The surrounding cluster

Finally, we discuss the gross properties of the ICM emission. We extracted a spectrum from a region centered on 3C 401 with an extraction radius of 32arcsec (108kpc). A background spectrum was formed from blank sky observations. After background subtraction, this spectrum possesses 3360 photons. After binning the spectrum to at least 15 photons per energy bin, we fit the 0.5-8keV spectral data with a thermal plasma model modified for the effects of Galactic and instrumental absorption (as discussed in Section 3.3). The best fit parameters are: plasma temperature $kT=2.9\pm 0.3{\rm\thinspace keV}$, plasma abundance $Z=0.43^{+0.20}_{-0.16}\,Z_\odot$, observed 0.5-10keV flux $F_{0.5-10}=3.7\times 10^{-13}\hbox{${\rm\thinspace erg}{\rm\thinspace cm}^{-2}{\rm\thinspace s}^{-1}\,$}$, and intrinsic (unabsorbed) 0.5-10keV luminosity $L_{0.5-10}=5.6\times 10^{43}\hbox{${\rm\thinspace erg}{\rm\thinspace s}^{-1}\,$}$, with a goodness of fit parameter $\chi^2/{\rm dof}=116/120$. The emission measure (EM) for this plasma is measured to be $EM=4.3\times 10^{66}\hbox{${\rm\thinspace cm}^{-3}\,$}$.

It is also interesting to examine the spatial structure of the cluster. By combining the two radial surface brightness profiles discussed in Section 3.2 (also Fig. 3) we have produced the azimuthally-averaged surface brightness profile. To this profile, we fit a standard $\beta$-model in which the surface brightness is given by

$$S(r)=\frac{S_0}{\left[1+(r/r_0)\right]^{3\beta-1/2}}.$$ 1

In a free fit, we obtain $r_0=36\pm 8{\rm\thinspace kpc}$ and $\beta=0.46^{+0.03}_{-0.02}$ ($\chi^2=11.4$ for 17 degrees of freedom). This is a rather flat density profile and small core radius for such a cluster to possess. If we fix $\beta=0.67$, the canonical value measured in rich clusters of galaxies, the fit is substantially worse ($\chi^2=80$ for 18 degrees of freedom) due to a underprediction of surface brightness at the smallest radii ($<5\arcsec$) and largest radii ($>30\arcsec$) and an overprediction of the surface brightness in the range 10-20arcsec.

Inverting eqn. 1 to give the radial dependence of the volume emissivity, and normalizing using the value of $EM$ determined from the spectral fit allows us to deduce the approximate radial run of density $n(r)$ and pressure $p(r)$ (assuming that the ICM is isothermal with $kT=2.9{\rm\thinspace keV}$). The result of this exercise is

Knowing the absolute values of density and pressure is essential for examining the energetics of the radio-galaxy interaction, a topic that we shall address in the next Section.

We finish our discussion of surface brightness profiles by returning to the issue of the large scale spurs or cross-like structure noted in the adaptively smoothed surface brightness map (Fig. 1). Due to the four-fold symmetry, we do not expect these features to be clearly revealed in the quadrant analysis presented above. To examine a putative structure with four-fold symmetry requires that we perform the following tailored surface brightness profile analysis. We divide the image plane into eight equal and non-overlapping 45degree sectors centered on the core of 3C 401. This ``wheel'' of sectors is aligned so that the radio-axis of 3C 401 lies on the mid-line of one back-to-back pair of sectors. We then form an average radial surface brightness profile using the four (alternating) sectors that lie either along or perpendicular to the radio axis (Fig. b; dashed line). The adaptively smoothed image suggests that these sectors should coincide with the four spurs of the cross-like structure. We compare this with the average radial surface brightness profile using the other four sectors which, according to the adaptively smoothed image, should lie in the inter-spur gaps (Fig. b; solid line). This analysis reveals a clear excess of counts in the on-spur surface brightness profile as compared with the off-spur case at radii of 20-50arcsec (70-170kpc). Thus, we conclude that the cross-like structure is not an artefact of the adaptive smoothing.