Volume 570, October 2014
|Number of page(s)||16|
|Section||Cosmology (including clusters of galaxies)|
|Published online||31 October 2014|
We have performed a detailed analysis of the temperature structure of the regions of interest in A496 (annular sectors and polygons), searching for possible multitemperature components in the ICM spectra.
In this Appendix we present the results from the analysis of each spectrum with the two different spectral models described in Sect. 2.2: the one-temperature vapec model (1T model), and the multitemperature GDEM model (Buote et al. 2003).
In Fig. A.1 we show the relative differences between the temperatures estimated with the 1T model, T1T, and the GDEM model, TGDEM, that is (T1T − TGDEM) /TGDEM, plotted as a function of the physical distance from the cluster center of the regions for the 98 polygons used to extract the spectra (see Sect. 3.4 and Fig. 8). In Fig. A.1 only the central bin shows a temperature difference significantly larger than ~ 5%, while in all other bins the differences are around 3 − 6% and consistent with this value within 1 − 2σ. The best-fitting constant model, with the exclusion of the first bin, gives 0.038 ± 0.002 and is plotted in Fig. A.1 as a solid line.
The relative Fe abundance differences, (ZFe,1T − ZFe,GDEM) /ZFe,GDEM, give similar results (see Fig. A.2). In this case, the best-fitting constant model gives 0.035 ± 0.01.
We can ascribe the small ~ 3% bias toward slightly higher temperatures and Fe abundances from the 1T model to well-known calibration problems in the EPIC detector between the soft (0.7−2 keV) and hard (2.–8. keV) X-ray bands (e.g., Nevalainen et al. 2010).
From the negligible differences between temperatures and Fe abundances in the two spectral models it is clear that, if present, a multitemperature component in the ICM contributes only modestly to the total emission. More interestingly for the purposes of our work, the value of the measured Fe abundance is essentially unaffected by a possible multitemperature structure.
We excluded from our analysis the central bin, which is the only one where the relative differences are significant in both cases. This central cluster region might be contaminated by the central AGN or by a true multiphaseness of the ICM.
Relative temperature differences between the 1T and GDEM models as a function of the distance from the center of the cluster. Red marks the IN, black the OUT polygons.
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Relative Fe abundance differences between the 1T and GDEM models as a function of the distance from the center of the cluster. Red marks the IN, black the OUT polygons.
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In Sect. 3.2 we derived the pressure jump across the main cold fronts: NNW, divided into two sectors 30°−75° and 75°−120° to account for its boxy morphology, and S2.
To a first approximation, we derived the pressure jump across the front by using the electron density and the temperature in the two bins just inside and outside each edge. Namely, we modeled the electron density profile with a broken power law: (B.1)where nin and nout are the electron densities at the cold-front position rCF on the inner and outer side of the edge. We projected the emissivity along the line of sight and fit the surface brightness profiles of each sector of interest to derive the values of nin, nout, αin, and αout. The fitting process was divided into two steps: we initially fit only the outer part of the profile (outside the cold front) where only the external component is present and derived the nout and αout parameters. Then, we fixed the external component and fit the whole profile to derive the inner component parameters. Finally, we derived the pressure jump pin/pout = ninTin/noutTout where the temperature values Tin and Tout in the two bins close to the front position were obtained through the spectral analysis (see Fig. 7). The pressure jumps obtained through this method are reported in the second column (approx pressure jump) of Table B.1.
Pressure (arbitrary units) profiles obtained with the two different methods (see text) in the three cold-front sectors 30° − 75° (left panel), 75° − 120° (middle panel) and 240° − 285° (right panel). The solid line is the pressure profile obtained by using the interpolated temperature profile, filled black circles correspond to the pressure obtained by using the original T profile.
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A more accurate estimate for the pressure profile can be obtained by multiplying the electron density profile with the temperature profile. However, the temperature profiles (see Fig. 7) are evaluated in bins that are significantly larger than the bins available for surface brightness (and electron density) profiles. We then interpolated the temperature profiles to reconstruct a temperature profile from the same bins that were used for the density profile. We performed two independent interpolations for the points inside and outside the cold front. For the outer regions we excluded the points close to the cold front to keep far away from the stagnation point; profiles in this region were computed by extrapolating measures at larger radii. We note that since bins used for the temperature profiles are large to allow reliable spectrum fitting and the number of bins is quite small, we did not deproject the temperature.
Pressure jumps for the three cold-front sectors
In Fig. B.1 we plot the pressure profiles (solid line) derived for the three cold-front sectors. The corresponding pressure jumps are reported in the last column of Table B.1. As expected, the jumps measured from the pressure profiles are slightly larger than the approximated ones: ~ 7% and ~ 5% for the two NNW sectors and 0.7 % for S2.
In Fig. B.1 we also overplot the nT profiles obtained from the original temperature profiles. The figure confirms that the two profiles match and that the differences between the results obtained with the two procedures are small.
In this appendix we address the robustness of the correlation (K-Fe) between entropy and metal abundance. We wish to investigate whether the match between IN and OUT regions in the K-Fe plot might be due to the single-temperature model employed to fit the spectra. If, in the regions on the spiral there were some gas mixing, two different gas phases would coexist and the 1T fitting might provide an averaged value for T, Z, ne which could preserve the correlation even if the gas were made up of two distinct components. Moreover, even if the gas whitin the spiral is not affected by mixing, projection effects can lead to the same bias since the analyzed spectrum would contain the two components. We fitted the spectra with a two-temperature model, but using this model did not improve the quality of the fit. We therefore took a different approach: we built a composite spectrum that contained the spectra of two different regions at opposite sides in the K-Fe plot. This simulates both a region containing mixed gas and a region affected by projection.
We chose regions #2 and #71 (see Fig. C.1). The lowest temperature region (#2) is on the spiral feature at the center of the cluster, while region #71 is outside the spiral north ~ 200″ (~ 120 kpc) of the center.
Best-fit values for temperature and metal abundance obtained using the 1T and 2T model for regions #2, #71 and for the composite spectrum #2 + #71.
K-Fe correlation. Red marks the IN, black the OUT polygons. Green points mark regions #2 and #71 used for the test, the purple point represents the composite region #2 + #71.
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We checked the count rates of both regions #2 and #71 and verified that they have similar values, so that the two regions contribute at the same level to the total spectrum. This mimics a region where mixing occurs with similar filling factors for the two different gas phases. We first fit the composite spectrum with a 1T model and found, as expected, best-fit values of the temperature and of the metal abundance (see Table C.1) that are in between those measured for regions #2 and #71. This also leads to a point in the K-Fe plot that is indeed still on the relation (see Fig. C.1), but in this case, the fitting procedure returns a much higher χ2, 760.3 for 676 d.o.f. against χ2 = 576.2 for 455 d.o.f. for region #2 and χ2 = 520.5 for 540 d.o.f. for region #71. Furthermore, visual inspection of the residuals clearly indicates that there is more than one spectral component. We then fit the composite spectrum with a 2T model, leaving normalization, temperature and Fe abundance as free parameters for both components. This resulted in a highly significant improvement in the fit (χ2 of 652.5 vs. 673 d.o.f.) and in the disappearance of the structures in the residuals found in the 1T fit. We performed the same 2T fitting also on the spectra extracted from regions #2 and #71. Here, including a second component provided improvements that are significantly smaller than those found for the composite region (see Table C.1). These improvements, while formally statistically significant, as indicated by the results of the F-test (see Table C.1), can be ascribed to the known EPIC calibration mismatch between soft and hard spectral bands (e.g., Nevalainen et al. 2010).
We conducted the same analysis on other pairs of spectra and found similar results.
We conclude that while mixing of different phases can lead to spectra whose 1T best fits lie on the K-Fe correlation, such composite spectra would be easily identified with a multitemperature analysis. The lack of any evidence of multiphaseness, beyond the modest level expected from the known EPIC calibration issues, tells us that mixing must at the most be modest in the gas located within the spiral.
© ESO, 2014
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