Weak lensing corrections to tSZ-lensing cross correlation

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 $\ell \gtrsim 3000$.

20 pages, 2 figures; matches version accepted by JCAP

References in corpus (5)

• Extended Limber Approximation
• The Search for the Missing Baryons at Low Redshift
• Do Hot Haloes Around Galaxies Contain the Missing Baryons?
• CFHTLenS: Cosmological constraints from a combination of cosmic shear two-point and three-point correlations
• Simulations of Weak Gravitational Lensing - II : Including Finite Support Effects in Cosmic Shear Covariance Matrices