Contour binning: a new technique for spatially resolved X-ray spectroscopy applied to Cassiopeia A

J. S. Sanders 0 0 Institute of Astronomy , Madingley Road, Cambridge CB3 0HA A B S T R A C T We present a new technique for choosing spatial regions for X-ray spectroscopy, called 'contour binning'. The method chooses regions by following contours on a smoothed image of the object. In addition, we re-explore a simple method for adaptively smoothing X-ray images according to the local count rate, we term 'accumulative smoothing', which is a generalization of the method used by FADAPT. The algorithms are tested by applying them to a simulated cluster data set. We illustrate the techniques by using them on a 50 ks Chandra observation of the Cassiopeia A supernova remnant. Generated maps of the object showing abundances in eight different elements, absorbing column density, temperature, ionization time-scale and velocity are presented. Tests show that contour binning reproduces surface brightness considerably better than other methods. It is particularly suited to objects with detailed spatial structure such as supernova remnants and the cores of galaxy clusters, producing aesthetically pleasing results. 1 I N T R O D U C T I O N Many X-ray telescopes such as XMMNewton, Chandra and ROSAT contain detectors which capture individual photons, recording their energy and position on the detector. Therefore, unlike conventional optical observing techniques, we simultaneously collect imaging and spectroscopic data for each part of the object. In addition, the Chandra X-ray Observatory has very high spatial resolution (1 arcsec), allowing the properties of the emitting object to be studied in unprecedented detail. With this spectroscopic and imaging information, we can select events from the observation corresponding to a particular part of an object with a region filter. From these events, a spectrum can be built-up. An X-ray spectral package such as XSPEC (Arnaud 1996) can then be used to fit a physical model to the spectrum. Conventionally simple geometric shapes, such as annuli, sectors, boxes or ellipses, are used to define a region filter. Using sectors, for example, and assuming spherical or elliptical symmetry, one can account for projection in a cluster of galaxies. However, most extended objects are not symmetric when observed in detail [e.g. the Perseus cluster, Fabian et al. (2000), Sanders et al. (2004); the Cassiopeia-A supernova remnant, Hwang et al. (2004) and Abell 2052, Blanton, Sarazin & McNamara (2003)]. Given the morphological diversity of extended X-ray sources, it is important to have techniques which allow us to analyse the spectral variation of a source over its extent. We first investigated this problem when looking for cool gas in a sample of X-ray clusters using ROSAT Position Sensitive Proportional Counter (PSPC) archival data (Sanders, Fabian & Allen 2000). We devised a technique which used adaptively smoothed maps (Ebeling, White & Rangarajan 2006) to define contours in surface brightness. The ratio of the number of counts in different energy bands between each contour was used to define an X-ray colour. By using a grid of models, the absorption and temperature of the gas could be estimated between the contours. We approached this problem again with the advent of data from Chandra with its high spatial resolution. We created an algorithm called adaptive binning (Sanders & Fabian 2001) which used the uncertainty on the number of counts or the error on the ratio of counts in different bands to define the size of binning region used. The process was simple: pass over the image, copying those pixels which have a small enough uncertainty on the number of counts or colour to an output image. Bin up the remaining pixels by a factor of 2. Repeat until all the pixels have been binned. On the final pass, we bin any pixels which are not yet binned. This simple approach works well and was used by us and other authors on data from several clusters of galaxies (e.g. Centaurus Sanders & Fabian 2002; Perseus Fabian et al. 2000; Abell 4059 Choi et al. 2004). The disadvantage of this approach is that the binning scale varies by a factor of 2. It is very notable where the scale changes, and some regions are overbinned. Therefore, we started using the bin accretion algorithm of Cappellari & Copin (2003). The algorithm adds pixels to a bin until a signal-to-noise threshold is reached. After all the pixels have been accreted, it uses Voronoi tessellation to make tessellated regions based on the weighted position of the original bins. This technique has the advantage of creating bins which are compact, varying in size smoothly with the surface brightness, and also provides bins with similar signal-to-noise ratios. We applied the method to X-ray observations of the Perseus cluster (Sanders et al. 2004). Rather than use X-ray colours, we extracted spectra for each of the regions and used spectral fitting to derive, for example, temperature and abundance maps. Recently, Diehl & Statler (2006) have generalized this algorithm to allow for data whose signal-tonoise ratio does not add in quadrature. The motivation for further work in this area is that the methods above do not use the surface brightness distribution to change the shape of each bin. Physical parameters (e.g. density, temperature and abundance) usually change in the direction of surface brightness changes. The method we describe here uses the surface brightness to define bins which cover regions of similar brightness. Other methods have been presented for mapping the parameters of the intracluster medium. These included wavelet techniques (Bourdin et al. 2004) and Monte Carlo methods (Peterson, Jernigan & Kahn 2004). The advantage of binning techniques is that they provide errors on individual spectral fit parameters, or colours, from a particular part of the sky. The individual measurements made using binning methods are independent, making it easy to measure the significance of individual spatial features. The techniques presented in this paper have already been applied to a number of Chandra observations of clusters, including a deep observation of the complex structure of the Centaurus cluster (Fabian et al. 2005), the possible detection of non-thermal radiation and the identification of a high metal shell likely to be associated with a fossil radio bubble in the Perseus cluster (Sanders, Fabian & Dunn 2005b), a sample of moderate redshift clusters (Bauer et al. 2005), and a 900-ks observation of the Perseus cluster (Fabian et al. 2006), finding little evidence for temperature changes associated with shock-like features, and producing evidence of a substantial reservoir of cool X-ray emitting material. We first present a simple smoothing method (accumulative smoothing), and then present the binning method based on the smoothed image (contour binning). 2 AC C U M U L AT I V E S M O O T H I N G In order to bin using the surface brightness, it was necessary for us to get an estimate of the surface b (...truncated)