The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the YSZ – M500 relation

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Table B.1:

Power law relations to convert physical parameters of REXCESS clusters from those derived using the empirical $M_{500} - Y_{\rm X}$ relation (Eq. (2)) to those derived using the standard slope relation (Eq. (3))^*.
Relation	C	$\alpha$
$M_{\rm 500}^{\rm ST}- M_{\rm 500}$	0.968	1.089
$T_{\rm X}^{\rm ST} - T_{\rm X}$	1.002	0.992
$Y_{\rm X}^{\rm ST} - Y_{\rm X}$	0.995	1.017
$Y_{\rm sph}^{\rm ST}(R_{500}) - Y_{\rm sph}(R_{500})$	0.991	1.031

Notes. ^(*)For each observable, Q, the conversion follows the form $(Q^{\rm ST}/Q_0)= C(Q/Q_0)^\alpha$ where the pivot, Q₀ is 3 $\times$ $10^{14}~{M_{\odot}}$ , $5~\rm keV$ , 2 $\times$ $10^{14}~{M_{\odot}}~\rm keV$ and 2 $\times$ $10^{-5}~{\rm Mpc^2}$ for $M_{\rm 500}$ , $T_{\rm X}$ , $Y_{\rm X}$ and $Y_{\rm sph}(R_{500})$ , respectively.

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