Virial quantities of galaxy clusters from extrapolating strong-lensing mass profiles

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Volume 698 (June 2025)

A&A, 698 (2025) A272

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Table 6.

Results of the increasing radius tests.

M0329	ρ₀	r_S		M(< 500 kpc)	χ²
R = 50″	$9 . 68_{- 0.58}^{+ 0.39} \times 10^{6}$ $9.68^{+0.39}_{-0.58} \times 10^{6}$	$8 . 00_{- 0.20}^{+ 0.33} \times 10^{2}$ $8.00^{+0.33}_{-0.20} \times 10^{2}$		$5 . 42_{- 0.07}^{+ 0.47} \times 10^{14}$ $5.42^{+0.47}_{-0.07} \times 10^{14}$	48.5
R = 150″	$9 . 82_{- 0.35}^{+ 0.37} \times 10^{6}$ $9.82^{+0.37}_{-0.35} \times 10^{6}$	$7 . 95_{- 0.19}^{+ 0.19} \times 10^{2}$ $7.95^{+0.19}_{-0.19} \times 10^{2}$		$5 . 37_{- 0.06}^{+ 0.06} \times 10^{14}$ $5.37^{+0.06}_{-0.06} \times 10^{14}$	38.2
R = 200″	$9 . 73_{- 0.35}^{+ 0.40} \times 10^{6}$ $9.73^{+0.40}_{-0.35} \times 10^{6}$	$8 . 00_{- 0.21}^{+ 0.19} \times 10^{2}$ $8.00^{+0.19}_{-0.21} \times 10^{2}$		$5 . 28_{- 0.05}^{+ 0.05} \times 10^{14}$ $5.28^{+0.05}_{-0.05} \times 10^{14}$	36.7
R = 250″	$9 . 60_{- 0.34}^{+ 0.39} \times 10^{6}$ $9.60^{+0.39}_{-0.34} \times 10^{6}$	$8 . 08_{- 0.21}^{+ 0.19} \times 10^{2}$ $8.08^{+0.19}_{-0.21} \times 10^{2}$		$5 . 51_{- 0.07}^{+ 0.05} \times 10^{14}$ $5.51^{+0.05}_{-0.07} \times 10^{14}$	37.2
R = 300″	$9 . 48_{- 0.36}^{+ 0.39} \times 10^{6}$ $9.48^{+0.39}_{-0.36} \times 10^{6}$	$8 . 14_{- 0.21}^{+ 0.21} \times 10^{2}$ $8.14^{+0.21}_{-0.21} \times 10^{2}$		$5 . 52_{- 0.07}^{+ 0.08} \times 10^{14}$ $5.52^{+0.08}_{-0.07} \times 10^{14}$	37.7

A2744	ρ₀	r_S	β	M(< 500 kpc)	χ²

NFW	$5 . 57_{- 0.14}^{+ 0.13} \times 10^{5}$ $5.57^{+0.13}_{-0.14} \times 10^{5}$	$7 . 83_{- 0.13}^{+ 0.14} \times 10^{2}$ $7.83^{+0.14}_{-0.13} \times 10^{2}$	–	$6 . 04_{- 0.04}^{+ 0.03} \times 10^{14}$ $6.04^{+0.03}_{-0.04} \times 10^{14}$	51.8
NFW-T3	$6 . 35_{- 0.24}^{+ 0.24} \times 10^{5}$ $6.35^{+0.24}_{-0.24} \times 10^{5}$	$7 . 13_{- 0.19}^{+ 0.20} \times 10^{2}$ $7.13^{+0.20}_{-0.19} \times 10^{2}$	–	$5 . 91_{- 0.07}^{+ 0.08} \times 10^{14}$ $5.91^{+0.08}_{-0.07} \times 10^{14}$	77.7
NIS	$1 . 92_{- 0.03}^{+ 0.03} \times 10^{8}$ $1.92^{+0.03}_{-0.03} \times 10^{8}$	$6 . 29_{- 0.07}^{+ 0.08} \times 10^{1}$ $6.29^{+0.08}_{-0.07} \times 10^{1}$	–	$5 . 18_{- 0.03}^{+ 0.02} \times 10^{14}$ $5.18^{+0.02}_{-0.03} \times 10^{14}$	183.36
NIS-T3	$2 . 29_{- 0.04}^{+ 0.04} \times 10^{8}$ $2.29^{+0.04}_{-0.04} \times 10^{8}$	$5 . 51_{- 0.07}^{+ 0.07} \times 10^{1}$ $5.51^{+0.07}_{-0.07} \times 10^{1}$	–	$4 . 88_{- 0.03}^{+ 0.03} \times 10^{14}$ $4.88^{+0.03}_{-0.03} \times 10^{14}$	179.2
Hernquist	$3 . 95_{- 0.10}^{+ 0.11} \times 10^{6}$ $3.95^{+0.11}_{-0.10} \times 10^{6}$	$1 . 36_{- 0.03}^{+ 0.03} \times 10^{3}$ $1.36^{+0.03}_{-0.03} \times 10^{3}$	–	$6 . 00_{- 0.04}^{+ 0.04} \times 10^{14}$ $6.00^{+0.04}_{-0.04} \times 10^{14}$	54.1
Hernquist-T3	$4 . 63_{- 0.15}^{+ 0.17} \times 10^{6}$ $4.63^{+0.17}_{-0.15} \times 10^{6}$	$1 . 21_{- 0.03}^{+ 0.03} \times 10^{3}$ $1.21^{+0.03}_{-0.03} \times 10^{3}$	–	$5 . 80_{- 0.08}^{+ 0.07} \times 10^{14}$ $5.80^{+0.07}_{-0.08} \times 10^{14}$	78.2
Beta	$1 . 19_{- 0.41}^{+ 0.39} \times 10^{9}$ $1.19^{+0.39}_{-0.41} \times 10^{9}$	$9 . 22_{- 1.93}^{+ 3.89} \times 10^{0}$ $9.22^{+3.89}_{-1.93} \times 10^{0}$	$0 . 495_{- 0.004}^{+ 0.009}$ $0.495^{+0.009}_{-0.004}$	$6 . 85_{- 0.15}^{+ 0.07} \times 10^{14}$ $6.85^{+0.07}_{-0.15} \times 10^{14}$	76.3
Beta-T3	$9 . 34_{- 5.57}^{+ 14.26} \times 10^{9}$ $9.34^{+14.26}_{-5.57} \times 10^{9}$	$1 . 66_{- 0.81}^{+ 1.61} \times 10^{0}$ $1.66^{+1.61}_{-0.81} \times 10^{0}$	$0 . 466_{- 0.002}^{+ 0.002}$ $0.466^{+0.002}_{-0.002}$	$7 . 89_{- 0.02}^{+ 0.15} \times 10^{14}$ $7.89^{+0.15}_{-0.02} \times 10^{14}$	67.7

Notes. The parameter values of the models marked with T3 are those reported in Table 3 as reference. The central mass densities are expressed in M_⊙/kpc³ and the length scales are listed in kpc. The total mass values are expressed in M_⊙.

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