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We conduct a pseudo-$C_\ell$ analysis of the tomographic cross-correlationbetween 1000 deg$^2$ of weak lensing data from the Kilo-Degree Survey(KiDS-1000) and the thermal Sunyaev-Zeldovich (tSZ) effect measured by Planckand the Atacama Cosmology Telescope (ACT). Using HMx, a halo-model-basedapproach that consistently models the gas, star, and dark matter components, weare able to derive constraints on both cosmology and baryon feedback for thefirst time from these data, marginalising over redshift uncertainties,intrinsic alignment of galaxies, and contamination by the cosmic infraredbackground (CIB). We find our results to be insensitive to the CIB, whileintrinsic alignment provides a small but significant contribution to thelensing--tSZ cross-correlation. The cosmological constraints are consistentwith those of other low-redshift probes and prefer strong baryon feedback. Theinferred amplitude of the lensing--tSZ cross-correlation signal, which scalesas $\sigma_8(\Omega_\mathrm{m}/0.3)^{0.2}$, is low by $\sim 2\,\sigma$ comparedto the primary cosmic microwave background constraints by Planck. Thelensing--tSZ measurements are then combined with pseudo-$C_\ell$ measurementsof KiDS-1000 cosmic shear into a novel joint analysis, accounting for the fullcross-covariance between the probes, providing tight cosmological constraintsby breaking parameter degeneracies inherent to both probes. The joint analysisgives an improvement of 40% on the constraint of$S_8=\sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$ over cosmic shear alone, whileproviding constraints on baryon feedback consistent with hydrodynamicalsimulations, demonstrating the potential of such joint analyses with baryonictracers such as the tSZ effect. We discuss remaining modelling challenges thatneed to be addressed if these baryonic probes are to be included in futureprecision-cosmology analyses.

astronomy and astrophysics

Joint constraints on cosmology and the impact of baryon feedback:  combining KiDS-1000 lensing with the thermal Sunyaev-Zeldovich effect from  Planck and ACT