A clustering-based self-calibration of the richness-to-mass relation of CAMIRA galaxy clusters out to $z\approx1.1$ in the Hyper Suprime-Cam survey

We perform a self-calibration of the richness-to-mass ($N$-$M$) relation of CAMIRA galaxy clusters with richness $N\geq15$ at redshift $0.2\leq z<1.1$ by modeling redshift-space two-point correlation functions. These correlation functions are $\xi_{\mathrm{cc}}$ of CAMIRA clusters, the auto-correlation function $\xi_{\mathrm{gg}}$ of the CMASS galaxies spectroscopically observed in the BOSS survey, and the cross-correlation function $\xi_{\mathrm{cg}}$ between these two samples. We focus on constraining the normalization $A_{\mathrm{N}}$ of the $N$-$M$ relation in a forward-modeling approach, carefully accounting for the redshift-space distortion, the Finger-of-God effect, and the uncertainty in photometric redshifts of CAMIRA clusters. The modeling also takes into account the projection effect on the halo bias of CAMIRA clusters. The parameter constraints are shown to be unbiased according to validation tests using a large set of mock catalogs constructed from N-body simulations. At the pivotal mass $M_{500}=10^{14}h^{-1}M_{\odot}$ and the pivotal redshift $z_{\mathrm{piv}} = 0.6$, the resulting normalization $A_{\mathrm{N}}$ is constrained as $13.8^{+5.8}_{-4.2}$, $13.2^{+3.4}_{-2.7}$, and $11.9^{+3.0}_{-1.9}$ by modeling $\xi_{\mathrm{cc}}$, $\xi_{\mathrm{cc}}+\xi_{\mathrm{cg}}$, and $\xi_{\mathrm{cc}} + \xi_{\mathrm{cg}} + \xi_{\mathrm{gg}}$, with average uncertainties at levels of $36\%$, $23\%$, and $21\%$, respectively. We find that the resulting $A_{\mathrm{N}}$ is statistically consistent with those independently obtained from weak-lensing magnification and from a joint analysis of shear and cluster abundance, with a preference for a lower value at a level of $\lesssim1.9\sigma$. This implies that the absolute mass scale of CAMIRA clusters inferred from clustering is mildly higher than those from the independent methods. [abridged]