Table 1.
Gas model parameters.
| Parameter | Units | Description | Default prior |
|---|---|---|---|
| Geometrical parameters of a triaxial ellipsoid (Eqs. (1) and (4)) | |||
| qICM, 1 | Minor-to-major axial ratio of the ICM distribution | 𝒰(0, 1) | |
| qICM, 2 | Intermediate-to-major axial ratio of the ICM distribution | 𝒰(qICM, 1, 1) | |
| cos θ | Cosine of the inclination angle of the ellipsoid major axis | 𝒰(0, 1) | |
| φ | deg | Second Euler angle | 𝒰 (–π/2, π/2) |
| ψ | deg | Third Euler angle | 𝒰 (–π/2, π/2) |
| Electron density profile (Eq. (14)) | |||
| n0 | cm−3 | Central scale density of the distribution of electrons | 𝒰(10−6, 10) |
| ζc | kpc | Ellipsoidal core radius of the gas distribution | 𝒰(0, 103) |
| ζt | Mpc | Ellipsoidal truncation radius of the gas distribution (ζt > ζc) | 𝒰 (ζc/103, 3) |
| βe | Slope of the gas distribution (in the intermediate region) | 𝒰(0, 3) | |
| ηe | Slope of the gas distribution (inner) | 𝒰(0, 1) | |
| γe | Slope of the gas distribution (outer) | 𝒰(0, 5) | |
| Gas pressure profile (Eq. (15)) | |||
| P0 | Normalization for the gNFW pressure profile | 𝒰(0, 102) | |
| c500 | Pressure profile concentration (r ∼ rs = R500/c500) | δ(1.4) | |
| γp | Slope parameter for central region (r ≪ rs) | δ(0.3) | |
| αp | Slope parameter for intermediate region (r ∼ rs) | 𝒰(0, 5) | |
| βp | Slope parameter for outer region (r ≫ rs) | 𝒰(0, 15) (a) | |
Notes. We consider five geometric parameters (qICM, 1, qICM, 2, θ, φ, ψ), six electron density parameters (n0, ζc, ζt, βe, ηe, γe), and five gas pressure parameters (P0, c500, γp, αp, βp). For the geometric and electron pressure profile parameters, we primarily adopt the priors in Sereno et al. (2018). We also assign delta priors to c500 (=1.4), and γp (=0.3) as a default, resulting in 14 free parameters. In the default prior column, 𝒰 refers to a uniform prior and δ refers to a delta function that fixes the parameter for the model fit.
For the cluster PSZ2 G313+61.13, to which we applied the model fit in this paper (Sect. 3), we employed a delta prior (Eq. (17)) because we limited the map size to be within R500, which results in very little sensitivity to βp (Sayers et al. 2023).
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