A comparative test of different pressure profile models in clusters of galaxies using recent ACT data

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Table 3.

Parameter estimation results for the BMP parameterization.

BMP	Priors:	[1.0, 3.0]	[0.1, 20.0]	[0.1, 2.0]
Redshift	Mass	c₅₀₀	P₀	β	χ_r²
z ∈ [0.0, 0.4]	M_500c ∈ [10^14.0,10^14.3] M_⊙	$2 . 28_{- 0.04}^{+ 0.05}$ $Mathematical equation: $ 2.28^{+0.05}_{-0.04} $$	$5 . 8_{- 0.3}^{+ 0.4}$ $Mathematical equation: $ 5.8^{+0.4}_{-0.3} $$	$1 . 07_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 1.07^{+0.03}_{-0.03} $$	0.07
z ∈ [0.0, 0.4]	M_500c ∈ [10^14.3,10^14.6] M_⊙	$2 . 42_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 2.42^{+0.03}_{-0.03} $$	$6 . 0_{- 0.3}^{+ 0.3}$ $Mathematical equation: $ 6.0^{+0.3}_{-0.3} $$	$1 . 08_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.08^{+0.02}_{-0.02} $$	1.02
z ∈ [0.0, 0.4]	M_500c ∈ [10^14.6,10^15.1] M_⊙	$2 . 49_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 2.49^{+0.03}_{-0.03} $$	$8 . 1_{- 0.5}^{+ 0.5}$ $Mathematical equation: $ 8.1^{+0.5}_{-0.5} $$	$1 . 29_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 1.29^{+0.03}_{-0.03} $$	0.11
z ∈ [0.0, 0.4]	All masses	$2 . 52_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 2.52^{+0.02}_{-0.02} $$	$6 . 7_{- 0.3}^{+ 0.3}$ $Mathematical equation: $ 6.7^{+0.3}_{-0.3} $$	$1 . 10_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.10^{+0.02}_{-0.02} $$	0.45

z ∈ [0.4, 0.8]	M_500c ∈ [10^14.0,10^14.3] M_⊙	$2 . 49_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 2.49^{+0.04}_{-0.04} $$	$5 . 0_{- 0.4}^{+ 0.4}$ $Mathematical equation: $ 5.0^{+0.4}_{-0.4} $$	$0 . 99_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 0.99^{+0.03}_{-0.03} $$	0.38
z ∈ [0.4, 0.8]	M_500c ∈ [10^14.3,10^14.6] M_⊙	$2 . 08_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 2.08^{+0.02}_{-0.02} $$	$4 . 6_{- 0.2}^{+ 0.2}$ $Mathematical equation: $ 4.6^{+0.2}_{-0.2} $$	$1 . 18_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.18^{+0.02}_{-0.02} $$	1.73
z ∈ [0.4, 0.8]	M_500c ∈ [10^14.6,10^15.1] M_⊙	$2 . 18_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 2.18^{+0.03}_{-0.03} $$	$5 . 4_{- 0.3}^{+ 0.3}$ $Mathematical equation: $ 5.4^{+0.3}_{-0.3} $$	$1 . 19_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.19^{+0.02}_{-0.02} $$	2.29
z ∈ [0.4, 0.8]	All masses	$2 . 11_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 2.11^{+0.02}_{-0.02} $$	$4 . 9_{- 0.2}^{+ 0.2}$ $Mathematical equation: $ 4.9^{+0.2}_{-0.2} $$	$1 . 18_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.18^{+0.02}_{-0.02} $$	1.76

z ∈ [0.8, 2.0]	M_500c ∈ [10^14.0,10^14.3] M_⊙	$2 . 50_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 2.50^{+0.04}_{-0.04} $$	$3 . 8_{- 0.6}^{+ 0.7}$ $Mathematical equation: $ 3.8^{+0.7}_{-0.6} $$	$0 . 90_{- 0.06}^{+ 0.06}$ $Mathematical equation: $ 0.90^{+0.06}_{-0.06} $$	0.41
z ∈ [0.8, 2.0]	M_500c ∈ [10^14.3,10^14.6] M_⊙	$2 . 28_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 2.28^{+0.03}_{-0.03} $$	$4 . 2_{- 0.3}^{+ 0.3}$ $Mathematical equation: $ 4.2^{+0.3}_{-0.3} $$	$1 . 08_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 1.08^{+0.03}_{-0.03} $$	0.57
z ∈ [0.8, 2.0]	M_500c ∈ [10^14.6,10^15.1] M_⊙	$2 . 64_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 2.64^{+0.04}_{-0.04} $$	$7 . 6_{- 0.9}^{+ 1.0}$ $Mathematical equation: $ 7.6^{+1.0}_{-0.9} $$	$1 . 18_{- 0.05}^{+ 0.05}$ $Mathematical equation: $ 1.18^{+0.05}_{-0.05} $$	0.92
z ∈ [0.8, 2.0]	All masses	$2 . 50_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 2.50^{+0.02}_{-0.02} $$	$4 . 5_{- 0.4}^{+ 0.4}$ $Mathematical equation: $ 4.5^{+0.4}_{-0.4} $$	$1 . 00_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 1.00^{+0.03}_{-0.03} $$	0.65

All redshifts	M_500c ∈ [10^14.0,10^14.3] M_⊙	$2 . 36_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 2.36^{+0.03}_{-0.03} $$	$4 . 8_{- 0.4}^{+ 0.4}$ $Mathematical equation: $ 4.8^{+0.4}_{-0.4} $$	$1 . 00_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 1.00^{+0.03}_{-0.03} $$	0.16
All redshifts	M_500c ∈ [10^14.3,10^14.6] M_⊙	$2 . 01_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 2.01^{+0.01}_{-0.01} $$	$4 . 5_{- 0.2}^{+ 0.2}$ $Mathematical equation: $ 4.5^{+0.2}_{-0.2} $$	$1 . 19_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.19^{+0.02}_{-0.02} $$	1.01
All redshifts	M_500c ∈ [10^14.6,10^15.1] M_⊙	$2 . 37_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 2.37^{+0.02}_{-0.02} $$	$7 . 1_{- 0.4}^{+ 0.4}$ $Mathematical equation: $ 7.1^{+0.4}_{-0.4} $$	$1 . 26_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 1.26^{+0.03}_{-0.03} $$	0.07
All redshifts	All masses	$2 . 16_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 2.16^{+0.01}_{-0.01} $$	$5 . 2_{- 0.3}^{+ 0.3}$ $Mathematical equation: $ 5.2^{+0.3}_{-0.3} $$	$1 . 17_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 1.17^{+0.02}_{-0.02} $$	0.27

Notes. The table quotes the best-fit estimates for the BMP parameters as obtained from the multistage fit. Uncertainties are quoted at the 68% confidence level; for c₅₀₀, the error bars have been rescaled using a Fisher-matrix correction as discussed in Sec. 6.1.

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