Free Access
Volume 575, March 2015
Article Number A30
Number of page(s) 25
Section Cosmology (including clusters of galaxies)
Published online 17 February 2015

Online material

Appendix A: Tables

Table A.1

63 HIFLUGCS clusters (without Abell 2244).

Table A.2

Best-fit temperatures and 68% confidence levels for the 4 different detectors (plus EPIC combined) in the (0.7−7) keV band.

Table A.3

Spline parameters (e.g., Press et al. 1992, Chap. 3.3) for the stacked residual ratios.

Appendix B: Temperature comparison

thumbnail Fig. B.1

Best-fit temperatures of the HIFLUGCS clusters in an isothermal region for all detector combinations in the (0.7−7.0) keV energy band and with NH frozen to the radio value of the LAB survey. The parameters of the best-fit powerlaw (black line) are also shown in Fig. B.4.

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thumbnail Fig. B.2

Same as Fig. B.1 but for the (0.7−2.0) keV band.

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thumbnail Fig. B.3

Same as Fig. B.1 but for the (2.0−7.0) keV band.

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thumbnail Fig. B.4

Fit parameter (see Eq. (3)) degeneracy for the 1, 3, and 5σ levels of the different detector combinations for the full (gray triangle), soft (red square), and hard (green circle) energy bands. Equality of temperatures for two instruments is given for a = 1 and b = 0. The deviation in σ from equality is given in the legend.

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thumbnail Fig. B.5

Left: fit parameter degeneracy for the 1, 3, and 5σ levels of ACIS – PN for the (0.7−7) keV energy band. ACIS-I (red square) and ACIS-S (black triangle) HIFLUGCS subsamples are shown versus the PN data (for all ACIS data combined, see Fig. B.4, top left panel, gray ellipse). Equality of temperatures for two instruments is given for a = 1 and b = 0. The deviation in σ from equality is given in the legend. Right: as in the left panel but only 3σ levels (gray and red ellipses) of ACIS – PN with temperatures taken from N10 (0.5−7 keV energy band, black triangle) and complete ACIS – PN of this work (0.7−7 keV energy band, red square).

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Appendix C: Self consistency test

In Sect. 6.2 we compared the best-fit temperatures of different instruments in the same energy band. In the case of purely isothermal emission and a very accurately calibrated effective area, the temperatures obtained in different energy bands of the same instrument should also be equal. By comparing temperatures of one instrument in different bands it is thus possible to quantify the absolute calibration uncertainties, if the assumption of isothermal emission is fulfilled.

In Fig. C.1 we demonstrate how self consistent the instruments are in terms of soft and hard band temperatures. We also quantify the expected deviation from equality of soft and hard band temperatures for a given two-temperature plasma.

Only for ACIS the temperature deviation (quoted σ value in the legend of Fig. C.1) is less than 3σ in comparing the soft and hard energy bands. By performing simulations similar to those shown in Sect. 7.1.1, we can quantify the expected difference between soft and hard band temperatures of the same instrument in the presence of a multitemperature structure. This is shown in Fig. C.1, where we indicate this result from simulations including a cold component with 1 keV and an EMR of 0.01, 2 keV and an EMR of 0.05, and 1 keV and an EMR of 0.05; i.e., the new symbols represent the new expected “zero points” given the multiple temperature components.

We conclude that the multitemperature structure has a strong influence on the results of this test and prevents firm conclusions on the absolute calibration. For a cold component with a temperature of ~1 keV and EMR higher than 0.01, the EPIC-PN instrument seems to agree with the simulations.

We want to emphasize that the non-detection of an effect of multitemperature ICM on comparing different instruments (as suggested in Sect. 7) is unrelated to multitemperature effects on the soft and hard band temperatures of the same instrument presented here, since the multitemperature influence may be much stronger.

thumbnail Fig. C.1

Fit parameter degeneracy for the 1, 3, and 5σ levels of each instrument in different energy bands. The green contours (circles) refer to the soft vs hard band. Equality of temperatures for two bands is given for a = 1 and b = 0. The deviation in σ from equality is given in the legend, as well as the expectations (blue pentagon, black square, and red diamond) for a multitemperature ICM with the parameters (temperature, emission measure ratio) of the cold component given.

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Appendix D: XMM-Newton and Chandra cross-calibration formulae

There are several methods of performing a cross-calibration between two instruments such as Chandra/ACIS and XMM-Newton/EPIC using galaxy clusters. In this work we show:

  • A correction formula for the effective area obtained using the stacked residual ratio method (Sect. 6.1 and Table A.3). For example to rescale the effective area of ACIS to give EPIC-PN consistent temperatures, one has to multiply the ACIS effective area by the spline interpolation of the ACIS/PN column of Table A.3.

  • A correction formula for the best-fit ICM temperature (Eq. (3) and Table 2); for example, for an ACIS-PN conversion in the full energy band, one has to use a = 0.836 and b = 0.016 for the parameters in Eq. (3) (with ACIS as X and PN as Y).

  • A linear relation for the hydrostatic masses (see below). The Chandra masses were calculated using the temperature and surface brightness profiles of the HIFLUGCS clusters, while the XMM-Newton masses were adopted from the rescaled Chandra temperature profiles (using Eq. (3) and Table 2).

The hydrostatic masses are shown in Fig. D.1. We found the following relation: (D.1)This result agrees with the derived relations in Mahdavi et al. (2013) and is also in rough agreement with Israel et al. (2014b). In Israel et al. (2014b), the authors obtained Chandra masses by using Chandra cluster temperatures assuming temperature profiles (from a scaling relation from Reiprich et al. 2013), while the XMM-Newton masses are calculated from the rescaled temperature profiles following the temperature scaling relation presented in this work. In Mahdavi et al. (2013), the authors find similar results concerning the temperature differences and also give a conversion for the hydrostatic masses between XMM-Newton and Chandra (see Fig. D.1).

The three methods presented in this work for converting between XMM-Newton and Chandra are obviously not exactly equivalent in the context of cosmological results.

thumbnail Fig. D.1

Comparison between Chandra and XMM-Newton in terms of hydrostatic masses in logspace (left) and realspace (right). Gray circles: Hydrostatic masses for Chandra (derived from data) and XMM-Newton (from rescaled Chandra temperature profiles). A best-fit relation (derived in logspace) is shown in black (Eq. (5)), along with the results from Israel et al. (2014b; red dashed line) and Mahdavi et al. (2013; green dotted dashed line).

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© ESO, 2015

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