Table 3.
Best fit parameters of the functional forms describing the universal thermodynamic quantities.
| Density: Eq. (7) | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Data | log(n0) | log(rc) | log(rs) | α | β | ϵ | σ1 | x0 | σ0 |
| Priors | U(−7, −2) | U(−7, −2) | U(−2.5, 2.5) | U(0, 5) | U(0, 5) | U(0, 5) | U(0, 0.5) | U(0, 1) | U(0, 0.5) |
| ALL | −4.4 ± 0.5 | −3.0 ± 0.5 | −0.29 ± 0.15 | 0.89 ± 0.59 | 0.43 ± 0.02 | 2.86 ± 0.38 | 0.09 ± 0.01 | 0.43 ± 0.02 | 0.16 ± 0.01 |
| CC | −3.9 ± 0.4 | −3.2 ± 0.3 | 0.17 ± 0.07 | 0.80 ± 0.61 | 0.49 ± 0.01 | 4.67 ± 0.36 | 0.04 ± 0.01 | 0.88 ± 0.10 | 0.13 ± 0.01 |
| NCC | −4.9 ± 0.4 | −2.7 ± 0.5 | −0.51 ± 0.17 | 0.70 ± 0.48 | 0.39 ± 0.04 | 2.60 ± 0.27 | 0.10 ± 0.01 | 0.38 ± 0.02 | 0.16 ± 0.01 |
| Pressure: Eq. (9) | |||||||||
| Data | P0 | c500 | γ | α | β | σ1 | x0 | σ0 | |
| Priors | U(0, 14) | U(0, 5) | U(0, 0.8) | fix | U(2, 8) | U(0, 0.5) | U(0, 2) | U(0, 0.5) | |
| ALL | 5.68 ± 1.77 | 1.49 ± 0.30 | 0.43 ± 0.10 | 1.33 | 4.40 ± 0.41 | 0.02 ± 0.01 | 1.63 ± 0.36 | 0.25 ± 0.02 | |
| CC | 6.03 ± 1.61 | 1.68 ± 0.23 | 0.51 ± 0.10 | 1.33 | 4.37 ± 0.26 | 0.03 ± 0.01 | 1.52 ± 0.33 | 0.00 ± 0.00 | |
| NCC | 7.96 ± 2.54 | 1.79 ± 0.38 | 0.29 ± 0.11 | 1.33 | 4.05 ± 0.41 | 0.01 ± 0.01 | 1.28 ± 0.52 | 0.30 ± 0.03 | |
| Temperature: Eq. (11) | |||||||||
| Data | T0 | log(rcool) | rt |
 |
acool | c/2 | σ1 | x0 | σ0 |
| Priors | U(0, 2) | U(−7, 0) | U(0, 1) | U(0, 1.5) | U(0, 3) | U(0, 1) | U(0, 0.5) | U(0, 3) | U(0, 0.5) |
| ALL | 1.21 ± 0.23 | −2.8 ± 1.1 | 0.34 ± 0.10 | 0.50 ± 0.24 | 1.03 ± 0.78 | 0.27 ± 0.04 | 0.01 ± 0.01 | 2.13 ± 0.67 | 0.09 ± 0.01 |
| CC | 1.32 ± 0.25 | −2.8 ± 0.7 | 0.40 ± 0.10 | 0.22 ± 0.17 | 0.74 ± 0.30 | 0.33 ± 0.06 | 0.01 ± 0.01 | 0.08 ± 0.04 | 0.03 ± 0.01 |
| NCC | 1.09 ± 0.10 | −4.4 ± 1.8 | 0.45 ± 0.14 | 0.66 ± 0.32 | 1.33 ± 0.89 | 0.30 ± 0.07 | 0.01 ± 0.01 | 2.22 ± 0.63 | 0.11 ± 0.01 |
| Entropy: Eq. (13) | |||||||||
| Data | log(K0) | K1 | α | σ1 | x0 | σ0 | |||
| Priors | U(−7, 0) | U(1, 2) | U(0, 2) | U(0, 0.5) | U(0, 1) | U(0, 0.5) | |||
| ALL | −3.98 ± 1.22 | 1.21 ± 0.03 | 0.83 ± 0.04 | 0.06 ± 0.02 | 0.56 ± 0.11 | 0.14 ± 0.01 | |||
| CC | −5.50 ± 1.10 | 1.35 ± 0.06 | 0.93 ± 0.04 | 0.03 ± 0.02 | 0.60 ± 0.22 | 0.17 ± 0.03 | |||
| NCC | −2.77 ± 0.55 | 1.14 ± 0.03 | 0.84 ± 0.07 | 0.05 ± 0.02 | 0.57 ± 0.16 | 0.14 ± 0.01 | |||
Notes. In all cases, we provide the results of the fit to the entire population (ALL) and to the cool-core (CC) and non-cool-core (NCC) populations separately. σ1, σ0, and x0 are the parameters of the log-parabola describing the behavior of the intrinsic scatter. We indicate the priors adopted on the parameters, indicating uniform priors between a and b with U(a, b).
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