3 Morphology

3.1 Image

We show in Fig. 1 the MOS1+MOS2 image of the cluster, produced simply by adding the data from each camera without accounting for vignetting. The image is striking: the cluster displays an unmistakably elliptical shape, with a clear brightness enhancement directly to the south, and there are a large number of sources in the field of view.

Figure 1: The MOS1 + MOS2 counts image of the whole field of view of the A1413 observation. Note the large number of sources and in particular, what appears to the an extended source to the south of the cluster itself.

3.2 2D ${\beta }$-model fitting

Motivated by the apparent excess of counts to the south of the cluster (see Fig. 1) we fitted the MOS1 +MOS2 image with a 2D ${\beta }$-model in order to quantify the significance of this feature. In fitting the image, we followed closely the procedure described in Neumann & Böhringer (1997). Images were extracted in the (0.3-1.4) keV band from the weighted MOS event files in pixels of size 3 $.\!\!^{\prime\prime}$4 and added to make a combined MOS image. Since in the case of weighted events Poissonian errors do not apply, errors were correctly calculated from the weights using $\sigma = \sqrt{\Sigma_{j} w_j^2}$ (see Arnaud et al. 2001b). An error image was generated for each instrument, and these images were added quadratically. The fitting procedure described below was tested and optimised on simulated data before application to the real data.

The $\chi^2$ test used in the fitting procedure assumes Gaussian statistics, for which the mean is the most likely value. The statistics are actually not Gaussian in the external regions of the field of view, dominated by the background. In these regions the number of photons per pixel is low and follows a Poisson distribution for which the mean is larger than the most likely value. If the image is not smoothed before fitting, there is thus a tendency to underestimate the mean background level, leading to erroneous values for the fitted cluster parameters. The combined MOS image was thus smoothed with a Gaussian of with $\sigma = 10\hbox{$^{\prime\prime}$ }$ before fitting. The error image was treated according to the error propagation function for Gaussian filtered images described in Neumann & Böhringer (1997). We fix all error pixels with a value of 0 to have a value of 1 before fitting, meaning that we can use $\chi^2$ fitting but are unable to determine confidence parameters on the fit. The data were then fitted with a 2D ${\beta }$-model of the form:

$$S(x,y) = S_0 (1+ F_1 +F_2)^{-3\beta +\frac{1}{2}} + B$$ (1)

where

$$F_1 = \frac{[ \cos{\alpha} (x - x_0) + \sin{\alpha} (y-y_0)]^2}{a_1^2}$$

$$F_2 = \frac{[-\sin{\alpha} (x - x_0) + \cos{\alpha} (y-y_0)]^2}{a_2^2}\cdot$$

Here, x₀,y₀ is the position of the centre of the cluster; x,y are the coordinate positions of each pixel; a₁,a₂are the major and minor core radii; $\alpha$ is the position angle; and the background is included in the model via the parameter B.

We fit the image between $1\hbox{$.\mkern-4mu^\prime$ }3$ (see below) and $13\hbox{$^\prime$ }$from the cluster center, excluding obvious point sources. The results of the 2D fit are shown in Table 1. Note that the fitted parameters are slightly dependent on the outer radius and the $\sigma$of the Gauss filter, but the results are always in good agreement with the 1D fit, described below.

 

 

Table 1: 2D ${\beta }$-model fits, $1\hbox {$.\mkern -4mu^\prime $ }3{'-} 13'$, MOS image.

Parameter
${\beta }$	0.72
$r_{\rm c}$ long	284.6 kpc
$r_{\rm c}$ short	201.2 kpc
PA	2$^\circ$26$^\prime$
Centre $\alpha$	11$^{\rm h}$55$^{\rm m}$18 $.\!\!^{\rm s}$9
Centre Dec	23$^\circ$24$^\prime$13 $.\!\!^{\prime\prime}$8

In order to quantify the significance of the excess of flux to the south of the cluster, we subtract the 2D ${\beta }$-model from the data and calculate the significance of the residuals using the prescription described in the Appendix of Neumann & Böhringer (1997). The excess is an extended source detected at >$10\sigma$, as shown in Fig. 2.

Figure 2: Residuals after subtraction of the 2D ${\beta }$-model, smoothed with a Gaussian with $\sigma = 5/\sqrt {2}$ pixels ($\sim$ $12\hbox {$^{\prime \prime }$ }$). This is a zoomed image where the centre of the cluster is the bright elliptical region at the centre of the image (a possible cooling flow?). The dynamic range is from -10 to +20$\sigma$, where areas of low $\sigma$are black and areas of high $\sigma$ are white. Contours are between +2 and +10$\sigma$, in steps of 2.

We extracted the spectrum from a circular region of radius $\sim$ $1\hbox{$^\prime$ }$ centred on the excess. This spectrum unfortunately does not contain sufficiently strong line emission for a redshift estimate, so we fitted using a MEKAL model with the same redshift as A1413, absorbed with the galactic column density toward the cluster ( $2.19 \times 10^{20}$ cm^-2 from Dickey & Lockman 1990). We find $kT = 3.1~\rm keV$. An overlay of the significance contours on the DSS plate of the image did not reveal any obvious sources associated with the excess, and a hardness ratio map did not reveal any interaction with the main cluster. Our tentative conclusion is that the source is either a foreground or background cluster: deeper optical observations of the region should resolve the issue.