Table 2.
Cluster scaling laws used in the first part of the paper.
| Law | X0 | α | γ | Scatter |
|---|---|---|---|---|
| (natural log) | ||||
| M500, WL − T300 kpc | (2.6 ± 0.55)×1013 M⊙ h−1 | 1.67 | −1.0 | − |
 |
8.24 × 1041 erg s−1 | 3.17 | 0.47 ± 0.68 | 0.67 |
| rc − r500 | 0.15 | − | − | − |
Notes. To keep the same configuration as in XXL Paper XXV, we include scatter only in the luminosity distribution. We use a log-normal scatter, with the value indicated in the table, as in the previous XXL cosmological analyses (XXL Paper XXV). Uncertainties on parameters indicate that these parameters are kept free during the analysis and are in a Gaussian prior range with σ given by the uncertainties and then marginalised over. The mass–temperature relation was published in the first XXL release (Lieu et al. 2016, hereafter XXL Paper IV) and the luminosity–temperature relation in the second XXL release, XXL Paper XX.
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