  We present the results of a systematic X-ray analysis of optically rich
galaxy clusters detected by the Subaru HSC survey in the eROSITA eFEDS field.
Through a joint analysis of SRG/eROSITA and Subaru/HSC surveys, we aim to study
the dynamical status of the optically selected clusters and derive the cluster
scaling relations. The sample consists of 43 optically selected galaxy clusters
with a richness $>40$ in $0.16<z<0.89$. We systematically analyzed the X-ray
images and spectra using the eROSITA data. We identified the BCG using the
optical and far-infrared databases. We evaluated the cluster's dynamical status
by measuring the offset between the X-ray peak and BCG position, the gas
concentration, and the number of galaxy-density peaks. We studied the
luminosity-temperature and mass-luminosity relations based on eROSITA X-ray
spectra and HSC weak-lensing data analyses. Based on the these measurements,
the fraction of relaxed clusters is $2(<39)$%, which is smaller than that of
the X-ray-selected cluster samples. After correcting for a selection bias due
to the richness cut, we obtained a shallow $L-T$ slope of $2.1\pm0.5$, which is
consistent with the predictions of the self-similar model and the baseline
model incorporating a mass-concentration relation. The $L-M$ slope of
$1.5\pm0.3$ agrees with the above theoretical models and that of the
shear-selected clusters in the eFEDs field. Our analysis of high-richness
optical clusters yields a small fraction of relaxed clusters and a shallow
slope for the luminosity-temperature relation. This suggests that the average
X-ray properties of the optical clusters are likely to be different from those
observed in the X-ray samples. Thus, the joint eROSITA and HSC observations are
a powerful tool in extending the analysis to a larger sample and understanding
the selection effect with a view to establish cluster scaling relations.
