Free Access
Issue
A&A
Volume 556, August 2013
Article Number A44
Number of page(s) 16
Section Cosmology (including clusters of galaxies)
DOI https://doi.org/10.1051/0004-6361/201321319
Published online 23 July 2013

Online material

Appendix A: Modeling of the surface brightness profile in the SE sector

thumbnail Fig. A.1

EPIC/pn surface brightness profile in the SE sector (position angles 180–250°) in the 0.5–2.0 keV band. The panel below each profile shows the residuals (Δχ2) of data from the best fit model. The insets show the density models used to fit the data: a single power-law (upper left panel), a double power-law (upper right panel), a broken power-law (lower left panel), and a triple power-law (lower right panel).

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Since the SE large scale feature we detected in A2142 could be the first cold front observed with XMM-Newton at a distance as large as 1 Mpc from the cluster center in low surface brightness regions, a detailed modeling of the profile is necessary to exclude other possible interpretations. We extracted the SB profile in the SE sector (position angles 180–250°) from the EPIC/pn image in the 0.5–2 keV energy range. We corrected for vignetting using the exposure map and we masked out bright point sources. We then assumed different models for the shape of the density profile that we project, assuming an elliptical symmetry as in Owers et al. (2009), to fit the surface brightness data in the radial range 3–15 ′ after convolving with the XMM-Newton PSF. We started using two simple models that do not assume any discontinuity in the profile: a single power law, which would be the normal behavior of the density profile in the undisturbed outskirts of a cluster, and a double power law, which could model a steepening in the density profiles at rbreak. As shown in the upper panels in Fig. A.1, these simple models fail to reproduce the complex shape of the profile ( and respectively). Then, we fitted the profile with the standard broken power-law density model used with cold fronts (e.g. Owers et al. 2009): (A.1)As discussed in Sect. 3.1.1, the profile does not extend at large radii, so we fixed the slope of the outer component at the value αout = 2.05 that we derived from the analysis of the ROSAT/PSPC profile. This model reproduces the shape of the profile well (lower left panel in Fig. A.1). The best fit parameters are provided in Table 1. Although the fit with this model is satisfactory (), we also used a fourth, more complicated density model, namely a combination of three power-laws: (A.2)with the continuity condition at the breaks r1 and r2We fixed α3 = 2.05, as in the previous case, and r2 = 10′ while we left as free parameters α1, α2, r1 and the overall normalization. This model provides an improved fit of the data (lower right panel in Fig. A.1) with . It is interesting to note that the model in Eq. (A.1) can be considered a limiting case for the triple power law model (Eq. (A.2)), where the slope α2 tends to infinity and the first break tends to coincide with the second one. In principle, we could compare the χ2 of the two fits and find that the triple power-law model provides a better description to the data than the double model at a confidence level of more than 99% (Δχ2 = 12.1) but this approach is limited by the fact that it considers only statistical errors. Systematic uncertainties, such as those due to the assumption of an idealized geometry or to an imperfect modeling of the PSF, are likely dominant, and therefore, it is difficult to clearly distinguish between the two models. Moreover, the fit of the profile with Eq. (A.2), requires the slope of the central power law to be extremely steep: α2 = 6.2 ± 0.5 is higher both than the slopes in the inner and outer part of the profile (α1 = 1.09 ± 0.01 and α3 = 2.05) and than the density slopes typically observed in the external regions of galaxy clusters (α in the range 2–3 Eckert et al. 2012). The fit also provides the position of the first break, r1 = 8.68 ± 0.08 arcmin, which implies that the region where the profile is described by the steep power-law is a thin shell of width 130 kpc. This best fit model describes a density distribution where the gas properties change very rapidly in a small shell, which is not much different from the sharp transition between two phases of the gas of the broken power law model (Eq. (A.1)), as clearly seen in the insets of the bottom panels in Fig. A.1. Therefore, the comparison of these two models supports the presence of a discontinuity in the SE profile of A2142.

The triple power-law model may also be explained by assuming that it is caused by a broken power-law model, where the discontinuity is not in the plane of the sky but has an inclination θ. Projection of this model in this geometry induces a smoothing on the surface brightness profile, which in the plane of the sky would appear sharp. The smoothing scale can be used in combination of the azimuthal extension of the front to derive the inclination θ under cylindrical approximation (i.e., assuming that the extension of the front along the line of sight is the same as in the plane of the sky). We used the width of the shell where the density profile is described by the steep power law (130 kpc) as smoothing length and 1.2 Mpc (Sect. 3.1.1) as extension of the edge and we found an inclination of about 6°. If the systematics were not dominating, we could therefore infer that the discontinuity is seen with a small, but non zero, angle with respect to the plane of the sky.

Appendix B: Spectral background modeling in the MOS detectors

We applied a method similar to the one described in Leccardi & Molendi 2008 (hereafter LM08) to model the background in the two regions at the southeastern cold front and restricted our analysis to the MOS detectors, since their background was found to be more predictable than for the pn (see LM08). While LM08 used the outermost annulus of the MOS image to model the local sky background components (cosmic X-ray background or CXB, Galactic halo, and local hot bubble), the source in our case is filling the entire FOV, such that the sky components must be estimated from another instrument. Therefore, we used the ROSAT/PSPC observation and extracted the spectrum of a background region located 50′ SE of the cluster core. We used the ftool Xselect to extract the spectrum of this region from the event files and computed the appropriate effective area using the pcarf tool. We subtracted the particle background with the help of the pcparpha executable. We fitted the resulting spectrum with a model composed by: i) a power law with a photon index fixed to 1.4 for the CXB (De Luca & Molendi 2004), absorbed by the Galactic NH (NH = 3.8 × 1020 cm2, Kalberla et al. 2005); ii) an absorbed APEC model with temperature fixed to 0.22 keV for the Galactic halo; and iii) an unabsorbed APEC model at a temperature of 0.11 keV for the local hot bubble (Snowden et al. 1998). The PSPC spectrum is well represented by this model (see Fig. B.1), and the normalization of the CXB component agrees with the value in De Luca & Molendi (2004).

thumbnail Fig. B.1

ROSAT/PSPC spectrum of the background region, that is located 50′ SE of the X-ray peak of A2142. The various components show the best-fit spectra for the local bubble (red), the Galactic halo (green), and the CXB (blue).

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To model the non-X-ray background (NXB), we used the spectra from the unexposed areas of the corners of the MOS detectors and fitted them with a phenomenological model made of a broken power law and a number of Gaussian emission lines (see Appendix A of LM08). This function was then used to model the NXB spectrum for the IN and OUT regions (see Fig. 3). The spectral shape of the NXB model was fixed to that found in the corners of the MOS, but the overall normalization of the model and the normalization of the prominent Al and Si emission lines were treated as free parameters. In both cases, the NXB dominates the source contribution above ~6 keV; therefore, the normalization of the NXB component is very well constrained by the high-energy data. The sky components were taken from our ROSAT background region (see Fig. B.1) and rescaled to the proper area, accounting for CCD gaps and dead pixels. The normalization of the local components was fixed, but the CXB component was allowed to vary by ±15% to account for cosmic variance. In any case, we note that the sky components are relatively unimportant at all energies, so our results are unaffected by local variations of the sky background. In addition, we also modeled the spectral component from quiescent soft protons (QSPs), following the method described in Appendix B of LM08. Namely, we computed the ratio between the mean count rate inside and outside the FOV of the detectors and used the phenomenological formula derived by LM08 to derive the normalization of the QSP component. The spectral shape of the QSP component was fixed to that found in LM08.

Four offset observations in the outskirts of A2142 were recently perfomed by XMM-Newton (P. I. D. Eckert) during AO11 (Eckert et al., in prep.). We extracted spectra using these observations in external sectors to model the sky-background components and verify our estimate of the normalizations based on the ROSAT/PSPC data. XMM-Newton data should grant us a better spectral resolution and thus a more detailed spectral modeling. However, the spectra in the external regions are dominated by the instrumental background (much larger in XMM-Newton than in ROSAT) even at low energies. Nonetheless, we verified that the normalizations of the sky components with the XMM-Newton offset observations are consistent with those we obtained with the ROSAT/PSPC modeling and do not have a significant impact on the spectral parameters that we measured in Sect. 3.1.2.

Appendix C: Estimate of the sloshing energy

thumbnail Fig. C.1

Left: pseudo-entropy profiles in the excess (red) and in the unperturbed region (black). Dashed lines show the entropy profiles in the elliptical simulation (rescaled for clarity) for the “excess” (red) and unperturbed (black) region. Right: corresponding radius c(r) for which the pseudo-entropy in the unperturbed region is equal to that in the spiral region. Circles are obtained by neglecting the ellipticity, while triangles are the values corrected assuming that the ellipticity is entirely intrinsic. The dashed line shows the one-to-one relation.

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We defined a “sloshing” region in the residual map (Fig. 6, right panel) by selecting regions corresponding to brightness excesses). We extracted surface brightness profiles in circular annuli, which were intersected with this region, and a temperature profile in spherical sectors, which resemble closely the mask file. We then combined these quantities to make pseudo-entropy profiles, which we show in the left panel of Fig. C.1, and compared them with the entropy profile in the “undisturbed” complementary region, K(r). As expected, the pseudo-entropy in the excess region is always lower than the mean profile of the cluster. For each radius ri of the entropy profile, we defined a corresponding radius c(ri) ≤ ri such that (C.1)Assuming that the gas in the excess region was transported outwards by the sloshing mechanism without modifying its entropy, the radius c(r) thus gives the radius where the gas at radius r was originally located before the sloshing mechanism set in. In Fig. C.1 (right panel) we plot the starting radius c(r) as a function of the actual position r: the gas is never displaced radially by more than a factor of ~2, as predicted by simulations (Ascasibar & Markevitch 2006).

We consider a bubble of gas of density ρin traveling outwards in the potential well of the cluster. At each radius r, some gas with density ρ(r) travels inward to fill the bubble volume V. The force applied on the bubble is thus given by (C.2)where g is the gravity acceleration. If the process is adiabatic, the bubble expands at each radius r, and the density decreases, preserving the entropy, such that (C.3)where r0 is the initial position of the bubble. We can write its density (C.4)Inserting this into Eq. (C.2) and introducing Mgas = ρ0V, we find where g(r) is the gravity acceleration with modulus GMtot( < r)/r2. We calculated the total mass profile using the best fit NFW profile by Ettori et al. (2002). The total energy needed to move the bubble from radius r0 to r1 is thus given by the integral of the force, (C.5)The energy of the sloshing gas is then obtained by summing the contribution of each gas bubble (Eq. (C.5)) for all radii in the excess region: (C.6)where c(r) is the starting radius for each gas particle at radius r that we obtained from the entropy profile. The gas mass Mgas(ri) in Eq. (C.6) is calculated as the product of the projected gas density in the ith shell of the profile with the volume, which is defined as the intersection of spherical and cylindrical shells multiplied by the fraction of the azimuth (f) considered (4/3π(4ridri)3/2 ∗ f). Using Eq. (C.6), we find Etot ~ 3.5 × 1061 erg.

thumbnail Fig. C.2

Simulated image of an elliptical entropy distribution to which we overlaid circular annuli to qualitatively show the effect of the assumption of spherical symmetry, compared with the mask used to select “excess” regions.

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In the previous calculation, we estimated the energy spent against the gravitational potential under the assumption of spherical symmetry. This calculation may be biased by the large ellipticity of A2142, inducing an overestimate of the displacement of gas particles and therefore of the energy. If the entropy distribution is intrinsically elliptical and we calculate profiles in circular annuli, along the major axis of the ellipse, we will invariably find gas with lower entropy

compared to regions at the same distance from the center but along the minor axis (see Fig. C.2, left panel). To quantify this effect, we generated an image of an elliptical entropy distribution (left panel of Fig. C.2): starting from the pseudo-entropy in the “unperturbed” region, we used the ellipticity and inclination of the X-ray image of A2142 as geometrical parameters. We then extracted profiles in the “excess” and “unperturbed” regions, using the mask shown in Fig. C.2 (right panel) and compared them to measure the displacement c(r). As shown in Fig. C.1 (left panel, dashed lines), the profile extracted along the “excess” region is consistent with the “unperturbed” one at small radii, but the two profiles differ significantly at r > 3 arcmin, although their difference is smaller than the one observed with real data (Fig. C.1). Using these entropy profile, we calculated the displacements induced by the ellipticity, and we subtracted them from the c(r) values calculated before (Fig. C.1, right panel).

We note that the correction we calculated in this way may result as an overcorrection, since it assumes that all the ellipticity is intrinsic and not associated to the sloshing itself. For this reason the corrected value should be considered as a lower limit, while the uncorrected one, which completely neglects the ellipticity of the gas, should be considered as a upper limit.


© ESO, 2013

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