Distinguishing standard reionization from dark matter models

The Wilkinson Microwave Anisotropy Probe (WMAP) experiment has detected reionization at the $5.5\sigma$ level and has reported a mean optical depth of $0.088\pm 0.015$. A powerful probe of reionization is the large-angle $EE$ polarization power spectrum, which is now (since the first five years of data from WMAP) cosmic variance limited for $2\le l\le 6$. Here we consider partial reionization caused by weakly interacting massive particle dark matter annihilation, and calculate the expected polarization power spectrum. We compare the dark matter models with a standard two-step reionization theory, and examine whether the models may be distinguished using current, and future cosmic microwave background (CMB) observations. We consider dark matter annihilation at intermediate redshifts ($z<60$) due to halos, as well as annihilation at higher redshifts due to free particles. In order to study the effect of high redshift dark matter annihilation on CMB power spectra, it is essential to include the contribution of residual electrons (left over from recombination) to the ionization history. Dark matter halos at redshifts $z<60$ influence the low multipoles $l<20$ in the $EE$ power spectrum, while the annihilation of free particle dark matter at high redshifts $z>100$ mainly affects multipoles $l>10$.

Figure 1

Inverse Compton scattering of a single electron of energy 1 GeV with the CMB at $z=500$. The curves show the photon spectrum at times when 1%, 50%, 90%, and 99% of the initial electron energy has been lost to the CMB.

Figure 2

Estimating the initial value of $x_{\mathrm{ion}}$ for the different dark matter models in the absence of residual electrons. The solid line is the power law fit, while the dashed lines are drawn for different values of $x_{\mathrm{init}}$.

Figure 3

Comparing the three dark matter models with baryonic model A. For $z<25$, the dark matter models are identical to model A, and have an optical depth $\tau (0,25)=0.087$. For $z>25$, the dark matter models feature partial ionization due to halos and free particles. Also shown for comparison is a “sudden” reionization model. Part (a) shows the ionization history for the different models. Part (b) shows the respective polarization power spectra ($EE$), with $1\sigma$ cosmic variance error bars computed using the power spectrum of model A. Part (c) shows the $\sigma (l)$ deviations of the different models ($EE$ power spectra), all compared to model A. The solid (black) curve denotes the “sudden” reionization model, while the three dashed curves are drawn for the three dark matter models. DM model #1 is indistinguishable from model A.

Figure 4

The $TT$ power spectrum. Partial ionization by dark matter results in a larger optical depth, causing a suppression of power (top panel). Decreasing the amplitude of the primordial scalar power $A_{\mathrm{s}}$ by $\sim 5\%$ can mimic the effect of $\tau (z)$ (bottom panel).

Figure 5

The large-angle $EE$ (top panel) and $TE$ (bottom panel) power spectra. The $1\sigma$ cosmic variance error bars are drawn for baryonic model A. The solid (black) curve is drawn for the baryonic model with reduced $A_{\mathrm{s}}$. The dashed curve (blue) is plotted for dark matter model #3 ($m_{\chi }=10\mathrm{GeV}$, $c=15$). It is harder to distinguish different models using the $TE$ power spectrum because $C_l^{TE}\propto \tau (z)$, while $C_l^{EE}\propto \tau (z{)}^2$. Following the WMAP convention, the bottom panel shows $(l+1)C_l^{TE}/2\pi$ and not $l(l+1)C_l^{TE}/2\pi$.