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Table A.1.

Priors used for the forwarded modeling. In the case of a Gaussian prior, we report the range at a ±1σ–level.

Parameter Prior Type Min – Max Parameter Prior Type Min – Max
Empirical formalism Theoretical-formalism
RA [deg] Uniform 34.425921 – 34.442521 RA [deg] Uniform 34.425921 – 34.442521
Dec [deg] Uniform -3.768419 – -3.751819 Dec [deg] Uniform -3.768419 – -3.751819
M500, c [M] Log-Uniform 1013.4 − 1014.6 P0 [keV cm−3] Uniform 0.0001 – 1.0
eccentricity Uniform 0.0 – 1.0 rs [arcsec] Uniform 1.1772 – 120.024
Position angle [deg] Uniform -90.0 – 90.0 eccentricity Uniform 0.0 – 1.0
z Gaussian 1.977 – 1.979 Position angle [deg] Uniform -90.0 90.0
αACA, B3 Gaussian 0.95 – 1.00 α Uniform 0.5–10.0
αALMA, B3 Gaussian 0.95 – 1.00 β Uniform 0.5–10
Point Source γ Uniform -1.0 – 5.0
RA [deg] Uniform 34.42588105 – 34.45717415 z Gaussian 1.977 – 1.979
Dec [deg] Uniform -3.7905406 – -3.7377484 αACA, B3 Gaussian 0.95 – 1.00
Amplitude [Jy] Uniform 0.0 – 1.0 αALMA, B3 Gaussian 0.95 – 1.00
Spectral slope Uniform -5.0 – 10
αACA, B3 Gaussian 0.95 – 1.00
αALMA, B3 Gaussian 0.95 – 1.05
αALMA, B4 Gaussian 0.95 – 1.05

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