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Cross-correlating Sunyaev–Zel’dovich and weak lensing maps

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posted on 2023-06-08, 17:56 authored by Dipak MunshiDipak Munshi, Joudaki Shahab, Peter Coles, Joseph Smidt, Scott T Kay
We present novel statistical tools to cross-correlate frequency cleaned thermal Sunyaev-Zel'dovich (tSZ) maps and tomographic weak lensing (wl) convergence maps. Moving beyond the lowest order cross-correlation, we introduce a hierarchy of mixed higher-order statistics, the cumulants and cumulant correlators, to analyze non-Gaussianity in real space, as well as corresponding polyspectra in the harmonic domain. Using these moments, we derive analytical expressions for the joint two-point probability distribution function (2PDF) for smoothed tSZ (y_s) and convergence (\kappa_s) maps. The presence of tomographic information allows us to study the evolution of higher order {\em mixed} tSZ-weak lensing statistics with redshift. We express the joint PDFs p_{\kappa y}(\kappa_s,y_s) in terms of individual one-point PDFs (p_{\kappa}(\kappa_s), p_y(y_s)) and the relevant bias functions (b_{\kappa}(\kappa_s), b_y(y_s)). Analytical results for two different regimes are presented that correspond to the small and large angular smoothing scales. Results are also obtained for corresponding {\em hot spots} in the tSZ and convergence maps. In addition to results based on hierarchical techniques and perturbative methods, we present results of calculations based on the lognormal approximation. The analytical expressions derived here are generic and applicable to cross-correlation studies of arbitrary tracers of large scale structure including e.g. that of tSZ and soft X-ray background.

History

Publication status

  • Published

File Version

  • Published version

Journal

Monthly Notices of the Royal Astronomical Society

ISSN

0035-8711

Publisher

Wiley-Blackwell

Volume

442

Page range

69-91

Department affiliated with

  • Physics and Astronomy Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2014-07-24

First Open Access (FOA) Date

2014-07-24

First Compliant Deposit (FCD) Date

2014-07-24

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