significantly lower, because of its lack of high $S/N$ polarization measurements, but it can strongly constrain $\mathcal{O}(\mathrm{MeV})$ particles such as those proposed by Boehm et al. (2004).

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, and photon-photon scattering. All the curves (except the dotted curve) assume a neutral IGM, with a density of $2\times {10}^{-7}{\mathrm{cm}}^{-3}$ atoms today. The dotted curve shows the pair production rate for a completely ionized IGM. Regions where $t_{\mathrm{H}}/t_{\mathrm{cool}}<1$ are transparent; photons injected at these energies lose their energy by redshifting. Note that photon-photon scattering does not transfer the energy to electrons, but simply redistributes it to lower energies. This figure ignores pair production off CMB photons since this process is subdominant for the energy range considered here; it however dominates at higher energies.

Figure 2

The injection of energy from dark matter annihilation into the IGM, via the creation of electromagnetic cascades. Energy transfer to the IGM takes place principally through the ionization and collisional processes.

Figure 3

The ionization fraction $x_e$ (top), matter temperature (center), and visibility function (bottom) as a function of ${ϵ}_{\mathrm{DM}}$. The heavy solid lines show the fiducial model with ${ϵ}_{\mathrm{DM}}=0$; from bottom to top, ${ϵ}_{\mathrm{DM},0}=5,10,100,500\times {10}^{-25}\mathrm{eV}/s$. The thin dashed line in the center plot shows the evolution of CMB temperature, $T(z)=T_0(1+z)$. Note that the injection of additional energy does not slow recombination, but increases the residual ionization; this leaves the peak of the visibility function unchanged but broadens the surface of last scattering.

Figure 4

The TT, TE, and EE angular power spectra for our fiducial cosmological model, with no DM annihilation (solid and dotted lines), and with ${ϵ}_{\mathrm{DM},0}={10}^{-22}\mathrm{eV}/\mathrm{s}$. Also shown are the polarization noise spectra, for the WMAP V band, the Planck 143 Ghz channel, and a hypothetical high resolution polarization experiment (see Table  for details).

Figure 5

(Top) The heavy lines show the ratio of damping functions $D(k)/D_0(k)$ for ${ϵ}_{\mathrm{DM},0}$ of 100, (solid), 500 (dotted), and $1000\times {10}^{-25}\mathrm{eV}/\mathrm{s}$ (dashed) and our fiducial cosmology. The light lines show this same ratio divided by $(k/k_{\mathrm{fid}}{)}^{-\alpha }$ where $k_{\mathrm{fid}}=0.05{\mathrm{Mpc}}^{-1}$. The horizontal dotted lines are a visual guide. (Bottom) The solid line shows the ratio of a model with no DM annihilation, but with $n_s$ altered using the analytic calculation above, to our fiducial model with ${ϵ}_{\mathrm{DM},0}=500\times {10}^{-25}\mathrm{eV}/\mathrm{s}$. The dashed line has the same ratio, except that all the cosmological parameters are adjusted to best fit the model with DM annihilation.

Figure 6

The detectability of a given injection energy, ${ϵ}_{\mathrm{DM},0}$, for the different experimental specifications of Table , assuming a maximum multipole, $l_{\max }=2500$. The lines, from left to right, are for cosmic variance, HiRes POL, the Planck 143 Ghz channel, and the WMAP V band. The dashed line shows the cosmic variance detectability for $l_{\max }=1500$, while the dot-dashed lines show it for 20% and 50% sky coverage. The dotted line uses the parameters for HiRes POL, but with no polarization information. Also shown are the 68%, 90%, and 99% levels.

Figure 7

The 90% exclusion region in the $M_{\mathrm{DM}}-f$ plane, for (from top to bottom) WMAP , Planck, and HiRes POL; regions above the lines can be excluded by these experiments. This assumes our fiducial cosmology, and Eq. (6) to relate $f$ and $M_{\mathrm{DM}}$ to ${ϵ}_{\mathrm{DM}}$; $⟨{\sigma }_{A}v⟩$ is set to the value required for a thermal relic density, but deviations from this can be absorbed into $f$. The dotted lines also show the 68% and 99% exclusion regions for our hypothetical polarization experiment.

Figure 8

Contours in the ${\Omega }_{\mathrm{DM}}–⟨{\sigma }_{A}v⟩$ plane with ${ϵ}_{\mathrm{DM},0}={10}^{-24}\mathrm{eV}/\mathrm{s}$, for $M_{\mathrm{DM}}/f=1\mathrm{TeV}$, 1 GeV, and 1 MeV (solid), and 10 TeV, 10 GeV, and 10 MeV (dashed). Regions above these contours are accessible to an experiment with the sensitivity to measure ${ϵ}_{\mathrm{DM},0}={10}^{-24}\mathrm{eV}/\mathrm{s}$. The shaded region shows the region excluded by our fiducial model.