Weak lensing corrections to tSZ-lensing cross correlation

TL;DR

This paper investigates higher order gravitational lensing effects on the tSZ-lensing cross correlation, finding that corrections are significant only at very small angular scales, thus refining the interpretation of observational data.

Contribution

It extends previous calculations to include higher order lensing corrections for tSZ-lensing cross correlations, providing a more accurate theoretical model.

Findings

Reduced shear correction exceeds 1% at multipoles above 3000

Higher order effects like Born and lens-lens coupling are quantified

Redshift distortions and vector modes are negligible at this order

Abstract

The cross correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and gravitational lensing in wide field has recently been measured. It can be used to probe the distribution of the diffuse gas in large scale structure, as well as inform us about the missing baryons. As for any lensing-based quantity, higher order lensing effects can potentially affect the signal. Here, we extend previous higher order lensing calculations to the case of tSZ-lensing cross correlations. We derive terms analogous to corrections due to the Born approximation, lens-lens coupling, and reduced shear up to fourth order in the Newtonian potential. Redshift distortions and vector modes are shown to be negligible at this order. We find that the dominant correction due to the reduced shear exceeds percent-level only at multipoles of $\ell \gtrsim 3000$.