Complex angular structure of three elliptical galaxies from high-resolution ALMA observations of strong gravitational lenses

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Volume 688 (August 2024)

A&A, 688 (2024) A110

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Table 2.

Posterior distributions of the parameters of lens models.

	SDP 81		SPT 0532−50		SPT 0538−50

	PL	PL+MP	PL	PL+MP	PL	PL+MP
x_l	$0 . 542_{- 0.011}^{+ 0.003}$ $0.542^{+0.003}_{-0.011}$	$0 . 560_{- 0.003}^{+ 0.003}$ $0.560^{+0.003}_{-0.003}$	$2 . 1043_{- 0.0007}^{+ 0.0003}$ $2.1043^{+0.0003}_{-0.0007}$	$2 . 1003_{- 0.0003}^{+ 0.0004}$ $2.1003^{+0.0004}_{-0.0003}$	$0 . 1896_{- 0.0008}^{+ 0.0008}$ $0.1896^{+0.0008}_{-0.0008}$	$0 . 1907_{- 0.0026}^{+ 0.0007}$ $0.1907^{+0.0007}_{-0.0026}$
y_l	$- 0 . 170_{- 0.009}^{+ 0.005}$ $-0.170^{+0.005}_{-0.009}$	$- 0 . 149_{- 0.004}^{+ 0.003}$ $-0.149^{+0.003}_{-0.004}$	$1 . 8706_{- 0.0003}^{+ 0.0001}$ $1.8706^{+0.0001}_{-0.0003}$	$1 . 8700_{- 0.0003}^{+ 0.0004}$ $1.8700^{+0.0004}_{-0.0003}$	$- 0 . 0277_{- 0.0016}^{+ 0.0009}$ $-0.0277^{+0.0009}_{-0.0016}$	$- 0 . 0254_{- 0.0011}^{+ 0.0013}$ $-0.0254^{+0.0013}_{-0.0011}$
R_E	$1 . 609_{- 0.002}^{+ 0.007}$ $1.609^{+0.007}_{-0.002}$	$1 . 611_{- 0.002}^{+ 0.003}$ $1.611^{+0.003}_{-0.002}$	$0 . 5420_{- 0.0001}^{+ 0.0001}$ $0.5420^{+0.0001}_{-0.0001}$	$0 . 5420_{- 0.0002}^{+ 0.0002}$ $0.5420^{+0.0002}_{-0.0002}$	$1 . 7237_{- 0.0010}^{+ 0.0003}$ $1.7237^{+0.0003}_{-0.0010}$	$1 . 7243_{- 0.0004}^{+ 0.0004}$ $1.7243^{+0.0004}_{-0.0004}$
q	$0 . 794_{- 0.031}^{+ 0.010}$ $0.794^{+0.010}_{-0.031}$	$0 . 832_{- 0.008}^{+ 0.009}$ $0.832^{+0.009}_{-0.008}$	$0 . 816_{- 0.008}^{+ 0.005}$ $0.816^{+0.005}_{-0.008}$	$0 . 840_{- 0.005}^{+ 0.005}$ $0.840^{+0.005}_{-0.005}$	$0 . 894_{- 0.003}^{+ 0.008}$ $0.894^{+0.008}_{-0.003}$	$0 . 876_{- 0.004}^{+ 0.004}$ $0.876^{+0.004}_{-0.004}$
θ_q	$12_{- 2}^{+ 4}$ $12^{+4}_{-2}$	$6_{- 1}^{+ 2}$ $6^{+2}_{-1}$	$28 . 3_{- 0.3}^{+ 1.3}$ $28.3^{+1.3}_{-0.3}$	$23 . 6_{- 0.6}^{+ 0.5}$ $23.6^{+0.5}_{-0.6}$	$152_{- 1}^{+ 1}$ $152^{+1}_{-1}$	$153_{- 1}^{+ 1}$ $153^{+1}_{-1}$
γ	$1 . 97_{- 0.13}^{+ 0.04}$ $1.97^{+0.04}_{-0.13}$	$2 . 00_{- 0.07}^{+ 0.03}$ $2.00^{+0.03}_{-0.07}$	$2 . 19_{- 0.03}^{+ 0.04}$ $2.19^{+0.04}_{-0.03}$	$2 . 20_{- 0.02}^{+ 0.04}$ $2.20^{+0.04}_{-0.02}$	$2 . 22_{- 0.06}^{+ 0.03}$ $2.22^{+0.03}_{-0.06}$	$2 . 23_{- 0.03}^{+ 0.02}$ $2.23^{+0.02}_{-0.03}$
Γ	$0 . 032_{- 0.019}^{+ 0.005}$ $0.032^{+0.005}_{-0.019}$	$0 . 037_{- 0.007}^{+ 0.004}$ $0.037^{+0.004}_{-0.007}$	$0 . 015_{- 0.002}^{+ 0.002}$ $0.015^{+0.002}_{-0.002}$	$0 . 022_{- 0.001}^{+ 0.003}$ $0.022^{+0.003}_{-0.001}$	$0 . 012_{- 0.001}^{+ 0.001}$ $0.012^{+0.001}_{-0.001}$	$0 . 011_{- 0.001}^{+ 0.001}$ $0.011^{+0.001}_{-0.001}$
θ_Γ	$- 8_{- 12}^{+ 4}$ $-8^{+4}_{-12}$	$8_{- 2}^{+ 2}$ $8^{+2}_{-2}$	$13_{- 6}^{+ 2}$ $13^{+2}_{-6}$	$26_{- 1}^{+ 1}$ $26^{+1}_{-1}$	$15_{- 4}^{+ 3}$ $15^{+3}_{-4}$	$19_{- 2}^{+ 2}$ $19^{+2}_{-2}$
A₃	–	$0 . 0018_{- 0.0009}^{+ 0.0009}$ $0.0018^{+0.0009}_{-0.0009}$	–	$0 . 0047_{- 0.0004}^{+ 0.0003}$ $0.0047^{+0.0003}_{-0.0004}$	–	$- 0 . 0078_{- 0.0013}^{+ 0.0006}$ $-0.0078^{+0.0006}_{-0.0013}$
B₃	–	$0 . 0034_{- 0.0007}^{+ 0.0006}$ $0.0034^{+0.0006}_{-0.0007}$	–	$- 0 . 0019_{- 0.0003}^{+ 0.0003}$ $-0.0019^{+0.0003}_{-0.0003}$	–	$0 . 0049_{- 0.0009}^{+ 0.0022}$ $0.0049^{+0.0022}_{-0.0009}$
A₄	–	$- 0 . 0032_{- 0.0013}^{+ 0.0015}$ $-0.0032^{+0.0015}_{-0.0013}$	–	$- 0 . 0037_{- 0.0007}^{+ 0.0006}$ $-0.0037^{+0.0006}_{-0.0007}$	–	$- 0 . 0033_{- 0.0009}^{+ 0.0012}$ $-0.0033^{+0.0012}_{-0.0009}$
B₄	–	$0 . 0041_{- 0.0014}^{+ 0.0016}$ $0.0041^{+0.0016}_{-0.0014}$	–	$- 0 . 0060_{- 0.0007}^{+ 0.0007}$ $-0.0060^{+0.0007}_{-0.0007}$	–	$- 0 . 0078_{- 0.0021}^{+ 0.0014}$ $-0.0078^{+0.0014}_{-0.0021}$

𝒦	≡0	28	≡0	75	≡0	120

Notes. The uncertainties given are the weighted 1st and 99th percentile ranges of the marginalised posterior sampling with MultiNest. Positions are given relative to the observation phase centre, given in Table 1. The Bayes factor (𝒦) is relative to the PL model. All angles are defined east of north.

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