Detailed X-ray spectral study of annuli

Motivated by the above analysis, we have examined the spectra for annular regions in the cluster. Source spectra, background spectra, response matrices and ancillary files were generated for each annular region, as in § 3.4.1. Finally, the spectra were binned so as to possess a minimum of 20 counts per bin, thereby allowing the use of $\chi ^2$ fitting techniques. We fitted each spectrum to a variety of models in the energy range of 0.8-8.0keV⁴: a single-phase emission model and two multi-phase emission models. For a single-phase emission model (hereafter, model-S), the spectrum is fitted with single-temperature MEKAL model, and for multiphase emission models, with two-temperature MEKAL model (model-T) or a single temperature plasma plus cooling flow model (model-SCF). In the cooling flow model, we set the upper (initial) temperature of the cooling material to be equal to the temperature of the single plasma component. The lower ``cutoff'' temperature of the cooling flow model is set to 0.1keV (i.e., significantly below our bandpass). In this analysis, the intervening neutral absorption column density is left as a free parameter. For reference, the Galactic absorption column density is $N_{\rm H,Gal} = 1.45 \times 10^{20}$ cm$^{-2}$.

Figure 7: Temperature, absorbing column density, metallicity, and the appropriate reduced $\chi ^2$ value as a function of radius fitted with the single temperature MEKAL model (model-S; panel a), two temperature MEKAL model (model-T; panel b), and single temperature plasma plus cooling flow model (model-SCF; panel c). Error bars are shown at the 1-$\sigma$ level for one interesting parameter ($\Delta \chi ^2=1$). Open square and cross show the results with metallicity fixed to the 0.4 times solar value and with metallicity free, respectively. For model-T, the metallicities of the two phases were fixed to be same.

The results of this analysis are shown in Fig. 7, together with the 90% confidence ranges for one interesting degree of freedom ($\Delta\chi^2=2.7$). Here, we report the results for both the fixed abundance fits (open squares) and variable abundance fits (diagonal crosses).

When fitted with a single temperature component plasma model (parameterized by a single temperature and a single emission measure; Fig. 7a), some clear trends are seen. The temperature decreases from 4keV in the outer regions of the cluster to 2keV in the central regions. When applying model-S with metallicity as a free parameter, we find an enhanced metallicity (approaching almost cosmic abundances) at intermediate radii (20-50kpc), with metallicities decreasing to $0.4-0.5Z_\odot$ of the cosmic value at smaller and large radii. The goodness-of-fit is, however, rather poor when applying model-S to the cluster center. Much of the poor goodness of fit is due to an underprediction of the soft flux by the single temperature model. It is this mis-match that is responsible for the unphysically small absorption (i.e. less that $N_{\rm H,Gal}$) implied by these fits.

The two temperature model (model-T; Fig. 7b) is a much better description of the spectral data, especially within the inner 50kpc. The actual values of the two temperatures seem to be weak functions of radius, with $kT_{\rm high}\approx 4-5{\rm\thinspace keV}$ and $kT_{\rm low}\approx 1-2{\rm\thinspace keV}$ in most of the radial bins. Apparent exceptions to this are the 20-40kpc radial bins which, in the fixed abundance fits, both appear to have $kT_{\rm high}>7{\rm\thinspace keV}$. However, variable abundance fits suggest that the abundance strongly deviates from $Z=0.4Z_\odot$ at these radii and, once that is accounted for, the upper plasma temperature is also approximately 4keV. The principal qualitative difference between the one and two temperature fits lies in the abundance profile. In the one temperature fits, there is a pronounced drop in the metallicity as one proceeds from 30kpc into the center of the cluster. On the other hand, the two temperature fits show a jump in the metallicity at about 40kpc, with the metallicity displaying an approximately flat radial dependence within this radius. Thus, the metallicity peak noted in the single temperature fits is probably an artifact of the model (also see case of the Virgo Cluster, Molendi & Gastaldello, 2001). Due to the better quality of these fit (especially in the soft band), the measured absorption column is more meaningful for model-T. We see that all radii are consistent with Galactic absorption, i.e., there is no evidence for intrinsic absorption in this cluster.

The cooling flow model (model-SCF) is a poorer description of these data than the two temperature model (model-T). This is due to the fact that the model includes gas at all temperature from the ambient temperature down to 0.1keV whereas, as noted in the introduction, the cooling in many clusters (including A4059; Peterson et al. 2003) is truncated at 1-2keV by some process. With this caveat, we note that the cooling flow model reproduces the temperature structure of model-S and the metallicity behaviour of model-T.