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The thermal Sunyaev-Zel'dovich (tSZ) effect signal is widely recognized as arobust 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 scatterpredicted from numerical simulations. This raises a question as to whether wecan realize the full statistical power of ongoing and upcoming tSZ-WLobservations of galaxy clusters. In this work, we investigate the origin ofobserved scatter in the tSZ-WL scaling relation, using mock maps of galaxyclusters extracted from cosmological hydrodynamic simulations. We show that theinferred intrinsic scatter from mock tSZ-WL analyses is considerably largerthan the intrinsic scatter measured in simulations, and comparable to thescatter in the observed tSZ-WL relation. We show that this enhanced scatteroriginates from the combination of the projection of correlated structuresalong the line of sight and the uncertainty in the cluster radius associatedwith WL mass estimates, causing the amplitude of the scatter to depend on thecovariance between tSZ and WL signals. We present a statistical model torecover the unbiased cluster scaling relation and cosmological parameter bytaking into account the covariance in the tSZ-WL mass relation frommulti-wavelength cluster surveys.

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