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Table 2:

Best fitting parameters for the entropy-temperature and entropy-mass relations.
Radius C $\alpha $ $\sigma_{\ln{K}}$
  (keV cm-2)   raw int
Entropy-temperature relation        
0.1 R200 $347\pm23$ $0.89\pm0.15$ $0.262\pm0.040$ $0.254\pm0.041$
R2500 $783\pm15$ $0.76\pm0.06$ $0.120\pm0.021$ $0.083\pm0.118$
R1000 $1152\pm27$ $0.83\pm0.06$ $0.093\pm0.015$ ...
R500 $1489\pm125$ $0.92\pm0.24$ $0.265\pm0.055$ ...
Entropy-mass relation        
R2500 $864\pm27$ $0.42\pm0.05$ $0.155\pm0.025$ $0.136\pm0.031$
R1000 $1308\pm52$ $0.48\pm0.04$ $0.119\pm0.017$ $0.052\pm0.162$
R500 $1748\pm237$ $0.62\pm0.17$ $0.265\pm0.055$ $0.221\pm0.160$

Notes. T is the spectroscopic temperature in the [0.15-0.75] R500 region; masses are estimated from the $M{-}Y_{\rm X}$ relation given in Eq. (1). Data were fitted with a power law of the form $E(z)^{n} K = C \times (A/A_0)^\alpha$, with A0 = 5 keV and $5.3\times10^{14}~M_\odot$, and n= 4/3 and 2/3, for temperature and mass repectively. Fits used orthogonal BCES regression with errors estimated using bootstrap resampling. The raw and intrinsic logarithmic scatter about the best fitting relations are given in the final two columns.


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