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

Context. 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). Aims. 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. Methods. We analyzed a sample of 997 CAMIRA clusters with a richness of N > 15 and redshifts of 0.1 < z < 1.3. Using bolometric luminosities derived from count rates and a weak-lensing mass calibration, we studied the L-M and N-M scaling relations through stacking analysis, while accounting for selection effects and redshift evolution. We also compared clusters with and without X-ray counterparts in the eFEDS catalog in terms of their scaling relations and surface-brightness profiles. Results. The best-fit L-M slope (1.56^ +0.14 _ -0.12 ) is slightly steeper than the self-similar prediction, yet it 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 marginally steeper L-M slope, higher central surface brightness, and more centrally concentrated X-ray profiles than undetected systems. Conclusions. 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 such as eROSITA and Subaru HSC.