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Table 1.

Priors on the model parameters employed in our analysis.

Param. Prior Details Ref.
gNFW pressure model
RA Delta 1
Dec Delta 1
Pe, us Split-normal μ = 8.65 × 10−3 keV cm−3 2
σ = (0.92 × 10−3 keV cm−3,
1.29 × 10−3 keV cm−3)
Te, us Split-normal μ = 9.40 keV 2
σ = (1.00 keV, 1.40 keV)

Shock front
RA Split-normal 3
Dec Split-normal 3
θ Split-normal 3
Uniform min = 1, max = 10
α Uniform min = −10, max = 0

Calibration
κACA Normal μ = 1.00, σ = 0.05
κALMA Normal μ = 1.00, σ = 0.05

Notes. μ and σ are the mode and the standard deviation of the probability distributions. The two values reported for σ in the case of split-normal priors represent the standard deviations of the lower and upper halves of the corresponding distributions. The parameters (RA, Dec)gNFW, Pe, us, and Te, us respectively define the centroid of the gNFW profile describing the upstream pressure distribution, and the upstream pressure, and the temperature normalization (see Sect. 2.2.2 for a discussion). For the shock front, we use its nose position (RA, Dec)shock as the reference point. Further, θ and ℳ are the orientation of the shock axis and the Mach number (Sect. 2.2.1), while α is the slope of the downstream power-law profile (Sect. 2.2.2). Finally, κACA and κALMA are the ACA and ALMA calibration hyperparameters (Sect. 2.2.2).

References. (1) Clowe et al. 2006; (2) X-ray model from Markevitch 2006 and Markevitch & Vikhlinin 2007; (3) this work (see Sect. 2.2).

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