The SRG/eROSITA All-Sky Survey Weak lensing of eRASS1 galaxy clusters in KiDS-1000 and consistency checks with DES Y3 and HSC-Y3

Aims. We aim to participate in the calibration of the X-ray photon count rate to halo mass scaling relation of galaxy clusters selected in the first eROSITA All-Sky Survey on the western Galactic hemisphere (eRASS1) using weak-lensing (WL) data from the fourth data release of the Kilo-Degree Survey (KiDS-1000). We therefore measured the radial shear profiles around eRASS1 galaxy clusters using background galaxies in KiDS-1000 as well as the cluster member contamination. Furthermore, we provide consistency checks with the other stage-III weak-lensing surveys that take part in the eRASS1 mass calibration, the Dark Energy Survey Year 3 (DES Y3) and Hyper Suprime-Cam Year 3 (HSC-Y3), as KiDS-1000 has overlap with both surveys. Methods. We determined the cluster member contamination of eRASS1 clusters present in KiDS-1000 based on background galaxy number density profiles, where we accounted for the optical obscuration caused by cluster galaxies. The extracted shear profiles, together with the result of the contamination model and the lens sample selection, were then analysed through a Bayesian population model. We calibrated the WL mass bias parameter by analysing realistic synthetic shear profiles from mock cluster catalogues. Our consistency checks between KiDS-1000 and DES Y3 and HSC-Y3 include the comparison of contamination-corrected density contrast profiles and amplitudes by employing the union of background sources around common clusters as well as the individual scaling relation results. Results. We present a global contamination model for eRASS1 clusters in KiDS-1000 and the calibration results of the X-ray photon count rate to halo mass relation. The results of the WL mass bias parameter b_WL obtained through mock observations show that hydro-dynamical modelling uncertainties only play a sub-dominant role in KiDS-1000. The uncertainty of the multiplicative shear bias dominates the systematic error budget at low cluster redshifts, while the uncertainty of our contamination model does so at high ones. The crosschecks between the three WL surveys show that they are for the most part statistically consistent with each other. This enables, for the first time, cosmological constraints from clusters calibrated by three state-of-the-art weak-lensing surveys.