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Appendix A: Clusters included in the combined sample

Appendix B: L-z distribution of the cluster sample

	Fig. B.1 Bolometric X-ray luminosity LX of the clusters included in the combined cluster sample.
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Appendix C: Comparison of cluster properties for systems included in more than one subsample

	Fig. C.1 Comparison of cluster properties for z < 0.3-systems included in more than one subsample.
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	Fig. C.2 Distribution of deviations from the mean value for the z < 0.3-clusters included in more than one subsample in units of the assumed error σ. Top panel: mass deviations. Middle panel: LX deviations. Bottom panel: ICM temperature deviations.
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Several of the clusters in our combined sample are included in more than one source publication, either relying on completely independent measurement data or using the same X-ray data reanalyzed according to the strategy that was chosen by the different authors. These measurements of cluster observables can be compared to each other after correcting for different analysis schemes and provide a useful tool to test the applied homogenization scheme. Furthermore, the comparison analysis gives an estimate of whether the error budget assumed in the different publications is realistic and reveals systematic differences between the results derived by the various studies.

Figure C.1 shows the cluster properties of the low redshift (z < 0.3) overlap sample. In Fig. C.2, we present the deviations of the individual measured values from the mean value in units of σ, and the error estimated in the individual publications. Note that the true values of the cluster observables are unknown. The comparison to the mean value therefore does not allow any statements about the reliability of the results derived in the different studies. Figure C.2 instead provides an insight into the systematic differences between the results of different studies and whether the assumed error estimates are realistic.

The derived spectroscopic temperatures agree well for most of the clusters. As visible in the bottom panel of Fig. C.2, the majority of the measured values deviate less than 1σ from the mean value. In detail, 59% of the measurements lie within 1σ and 82% within 2σ of the mean. Only 5% of the results deviate by more than 5σ. This indicates that the spectral fitting method generally leads to secure and consistent results, that the probability of severe misestimations is low, and that the assumed error budgets are likely to be realistic. Differences may result from different spectral extraction regions or different treatments of parameters, such as the ICM metallicity or the background subtraction process. However, these different measurement schemes do not lead to completely incomparable data sets. The temperature differences between the subsamples are rather uncorrelated and reveal no systematic trends between different studies. We note that for the samples of Zhang07, Zhang08, and Arnaud05 only core-excised temperatures were available. However, comparing those to the core-included temperatures given in other studies (e.g. Mantz09), the observed differences remain small.

For the X-ray luminosity L_X, the situation is clearly different. As visible in the middle panel of Fig. C.1, most of the derived luminosities do not agree within the errors. Furthermore, the differences between the results of some studies clearly show systematic trends. In terms of the deviations from the mean value, only 19% of the values lie within 1σ and 29% within 2σ, while 39% of the measurements show deviations of more than 5σ. The different samples exhibit systematic differences when compared to each other, especially for the Mantz09-Zhang08 overlap but to a lesser degree also for the common clusters of Zhang08 and OHara07. The reason for these deviations remains unclear since all known systematic differences, such as the definition of cluster radii and the different energy bands used, were corrected for. These deviations therefore imply that there are additional systematic differences between the samples. However, for the central goal of this work, constraining the redshift evolution of scaling relations, this open question is of negligible importance because systematic differences mostly occur for low-redshift samples and the choice of sample from which multiply analyzed clusters are taken has no significant influence on the evolution results. In addition to systematic trends, even for samples that show no trends at all, the differences between the results considerably exceed the estimated errors. This indicates that the error estimations made by the different studies are too optimistic or that there are additional sources of measurement errors not included in the error budget.

Similar but less significant systematic trends are also visible when comparing the results for cluster masses. As visible in the top panel of Fig. C.2, 51% of the results deviate by less than 1σ from the mean value, while 89% lie within 2σ and no measurement shows deviations of more than 5σ. However, apart from these systematic trends the estimated errors for cluster mass seem realistic as most measurements deviate by less than 1σ from the mean. The masses derived in Pratt09 based on the Y_X-parameter and the Y_X–M relation show no significant systematic difference from the hydrostatic mass estimates. However, owing to the small overlap sample of five clusters, the comparison analysis provides no suitable tool to identify these differences.

	Fig. C.3 Comparison of cluster properties for z > 0.3-systems included in more than one subsample.
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In Fig. C.3, the derived cluster properties of the z > 0.3 overlap sample are compared. The typical observational errors for distant systems are larger, although within these errors the results are in closer agreement than for the local overlap sample.

The deviations from the mean temperature plotted in the bottom panel of Fig. C.4 lie below the estimated errors for most systems. In detail, 72% of the results deviate by less than 1σ and 90% by less than 2σ from the mean value, while no deviations of more than 5σ occur. As for the low-redshift clusters, the measured temperatures show no systematic trends for single subsamples, i.e. the spectroscopic fitting procedure also seems reliable for distant clusters and there appears to be no major systematic effects that have to be corrected. Furthermore, according to the mostly small deviations in units of the assumed error, the estimated error budget is likely to be realistic.

Luminosities agree on average more strongly for the high-z clusters than for the local sample, for instance the Ettori04 and OHara07 results are consistent for 12 of the 18 clusters in common (see middle panel of Fig. C.3). In contrast to the local overlap sample, no significant systematic trends between the different studies are visible. The deviations from the mean value plotted in the middle panel of Fig. C.4 are smaller than 1σ for 53% of the results and below 2σ for 62% of the measurements. We have found that 12% of the results deviate by more than 5σ. The distribution of deviations implies that the error budget might have been previously underestimated by the different studies, although by no means as significantly as for the local systems.

The masses derived by Ettori04, Maughan06, and Kotov05 plotted in the top panel of Fig. C.3 are consistent within the errors for all shared clusters, all results deviate by less then 1σ from the mean value. The estimated errors are therefore likely realistic. However, the small size of the overlap sample of only four clusters does not allow us to peform a robust analysis of the systematic differences between the different studies.

	Fig. C.4 Distribution of deviations from the mean value for the z > 0.3-clusters included in more than one subsample in units of the assumed error σ. Top panel: mass deviations. Middle panel: LX deviations. Bottom panel: ICM temperature deviations.
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Appendix D: Local scaling relations for the combined cluster sample

Figure D.1–D.3 show the z < 0.3-clusters included in the combined cluster samples and the local scaling relations fitted to this sample using different BCES fitting schemes in comparison to the relations derived by Pratt09 which were adopted for the evolution study in our work.

	Fig. D.1 Local cluster sample: M–T relation. The red line shows the BCES(T|M) best-fit relation for the combined cluster sample, and the grey lines the BCES(M|T) and BCES orthogonal relations. The blue line shows the Pratt09 relation (see Sect. 3.1).
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	Fig. D.2 Local cluster sample: LX–T relation. The red line shows the BCES(L|T) best-fit relation for the combined cluster sample, and the grey lines the BCES(T|L) and BCES orthogonal relations. The blue line shows the Pratt09 relation (see Sect. 3.1).
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	Fig. D.3 Local cluster sample: M–LX relation. The red line shows the BCES(L|M) best fit relation from the combined cluster sample, the grey lines the BCES(M|L) and BCES orthogonal relations. The blue line shows the Pratt09 relation (see Sect. 3.1).
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© ESO, 2011