Table 4: The best-fit values of the evolution parameter B, Bz (see Eqs. (6) and (7) and comments in Sect. 4) are obtained by comparing to the local best-fit results, indicated in the second column and discussed in the text, the 28, 16 and 11 clusters with redshift larger than 0.4, 0.6 and 0.8, respectively. The case of no evolution corresponds to a value of Bz equal to 0. The L-T relation has been studied also not including the correction by Ez. This relation is then expected to be proportional to Ez and B should be measured in the range 0.6-0.9 in the adopted cosmology.
RelationLocal ref. $(z\ge0.4)$$(z\ge0.6)$$(z\ge0.8)$
   B
L-TMarkevitch (1998)  $0.62 (\pm0.28)$ $0.04 (\pm0.33)$ $0.04 (\pm0.39)$
(Fig. 4)Arnaud & Evrard (1999)  $0.98 (\pm0.20)$ $0.22 (\pm0.25)$ $0.24 (\pm0.30)$
 Novicki et al. (2002) (z<0.3)  $0.54 (\pm0.31)$ $-0.06 (\pm0.37)$ $-0.02 (\pm0.43)$
 Novicki et al. (2002) (0.3<z<0.6)  $0.10 (\pm0.62)$ $-0.48 (\pm0.73)$ $-0.34 (\pm0.83)$
   Bz
Ez-1 L-TEttori et al. (2002)  $-1.04 (\pm0.32)$ $-1.48 (\pm0.38)$ $-1.46 (\pm0.44)$
(Fig. 4)Allen et al. (2001c)  $-0.16 (\pm0.23)$ $-0.72 (\pm0.28)$ $-0.78 (\pm0.32)$
$E_z M_{\rm tot}-T$Ettori et al. (2002)  $-0.12 (\pm0.39)$ $-0.14 (\pm0.46)$ $-0.06 (\pm0.52)$
(Fig. 5)Finoguenov et al. (2001)  $-0.26 (\pm0.17)$ $-0.16 (\pm0.21)$ $-0.12 (\pm0.26)$
 Allen et al. (2001c)  $0.02 (\pm0.39)$ $0.04 (\pm0.45)$ $0.06 (\pm0.52)$
$E_z M_{\rm gas}-T$Ettori et al. (2002)  $-0.26 (\pm0.23)$ $-0.54 (\pm0.27)$ $-0.54 (\pm0.32)$
(Fig. 6)Mohr et al. (1999)  $-0.10 (\pm0.20)$ $-0.42 (\pm0.24)$ $-0.42 (\pm0.28)$
$E_z^{-1} L-E_z M_{\rm tot}$Ettori et al. (2002)  $-0.60 (\pm0.17)$ $-1.10 (\pm0.20)$ $-1.12 (\pm0.25)$
(Fig. 7)Reiprich & Böhringer (2002)  $0.18 (\pm0.20)$ $-0.86 (\pm0.25)$ $-0.78 (\pm0.32)$


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