Covariance in the Thermal SZ-Weak Lensing Mass Scaling Relation of Galaxy Clusters

TL;DR

This paper investigates the increased scatter in the tSZ-WL mass scaling relation of galaxy clusters, attributing it to projection effects and radius uncertainties, and proposes a statistical model to correct for this covariance.

Contribution

It introduces a statistical model that accounts for covariance between tSZ and weak lensing signals to recover unbiased cluster scaling relations.

Findings

Enhanced scatter arises from line-of-sight projection and radius uncertainties.

The proposed model effectively corrects for covariance effects.

Results improve the accuracy of mass estimates in multi-wavelength surveys.

Abstract

The thermal Sunyaev-Zel'dovich (tSZ) effect signal is widely recognized as a robust mass proxy of galaxy clusters with small intrinsic scatter. However, recent observational calibration of the tSZ scaling relation using weak lensing (WL) mass exhibits considerably larger scatter than the intrinsic scatter predicted from numerical simulations. This raises a question as to whether we can realize the full statistical power of ongoing and upcoming tSZ-WL observations of galaxy clusters. In this work, we investigate the origin of observed scatter in the tSZ-WL scaling relation, using mock maps of galaxy clusters extracted from cosmological hydrodynamic simulations. We show that the inferred intrinsic scatter from mock tSZ-WL analyses is considerably larger than the intrinsic scatter measured in simulations, and comparable to the scatter in the observed tSZ-WL relation. We show that this enhanced scatter originates from the combination of the projection of correlated structures along the line of sight and the uncertainty in the cluster radius associated with WL mass estimates, causing the amplitude of the scatter to depend on the covariance between tSZ and WL signals. We present a statistical model to recover the unbiased cluster scaling relation and cosmological parameter by taking into account the covariance in the tSZ-WL mass relation from multi-wavelength cluster surveys.