The SRG/eROSITA All-Sky Survey - Tracing the large-scale structure with a clustering study of galaxy clusters

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Volume 686 (June 2024)

A&A, 686 (2024) A196

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Table B.1.

Priors and posteriors of the HOD and the derived parameters for the test about the choice of the priors.

Parameter	Large Prior		Standard Prior		Small Prior		Diagonal error
M_min	𝒰(12.0, 16.5)	14.95 $_{- 0.30}^{+ 0.89}$ $^{+0.89}_{-0.30}$	𝒰(13.0, 16.0)	14.94 $_{- 0.26}^{+ 0.84}$ $^{+0.84}_{-0.26}$	𝒰(13.5, 15.8)	14.83 $_{- 0.21}^{+ 0.68}$ $^{+0.68}_{-0.21}$	𝒰(13.0, 16.0)	14.95 $_{- 0.28}^{+ 0.82}$ $^{+0.82}_{-0.28}$
σ_{log M}	𝒰(0.005, 2.5)	0.62 $_{- 0.35}^{+ 0.47}$ $^{+0.47}_{-0.35}$	𝒰(0.01, 2.0)	0.62 $_{- 0.32}^{+ 0.46}$ $^{+0.46}_{-0.32}$	𝒰(0.05, 1.2)	0.58 $_{- 0.27}^{+ 0.41}$ $^{+0.41}_{-0.27}$	𝒰(0.01, 2.0)	0.59 $_{- 0.31}^{+ 0.41}$ $^{+0.41}_{-0.31}$
α_sat	𝒰(0.05, 3.5)	1.45 $_{- 0.61}^{+ 0.86}$ $^{+0.86}_{-0.61}$	𝒰(0.1, 3.0)	1.41 $_{- 0.58}^{+ 0.82}$ $^{+0.82}_{-0.58}$	𝒰(0.3, 2.5)	1.35 $_{- 0.50}^{+ 0.67}$ $^{+0.67}_{-0.50}$	𝒰(0.1, 3.0)	1.47 $_{- 0.60}^{+ 0.83}$ $^{+0.83}_{-0.60}$
M_sat	𝒰(12.0, 16.5)	15.64 $_{- 0.30}^{+ 0.30}$ $^{+0.30}_{-0.30}$	𝒰(13.0, 16.5)	15.63 $_{- 0.28}^{+ 0.29}$ $^{+0.29}_{-0.28}$	𝒰(14.0, 16.0)	15.58 $_{- 0.22}^{+ 0.23}$ $^{+0.23}_{-0.22}$	𝒰(13.0, 16.5)	15.67 $_{- 0.23}^{+ 0.29}$ $^{+0.29}_{-0.23}$

Notes. Different results for the HOD fit of the projected correlation function for the S2 sample (0.1 < z < 0.4, L_X > 10^43.4 erg/s/cm²). We compare the posterior from the standard analysis to different choices of the prior and only using the diagonal error of the covariance matrix. 𝒰(min, max) indicates a uniform prior between the minimum and maximum values.

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