4.5 Cluster morphology
4.5.1 X-ray morphology
Following the work of Cassano et al. (2010), we use three parameters to estimate the level of substructure in J0256 from theXMM-Newtoncombined EPIC image shown in Figure 4.8. This image is produced by following the ESA reduction thread for extended X-ray sources2 and is both exposure-corrected and background-subtracted. To determine the measurement uncertainty on each of our parameters, we adopt the simulation method of B¨ohringer et al. (2010) whereby a Poisson resampled X-ray image is used to compute the standard deviation of a parameter mea- surement, which is then used to estimate the measurement uncertainty.
4.5.1.1 Concentration parameter,cSB
The concentration parameter, proposed by Santos et al. (2008) as a probe of cluster substructure, is the ratio of the cluster core and the larger-scale X-ray surface brightnesses. We calculate the concentration parameter as
cSB = S(<100kpc)
S(<500kpc), (4.3)
whereSis the X-ray surface brightness within a particular radius, centred on the X-ray peak. Be- fore calculatingcSB, we smooth the X-ray image using a Gaussian filter with a standard deviation ofσ = 3. We determine a value ofcSB = 0.16±0.12for J0256.
4.5.1.2 Centroid shift,w
Poole et al. (2006) show that, compared to other X-ray morphological estimators, the centroid shift is the most sensitive to cluster dynamical state and least sensitive to cluster image noise. It is defined as the rms deviation of the projected separation between the X-ray peak and the centre of mass in units of the aperture radius,Rap, computed in a series of concentric circular apertures centred on the cluster X-ray peak (Mohr et al., 1993; O’Hara et al., 2006; Maughan et al., 2008).
2http://xmm.esac.esa.int/sas/current/documentation/threads/esasimage_
thread.shtml
Following Cassano et al. (2010), the aperture radius is decreased in steps of 5% from a maximum aperture of radiusRap = 500kpc to 0.05Rap. We compute the centroid shift as
w=
"
1 N −1
X
i
(∆i− h∆i)2
#1/2
× 1
Rap, (4.4)
where∆i is the distance between the X-ray peak and the centroid of theith aperture. Following Poole et al. (2006) we excise the central 30 kpc around the X-ray peak when determining the centroid so as to reduce the bias towards a central core. We measure a value ofw= 0.054±0.005 for J0256.
4.5.1.3 Power ratio,P3/P0
The power ratio of a cluster is calculated using a multipole decomposition of the potential of the two-dimensional projected mass distribution. The idea of using the power ratio of the X- ray surface brightness to probe the underlying mass distribution was first introduced by Buote and Tsai (1995) and has since been widely used as an indication of substructure within a cluster (Jeltema et al., 2005; Ventimiglia et al., 2008; B¨ohringer et al., 2010; Cassano et al., 2010).
The multipole moments are determined as follows:
P0 = [a0ln (Rap)]2, (4.5) Pm = 1
2m2R2map a2m+b2m
, (4.6)
where Rap is the radius of the aperture within which the moments are computed. We use an aperture of radiusRap = 500 kpc centred on the X-ray cluster centroid. The parametersam and bm are determined using:
am(R) = Z
R06Rap
S(x0)R0mcosmφ0d2x0 (4.7) and
bm(R) = Z
R06Rap
S(x0)R0msinmφ0d2x0. (4.8)
As X-ray images are pixelised, the integral in equations 4.7 and 4.8 becomes a sum over all pixels, labelled by(x, y), within the radiusRap, whereS(x, y)is the surface brightness in that pixel. The zeroth momenta0given in equation 4.5 is thus the total X-ray intensity insideRap.
We use the normalised hexapole moment, P3/P0, which is the lowest power ratio moment providing a clear measure of substructure (B¨ohringer et al., 2010). For J0256, we calculate a value ofP3/P0 = (10.0±11.7)×10−6.
4.5.1.4 Comparison with the literature
Using the methods described in sections 4.5.1.1–4.5.1.3, Cassano et al. (2010) study the morpho- logical parameters for all clusters in the GMRT Radio Halo Survey (Venturi et al., 2007, 2008) and find a link between cluster dynamical state and the presence of a radio halo. They define a cluster to be dynamically disturbed if its morphological parameters satisfy the following condi- tions: cSB <0.2,w > 0.012andP3/P0 > 1.2×10−7. The majority of dynamically disturbed clusters are found to show radio halo emission. All of the parameter values we determine in our analysis of J0256 (cSB = 0.16±0.12,w = 0.054±0.005andP3/P0 = (10.0±11.7)×10−6) satisfy the above conditions for a merging cluster.
However, the X-ray parameters in the literature are calculated using images from Chandra, which has a significantly higher resolution compared toXMM-Newton. To investigate the effect of the different telescope properties on the morphological parameters, we select a cluster, A2631, with archival data from both instruments and create exposure-corrected, background subtracted images from each telescope. We compute the morphological parameters for each image over a range of resolutions and find that the power ratio from theXMM-Newton image is up to five times larger than that from theChandraimage, whereas the other two parameters are compara- ble between images. By convolving the images to the same resolution, all parameters are now consistent within the error bars. We thus conclude that our power ratio measurement for J0256 should be taken as an upper limit, as we’d expect the result to decrease if we viewed the clus- ter with Chandra resolution. Nevertheless, a visual inspection of the X-ray image does suggest distinct substructure and if we reduce the measured J0256P3/P0 value by the maximal factor of
−3000 −2000 −1000 0 1000 2000 3000 Velocity (km/s)
0 2 4 6 8 10 12 14 16
Counts
0.350 0.355 0.360 Redshift0.365 0.370 0.375
Figure 4.9: Histogram showing the redshift distribution for 78 spectroscopically confirmed cluster members. Here v = 0 is defined as the cluster systemic redshift of z = 0.363, and the bin width is 420 km s−1. A bimodal fit of two Gaussians, defined by the thick red (main component; µ = 0.361 ± 0.001, σ = 0.004 ± 0.001) and thin blue (subcluster;
µ = 0.369 ±0.002, σ = 0.003± 0.001) curves, is shown as the dotted black curve. A sin- gle Gaussian fit (µ = 0.363 ±0.002, σ = 0.005 ±0.001) is shown by the dot-dashed black curve. The vertical thick red (thin blue) dashed line shows the velocity of the BCG for the main (subcluster) component.
five, as found with our test cluster, the value is still in the “disturbed” region of the parameter space.