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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))*.

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.

Source LaTeX | All tables | In the text

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