Dynamical models of cluster members to probe the total mass properties of cluster subhalos - I. A comparison with parametric strong lensing models

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Volume 711 (July 2026)

A&A, 711 (2026) A291

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Table 1.

Comparison of the parameters of the F-J scaling relation obtained from the dynamical models, the SL models optimizations, and previous literature kinematic measurements, for the clusters of galaxies A2744 and M0416.

A2744
Model	α	σ_r [km s⁻¹]	Δσ_r [km s⁻¹]

SL: B+23a	0.40	$289_{- 16}^{+ 27}$ $Mathematical equation: $ 289^{+27}_{-16} $$	−
Kin “FS”: B+23a	$0 . 33_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 0.33^{+0.03}_{-0.03} $$	$217_{- 12}^{+ 12}$ $Mathematical equation: $ 217^{+12}_{-12} $$	$33_{- 3}^{+ 3}$ $Mathematical equation: $ 33^{+3}_{-3} $$
Kin “RS”: B+23a	$0 . 30_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 0.30^{+0.04}_{-0.04} $$	$210_{- 16}^{+ 16}$ $Mathematical equation: $ 210^{+16}_{-16} $$	$36_{- 3}^{+ 4}$ $Mathematical equation: $ 36^{+4}_{-3} $$
Dynamical	$0 . 26_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 0.26^{+0.04}_{-0.04} $$	$262_{- 20}^{+ 20}$ $Mathematical equation: $ 262^{+20}_{-20} $$	$47_{- 4}^{+ 5}$ $Mathematical equation: $ 47^{+5}_{-4} $$
Dynamical “2p”	$0 . 24_{- 0, 06}^{+ 0.06}$ $Mathematical equation: $ 0.24^{+0.06}_{-0,06} $$	$269_{- 24}^{+ 24}$ $Mathematical equation: $ 269^{+24}_{-24} $$	$55_{- 6}^{+ 8}$ $Mathematical equation: $ 55^{+8}_{-6} $$

M0416

Model	α	σ_r [km s⁻¹]	Δσ_r [km s⁻¹]

SL: B+23b	0.30	$281_{- 19}^{+ 12}$ $Mathematical equation: $ 281^{+12}_{-19} $$	−
Kin “FS”: B+21	$0 . 31_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 0.31^{+0.03}_{-0.03} $$	$272_{- 14}^{+ 14}$ $Mathematical equation: $ 272^{+14}_{-14} $$	$32_{- 3}^{+ 3}$ $Mathematical equation: $ 32^{+3}_{-3} $$
Kin “RS”: B+21	$0 . 28_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ 0.28^{+0.03}_{-0.03} $$	$268_{- 22}^{+ 23}$ $Mathematical equation: $ 268^{+23}_{-22} $$	$30_{- 3}^{+ 4}$ $Mathematical equation: $ 30^{+4}_{-3} $$
Dynamical	$0 . 25_{- 0.05}^{+ 0.04}$ $Mathematical equation: $ 0.25^{+0.04}_{-0.05} $$	$321_{- 28}^{+ 29}$ $Mathematical equation: $ 321^{+29}_{-28} $$	$41_{- 5}^{+ 6}$ $Mathematical equation: $ 41^{+6}_{-5} $$
Dynamical “2p”	$0 . 20_{- 0, 05}^{+ 0.05}$ $Mathematical equation: $ 0.20^{+0.05}_{-0,05} $$	$307_{- 30}^{+ 33}$ $Mathematical equation: $ 307^{+33}_{-30} $$	$41_{- 6}^{+ 9}$ $Mathematical equation: $ 41^{+9}_{-6} $$

Notes. We report the slope, α, normalization, σ_r, and scatter, Δσ_r, obtained from the kinematic measurements performed in B+23a and B+21, reported as “Kin”; strong lensing measurements from B+23a and B+23b, listed as “SL”; and our dynamical model measurements, labeled as “Dynamical”. The “FS” and “RS” labels indicate that the full and restricted samples of galaxies from the listed papers were used to calibrate the scaling relations, respectively. The RS sample, further restricted to the galaxies with more than two kinematic measurements, is labeled as “2p”.

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