We perform a self-calibration of the richness-to-mass ( N – M ) relation of CAMIRA galaxy clusters with richness N \geq 15 at redshift 0.2 \leq z < 1.1 by modeling redshift-space two-point correlation functions , namely , the auto-correlation function \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 { c } \mathrm { g } } between these two samples .
We focus on constraining the normalization A _ { 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 } \mathrm { M } _ { \odot } and the pivotal redshift z _ { \mathrm { piv } } = 0.6 , the resulting normalization A _ { 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 { c } \mathrm { g } } , and \xi _ { \mathrm { cc } } + \xi _ { \mathrm { c } \mathrm { g } } + \xi _ { \mathrm { gg } } , with average uncertainties at levels of 36 \% , 23 \% , and 21 \% , respectively .
We find that the resulting A _ { 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 \lesssim 1.9 \sigma .
This implies that the absolute mass scale of CAMIRA clusters inferred from clustering is mildly higher than those from the independent methods .
We discuss the impact of the selection bias introduced by the cluster finding algorithm , which is suggested to be a subdominant factor in this work .