Table 1. Open in new tab Model...

Component	Δα	Δδ	e	θ	r_core	r_cut	σ
MACS0416-like, z = 0.35
\|$N_{\mathrm{ s}} = 26$\|⁠, z_{s, toy} = {1.6, 3.5, 6.1}
Cluster halo 1	−0.22	0.06	0.81	143	37.4	988	615
Cluster halo 2	22.67	−34.27	0.89	136	26.3	988	466
Cluster halo 3	−32.45	8.80	0.00	0	34.2	988	308
Cluster halo 4	22.80	−48.15	0.76	122	66.7	988	707
Perturber 1	31.96	−65.55	0.00	0	4.9	274	77
Perturber 2	13.34	2.62	0.60	−46	4.9	65	106
Scaling relations	N(gal) = 212	m^ref = 17.02	\|$r_{\rm core}^{\rm ref}$\| = 0.74 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 74 kpc	σ^ref = 210.00 km s⁻¹
A2744-like, z = 0.4
\|$N_{\mathrm{ s}} = 22$\|⁠, z_{s, toy} = {1.5, 2.4, 3.8}
Cluster halo 1	−1.42	0.55	0.59	91	28.6	1500	515
Cluster halo 2	−17.85	−15.22	0.40	54	34.1	1600	632
Ext. clump 1	99.49	85.97	0.00	0	1.3	800	111
Ext. clump 2	138.28	99.87	0.00	0	1.4	800	372
Ext. clump 3	24.23	155.84	0.00	0	1.4	800	294
BCG-N	0.0	0.0	0.28	133	1.3	800	208
BCG-S	−17.95	−20.05	0.74	26	0.2	178	308
Scaling relations	N(gal) = 223	m^ref = 17.34	\|$r_{\rm core}^{\rm ref}$\| = 0.15 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 19.52 kpc	σ^ref = 252.66 km s⁻¹
MACS1206-like, z = 0.45
\|$N_{\mathrm{ s}} = 25$\|⁠, z_{s, toy} = {1.9, 4.2, 5.7}
Cluster halo 1	−1.40	0.14	0.72	19	35.2	1152	748
Cluster halo 2	9.20	3.63	0.46	117	77.6	1152	663
Ext. clump 1	−28.87	−6.83	0.33	−25	70.9	1152	501
Scaling relations	N(gal) = 258	m^ref = 17.19	\|$r_{\rm core}^{\rm ref}$\| = 0.86 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 86 kpc	σ^ref = 210.0 km s⁻¹
AS1063-like, z = 0.5
\|$N_{\mathrm{ s}} = 23$\|⁠, z_{s, toy} = {2.4, 3.3, 4.3}
Cluster halo 1	1.44	−0.73	0.63	−39	111.3	1220	1165
Cluster halo 2	−48.60	26.26	0.01	0	30.5	1220	213
Ext. clump 1	18.90	−73.36	0.80	−162	8.6	1155	356
BCG	−18.05	13.47	0.13	−28	221.7	2070	443
Perturber	0.20	−1.24	0.34	−15	88.1	610	250
Scaling relations	N(gal) = 222	m^ref = 16.18	\|$\rm r_{\rm core}^{\rm ref}$\| = 0.91 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 92 kpc	σ^ref = 210.0 km s⁻¹

Component

Δα

Δδ

r_core

r_cut

[arcsec]

[deg]

[kpc]

[km s⁻¹]

MACS0416-like, z = 0.35

|$N_{\mathrm{ s}} = 26$|⁠, z_{s, toy} = {1.6, 3.5, 6.1}

Cluster halo 1

−0.22

0.06

0.81

143

37.4

988

615

Cluster halo 2

22.67

−34.27

0.89

136

26.3

988

466

Cluster halo 3

−32.45

8.80

0.00

34.2

988

308

Cluster halo 4

22.80

−48.15

0.76

122

66.7

988

707

Perturber 1

31.96

−65.55

0.00

4.9

274

Perturber 2

13.34

2.62

0.60

−46

4.9

106

Scaling relations

N(gal) = 212

m^ref = 17.02

|$r_{\rm core}^{\rm ref}$| = 0.74 kpc

|$\rm r_{\rm cut}^{\rm ref}$| = 74 kpc

σ^ref = 210.00 km s⁻¹

A2744-like, z = 0.4

|$N_{\mathrm{ s}} = 22$|⁠, z_{s, toy} = {1.5, 2.4, 3.8}

Cluster halo 1

−1.42

0.55

0.59

28.6

1500

515

Cluster halo 2

−17.85

−15.22

0.40

34.1

1600

632

Ext. clump 1

99.49

85.97

0.00

1.3

800

111

Ext. clump 2

138.28

99.87

0.00

1.4

800

372

Ext. clump 3

24.23

155.84

0.00

1.4

800

294

BCG-N

0.0

0.28

133

1.3

800

208

BCG-S

−17.95

−20.05

0.74

0.2

178

308

Scaling relations

N(gal) = 223

m^ref = 17.34

|$r_{\rm core}^{\rm ref}$| = 0.15 kpc

|$r_{\rm cut}^{\rm ref}$| = 19.52 kpc

σ^ref = 252.66 km s⁻¹

MACS1206-like, z = 0.45

|$N_{\mathrm{ s}} = 25$|⁠, z_{s, toy} = {1.9, 4.2, 5.7}

Cluster halo 1

−1.40

0.14

0.72

35.2

1152

748

Cluster halo 2

9.20

3.63

0.46

117

77.6

1152

663

Ext. clump 1

−28.87

−6.83

0.33

−25

70.9

1152

501

Scaling relations

N(gal) = 258

m^ref = 17.19

|$r_{\rm core}^{\rm ref}$| = 0.86 kpc

|$r_{\rm cut}^{\rm ref}$| = 86 kpc

σ^ref = 210.0 km s⁻¹

AS1063-like, z = 0.5

|$N_{\mathrm{ s}} = 23$|⁠, z_{s, toy} = {2.4, 3.3, 4.3}

Cluster halo 1

1.44

−0.73

0.63

−39

111.3

1220

1165

Cluster halo 2

−48.60

26.26

0.01

30.5

1220

213

Ext. clump 1

18.90

−73.36

0.80

−162

8.6

1155

356

BCG

−18.05

13.47

0.13

−28

221.7

2070

443

Perturber

0.20

−1.24

0.34

−15

88.1

610

250

Scaling relations

N(gal) = 222

m^ref = 16.18

|$\rm r_{\rm core}^{\rm ref}$| = 0.91 kpc

|$\rm r_{\rm cut}^{\rm ref}$| = 92 kpc

σ^ref = 210.0 km s⁻¹

Component	Δα	Δδ	e	θ	r_core	r_cut	σ
MACS0416-like, z = 0.35
\|$N_{\mathrm{ s}} = 26$\|⁠, z_{s, toy} = {1.6, 3.5, 6.1}
Cluster halo 1	−0.22	0.06	0.81	143	37.4	988	615
Cluster halo 2	22.67	−34.27	0.89	136	26.3	988	466
Cluster halo 3	−32.45	8.80	0.00	0	34.2	988	308
Cluster halo 4	22.80	−48.15	0.76	122	66.7	988	707
Perturber 1	31.96	−65.55	0.00	0	4.9	274	77
Perturber 2	13.34	2.62	0.60	−46	4.9	65	106
Scaling relations	N(gal) = 212	m^ref = 17.02	\|$r_{\rm core}^{\rm ref}$\| = 0.74 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 74 kpc	σ^ref = 210.00 km s⁻¹
A2744-like, z = 0.4
\|$N_{\mathrm{ s}} = 22$\|⁠, z_{s, toy} = {1.5, 2.4, 3.8}
Cluster halo 1	−1.42	0.55	0.59	91	28.6	1500	515
Cluster halo 2	−17.85	−15.22	0.40	54	34.1	1600	632
Ext. clump 1	99.49	85.97	0.00	0	1.3	800	111
Ext. clump 2	138.28	99.87	0.00	0	1.4	800	372
Ext. clump 3	24.23	155.84	0.00	0	1.4	800	294
BCG-N	0.0	0.0	0.28	133	1.3	800	208
BCG-S	−17.95	−20.05	0.74	26	0.2	178	308
Scaling relations	N(gal) = 223	m^ref = 17.34	\|$r_{\rm core}^{\rm ref}$\| = 0.15 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 19.52 kpc	σ^ref = 252.66 km s⁻¹
MACS1206-like, z = 0.45
\|$N_{\mathrm{ s}} = 25$\|⁠, z_{s, toy} = {1.9, 4.2, 5.7}
Cluster halo 1	−1.40	0.14	0.72	19	35.2	1152	748
Cluster halo 2	9.20	3.63	0.46	117	77.6	1152	663
Ext. clump 1	−28.87	−6.83	0.33	−25	70.9	1152	501
Scaling relations	N(gal) = 258	m^ref = 17.19	\|$r_{\rm core}^{\rm ref}$\| = 0.86 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 86 kpc	σ^ref = 210.0 km s⁻¹
AS1063-like, z = 0.5
\|$N_{\mathrm{ s}} = 23$\|⁠, z_{s, toy} = {2.4, 3.3, 4.3}
Cluster halo 1	1.44	−0.73	0.63	−39	111.3	1220	1165
Cluster halo 2	−48.60	26.26	0.01	0	30.5	1220	213
Ext. clump 1	18.90	−73.36	0.80	−162	8.6	1155	356
BCG	−18.05	13.47	0.13	−28	221.7	2070	443
Perturber	0.20	−1.24	0.34	−15	88.1	610	250
Scaling relations	N(gal) = 222	m^ref = 16.18	\|$\rm r_{\rm core}^{\rm ref}$\| = 0.91 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 92 kpc	σ^ref = 210.0 km s⁻¹

Table 1.

Open in new tab

Model parameters for the four cluster lens systems in the simulation. z represents the cluster redshift, |$N_{s}$| is the number of lensed sources put in the lens system, and z_{s, toy} denotes the source redshift distribution used in the analyses. Note that in each system, only three of the lensed sources are used for lens modelling due to computational constraints. Within a lensed system, each line provides the parameters for a specific component, where Δα and Δδ are the respective relative position to the cluster centre; e is the ellipticity of the clump calculated as e = 1 − b/a, a and b are the semimajor and semiminor axes; θ is the position angle; |$r_{\mathrm{ core}}$|⁠, |$r_{\mathrm{ cut}}$|⁠, and σ are the core radius, cut radius, and velocity dispersion; m^ref, |$r_{\rm core}^{\rm ref}$|⁠, |$r_{\rm cut}^{\rm ref}$|⁠, σ^ref are parameters for computing the scaling relations of member galaxies in equation (2).

Component	Δα	Δδ	e	θ	r_core	r_cut	σ
	[arcsec]	[arcsec]		[deg]	[kpc]	[kpc]	[km s⁻¹]
MACS0416-like, z = 0.35
\|$N_{\mathrm{ s}} = 26$\|⁠, z_{s, toy} = {1.6, 3.5, 6.1}
Cluster halo 1	−0.22	0.06	0.81	143	37.4	988	615
Cluster halo 2	22.67	−34.27	0.89	136	26.3	988	466
Cluster halo 3	−32.45	8.80	0.00	0	34.2	988	308
Cluster halo 4	22.80	−48.15	0.76	122	66.7	988	707
Perturber 1	31.96	−65.55	0.00	0	4.9	274	77
Perturber 2	13.34	2.62	0.60	−46	4.9	65	106
Scaling relations	N(gal) = 212	m^ref = 17.02	\|$r_{\rm core}^{\rm ref}$\| = 0.74 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 74 kpc	σ^ref = 210.00 km s⁻¹
A2744-like, z = 0.4
\|$N_{\mathrm{ s}} = 22$\|⁠, z_{s, toy} = {1.5, 2.4, 3.8}
Cluster halo 1	−1.42	0.55	0.59	91	28.6	1500	515
Cluster halo 2	−17.85	−15.22	0.40	54	34.1	1600	632
Ext. clump 1	99.49	85.97	0.00	0	1.3	800	111
Ext. clump 2	138.28	99.87	0.00	0	1.4	800	372
Ext. clump 3	24.23	155.84	0.00	0	1.4	800	294
BCG-N	0.0	0.0	0.28	133	1.3	800	208
BCG-S	−17.95	−20.05	0.74	26	0.2	178	308
Scaling relations	N(gal) = 223	m^ref = 17.34	\|$r_{\rm core}^{\rm ref}$\| = 0.15 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 19.52 kpc	σ^ref = 252.66 km s⁻¹
MACS1206-like, z = 0.45
\|$N_{\mathrm{ s}} = 25$\|⁠, z_{s, toy} = {1.9, 4.2, 5.7}
Cluster halo 1	−1.40	0.14	0.72	19	35.2	1152	748
Cluster halo 2	9.20	3.63	0.46	117	77.6	1152	663
Ext. clump 1	−28.87	−6.83	0.33	−25	70.9	1152	501
Scaling relations	N(gal) = 258	m^ref = 17.19	\|$r_{\rm core}^{\rm ref}$\| = 0.86 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 86 kpc	σ^ref = 210.0 km s⁻¹
AS1063-like, z = 0.5
\|$N_{\mathrm{ s}} = 23$\|⁠, z_{s, toy} = {2.4, 3.3, 4.3}
Cluster halo 1	1.44	−0.73	0.63	−39	111.3	1220	1165
Cluster halo 2	−48.60	26.26	0.01	0	30.5	1220	213
Ext. clump 1	18.90	−73.36	0.80	−162	8.6	1155	356
BCG	−18.05	13.47	0.13	−28	221.7	2070	443
Perturber	0.20	−1.24	0.34	−15	88.1	610	250
Scaling relations	N(gal) = 222	m^ref = 16.18	\|$\rm r_{\rm core}^{\rm ref}$\| = 0.91 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 92 kpc	σ^ref = 210.0 km s⁻¹

Component	Δα	Δδ	e	θ	r_core	r_cut	σ
	[arcsec]	[arcsec]		[deg]	[kpc]	[kpc]	[km s⁻¹]
MACS0416-like, z = 0.35
\|$N_{\mathrm{ s}} = 26$\|⁠, z_{s, toy} = {1.6, 3.5, 6.1}
Cluster halo 1	−0.22	0.06	0.81	143	37.4	988	615
Cluster halo 2	22.67	−34.27	0.89	136	26.3	988	466
Cluster halo 3	−32.45	8.80	0.00	0	34.2	988	308
Cluster halo 4	22.80	−48.15	0.76	122	66.7	988	707
Perturber 1	31.96	−65.55	0.00	0	4.9	274	77
Perturber 2	13.34	2.62	0.60	−46	4.9	65	106
Scaling relations	N(gal) = 212	m^ref = 17.02	\|$r_{\rm core}^{\rm ref}$\| = 0.74 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 74 kpc	σ^ref = 210.00 km s⁻¹
A2744-like, z = 0.4
\|$N_{\mathrm{ s}} = 22$\|⁠, z_{s, toy} = {1.5, 2.4, 3.8}
Cluster halo 1	−1.42	0.55	0.59	91	28.6	1500	515
Cluster halo 2	−17.85	−15.22	0.40	54	34.1	1600	632
Ext. clump 1	99.49	85.97	0.00	0	1.3	800	111
Ext. clump 2	138.28	99.87	0.00	0	1.4	800	372
Ext. clump 3	24.23	155.84	0.00	0	1.4	800	294
BCG-N	0.0	0.0	0.28	133	1.3	800	208
BCG-S	−17.95	−20.05	0.74	26	0.2	178	308
Scaling relations	N(gal) = 223	m^ref = 17.34	\|$r_{\rm core}^{\rm ref}$\| = 0.15 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 19.52 kpc	σ^ref = 252.66 km s⁻¹
MACS1206-like, z = 0.45
\|$N_{\mathrm{ s}} = 25$\|⁠, z_{s, toy} = {1.9, 4.2, 5.7}
Cluster halo 1	−1.40	0.14	0.72	19	35.2	1152	748
Cluster halo 2	9.20	3.63	0.46	117	77.6	1152	663
Ext. clump 1	−28.87	−6.83	0.33	−25	70.9	1152	501
Scaling relations	N(gal) = 258	m^ref = 17.19	\|$r_{\rm core}^{\rm ref}$\| = 0.86 kpc	\|$r_{\rm cut}^{\rm ref}$\| = 86 kpc	σ^ref = 210.0 km s⁻¹
AS1063-like, z = 0.5
\|$N_{\mathrm{ s}} = 23$\|⁠, z_{s, toy} = {2.4, 3.3, 4.3}
Cluster halo 1	1.44	−0.73	0.63	−39	111.3	1220	1165
Cluster halo 2	−48.60	26.26	0.01	0	30.5	1220	213
Ext. clump 1	18.90	−73.36	0.80	−162	8.6	1155	356
BCG	−18.05	13.47	0.13	−28	221.7	2070	443
Perturber	0.20	−1.24	0.34	−15	88.1	610	250
Scaling relations	N(gal) = 222	m^ref = 16.18	\|$\rm r_{\rm core}^{\rm ref}$\| = 0.91 kpc	\|$\rm r_{\rm cut}^{\rm ref}$\| = 92 kpc	σ^ref = 210.0 km s⁻¹

This Feature Is Available To Subscribers Only