Morphological Appearance

Figure 1a shows an adaptively smoothed image of the central 3 arcmin of A4059. Overlayed is the 8GHz image by (Taylor et al., 1994, , hereafter T94). While the large scale emission appears smooth (probably due to the larger smoothing length used by the csmooth algorithm), the core of A4059 is not relaxed: it is double peaked with one peak at the cluster center and the other 15arcsec south-west of the center. The smoothed image reveals a distorted hour-glass like structure (yellow regions in Fig. 1a), centered on the nucleus and oriented perpendicular to the radio axis.

Figure 1: ACIS-S image of A4059. Left panel: adaptively smoothed image of $c_{1}$ in units of $10^{-8}\ {\rm cts\ cm^{-2}\ pixel^{-1}\ s^{-1}}$ (significance $5-6\sigma$, $0.492\arcsec$ per pixel) with contours of 8GHz flux (from T94) and contours for statistical evaluation of cavities (§2.2). Right panel: adaptively smoothed representation of the central region (smoothed to $3-4\sigma$ significance, same units) and 8 GHz radio contours.

The most interesting detail of the X-ray image are the two X-ray holes already noticed by HS, clearly visible in the 5-sigma smoothed image. The higher quality CXO image confirms that these are real local brightness minima, not just a visual effect caused by a bright central bar perpendicular to the cluster elongation. A noticeable offset exists between the nucleus and the axis between the cavity centers, with the nucleus being shifted to the south-west by $\sim 12\arcsec$ from this axis. The cavity centers are roughly $50\arcsec$ apart.

To assess the significance of the cavities we extracted an azimuthally averaged radial surface brightness profile of the central region, excluding the cavity regions shown in Fig. 1a (a by-eye approximation) and calculated the expected surface brightness in the two cavities. Based on this estimate, the NW and SE cavities are significant to 26 and 5.3 sigma, respectively. However, because the central region of A4059 is strongly perturbed (roughly inward of 1 arcmin from the center), it is difficult to make a rigorous statement concerning the significance of the cavities this way.

However, the outer regions of the cluster appear relaxed. As an alternative method, we took radial surface brightness profiles from the combined SE- and NW quadrants and the combined SW-NE quadrants. As a first order correction for cluster ellipticity we shifted the radial SW-NE profile outward by a factor of 1.13, producing a good match at large radii with the SE-NW profile. Because the temperature at large $r$ is relatively uniform, we used an isothermal $\beta$-model to fit the surface brightness, which represents the outer cluster very well. Because the inner cluster regions are not well represented by a $\beta$-model, we only used points further than 60 arcsec from the center for the fit ($r_{\rm c} \sim 50\arcsec$, $\beta=0.52$, $\chi^{2}/dof=59/43=1.4$).

We then compared the flux measured inside the cavity contours in Fig. 1a to that expected from the $\beta$-model. The NW cavity has 33 sigma significance compared to the best fit $\beta$-model, while the less pronounced SE cavity has 13 sigma significance. Forcing the $\beta$-model normalization to be consistent with the observed cavity flux increases the reduced chisquare of the fit by a factor of 2.7 (NW cavity) and 1.9 (SE cavity), corresponding to a significance of 8.5 and 6 respectively.

The radio overlay in Fig. 1a shows that the 8GHz radio lobes are only partly coincident with the cavities. The NW lobe covers a good fraction of the NW cavity. The SE lobe is much smaller than the northern lobe and not spatially coincident with the SE cavity. We note, however, that low-frequency radio observations sensitive to spatial scales of $0.1-1$arcmin, which might reveal the full extent of the radio lobes, do not yet exist.

The central peak contains interesting sub-structure (Fig. 1b., smoothed to a S/N of 3-4). The brightest sub peak, which is well resolved by CXO and has a diameter of 3-4$\sim$ 3-4kpc, is coincident with the core of PKS 2354-35 (within the CXO pointing accuracy) and could be emission from the hot interstellar medium of the central galaxy. The three sub-peaks are located around a local brightness minimum. Our hardness ratio analysis (§2.3) suggests that this minimum is due to lack of emission rather than intervening absorption. The close correspondence between these peaks and the SE radio lobe suggests that this substructure might be caused by on-going interaction.