6 Properties of the central gas

Our best-fit polytropic model is an excellent description of the observed temperature profile barring the inner point, which is significantly lower. We examined if this temperature drop could be due to a cooling flow.

The cooling time, the enthalpy of the ICM divided by the energy loss due to X-rays, is calculated using:

$$t_{\rm cool} =2.9\times 10^{10}\ {\rm yrs} \sqrt{\frac{kT_{\r... ...V}}\ \left(\frac{n_{\rm H}}{10^{-3}~{\rm cm}^{-3}}\right)^{-1}$$ (11)

from Sarazin (1986). Using the central density derived from the KBB model fit (Table 2), we find $t_{\rm cool} \sim 2.4 \times 10^9$ yr, or about one quarter of the age of the Universe at the cluster redshift. This suggests that a CF should exist. Furthermore, the cooling radius, defined as the radius where the cooling time is equal to the age of the Universe, is $r_{\rm cool} \sim 0.6\hbox{$^\prime$ }$ meaning that any CF should reside in the central bin. This is consistent with the observed temperature drop.

 

 

Table 4: Multi-temperature and CF fits to the inner annulus. The F-test is computed against the fit for a single temperature absorbed mekal model.

Parameters	1T	2T	CF
$kT_1~(\rm keV)$	6.4	6.9	7.9
$kT_2~(\rm keV)$	-	0.61	-
$Z/Z_{\odot}$	0.33	0.35	0.35
$\dot{M}~(M_{\odot}~{\rm yr}^{-1})$	-	-	58.9
$\chi^2 / \nu$	1003.2/854	982.2/852	978.3/851
$F_{\rm prob}$	-	>$99.99\%$	>$99.99\%$

We thus fitted the spectrum of the inner bin with more complicated models:

• The sum of two MEKAL models absorbed by a common column density fixed at the galactic value. When fitting, the second temperature is limited to be less than or equal to the temperature of the main component, and the abundances of the two components are tied together.

• The sum of a MEKAL and a cooling flow model, again with a fixed common absorption. Here the abundance of the CF is tied to that of the thermal spectrum, and the upper temperature for the CF is limited to be the temperature of the thermal gas.

The results are shown in Table 4. Both the two temperature and the MEKAL +CFLOW models are better fits than the single temperature model at the >$99.99\%$ level. In addition, the MEKAL+CFLOW model is a better description of the data than the two-temperature model at the $93\%$ level.

The secondary temperatures and CF properties are not well constrained. More sophisticated modelling is needed, preferably including RGS data, which is beyond the scope of this paper.