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Table 1

Priors used on the free parameters in the fitting, divided into several parameter types for clarity.

Parameter Units Description Prior
• Cosmology
Ωm − Mean matter density at present time U$\[\mathcal{U}\]$(0.05, 0.95)
log10 As − Amplitude of the primordial power spectrum U$\[\mathcal{U}\]$(−10, −8)
H0 kmsMpc$\[\frac{\frac{\mathrm{km}}{\mathrm{s}}}{\mathrm{Mpc}}\]$ Hubble expansion rate at present time N$\[\mathcal{N}\]$(67.77, 0.6)
Ωb − Mean baryon density at present time U$\[\mathcal{U}\]$(0.046, 0.052)
ns − Spectra index of the primordial power spectrum U$\[\mathcal{U}\]$(0.92, 1.0)
w0 − Dark energy equation of state. Fixed to −1 in ΛCDM U$\[\mathcal{U}\]$(−2.5, −0.33)
∑ mv eV Summed neutrino masses. Fixed to 0 eV in ΛCDM U$\[\mathcal{U}\]$(0, 1)
• X-ray scaling relation
AX − Normalization of the M − CR scaling relation U$\[\mathcal{U}\]$(0.01, 3)
BX − Mass slope of the M − CR scaling relation U$\[\mathcal{U}\]$(0.1, 5)
DX − Luminosity distance evolution of the M − CR scaling relation Fixed to −2
EX − Scale factor evolution of the M − CR scaling relation Fixed to 2
FX − Redshift evolution of the mass slope of the M − CR scaling relation U$\[\mathcal{U}\]$(−5, 5)
GX − Redshift evolution of the normalization of the M − CR scaling relation U$\[\mathcal{U}\]$(−5, 5)
σX − Intrinsic scatter of the M − CR scaling relation U$\[\mathcal{U}\]$(0.05, 2)
• Weak lensing mass calibration
AWL − Scatter in the weak lensing bias from the first principal component N$\[\mathcal{N}\]$(0, 1)
BWL − Scatter in the weak lensing bias from the second principal component N$\[\mathcal{N}\]$(0, 1)
CWL − Standardize mass slope of the weak lensing bias N$\[\mathcal{N}\]$(0, 1)
DWL − Redshift dependent intrinsic scatter in the weak lensing bias N$\[\mathcal{N}\]$(0, 1)
ρMWL,CR − Intrinsic correlation between weak lensing mass and count rate U$\[\mathcal{U}\]$(−0.9, 0.9)
• Richness mass calibration
log Aλ − Normalization of the M − λ scaling relation U$\[\mathcal{U}\]$(1.4, 6)
Bλ − Mass slope of the M − λ scaling relation U$\[\mathcal{U}\]$(0, 2)
Cλ − Redshift evolution of the normalization of the M − λ scaling relation U$\[\mathcal{U}\]$(−2, 2)
Dλ − Redshift evolution of the mass slope of the M − λ scaling relation U$\[\mathcal{U}\]$(−2, 2)
σλ − Intrinsic scatter of the M − λ scaling relation U$\[\mathcal{U}\]$(0.05, 2)
ρλ,CR − Intrinsic correlation between richness and count rate U$\[\mathcal{U}\]$(−0.9, 0.9)
• Contamination modeling
fAGN − Fraction of AGN contaminants in the extended source sample U$\[\mathcal{U}\]$(0, 0.1)
fRS − Fraction of RS contaminants in the extended source sample U$\[\mathcal{U}\]$(0, 0.15)
• Redshift uncertainty
σz − Relative error on the measured redshift T$\[\mathcal{T}\]$ N$\[\mathcal{N}\]$ (0.0050, 0.0011, 0, 1)
bz − Systematic bias in our redshift estimate N$\[\mathcal{N}\]$(1.005, 0.037)
cz − Fraction of objects for which we measure a shifted redshift T$\[\mathcal{T}\]$ N$\[\mathcal{N}\]$(0.0013, 0.0010, 0, 1)
cshift,z − Amount of redshift shift for cz fraction of objects U$\[\mathcal{U}\]$(−0.1, 0.1)

Notes. With U$\[\mathcal{U}\]$(min, max) we indicate a uniform distribution between “min” and “max”. With N$\[\mathcal{N}\]$(μ, σ) we indicate a normal distribution centered on μ and with standard deviation σ. With T$\[\mathcal{T}\]$ N$\[\mathcal{N}\]$(μ, σ, min, max) we indicate a truncated normal distribution centered on μ and with standard deviation σ bounded between “min” and “max”.

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