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

Abstract

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 $\approx 140$ deg${}^2$, using the three-year (S19A) weak-lensing data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. In this work, a sample of $434$ optically confirmed galaxy clusters (and groups) at redshift $0.01\lesssim z\lesssim 1.3$ with a median of $0.35$ is studied, 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 modelling, we perform a blind analysis for the weak-lensing mass calibration by simultaneously modelling the observed count rate $\hat{I}\cdot$ and the shear profile $g$ of individual clusters through the count rate-to-mass-and-redshift ($\hat{I}\cdot$--$M_{500}$--$z$) and weak-lensing mass-to-mass-and-redshift ($M_{\mathrm{WL}}$--$M_{500}$--$z$) relations, 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 modelling of the scaling relations, as the ensemble mass spanning a range of $10^{13}{h}^{-1}{M}_{\odot }\lesssim M_{500}\lesssim 10^{15}{h}^{-1}{M}_{\odot }$ with a median of $\approx 10^{14}{h}^{-1}{M}_{\odot }$ 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 ($L_{\mathrm{X}}$ and $L_{\mathrm{b}}$), the emission-weighted temperature $T_{\mathrm{X}}$, the mass of intra-cluster medium $M_{\mathrm{g}}$, and the mass proxy $Y_{\mathrm{X}}$, which is the product of $T_{\mathrm{X}}$ and $M_{\mathrm{g}}$. (abridged)

Accepted for publication in A&A. Submitted to A&A for the Special Issue: The Early Data Release of eROSITA and Mikhail Pavlinsky ART-XC on the SRG Mission