Table 2: Observed scaling relations. For each observable set (B,A), we fitted a power law relation of the form $B = C(A/A_0)^\alpha $, with $A_0 = 5~{\rm keV}; 4\times10^{13}~M_{\odot}; 2\times10^{14}~M_{\odot}~\rm keV$ for $T_{\rm X}$, $M_{\rm g, 500}$ and $Y_{\rm X}$ respectively. $\sigma _{\rm log,r}$ and $\sigma _{\rm log,i}$ are the raw and intrinsic scatter about the best fitting relation in the $\log$-$\log$ plane. The M500-$T_{\rm X}$ relation is the same as that given in Arnaud et al. (2005).
Relation $\log_{10} C $ $\alpha$ $\sigma _{\rm log,r}$ $\sigma _{\rm log,i}$
h(z) M500-$T_{\rm X}$ $14.580 \pm 0.016$ $1.71 \pm 0.09$ 0.064 0.039
h(z)2/5 M500-$Y_{\rm X}$ $14.556 \pm 0.015$ $0.548 \pm 0.027$ 0.062 0.039
M500- $M_{\rm g, 500}$ $14.542 \pm 0.015$ $0.803 \pm 0.040$ 0.065 0.044
$h(z) M_{{\rm g},500}$-$T_{\rm X}$ $13.651 \pm 0.010$ $2.10 \pm 0.05$ 0.048 0.036
$h(z)^{2/5} M_{\rm g,500}$-$Y_{\rm X}$ $13.619 \pm 0.008$ $0.678 \pm 0.014$ 0.017 -
$f_{\rm g,500}$-$Y_{\rm X}$ $-0.939 \pm 0.016$ $0.133 \pm 0.028$ 0.067 0.044


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