Improved model of the Supernova Refsdal cluster MACS J1149.5+2223 thanks to VLT/MUSE

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Volume 689 (September 2024)

A&A, 689 (2024) A42

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Table 4.

Model parameter estimates, as the median values, with 68% CL (i.e., 1σ) uncertainties and the adopted prior ranges.

Profile	Parameter	Prior	Median ±1σ
1^st Halo	x_H [″]	[ − 60, 60]	−0.5 ± 0.3
	y_H [″]	[ − 60, 60]	$0 . 40_{- 0.20}^{+ 0.21}$ $0.40_{- 0.20}^{+ 0.21}$
	q_H	[0.2, 1]	$0 . 507_{- 0.020}^{+ 0.015}$ $0.507_{- 0.020}^{+ 0.015}$
	ϕ_H [rad]	( −∞, +∞)	0.60 ± 0.02
	θ_E,H [″]	[0, +∞)	$31 . 5_{- 3.0}^{+ 3.1}$ $31.5_{- 3.0}^{+ 3.1}$
	r_c,H [″]	[0, +∞)	$8 . 72_{- 0.84}^{+ 0.90}$ $8.72_{- 0.84}^{+ 0.90}$

2^nd Halo	x_H [″]	[ − 60, 60]	$- 22 . 6_{- 2.9}^{+ 1.6}$ $-22.6_{- 2.9}^{+ 1.6}$
	y_H [″]	[ − 60, 60]	$- 26 . 8_{- 2.9}^{+ 1.8}$ $-26.8_{- 2.9}^{+ 1.8}$
	q_H	[0.2, 1]	$0 . 67_{- 0.20}^{+ 0.11}$ $0.67_{- 0.20}^{+ 0.11}$
	ϕ_H [rad]	( −∞, +∞)	$0 . 53_{- 0.35}^{+ 0.15}$ $0.53_{- 0.35}^{+ 0.15}$
	θ_E,H [″]	[0, +∞)	$8 . 52_{- 1.65}^{+ 1.80}$ $8.52_{- 1.65}^{+ 1.80}$
	r_c,H [″]	[0, +∞)	7.1 ± 1.8

3^rd Halo	x_H [″]	[ − 60, 60]	$25 . 5_{- 1.0}^{+ 0.7}$ $25.5_{- 1.0}^{+ 0.7}$
	y_H [″]	[ − 60, 60]	$47 . 60_{- 0.25}^{+ 0.24}$ $47.60_{- 0.25}^{+ 0.24}$
	q_H	[0.2, 1]	$0 . 217_{- 0.014}^{+ 0.030}$ $0.217_{- 0.014}^{+ 0.030}$
	ϕ_H [rad]	( −∞, +∞)	0.60 ± 0.04
	θ_E,H [″]	[0, +∞)	9.8 ± 0.9
	r_c,H [″]	[0, +∞)	$0 . 93_{- 0.35}^{+ 0.40}$ $0.93_{- 0.35}^{+ 0.40}$

4^th Halo (H_4N)	x_H [″]	[0, 60]	$15 . 23_{- 0.40}^{+ 0.35}$ $15.23_{- 0.40}^{+ 0.35}$
	y_H [″]	[0, 60]	$59 . 6_{- 0.6}^{+ 0.3}$ $59.6_{- 0.6}^{+ 0.3}$
	θ_E,H [″]	[0, +∞)	4.5 ± 0.5

Scaling relation	θ_E,BCG [″]	[0, +∞)	1.57 ± 0.24
Scaling relation	r_t,BCG [″]	[0, +∞)	$15 . 8_{- 5.9}^{+ 13.0}$ $15.8_{- 5.9}^{+ 13.0}$

1^st member	q	[0.2, 1]	$0 . 8_{- 0.3}^{+ 0.2}$ $0.8_{- 0.3}^{+ 0.2}$
	ϕ [rad]	( −∞, +∞)	$1 . 45_{- 0.82}^{+ 1.05}$ $1.45_{- 0.82}^{+ 1.05}$
	θ_E [″]	[0, +∞)	$1 . 85_{- 0.83}^{+ 6.1}$ $1.85_{- 0.83}^{+ 6.1}$
	r_t [″]	[0, +∞)	$1 . 04_{- 0.83}^{+ 2.45}$ $1.04_{- 0.83}^{+ 2.45}$

2^nd member	q	[0.2, 1]	0.6 ± 0.3
	ϕ [rad]	( −∞, +∞)	$1 . 5_{- 1.0}^{+ 1.2}$ $1.5_{- 1.0}^{+ 1.2}$
	θ_E [″]	[0, +∞)	$2 . 2_{- 1.1}^{+ 4.6}$ $2.2_{- 1.1}^{+ 4.6}$
	r_t [″]	[0, +∞)	$0 . 39_{- 0.30}^{+ 0.71}$ $0.39_{- 0.30}^{+ 0.71}$

photo-z	z₆	[0, 6]	$2 . 76_{- 0.15}^{+ 0.20}$ $2.76_{- 0.15}^{+ 0.20}$
	z₇	[0, 6]	2.74 ± 0.06
	z₈	[0, 6]	$2 . 84_{- 0.05}^{+ 0.06}$ $2.84_{- 0.05}^{+ 0.06}$

Notes. The positions are given relative to the BCG, Einstein radii are given for a source redshift of infinity, and all position angle values, measured counterclockwise from the positive x-axis, are converted to the range [0, π]. For the prior ranges, square brackets indicates bounds included in the prior range, while round brackets indicate bounds excluded. The median values and 1σ uncertainties are computed by excluding the first 20 000 accepted iterations as burn-in points.

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