Constraining reionization with the first measurement of the cross-correlation between the CMB optical-depth fluctuations and the Compton y-map

Abstract

We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, $\delta \tau$, and the Compton $y$-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the $y$-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic SZ effect can not. We measure this new observable using a Planck $y$-map as well as a map of optical-depth fluctuations that we reconstruct from Planck CMB temperature data. We use our measurements to derive a first CMB-only upper limit on the temperature inside ionized bubbles, $T_{\mathrm{b}}\lesssim 7.0\times 10^5$K ($2\sigma$). We also present future forecasts, assuming a fiducial model with characteristic reionization bubble size $R_{\mathrm{b}}=5$Mpc and $T_{\mathrm{b}}=5\times 10^4$K. The signal-to-noise ratio of the fiducial cross-correlation using a signal dominated PICO-like $y$-map becomes $\simeq 7$ with CMB-S4 $\delta \tau$ and $\simeq 13$ with CMB-HD $\delta \tau$. For the fiducial model, we predict that the CMB-HD $-$ PICO cross-correlation should achieve an accurate measurement of the reionization parameters; $T_{\mathrm{b}}\simeq 49800_{-5100}^{+4500}$K and $R_{\mathrm{b}}\simeq 5.09_{-0.79}^{+0.66}$Mpc. Since the power spectrum of the electron density fluctuations is constrained by the $\delta \tau$ auto spectrum, the temperature constraints should be only weakly model-dependent on the details of the electron distributions and should be statistically representative of the temperature in ionized bubbles during reionization. This cross-correlation could, therefore, become an important observable for future CMB experiments.

arXiv comment13 pages, 9 figures, Accepted for publication in PRD

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