Table 2.
Parameters of all best-fitting lines derived with the procedure described at the end of Sect. 3.
| (X, Y) | a | b | σY|X |
|---|---|---|---|
| z = 0 | |||
| M500, T* | 0.10 ± 0.01 | 1.71 ± 0.03 | 0.07 ± 0.01 |
 |
0.52 ± 0.02 | 1.28 ± 0.06 | 0.16 ± 0.02 |
| M500, MBCG | 0.75 ± 0.01 | 0.66 ± 0.01 | 0.10 ± 0.01 |
| MBCG, MBH | −0.42 ± 0.03 | 1.16 ± 0.04 | 0.14 ± 0.01 |
| M500, MBH | 0.45 ± 0.02 | 0.76 ± 0.03 | 0.18 ± 0.02 |
 |
0.20 ± 0.02 | 0.73 ± 0.04 | 0.23 ± 0.02 |
 |
0.03 ± 0.02 | 0.83 ± 0.04 | 0.25 ± 0.02 |
| z = 0.5 | |||
| M500, T* | 0.05 ± 0.01 | 1.73 ± 0.04 | 0.08 ± 0.01 |
 |
0.48 ± 0.03 | 1.49 ± 0.11 | 0.24 ± 0.03 |
| M500, MBCG | 0.68 ± 0.01 | 0.69 ± 0.02 | 0.13 ± 0.01 |
| MBCG, MBH | −0.42 ± 0.03 | 1.25 ± 0.05 | 0.16 ± 0.02 |
| M500, MBH | 0.43 ± 0.02 | 0.86 ± 0.04 | 0.23 ± 0.02 |
 |
0.06 ± 0.03 | 0.92 ± 0.06 | 0.34 ± 0.04 |
 |
0.15 ± 0.03 | 0.90 ± 0.06 | 0.27 ± 0.03 |
| z = 1 | |||
| M500, T* | −0.07 ± 0.01 | 1.72 ± 0.05 | 0.06 ± 0.01 |
 |
0.46 ± 0.04 | 1.70 ± 0.22 | 0.22 ± 0.03 |
| M500, MBCG | 0.67 ± 0.01 | 0.73 ± 0.03 | 0.11 ± 0.01 |
| MBCG, MBH | −0.42 ± 0.04 | 1.45 ± 0.07 | 0.19 ± 0.02 |
| M500, MBH | 0.56 ± 0.04 | 1.06 ± 0.08 | 0.27 ± 0.03 |
 |
0.12 ± 0.04 | 1.21 ± 0.17 | 0.40 ± 0.09 |
 |
0.35 ± 0.05 | 1.07 ± 0.09 | 0.30 ± 0.03 |
| z = 1.5 | |||
| M500, MBCG | 0.69 ± 0.02 | 0.77 ± 0.05 | 0.12 ± 0.02 |
| MBCG, MBH | −0.38 ± 0.05 | 1.58 ± 0.10 | 0.22 ± 0.02 |
| M500, MBH | 0.71 ± 0.05 | 1.25 ± 0.11 | 0.30 ± 0.04 |
 |
0.55 ± 0.06 | 1.27 ± 0.11 | 0.33 ± 0.05 |
| z = 2 | |||
| M500, MBCG | 0.67 ± 0.02 | 0.75 ± 0.06 | 0.11 ± 0.03 |
| MBCG, MBH | −0.33 ± 0.08 | 1.76 ± 0.20 | 0.26 ± 0.05 |
| M500, MBH | 0.85 ± 0.08 | 1.35 ± 0.15 | 0.34 ± 0.04 |
 |
0.72 ± 0.10 | 1.37 ± 0.16 | 0.36 ± 0.04 |
Notes. For each (X, Y) pair of data, we fit the formula: log(Y/Y0) = a + b × log(X/X0) where the normalizations, X0 or Y0, are equal to 2 keV, 1014 M⊙, 1011 M⊙ and 109 M⊙, respectively, for T, M500, MBCG, and all SMBH masses: 
, and 
. The parameters a, b, and σ and their errors are the mean and standard deviation values of the distributions obtained by applying the procedure to ten thousand bootstrapping samples. The asterisks indicate that the analysis is performed to the temperature subsample.
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