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

Kavli Affiliate: Toshiya Namikawa

| First 5 Authors: Toshiya Namikawa, Anirban Roy, Blake D. Sherwin, Nicholas Battaglia, David N. Spergel

| Summary:

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, $deltatau$, 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, $T_{rm
b}lesssim 7.0times10^5,$K ($2,sigma$). We also present future forecasts,
assuming a fiducial model with characteristic reionization bubble size $R_{rm
b}=5,$Mpc and $T_{rm b}=5times10^4,$K. The signal-to-noise ratio of the
fiducial cross-correlation using a signal dominated PICO-like $y$-map becomes
$simeq7$ with CMB-S4 $deltatau$ and $simeq13$ with CMB-HD $deltatau$. For
the fiducial model, we predict that the CMB-HD $-$ PICO cross-correlation
should achieve an accurate measurement of the reionization parameters; $T_{rm
b}simeq 49800^{+4500}_{-5100},$K and $R_{rm b}simeq
5.09^{+0.66}_{-0.79},$Mpc. Since the power spectrum of the electron density
fluctuations is constrained by the $deltatau$ 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.

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