The eventful life journey of galaxy clusters - I. Impact of dark matter halo and intracluster medium properties on their full assembly histories

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Volume 699 (July 2025)

A&A, 699 (2025) A1

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Table A.2.

Fit parameters (α and β) for our three mass ranges to the functional form in Eq. (A.1).

Main branch of the merger tree: most bound

Mass range (at z = 0)	α	β	R_fit² / MRE

M_vir > 10¹⁴ M_⊙	$0 . 66_{- 0.44}^{+ 1.13}$ $0.66^{+1.13}_{-0.44}$	$- 1 . 58_{- 0.79}^{+ 0.24}$ $-1.58^{+0.24}_{-0.79}$	0.93
... Reference	0.36	−1.19	50%

5 × 10¹³ M_⊙ < M_vir < 10¹⁴ M_⊙	$0 . 73_{- 0.46}^{+ 1.26}$ $0.73^{+1.26}_{-0.46}$	$- 1 . 60_{- 0.91}^{+ 0.27}$ $-1.60^{+0.27}_{-0.91}$	0.70
... Reference	0.32	−1.09	51%

10¹³ M_⊙ < M_vir < 5 × 10¹³ M_⊙	$- 0 . 51_{- 0.26}^{+ 0.90}$ $-0.51^{+0.90}_{-0.26}$	$- 0 . 66_{- 0.55}^{+ 0.10}$ $-0.66^{+0.10}_{-0.55}$	0.99
... Reference	0.28	−0.95	27%

Main branch of the merger tree: most massive

Mass range (at z = 0)	α	β	R_fit² / MRE
M_vir > 10¹⁴ M_⊙	$0 . 10_{- 0.25}^{+ 0.87}$ $0.10^{+0.87}_{-0.25}$	$- 1 . 18_{- 0.56}^{+ 0.11}$ $-1.18^{+0.11}_{-0.56}$	0.99
... Reference	0.36	−1.19	29%

5 × 10¹³ M_⊙ < M_vir < 10¹⁴ M_⊙	$0 . 10_{- 0.30}^{+ 1.21}$ $0.10^{+1.21}_{-0.30}$	$- 1 . 14_{- 0.84}^{+ 0.16}$ $-1.14^{+0.16}_{-0.84}$	0.97
... Reference	0.32	−1.09	30%

10¹³ M_⊙ < M_vir < 5 × 10¹³ M_⊙	$- 0 . 01_{- 0.31}^{+ 0.94}$ $-0.01^{+0.94}_{-0.31}$	$- 0 . 96_{- 0.62}^{+ 0.14}$ $-0.96^{+0.14}_{-0.62}$	0.99
... Reference	0.28	−0.95	30%

Notes. The results are shown for the merger trees used in the paper results (top block), and for the merger trees computed from the most-massive method (bottom block). The reference values for α and β are obtained from Correa et al. (2015) at the median mass in each sub-sample. Within each pair of rows, in the rightmost column, the top row shows the coefficient of determination, while the bottom row shows the mean relative error between best-fit and Correa et al. (2015).

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