Adaptively binned image analysis

**Figure 5:** Maps of column density (panel a), temperature (panel b), gas density (panel c), metallicity (panel d), pressure (panel e), specific entropy (panel f), cooling time (panel g), and the appropriated reduced $\chi ^2$ value (panel h) for adaptively binned central image of A4059, with an intrinsic absorption single temperature MEKAL model. Dotted circle contour ( kpc) includes the bright hour-glass like structured region of the cluster.
$\begin{figure}\centerline{\hbox{ \psfig{figure=fig5.ps,width=0.9\textwidth}} } \end{figure}$

Given the asymmetries present in the cluster core, we must analyze the spectral properties of the cluster across the 2-dimensional image. We achieve this using the ``adaptive binning'' method of Sanders & Fabian (2001). The adaptive binning code, kindly provided by Jeremy Sanders², computes the optimal tiling across the image such that each tile possesses at least a specified number of photons. Spectra can then be extracted and analyzed for each tile. The major advantage of this method is that one can maintain high spatial resolution (i.e. small tiles) in the high count rate regions of the image.

The adaptive binning was set such that each tile possessed at least 600 counts, resulting in a fractional error on the net count rate of 0.04. Spectra and response matrices were extracted from each tile. Although an analysis using the

keV energy range could provide information on cold emission and intrinsic absorption in the cluster, such an analysis is severely hampered by calibration problems at the lowest energies, in particular the effects of contamination on the ACIS filter and charge-transfer inefficiency (CTI) in the CCD. Therefore, only data between

keV were included in this spectral analysis. The separate responses for each tile were weighted to account appropriately for instrumental response variations across the detector, using the mkwarf and mkrmf scripts implemented within CIAO. The original auxiliary response files created by CIAO tool mkwarf were corrected for degradation in the ACIS quantum efficiency (QE) using the software released by George Chartas and Konstantin Getman ³. Background spectra were generated using the blank sky fields (Markevitch 2000) for the same part of the detector. All spectra were grouped to have at least 20 photons per energy bin, thereby facilitating the use of $\chi ^2$ fitting.

For our canonical spectral fits, each spectrum was modelled with a single temperature optically-thin thermal plasma component (modeled using the MEKAL model as implemented in XSPEC; Mewe, Gronenschild & van den Oord 1985; Mewe, Lemen & van den Oord 1986; Kaastra 1992; Liedahl, Osterheld & Goldstein 1995) with a metallicity fixed at

and absorbed by the Galactic column density of $N_{H}=1.45\times10^{20}$ cm $^{-2}$ . Once we obtained the best- fit plasma emission measure and temperature for each bin, we derived the density, pressure and cooling time assuming that the plasma is single-phase and has a line-of-sight path length equal to the radial distance between the center of the bin and the center of the cluster (following the method of Fabian et al. 2001). We also studied the effect of relaxing the metallicity constraint and including the possibility of intrinsic absorption.

In Fig. 5, we show maps of the best fitting values of intrinsic absorption (for those fits that relax the absorption constraint), temperature, gas density, metallicity (for those fits that relax the metallicity constraint), pressure, entropy ( $s=p/n^{5/3}$ ), radiative cooling time and $\chi^2_\nu$ . We have overlaid the X-ray contour map to facilitate comparison. Significant complexity can be seen in these maps. Within the centralmost regions of the cluster (about

radius, see dotted circle contour in Fig. 5a), the gas density and pressure dramatically increase, reaching peak values of $n_{e}\sim 0.11$ cm $^{-3}$ and $p\sim 2.7\times10^{-10}$ erg cm $^{-3}$ , and the temperature decreases reaching down to a value of $kT \sim 1.4$ keV.

**Figure 6:** Radial distribution of the fitted parameters for the bins in Fig. 5 with 1- $\sigma$ errors. Each profile corresponds to the fitted values of NE and SW sides of the cluster center. The radius is the mean distance from the cluster center to the each bin.
$\begin{figure}\centerline{\hbox{ \psfig{figure=fig6.ps,width=0.8\textwidth}} } \end{figure}$

One of the most striking and unusual features within the core of Abell 4059 is the the bright ridge of emission stretching from the cluster core to the SW. Our temperature map (Fig. 5b) clearly shows that the ridge is composed of gas that is cool (with a temperature of $\sim 1.4{\rm\thinspace keV}$ ) and has low entropy. In order to investigate the spatial differences in the properties of X-ray emitting gas in and around this structure, Fig. 6 shows the best fitting parameters for the tile fits, averaged in radial bins, as a function of the distance from the center of the cluster. Fig. 6 distinguishes between the NE and SW sides of the cluster in order to study the nature of the bright SW ridge. The most significant result from Fig. 6 is that the radiative cooling time within the ridge is rather small (less than 1Gyr within 25kpc and about 0.1Gyr within the innermost few kpc).

The temperature and pressure maps in Fig. 5b and 5e exhibit no evidence for any hot gas in or around the cavities. We can see that the SW part adjacent to the central hour-glass like structure shows obviously sharp gradients in the fitted temperature, entropy, and radiative cooling time maps, while the NE shows a rather smooth profile. The oscillation of fitted values shown in Fig. 6 results from this non-axisymmetric feature.