Table 1.
Observed scaling relations.
| Scaling | Intrinsic scatter in X | Intrinsic scatter in Y | Scatter correlation | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Intercept | Slope | Evolution | Local scatter | Evolution | Local scatter | Evolution | Local correlation | Evolution | |||
| x | y | αY|Z | βY|Z | γY|Z | σX|Z, 0 | γσX|Z | σY|Z, 0 | γσY|Z | ρXY|Z, 0 | γρXY|Z | βss |
| t | l | −2.15 ± 0.18 | 2.78 ± 0.42 | −0.48 ± 1.25 | 0.03 ± 0.04 | [0] | 0.29 ± 0.08 | [0] | 0.20 ± 0.48 | [0] | 2 |
| t | l | −2.13 ± 0.18 | 2.70 ± 0.42 | −0.50 ± 1.29 | 0.03 ± 0.03 | 0.39 ± 0.34 | 0.29 ± 0.08 | 0.28 ± 0.28 | 0.28 ± 0.48 | 0.32 ± 0.66 | 2 |
| t | mg | −2.29 ± 0.06 | 1.53 ± 0.20 | 0.53 ± 0.53 | 0.10 ± 0.02 | [0] | 0.03 ± 0.03 | [0] | 0.64 ± 0.48 | [0] | 1 |
| t | mg | −2.27 ± 0.05 | 1.47 ± 0.17 | 0.67 ± 0.52 | 0.09 ± 0.02 | 0.23 ± 0.25 | 0.02 ± 0.02 | 0.45 ± 0.34 | 0.46 ± 0.52 | −0.05 ± 0.63 | 1 |
| mg | l | 2.32 ± 0.18 | 1.91 ± 0.09 | −0.44 ± 0.49 | 0.04 ± 0.02 | [0] | 0.12 ± 0.05 | [0] | 0.89 ± 0.20 | [0] | 2 |
| mg | l | 2.43 ± 0.14 | 1.97 ± 0.07 | −0.73 ± 0.42 | 0.02 ± 0.01 | 0.42 ± 0.33 | 0.06 ± 0.03 | 0.42 ± 0.33 | 0.31 ± 0.58 | 0.04 ± 0.63 | 2 |
Notes. Conventions and units are as in Sect. 2. Columns 1 and 2: variables of the regression procedure. Columns 3, 4, and 5: intercept, slope, and time evolution of the scaling relation. Columns 6 and 7: scatter of X and its time evolution. Columns 8 and 9: scatter of Y and its time evolution. Columns 10 and 11: correlation between the scatter and its time evolution. If the evolution is not considered (γσX|Z = γσY|Z = γρXY|Z = 0), scatter and correlations are meant as weighted averages over the redshift range. If the evolution is free, scatter and correlations are intended as local values at zref = 0.01. Column 12: self-similar slope (βss) for observable measured within fixed radii. Values in square brackets correspond to parameters kept fixed in the regression. Quoted values are biweight estimators of the marginalised distributions.
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