Joint X-ray/Sunyaev-Zel'dovich Analysis of the Intra-Cluster Medium
aa r X i v : . [ a s t r o - ph . C O ] A p r Joint X-ray/Sunyaev-Zel’dovich Analysis of theIntra-Cluster Medium
Kaustuv Basu ∗ ,† , Martin W. Sommer † and Yu-Ying Zhang † ∗ Max-Planck-Institut für Radioastronomie, Bonn, Germany † Argelander Institut für Astronomie, Bonn, Germany
Abstract.
We present results from a joint X-ray/Sunyaev-Zel’dovich modeling of the intra-cluster gas usingXMM-Newton and APEX-SZ imaging data. The goal is to study the physical properties of theintra-cluster gas with a non-parametric de-projection method that is, aside from the assumption ofspherical symmetry, free from modeling bias. We demonstrate a decrease of gas temperature in thecluster outskirts, and also measure the gas entropy profile, both of which are obtained for the firsttime independently of X-ray spectroscopy, using Sunyaev-Zel’dovich and X-ray imaging data. Thecontribution of the APEX-SZ systematic uncertainties in measuring the gas temperature at largeradii is shown to be small compared to the XMM-Newton and Chandra systematic spectroscopicerrors.
Keywords:
Galaxy clusters, Intra-cluster medium, Abell 2204, Abell 2163
PACS:
INTRODUCTION
Accurately determining the thermodynamic state of the intra-cluster medium (ICM) outto large radii in galaxy clusters is critical for understanding the link between the totalcluster mass and X-ray observables. For over a decade, observations of the thermalSunyaev-Zel’dovich Effect (tSZE, hereafter simply SZ; Sunyaev & Zel’dovich 1970)have been considered as a promising complement to X-ray observations for modelingthe ICM in galaxy clusters, yet only recently has it been possible to make meaningfulde-projections of gas temperature and density profiles using SZE imaging data frommulti-pixel bolometer arrays. The APEX-SZ experiment (Dobbs et al. 2006, Halversonet al. 2009) employs one of the first such powerful multi-pixel Transition-Edge Sensor(TES) bolometer cameras, enabling a joint analyses of the ICM properties using SZEand X-ray data. The first results of such analysis have been published by Nord et al.(2009) for the cluster Abell 2163, and Basu et al. (2010) for the prototypical relaxedcluster Abell 2204.
METHODS
We use publicly available X-ray imaging data in the 0.7–2 keV energy band from the
XMM-Newton observatory, and our Sunyaev-Zel’dovich effect imaging data at 150 GHzfrom the APEX-SZ experiment, to de-project the density and temperature profiles inclusters. The details of the X-ray and SZ data reductions are described in Nord et al.
00 200 300 400
APEX−SZ BEAM
FIGURE 1.
Left panel:
APEX-SZ map of Abell 2163 at 150 GHz, overlaid with XMM-Newton X-ray brightness contours in the 0.5-2 keV band.
Right panel:
XMM-Newton MOS1 image of Abell 2204overlaid with the contours from its APEX-SZ measurement. The SZ contour steps are -2, -4, -6 and -8 s with a spatial resolution of one arcminute and map size of 10 ×
10 arcmin. The black cross marks theflux weighted X-ray center, which matches with the peak location of the SZE map within the pointingaccuracy of the APEX telescope. (2009) and Basu et al. (2010). In Fig.1 we show examples of the SZ and X-ray imagingdata used in our analysis, for the clusters Abell 2163 and Abell 2204.The three-dimensional (de-projected) density and temperature profiles are obtaineddirectly using Abel’s integral inversion method, originally proposed by Silk & White(1978) for joint X-ray/SZ analyses of galaxy clusters. The high sensitivity and one ar-cminute resolution of the APEX-SZ images makes it possible to apply this method toperform a non-parametric analysis of the ICM properties in a real cluster. The uncertain-ties in the radial temperature profile are as yet dominated by the statistical uncertaintiesin the SZ measurement.
RESULTS
The primary outputs of the de-projection analysis are the three-dimensional density andtemperature profiles, from which the radial profiles of gas entropy and gas mass areobtained. The gas density profiles of the modeled clusters agree well with the X-rayderived isothermal b -models (Cavaliere & Fusco-Femiano 1978), confirming that in the0.5–2 keV energy band the X-ray surface brightness is practically independent of thegas temperature. The gas temperature profile within r in Abell 2163 is consistentwith being isothermal, whereas for the cool core cluster Abell 2204 a clear drop in thegas temperature near the cluster center is seen. By re-binning the data for Abell 2204, wecan also confirm a drop in the gas temperature in the cluster outskirts at 98% confidencelevel, which is obtained for the first time without using X-ray spectroscopy. The resultsfor the temperature modeling in Abell 2204 are shown in Fig.2.To compare the SZ-derived temperature profile in Abell 2204 with that obtained from
500 1000 1500 2000r (kpc)05101520 T e (r) ( k e V ) r r r k T ( k e V ) FIGURE 2.
Left panel:
De-projected temperature values and their 1 s statistical errors from the SZEmeasurement of the relaxed cluster Abell 2204. Over-plotted data points (red diamonds) are from the XMM-Newton analysis by Zhang et al. (2008).
Right panel:
SZ measurement of the temperature drop inthe outskirts of Abell 2204, shown in comparison with the results from cluster simulations by Hallman etal. 2007 (red dashed region), measurements of cooling core clusters from ASCA (gray shaded area) and
Chandra (blue solid line).
X-ray spectroscopic measurements, we obtained the “spectroscopic-like” temperaturefollowing Mazzotta et al. (2004). We also re-analyzed the
Chandra data (total exposuretime 88 ks) using the latest calibration updates (CALDB 4). The result for this com-parison is shown in Fig.3, together with the
Suzaku measurements for this same cluster.The
Suzaku measurements in the inner bins are affected by its large PSF (Reiprich etal. 2009). At r the Chandra measurements are dominated by systematic uncertaintiesdue to the background modeling; beyond that radius it is impossible to put meaning-ful constraints using the current
Chandra data. In comparison, the uncertainties on theSZE-derived temperatures are dominated by the statistical errors, out to r . The verylow and stable particle background in the Suzaku orbit makes its spectroscopic temper-ature measurements at large radii far superior. However, its large PSF is a problem formodeling clusters at higher redshifts ( z > . ) .We can compute the gas entropy profile, defined as K = T e n − / e , directly from the de-projected density and temperature profiles. A comparison between the entropy values inAbell 2163 and Abell 2204 shows a clear difference within the central 200 kpc, with thecore entropy in Abell 2163 being roughly an order of magnitude higher (Fig.3). Outsidethe core the entropy profile agrees with the power law K ( r ) (cid:181) r . expected from self-similar cluster models. The higher value of the “central entropy floor” in Abell 2163most likely indicates its merging nature. This entropy difference is again seen for the firsttime from SZ-derived temperature measurements independently of X-ray spectroscopy. CONCLUSIONS
The potential for joint X-ray/SZ analysis of the ICM properties is shown with the helpof APEX-SZ data, which allows for a non-parametric modeling of the temperature and
500 1000 1500 2000r (kpc)051015 k T ( k e V ) r r r K ( k e V c m ) A2204A2163
FIGURE 3.
Left panel:
Comparison of the projected gas temperature profile in Abell 2204 deducedfrom APEX-SZ data (blue, solid boundaries) with X-ray spectral measurements from
Chandra data (red,dashed boundaries). The hatched regions show the 1 s statistical uncertainties in each measurement, ontop of which the total uncertainties in each method are overplotted combining statistical and systematicerrors in quadrature. The three data points (black diamonds) are the Suzaku spectroscopic measurementsby Reiprich et al. (2009).
Right panel:
Comparison between the entropy profiles for Abell 2204 (blackdiamonds) and A2163 (blue squares). The higher entropy value in the central region of A2163 indicatesthe non-relaxed state of this cluster. density profiles out to the cluster virial radius. Apart from the assumption of sphericalsymmetry, the de-projection method is free from modeling biases. The uncertainties inthe gas temperature measurements near the virial radii is dominated by the statistical un-certainties in the SZ measurements. A demonstration of the decreasing gas temperaturein the cluster outskirts, and also the measurement of gas entropy profiles, are made fromthe SZ and X-ray imaging data without the use of X-ray spectroscopy.
ACKNOWLEDGMENTS
The authors thank H. Eckmiller, V. Jaritz, T. H. Reiprich, and the members of the APEX-SZ collaboration, for their contributions to this work.
REFERENCES
1. Basu, K., Zhang, Y.-Y., Sommer, M. W. et al.,