The eROSITA Final Equatorial-Depth Survey (eFEDS): X-ray observable-to-mass-and-redshift relations of galaxy clusters and groups with weak-lensing mass calibration from the Hyper Suprime-Cam Subaru Strategic Program survey

We present the first weak-lensing mass calibration and X-ray scaling relations of galaxy clusters and groups selected in the eROSITA Final Equatorial Depth Survey (eFEDS) observed by Spectrum Roentgen Gamma/eROSITA over a contiguous footprint with an area of 140 deg2, using the three-year (S19A) weak-lensing data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. In this work, we study a sample of 434 optically confirmed galaxy clusters (and groups) at redshift 0.01 1.3 with a median of 0.35, of which 313 systems are uniformly covered by the HSC survey to enable the extraction of the weak-lensing shear observable. In a Bayesian population modeling, we perform a blind analysis for the weak-lensing mass calibration by simultaneously modeling the observed count rate η and the shear profile g+ of individual clusters through the count-rate-to-mass-and-redshift (η-M500-z) relation and the weak-lensing-mass-to-mass-and-redshift (MWL-M500-z) relation, respectively, while accounting for the bias in these observables using simulation-based calibrations. As a result, the count-rate-inferred and lensing-calibrated cluster mass is obtained from the joint modeling of the scaling relations, as the ensemble mass spanning a range of 1013h-1M M500 with a median of for the eFEDS sample. With the mass calibration, we further model the X-ray observable-to-mass-and-redshift relations, including the rest-frame soft-band and bolometric luminosity (LX and Lb), the emission-weighted temperature TX, the mass of intra-cluster medium Mg, and the mass proxy YX, which is the product of TX and Mg. Except for LX with a steeper dependence on the cluster mass at a statistically significant level, we find that the other X-ray scaling relations all show a mass trend that is statistically consistent with the self-similar prediction at a level of Meanwhile, all these scaling relations show no significant deviation from the self-similarity in their redshift scaling. Moreover, no significant redshift-dependent mass trend is present. This work demonstrates the synergy between the eROSITA and HSC surveys in preparation for the forthcoming first-year eROSITA cluster cosmology.