Testing refracted gravity with the kinematics of galaxy clusters

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Table 2.

Best fit parameters from the MCMC analysis of MG-MAMPOSST for MACS 1206 and Abell S1063.

Cluster	𝒜₀	𝒜_∞	ϵ₀	log₁₀ ρ_c [M_⊙ Mpc⁻³]	Q	X_L [M_⊙/L_⊙]	ΔBIC
MACS 1206 (RG)	$1 . 38_{- 0.95}^{+ 1.42}$ $1.38^{+1.42 }_{-0.95}$	$2 . 84_{- 1.51}^{+ 2.03}$ $2.84^{+2.03 }_{-1.51}$	$0 . 18_{- 0.04}^{+ 0.04}$ $0.18^{+0.04 }_{-0.04}$	$14 . 92_{- 0.01}^{+ 0.01}$ $14.92^{+0.01 }_{-0.01}$	$5 . 21_{- 1.70}^{+ 1.85}$ $5.21^{+1.85 }_{-1.70}$	$4 . 45_{- 0.26}^{+ 0.24}$ $4.45^{+0.24 }_{-0.26}$	2.12
MACS 1206 (GR)	$1 . 65_{- 0.65}^{+ 0.83}$ $1.65^{+0.83 }_{-0.65}$	$3 . 19_{- 1.59}^{+ 1.72}$ $3.19^{+1.72 }_{-1.59}$				$4 . 48_{- 0.28}^{+ 0.26}$ $4.48^{+0.26 }_{-0.28}$	0

Abell S1063 (RG)	$2 . 06_{- 1.12}^{+ 1.94}$ $2.06^{+1.94 }_{-1.12}$	$1 . 01_{- 0.27}^{+ 0.31}$ $1.01^{+0.31 }_{-0.27}$	$0 . 13_{- 0.01}^{+ 0.01}$ $0.13^{+0.01 }_{-0.01}$	$14 . 787_{- 0.003}^{+ 0.002}$ $14.787^{+0.002 }_{-0.003}$	$23 . 62_{- 4.69}^{+ 5.00}$ $23.62^{+5.00 }_{-4.69}$	$4 . 88_{- 0.27}^{+ 0.28}$ $4.88^{+0.28 }_{-0.27}$	4.1
Abell S1063 (GR)	$1 . 35_{- 0.75}^{+ 2.16}$ $1.35^{+2.16 }_{-0.75}$	$1 . 89_{- 1.19}^{+ 2.27}$ $1.89^{+2.27 }_{-1.19}$				$4 . 15_{- 0.47}^{+ 0.44}$ $4.15^{+0.44 }_{-0.47}$	0

Notes. Best fits for MACS 1206 (first row) and Abell S1063 (second row). The last column indicates the ΔBIC with respect to the GR analysis of B23 (MACS 1206) and to our preliminary run based on S20 (Abell S1063), displayed in the third and fourth rows, respectively, for the parameters of interest. All the uncertainties are given at 95% C.L.

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