A new "temperature inversion" estimator to detect CMB patchy screening by large-scale structure

Thomson scattering of cosmic microwave background (CMB) photons imprints various properties of the baryons around galaxies on the CMB. One such imprint, called patchy screening, is a direct probe of the gas density profile around galaxies. It usefully complements the information from the kinematic and thermal Sunyaev-Zel'dovich effects and does not require individual redshifts. In this paper, we derive new estimators of patchy screening called the "temperature inversion" (TI) and "signed" estimators, analogous to the gradient inversion estimator of CMB lensing. Pedagogically, we clarify the relation between these estimators and the standard patchy screening quadratic estimator (QE). The new estimators trade optimality for robustness to biases caused by the dominant CMB lensing and foreground contaminants, allowing the use of smaller angular scales. We perform a simulated analysis to realistically forecast the expected precision of patchy screening measurements from four CMB experiments, ACT, SPT, Simons Observatory (SO) and CMB-S4, cross-correlated with three galaxy samples from BOSS, unWISE and the simulated Rubin LSST Data Challenge 2 catalog. Our results give further confidence in the first detection of this effect from the ACT$\times$unWISE data in the companion paper and show patchy screening will be a powerful observable for future surveys like SO, CMB-S4 and LSST. Implementations of the patchy screening QE and the TI and signed estimators are publicly available in our LensQuEst and ThumbStack software packages, available at https://github.com/EmmanuelSchaan/LensQuEst and https://github.com/EmmanuelSchaan/ThumbStack , respectively.