Enhanced strong-lensing model of MACS J0138.0–2155 based on new JWST and VLT/MUSE observations

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Table 2.

Input and output parameters of the reference lens model for the galaxy cluster MACS J0138.

	Input parameter values and assumed priors

	x [′′]	y [′′]	e	θ [°]	σ_LT [km s⁻¹]	r_core [′′]	r_cut [′′]	γ_ext	ϕ_ext [°]

Cluster-scale halo	−7.0 ÷ 7.0	−7.0 ÷ 7.0	0.0 ÷ 0.9	0.0 ÷ 180.0	400 ÷ 1500	0.0 ÷ 20.0	[2000.0]	–	–
External shear	–	–	–	–	–	–	–	0.0 ÷ 1.0	0.0 ÷ 180.0
JF-1	[ − 5.11]	[6.94]	[0.0]	[0.0]	40 ÷ 250	[0.001]	0.0 ÷ 30.0	–	–
JF-2	[ − 1.65]	[2.60]	[0.0]	[0.0]	40 ÷ 250	[0.001]	0.0 ÷ 30.0	–	–
JF-3	[19.09]	[ − 13.36]	[0.0]	[0.0]	40 ÷ 250	[0.001]	0.0 ÷ 30.0	–	–
BG	[6.87]	[3.84]	[0.0]	[0.0]	100 ÷ 300	[0.001]	0.0 ÷ 30.0	–	–
FG	[ − 0.87]	[ − 16.56]	[0.0]	[0.0]	20 ÷ 250	[0.001]	0.0 ÷ 30.0	–	–

Scaling relations	N_gal = 81	F160W^ref = 15.30	α = 0.21	$σ_{LT}^{ref} = 268 \pm 30$ $\boldsymbol{\sigma}_{\mathbf{LT}}^{\mathbf{ref}} = 268 \pm 30$	β = 0.78	$r_{cut}^{ref} = 1.0 \div 100.0$ $\boldsymbol{r}_{\mathbf{cut}}^{\mathbf{ref}} = 1.0 \div 100.0$	γ = 0.20	–	–

	Optimised parameter values

	x [′′]	y [′′]	e	θ [°]	σ_LT [km s⁻¹]	r_core [′′]	r_cut [′′]	γ_ext	ϕ_ext [°]

Cluster-scale halo	$0 . 44_{- 0.45}^{+ 0.52}$ $0.44^{+0.52}_{-0.45}$	$- 1 . 59_{- 0.90}^{+ 0.63}$ $-1.59^{+0.63}_{-0.90}$	$0 . 39_{- 0.04}^{+ 0.03}$ $0.39^{+0.03}_{-0.04}$	$138 . 5_{- 1.5}^{+ 1.8}$ $138.5^{+1.8}_{-1.5}$	$879_{- 59}^{+ 35}$ $879^{+35}_{-59}$	$9 . 9_{- 1.7}^{+ 1.0}$ $9.9^{+1.0}_{-1.7}$	[2000.0]	–	–
External shear	–	–	–	–	–	–	–	$0 . 11_{- 0.02}^{+ 0.02}$ $0.11^{+0.02}_{-0.02}$	$155 . 6_{- 5.8}^{+ 7.7}$ $155.6^{+7.7}_{-5.8}$

JF-1	[ − 5.11]	[6.94]	[0.0]	[0.0]	$69_{- 19}^{+ 33}$ $69^{+33}_{-19}$	[0.001]	$12 . 4_{- 8.9}^{+ 12.0}$ $12.4^{+12.0}_{-8.9}$	–	–
JF-2	[ − 1.65]	[2.60]	[0.0]	[0.0]	$243_{- 14}^{+ 5}$ $243^{+5}_{-14}$	[0.001]	$6 . 3_{- 2.1}^{+ 7.3}$ $6.3^{+7.3}_{-2.1}$	–	–
JF-3	[19.09]	[ − 13.36]	[0.0]	[0.0]	$56_{- 13}^{+ 53}$ $56^{+53}_{-13}$	[0.001]	$0 . 8_{- 0.7}^{+ 6.1}$ $0.8^{+6.1}_{-0.7}$	–	–
BG	[6.87]	[3.84]	[0.0]	[0.0]	$167_{- 20}^{+ 29}$ $167^{+29}_{-20}$	[0.001]	$20 . 4_{- 12.1}^{+ 6.9}$ $20.4^{+6.9}_{-12.1}$	–	–
FG	[ − 0.87]	[ − 16.56]	[0.0]	[0.0]	$54_{- 7}^{+ 23}$ $54^{+23}_{-7}$	[0.001]	$7 . 1_{- 6.2}^{+ 14.2}$ $7.1^{+14.2}_{-6.2}$	–	–

Scaling relations	N_gal = 81	$m_{F 160 W}^{ref} = 15.30$ $\boldsymbol{m}_{\mathbf{F160W}}^{\mathbf{ref}} = 15.30$	α = 0.21	$σ_{LT}^{ref} = 316_{- 29}^{+ 10}$ $\boldsymbol{\sigma}_{\mathbf{LT}}^{\mathbf{ref}} = 316^{+10}_{-29}$	β = 0.78	$r_{cut}^{ref} = 6 . 0_{- 1.6}^{+ 4.2}$ $\boldsymbol{r}_{\mathbf{cut}}^{\mathbf{ref}} = 6.0^{+4.2}_{-1.6}$	γ = 0.20	–	–

Notes. The x and y coordinates are expressed in arcseconds with respect to the position of the BCG, at RA = 24.51570318°, Dec = –21.92547911°. The values in square brackets were kept fixed during the model optimisation, and those that are separated by the ÷ symbol correspond to the lower and upper boundaries of the flat prior assumed in the model. The symbol ± instead specifies a Gaussian prior where we quote the mean and standard deviation of the distribution. We quote in the bottom table the median and the 16th and 84th percentiles from the model marginalised posterior distributions of the 20 free model parameters.

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