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Appendix A: Master table

In Table A.1 we give the list of clusters in common between the Planck and ROSAT samples. For the detailed properties of these clusters, we refer to Planck Collaboration (2011) and E12.

Appendix B: Comparison with literature temperature profiles

To ensure that the reconstruction of thermodynamic quantities from the X-ray density and the SZ pressure is giving correct results, we used the data for the 18 individual systems in common between the ROSAT and Planck samples (see Sect. 2.1 and Table A.1) and compared them with temperature profiles from XMM-Newton (Snowden et al. 2008) or Chandra (Cavagnolo et al. 2009). Given that the angular resolution of ROSAT is poorer than that of Chandra and XMM-Newton, we restricted our comparison to the radial range beyond 0.1   R₅₀₀. We also excluded the observational data points beyond R₅₀₀, since the techniques used to extract X-ray temperatures in large samples may not be valid in regions with a low signal-to-background ratio (see Ettori & Molendi 2011).

In Fig. B.1 we show the temperatures reconstructed using our method versus the observed temperatures for all available data points. The data were fit with a maximum-likelihood estimator that accounts for the scatter around the mean value, which needs to be computed simultaneously (see Maccacaro et al. 1988, and Paper II). The best-fit value for the data points in the [0.1 − 1] R₅₀₀ range gives (B.1)with a scatter of 9%. This analysis demonstrates that combining X-ray density profiles with SZ pressure profiles is an effective way of reconstructing thermodynamic quantities.

	Fig. B.1 Planck/ROSAT reconstructed temperature as a function of the observed temperature from XMM-Newton (Snowden et al. 2008) or Chandra (Cavagnolo et al. 2009) for the 18 objects in common between the two samples. The dashed red curve represents the best-fit function Trec = 0.97Tobs.
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Appendix C: Notes on individual objects

• A478: the line of sight of this system is known to exhibit a complex, varying column density (Pointecouteau et al. 2004). For this work, as in E12, we fixed N_H to the 21 cm value (Kalberla et al. 2005). This may result in a slightly incorrect density profile.

• A401: this system is in an early stage of merging with its neighbor A399, located ~35′ SW, and connected to it by a bridge of X-ray emission. The density profile was thus extracted in a sector excluding the direction connecting A401 to A399. Because it is unclear whether the same was done for the SZ profile, the resulting profiles may be unreliable.

• A2163: this very perturbed merging cluster may be out of hydrostatic equilibrium, which causes the mass estimates from X-rays to be overestimated by a factor of ~2 with respect to the mass derived from weak lensing and galaxy distribution (Soucail 2012). Therefore, the scaling factors (Eqs. (6) and (7)) may be incorrect, as well as the estimate of R₅₀₀ from Planck Collaboration (2011).

	Fig. C.1 Best fit to the Planck pressure profiles of the 18 systems (black points, from P13) with a GNFW profile (green lines), in the radial range of interest for this paper ([0.2 − 1.9] R500). The bottom panels show the ratio between the data and the model.
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	Fig. C.1 continued.
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	Fig. C.2 ROSAT density profiles of the 18 systems obtained through geometrical deprojection (black points) and parametric forward fitting (green-shaded areas), in the radial range of interest for this paper ([0.2 − 1.9] R500). The bottom panels show the ratio between the two methods.
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	Fig. C.2 continued.
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	Fig. C.3 Average entropy profiles for the total population obtained from the average profiles and for the median of the 18 systems in common. Similar to Fig. 5, but showing the differences between the parametric and deprojection techniques in both cases.
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© ESO, 2013