Patchy screening of the cosmic microwave background by inhomogeneous reionization

We derive a constraint on patchy screening of the cosmic microwave background from inhomogeneous reionization using off-diagonal $TB$ and $TT$ correlations in WMAP-7 temperature/polarization data. We interpret this as a constraint on the rms optical-depth fluctuation $\Delta \tau$ as a function of a coherence multipole $L_C$. We relate these parameters to a comoving coherence scale, of bubble size $R_C$, in a phenomenological model where reionization is instantaneous but occurs on a crinkly surface, and also to the bubble size in a model of “Swiss cheese” reionization where bubbles of fixed size are spread over some range of redshifts. The current WMAP data are still too weak, by several orders of magnitude, to constrain reasonable models, but forthcoming Planck and future EPIC data should begin to approach interesting regimes of parameter space. We also present constraints on the parameter space imposed by the recent results from the EDGES experiment.

Figure 1

The measurement of the power spectrum of fluctuations of the optical depth $\tau$ from $TB$ correlation with corresponding $1\sigma$ and $3\sigma$ confidence-level intervals for all multipoles up to the resolution limit of WMAP-7 is shown in the top two panels. A binned version with associated statistical uncertainty is shown in the bottom panel. The first two bins are $-0.0085\pm 0.1264$ at $L=26$, and $0.0029\pm 0.0056$ at $L=77$; they are omitted for the sake of clearer presentation. The measurements are consistent with zero at all multipoles.

Figure 2

Measurement of ${\widehat{C}}_L^{\tau \tau }$ from $TB$ correlation in WMAP-7 data. Results shown in black (filled circles) are obtained by using the analysis mask that covers all the point sources brighter than $\sim 1\mathrm{Jy}$, while the results in red (empty circles) are obtained after unmasking all the point sources. In spite of the large difference in the source contamination, the two results differ by much less than the statistical uncertainty, and no overall bias is observed.

Figure 3

Measurement of ${\widehat{C}}_L^{\tau \tau }$ from $TB$ correlation in WMAP-7 data. Black filled circles represent the measurements obtained from the foreground-reduced maps after applying the fiducial analysis mask (the fiducial result of Fig. 1). The rest of the data points correspond to the two test cases: the green x’s are obtained from the maps prior to foreground subtraction, but using the fiducial mask, while the red empty circles are measurements obtained from foreground-reduced maps after applying an extended mask. No overall bias is observed in the two cases, and all three results are consistent, within the estimated statistical uncertainty.

Figure 4

Family of simple patchy-reionization models given by Eq. (4) for $\Delta \tau =1$ and different values of $L_C$.

Figure 5

Shown are the $1\sigma$ confidence-level upper limits from WMAP-7 $TT$ and $TB$ correlations on the amplitude $(\Delta \tau {)}^2$ of the patchy-screening model given in Eq. (4) as a function of the coherence-scale parameter $L_C$. Also shown are sensitivity forecasts for experiments with map noise of $27\mu \mathrm{Karcmin}$ and $1\mu \mathrm{Karcmin}$, and beam width of $7^{\prime }$ and $5^{\prime }$, corresponding to Planck and EPIC-like mission, respectively. The values expected for a reionization surface that is crinkled on scales $R_C$ are indicated by the gray band. Also shown is the portion of this parameter space excluded by EDGES [9].