Constraining baryonic feedback and cosmology with weak-lensing, X-ray,
  and kinematic Sunyaev-Zeldovich observations
  Modern weak-lensing observations are becoming increasingly sensitive to
baryonic feedback processes which are still poorly understood. So far, this
challenge has been faced either by imposing scale-cuts in the data or by
modelling baryonic effects with simple, one-parameter models. In this paper, we
rely on a more general, seven-parameter prescription of baryonic feedback
effects, which is primarily motivated by observations and has been shown to
agree with a plethora of hydrodynamical simulations. By combining weak-lensing
data from the Kilo-Degree Survey (KiDS-1000) with observations of gas around
galaxy clusters, we are able to constrain baryonic parameters and learn more
about feedback and cosmology. In particular, we use cluster gas fractions from
X-ray data and gas profiles from kinematic Sunyaev-Zeldovich (kSZ) observations
to provide evidence for baryonic feedback that is stronger than predicted by
most hydrodynamical simulations. In terms of the matter power spectrum, we
report a beyond-percent effect at wave-modes above $k\sim 0.1-0.45$ h/Mpc and a
maximum suppression of $12-33$ percent at $k\sim7$ h/Mpc (68 percent confidence
level). Regarding the combined parameter
$\Sigma_8=\sigma_8(\Omega_m/0.3)^{0.58}$, we find the known tension with the
Planck satellite data to be reduced from 3.8 to 2.9 $\sigma$ once baryonic
effects are fully included in the analysis pipeline. The tension is further
decreased to 2.6 $\sigma$ when the weak-lensing data is combined with X-ray and
kSZ observations. We conclude that, while baryonic feedback effects become more
important in modern weak-lensing surveys, they are unlikely to act as the main
culprit for the observed $\Sigma_8$-tension.
