The eROSITA Final Equatorial-Depth Survey (eFEDS): X-ray stacking analysis of Subaru's optically selected clusters spanning low richness regime

TL;DR

This work extends X-ray scaling analyses to a large, low-richness sample of Subaru HSC CAMIRA clusters in the eFEDS field by stacking eROSITA data to derive L-M and N-M relations and to characterize ICM surface-brightness profiles. Using weak-lensing mass calibration and a hierarchical Bayesian framework, the authors find an L-M slope of $1.56^{+0.14}_{-0.12}$ and an N-M slope of $0.766^{+0.070}_{-0.060}$, with no strong evidence for evolution beyond self-similar expectations. Clusters with X-ray counterparts show steeper L-M and more concentrated gas profiles than undetected systems, indicating systematic differences between optically and X-ray selected samples and highlighting the importance of multi-wavelength surveys. The results demonstrate the viability of pushing scaling-relations studies to lower masses and luminosities and foreshadow tighter constraints with future eROSITA and Subaru HSC data.

Abstract

This is the second paper in a series exploring the X-ray properties of galaxy clusters optically selected by the Subaru Hyper Suprime-Cam (HSC) survey, using data from the SRG/eROSITA Final Equatorial-Depth Survey (eFEDS). We aim to investigate scaling relations between observable cluster properties and mass, and to study the radial X-ray profiles of a large sample of optically selected clusters. We analyze a sample of 997 CAMIRA clusters with richness $N > 15$ and redshifts of $0.1 < z < 1.3$. Using bolometric luminosities derived from count rates and a weak-lensing mass calibration, we study the $L-M$ and $N-M$ scaling relations through stacking analysis, while accounting for selection effects and redshift evolution. We also compare clusters with and without X-ray counterparts in the eFEDS catalog in terms of their scaling relations and surface brightness profiles. The best-fit $L-M$ slope ($1.56^{+0.14}_{-0.12}$) is slightly steeper than the self-similar prediction, yet remains consistent with our previous findings. The $N-M$ slope ($0.766^{+0.070}_{-0.060}$) broadly agrees with theoretical expectations and other optical samples. The data do not require any additional redshift evolution beyond the standard self-similar scaling, although current constraints on evolution remain weak. X-ray detected clusters exhibit a steeper $L-M$ slope, higher central surface brightness, and more centrally concentrated X-ray profiles than undetected systems. Our results highlight systematic differences in the X-ray properties between optically and X-ray selected cluster samples. This study extends scaling relation analyses into lower mass and luminosity regimes, demonstrating the value of combining deep X-ray and optical surveys like eROSITA and Subaru HSC.

Figures (12)

• Figure 1: Distribution of the CAMIRA clusters in the richness-redshift plane. Each point represents a cluster. Colors indicate the stacked groups used in the X-ray stacking analysis, defined by similar richness and redshift ranges (see Sects. \ref{['sec:sample']} and \ref{['subsec:stack_lumi']}).
• Figure 2: Scaling relations of the CAMIRA optically selected clusters. Each circle represents a stacked bin described in Sect. \ref{['subsec:stack_lumi']}, color-coded by its weighted average redshift. Solid lines show the best-fitting power-law models from the simultaneous fit: blue and magenta correspond to relations with respect to the WL masses and to the true masses, respectively. The shaded blue region indicates the $1\sigma$ uncertainty of the scaling relation with the WL masses. The $1-\sigma$ confidence ellipses indicate the posterior covariance of the stacked quantities, computed using either total uncertainties including intrinsic scatter (orange) or measurement error only (dashed black). The 32 data points are sorted by X-ray luminosity (left) or richness (right), grouped accordingly, and averaged within the group.
• Figure 3: Scaling relations of the CAMIRA clusters. Circles show stacked bins with approximately 500 X-ray counts. Blue (MATCH) and red (UNMATCH) markers indicate clusters with and without X-ray counterparts in eFEDS, respectively. Solid and dashed lines are best-fit power laws for detected and undetected samples. Best-fit relations are shown with respect to WL (blue/red) and true (green/black) masses. Shaded areas represent $1\sigma$ uncertainties for WL-based fits. The filled orange (X-ray detected) and green (X-ray undetected) ellipses have the same meaning as in Fig. \ref{['fig:scaling2']}.
• Figure 4: Radial surface brightness profiles of stacked CAMIRA clusters with and without X-ray detections are shown in blue and red circles, respectively. Arrows indicate upper limits. The richness bins are $15 \le N < 25$ (top), $25 \le N < 40$ (middle), and $40 \le N < 60$ (bottom). The left, middle, and right columns correspond to redshift ranges $0.1 \le z < 0.3$, $0.3 \le z < 0.6$, and $0.6 \le z < 1.2$, respectively. Best-fitting PSF-convolved $\beta$-models are plotted as blue and red solid lines, with shaded regions indicating their $1\sigma$ uncertainties. The underlying PSF and intrinsic $\beta$-model components are shown by dotted and dashed lines. The lower panels show the data/model ratios.
• Figure 5: Scaling relations of richness (left) and luminosity (right) with respect to true masses. The magenta solid lines and shaded regions show the best-fit relations and their uncertainties from this work. The green lines represent the results for individual CAMIRA clusters with $N>40$2023AA...669A.110O. The orange line shows the eRASS1 result Okabe25. The brown and gray dashed lines denote the stacked weak-lensing result of 2019PASJ...71...79O and our relation assuming no miscentering, respectively. All baseline relations are evaluated at $z=0.35$.