Table 2.
Priors on the MBProj2D analyses with the different models.
Description | Parameter | Prior |
---|---|---|
Standard (circular and other models) | ||
Central density | ln(n0/cm−3) | 𝒰(−14, 5) |
Outer slope | β | 𝒯𝒩(2/3, 1/3, 0.2, ∞) |
Inner slope | α | 𝒯𝒩(0, 5, −10, 10) |
Core radius | ln(rc/kpc) | 𝒯𝒩(ln400, 3, ln5, ln5000) |
Cluster RA shift ( * ) | δx/arcsec | 𝒩(0, 30) |
Cluster Dec. shift ( * ) | δy/arcsec | 𝒩(0, 30) |
Background | ln(B/ct/s/arcsec2) | 𝒰(−18.4, −8.4) |
Point source normalisation ( * *) | ln(N/photon/keV/cm2/s) | 𝒰(−17, −12) |
Elliptical | ||
Rotation angle ( † ) | θ0/° | 𝒰s(θfit − 90, θfit + 90) |
Ellipticity | ϵ | 𝒰s(0, 0.999) |
Slosh | ||
Rotation angle ( † ) | θ0/° | 𝒰s(θfit − 180, θfit + 180) |
Slosh | H | 𝒰s(0.001, 1) |
Multipole 1 | ||
Rotation angle ( † ) | θ0/° | 𝒰s(θfit − 180, θfit + 180) |
Multipole magnitude | M1 | 𝒰s(0, 1) |
Multipole 2 | ||
Rotation angle† | θ0/° | 𝒰s(θfit − 90, θfit + 90) |
Multipole magnitude | M2 | 𝒰s(0, 1) |
Multipole 3 | ||
Rotation angle ( † ) | θ0/° | 𝒰s(θfit − 60, θfit + 60) |
Multipole magnitude | M3 | 𝒰s(0, 1) |
Multipole 4 | ||
Rotation angle† | θ0/° | 𝒰s(θfit − 45, θfit + 45) |
Multipole magnitude | M4 | 𝒰s(0, 1) |
Notes. Here 𝒰(a, b) is a uniform prior between a and b. 𝒩(μ, σ) is a normal distribution centred on μ with width σ. 𝒯𝒩(μ, σ, a, b) is a truncated normal distribution with the peak at μ, with width σ, truncated below a or above b. 𝒰s(a, b) is a uniform distribution with softened edges, where the log prior is 1 − e(a − x)/0.01 if x < a, 1 − e(x − b)/0.01 if x > b, and zero otherwise. In this case, during model evaluation, the parameter was forced to the range of a to b. ( * )Only the main cluster position was allowed to vary from the source detection position during the MCMC run. Other cluster positions were fitted for once, then fixed to these positions. If fitted using the peak position, these parameters were frozen. ( * *)Normalisations defined at 1 keV assuming a power-law photon index of 1.7. ( † )The best fitting value of θ0 was used as θfit to reduce boundary issues when sampling. In the output catalogue, the value of θ0 was reduced to the range about θfit = 0.
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