Constraining reionization with the first measurement of the cross-correlation between the CMB optical-depth fluctuations and the Compton <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>y</mml:mi></mml:math> -map

We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in CMB optical depth which probes integrated electron density, $\delta\tau$, and Compton $y$-map pressure. This is much less contaminated than power spectrum by late-time cluster contributions. In addition, this can constrain temperature of ionized bubbles while optical-depth kinetic SZ effect not. measure observable using Planck as well map we reconstruct from data. use our measurements to derive first CMB-only upper limit on inside bubbles, $T_{\rm b}\lesssim 7.0\times10^5\,$K ($2\,\sigma$). also present future forecasts, assuming fiducial model with characteristic bubble size $R_{\rm b}=5\,$Mpc b}=5\times10^4\,$K. The signal-to-noise ratio signal dominated PICO-like becomes $\simeq7$ CMB-S4 $\delta\tau$ $\simeq13$ CMB-HD $\delta\tau$. For model, predict $-$ PICO should achieve an accurate measurement parameters; b}\simeq 49800^{+4500}_{-5100}\,$K 5.09^{+0.66}_{-0.79}\,$Mpc. Since density constrained auto spectrum, constraints be only weakly model-dependent details distributions statistically representative during reionization. could, therefore, become important for experiments.