Table 2.
Scaling relations and intrinsic scatter data from the multi-response regression, as described in Sect. 3.
Description | Relation | Parameter | Results | S − S |
---|---|---|---|---|
Intercept | Mgas, 300 kpc − Mgas, 300 kpc | ![]() |
[0] | – |
Intercept | T300 kpc − Mgas, 300 kpc | ![]() |
1.60 ± 0.17 | – |
intercept | ![]() |
![]() |
2.39 ± 0.13 | – |
Slope | Mgas, 300 kpc − Mgas, 300 kpc | ![]() |
[1] | 1 |
Slope | T300 kpc − Mgas, 300 kpc | ![]() |
0.71 ± 0.09 | 1 |
Slope | ![]() |
![]() |
1.94 ± 0.07 | 2 |
Time evolution | Mgas, 300 kpc − Mgas, 300 kpc | ![]() |
[0] | 0 |
Time evolution | T300kpc − Mgas, 300 kpc | ![]() |
0.68 ± 0.09 | 0 |
Time evolution | ![]() |
![]() |
0.15 ± 0.55 | 0 |
Intrinsic scatter | Mgas, 300 kpc|Z | ![]() |
0.03 ± 0.01 | – |
Intrinsic scatter | T300 kpc|Z | σt(Y)|Z | 0.09 ± 0.02 | – |
Intrinsic scatter | ![]() |
σl(Y)|Z | 0.05 ± 0.03 | – |
Scatter correlation | T300 kpc − Mgas, 300 kpc|Z | ![]() |
0.35 ± 0.52 | – |
Scatter correlation | ![]() |
![]() |
0.40 ± 0.43 | – |
Scatter correlation | ![]() |
ρt(Y)l(Y)|Z | 0.07 ± 0.70 | – |
Notes. The gas mass mg, the temperature t, and the luminosity l act as y1, y2, and y3, respectively. Y1 is an unbiased but scattered proxy of Z. Scatter data and correlations are meant as weighted averages over the redshift range. Values in square brackets are kept fixed in the regression. The last column lists the self-similar expectations. Quoted values are biweight estimators of the marginalised distributions.
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