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 2.

Priors and posteriors for the HOD and the derived parameters on the five volume-limited eRASS1 samples (see Table 1 and Fig. 1).

Parameter	Prior	Posterior
		S0	S1	S2	S3	S4
M_min	𝒰(13.0, 16.0)	14.73 $_{- 0.35}^{+ 0.93}$ $^{+0.93}_{-0.35}$	14.90 $_{- 0.24}^{+ 0.87}$ $^{+0.87}_{-0.24}$	14.94 $_{- 0.26}^{+ 0.84}$ $^{+0.84}_{-0.26}$	15.02 $_{- 0.63}^{+ 0.63}$ $^{+0.63}_{-0.63}$	15.04 $_{- 0.72}^{+ 0.61}$ $^{+0.61}_{-0.72}$
σ_logM	𝒰(0.01, 2.0)	0.82 $_{- 0.46}^{+ 0.49}$ $^{+0.49}_{-0.46}$	0.66 $_{- 0.34}^{+ 0.50}$ $^{+0.50}_{-0.34}$	0.62 $_{- 0.32}^{+ 0.46}$ $^{+0.46}_{-0.32}$	0.58 $_{- 0.40}^{+ 0.23}$ $^{+0.23}_{-0.40}$	0.57 $_{- 0.37}^{+ 0.20}$ $^{+0.20}_{-0.37}$
α_sat	𝒰(0.1, 3)	1.25 $_{- 0.54}^{+ 0.89}$ $^{+0.89}_{-0.54}$	1.48 $_{- 0.60}^{+ 0.85}$ $^{+0.85}_{-0.60}$	1.41 $_{- 0.58}^{+ 0.82}$ $^{+0.82}_{-0.58}$	1.65 $_{- 0.93}^{+ 1.04}$ $^{+1.04}_{-0.93}$	1.67 $_{- 1.08}^{+ 1.05}$ $^{+1.05}_{-1.08}$
M_sat	𝒰(13.0, 16.5)	15.32 $_{- 0.33}^{+ 0.34}$ $^{+0.34}_{-0.33}$	15.70 $_{- 0.27}^{+ 0.30}$ $^{+0.30}_{-0.27}$	15.63 $_{- 0.28}^{+ 0.29}$ $^{+0.29}_{-0.28}$	15.79 $_{- 0.30}^{+ 0.36}$ $^{+0.36}_{-0.30}$	15.76 $_{- 0.35}^{+ 0.42}$ $^{+0.42}_{-0.35}$
α_inc	Fixed	0.55	0.55	0.55	0.55	0.55
M_inc	Fixed	14.87	14.95	15.06	15.16	15.25

f_sat	–	< 14.9%	< 9.3%	< 9.9%	< 6.8%	< 8.1%
b	–	2.95 ± 0.21	3.35 ± 0.23	3.69 ± 0.27	4.15 ± 0.42	4.34 ± 0.62
$\bar{M_{halo}}$ $\overline{M_{\mathrm{halo}}}$ [10¹⁴ M_⊙]	–	3.09 ± 0.48	3.54 ± 0.51	3.83 ± 0.55	4.44 ± 0.89	4.38 ± 1.11
$\bar{L_{X}}$ $\overline{L_{\mathrm{X}}}$ [10⁴³ erg s⁻¹]	–	4.63 ± 0.97	7.38 ± 0.98	10.21 ± 0.98	13.68 ± 0.99	17.76 ± 0.99

Notes. 𝒰(min, max) indicates a uniform prior between minimum and maximum values. The parameters with fixed prior were estimated using the eRASS1 digital twin (Seppi et al. 2022). The bottom part of the table shows derived parameters: the fraction of satellites f_sat (see Eq. (9)), the large-scale halo bias, and the average halo mass. The average X-ray luminosity for each sample is reported in the last row. The upper limits extend to the 84th percentile.

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