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Table 1.
Priors used in the default modelling.
| Parameters | Priors |
|---|---|
| The X-ray count rate-to-mass-and-redshift (CR–M–z) relation | |
| Eq. (7) | |
| AX | 𝒰(0.001, 3.0) |
| BX | 𝒰(0.0, 5.0) |
| δX | 𝒰(−5.0, 5.0) |
| γX | 𝒰(−5.0, 5.0) |
| σX | 𝒰(0.05, 2.0) |
| The BCG stellar-mass-to-mass-and-redshift (M⋆, BCG–M–z) relation | |
| Eq. (8) | |
| ABCG | 𝒰(8.0, 13.0) |
| BBCG | 𝒰(0.0, 5.0) |
| δBCG | 𝒰(−5.0, 5.0) |
| γBCG | 𝒰(−5.0, 5.0) |
| σBCG | 𝒰(0.05, 2.0) |
| The weak-lensing mass bias-to-mass-and-redshift (bWL–M–z) relation | |
| Eq. (9) | |
| BWL | 𝒩(0.047,0.0212) and 𝒰(−1.0, 1.0) |
| δWL | 𝒩(0,12) and 𝒰(−5.0, 5.0) |
| γWL | 𝒩(0,12) and 𝒰(−5.0, 5.0) |
| σWL | 𝒩(0.23,0.032) and 𝒰(0.05, 2.0) |
| Miscentring | |
| fmis | 𝒩(0.32, 0.0432) and 𝒰(0.0,1.0) |
| lnσmis | 𝒩(−0.85, 0.182) and 𝒰(−2.0,1.0) |
| Correlated intrinsic scatter | |
| ρX, WL | 𝒰(−0.9, 0.9) |
| ρX, BCG | 𝒰(−0.9, 0.9) |
| ρBCG, WL | 𝒰(−0.9, 0.9) |
| Flat ΛCDM Cosmology | |
| Ωm | 𝒩(0.30,0.022) and 𝒰(0.1, 0.99) |
| σ8 | 𝒩(0.80,0.022) and 𝒰(0.45, 1.15) |
| h | 𝒩(0.7,0.052) and 𝒰(0.5, 0.9) |
| Ωb | 𝒰(0.03, 0.07) |
| ns | 𝒰(0.94, 1.0) |
Notes. The first column contains the names of the parameters, while the second column presents the priors. For a parameter with both flat and Gaussian priors, we allowed it to vary following the Gaussian prior within a range allowed by the flat prior.
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