Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D

Abstract

The thermal Sunyaev-Zel'dovich (tSZ) effect measures the line-of-sight projection of the thermal pressure of free electrons and lacks any redshift information. By cross correlating the tSZ effect with an external cosmological tracer we can recover a good fraction of this lost information. Weak lensing (WL) is thought to provide an unbiased probe of the dark Universe, with many WL surveys having sky coverage that overlaps with tSZ surveys. Generalising the tomographic approach, we advocate the use of the spherical Fourier-Bessel (sFB) expansion to perform an analysis of the cross-correlation between the projected (2D) tSZ Compton $y$-parameter maps and 3D weak lensing convergence maps. We use redshift dependent linear biasing and the halo model as a tool to investigate the tSZ-WL cross-correlations in 3D. We use the Press-Schechter (PS) and the Sheth-Tormen (ST) mass-functions in our calculations, finding that the results are quite sensitive to detailed modelling. We provide detailed analysis of surveys with photometric and spectroscopic redshifts. The signal-to-noise (S/N) of the cross-spectra ${\mathcal{C}}_{\ell }(k)$ for individual 3D modes, defined by the radial and tangential wave numbers $(k;\ell )$, remains comparable to, but below, unity though optimal binning is expected to improve this. The results presented can be generalised to analyse other CMB secondaries, such as the kinetic Sunyaev-Zel'dovich (kSZ) effect.

27 pages, 12 Figures. Published in MNRAS

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Cited by in corpus (5)

• Deconstructing Thermal Sunyaev-Zel'dovich - Gravitational Lensing Cross-Correlations: Implications for the Intracluster Medium
• Cross-correlating 2D and 3D galaxy surveys
• Extracting the late-time kinetic Sunyaev-Zel'dovich effect
• 3D Weak Lensing: Modified Theories of Gravity
• Galaxy Clustering in 3D and Modified Gravity Theories