Fixing model parameters

The absorbing column density was fixed at 1.64 × 1020atoms/cm−2(based on previous observations) as well as the redshift at 0.342. The elemental abundance for the thermal component was left as a free pa- rameter and fitted to the unshocked region, however the 3σ confidence interval was much too broad for the best fit value and un-physical. Therefore an abundance of 0.3×solar was chosen, since the expected value for cluster environments is 0.3-0.5× solar (Mushotzky et al., 1978; Mushotzky, 1984). Values of 0.5 and 0.7 ×solar were also tested, although varying results were obtained between both lobes (statistics improved for the western lobe for increasing abundance, while the opposite was true for eastern lobe). A fixed abundance of 0.3× solar was therefore used, as there is no a priori reason to use other values. The only free parameters for the thermal model were the temperature and thermal normalisation. The best fit values for these parameters were then used, by fitting them to both the shocked and un-shocked regions, to test the shock conditions. To check the consistency of the APEC model, a thermal mekal model was also fitted. This is a similar model to APEC in that it models the spectra from hot diffuse gas, but also incorporates line emission from several components. Similar statistics for this model were obtained, giving further confidence to the application of the APEC model.

A power-law component theoretically should have better fit statistics near the core of the cluster at the location of the radio galaxy, since we would expect a non-thermal emission contribution due to Inverse- Compton scattering and/or Synchrotron Self-Compton scattering. An absorbed thermal + power-law model was therefore fitted to the shocked region, with a fixed shock temperature from the previous tem- perature only fit. The data were an acceptable fit with a χ2∼0.9 and a similar normalisation to the temperature only fit (see Table 2.3), although the power law normalisation was consistent with zero and therefore an absorbed thermal component only was considered for the shocked region.

Further regions were also created at the location of the lobes (aided by overlaying the JVLA L-band radio contours of 3C320 over the Chandra X-ray data) with an off-source background and fitted with the various models. The power-law fit gave significantly better fit results for the lobes than a power law + thermal model and only a thermal model. The fitted steep photon index of γ ∼ 2.0 for the lobes of 3C320 agrees with that obtained for Suzaku X-ray satellite observations of Centaurus A (Stawarz et al. 2013). The fit statistics for a power-law model also agree with the expectation that there is predominantly non- thermal emission from the lobes. Consequently I also tested the shock region masking out the lobes and fitting a thermal model, which we would expect to yield better results if the lobes do indeed contain predominantly non-thermal material. However, I do not include these results here since masking out the lobe regions removes a significant amount of cluster emission through the line-of-sight, and therefore this region was subsequently discarded from my results. Note that the fit statistics with the mekal model were more or less similar to those with the APEC model, and subsequently the mekal model fitting was

dropped.

On a physical basis however, there may be a component of thermal emission in the lobes, as detected for the lobes of Centaurus A by Stawarz et al. (2013). Furthermore, it is difficult to entirely remove thermal foreground cluster emission in front of the lobes using only background subtraction. Therefore a power law plus thermal model is expected to provide the best physical description of the lobe region. Tests were made prior to this fit with the absorbed power-law plus thermal model component, but with a fixed photon index for a range of photon indices to see whether a variation in photon power-law index would give varying results for the other parameters. The other parameters such as temperature and thermal normalisation were also left free. Photon indices of γ = 1.5, 1.75 and 2.0 were used to fit to the spectrum of the lobes. The corresponding results are shown in Table 2.6. Then, the fits were made using a single fixed photon index of 1.75, corresponding to a synchrotron injection index of 0.75. This was a reasonable assumption to make since, as seen in Table 2.6, a change in the photon indices did not produce a significant difference in the fit statistics or the values of the fitted parameter. Furthermore, the lobe temperatures were fixed at the shocked temperature of kT = 3.560 from Table 2.3. These fit results are shown in Table 2.7, and were used to detect an inverse-Component component in the lobes—explained in Section 2.7.5.

TABLE2.3: Statistics, fitted parameters and calculated parameters for tight shock regions.

Region χ_red2 kT (keV) Norm (×10−4) ne (×102cm−3) Vol (×1070cm3) Pressure (×10−11Pa) Off-source background 1.006 3.569+0.502_−0.409 2.683+0.154_−0.150 1.84 ± 0.0521 2.033 2.364 ± 0.312 Tight on-source background 0.841 3.488+0.700_−0.542 2.138+0.176_−0.164 1.64 ± 0.0652 2.033 2.059 ± 0.375 Loose on-source background 0.885 3.560+0.553_−0.450 2.482+0.160_−0.153 1.77 ± 0.0560 2.033 2.268 ± 0.327

TABLE 2.4: Statistics, fitted parameters and calculated parameters for unshocked regions with tight shocked region masked and modelled as a cylinder. Note all background regions are taken as an annulus

just outside selected region.

Region χ_red2 kT (keV) Norm (×10−4) ne (×102cm−3) Vol (×1070cm3) Pressure (×10−11Pa) Circular 0.927 3.740+3.589_−1.460 0.573+0.131_−0.124 0.482 ± 0.0538 6.353 0.649 ± 0.427 Elliptical 1.031 2.773+2.260_−0.852 0.633+0.134_−0.136 0.428 ± 0.0456 8.890 ± 0.00295 0.427 ± 0.244

TABLE2.5: Statistics, fitted parameters and calculated parameters for lobe region fitted with an absorbed thermal APEC model. Note a circular on-source background region was taken in the vicinity of the

cluster emission (Figure 2.23).

Region χ_red2 kT (keV) Thermal norm (×10−5) Both lobes 0.613 3.384+0.923_−0.610 10.181+1.012_−0.999 Western 0.657 3.600+1.779_1.016 5.805+0.800_−0.731 Eastern 0.843 2.943+1.187_−0.756 4.383+0.669_−0.659

TABLE2.6: Statistics, fitted parameters and calculated parameters for lobe region fitted with a power- law plus thermal APEC model with fixed values of γ. γ is defined in the sense A(E) ∼ E−γ. Note a

circular on-source background region was taken (Figure 2.23).

Region χ_red2 γ PL norm (×10−5) kT (keV) Therm norm (×10−4) Both lobes 0.600 1.50 0.349+0.646 3.117+0.528_−0.762 0.851+0.149_−0.179 Both lobes 0.601 1.75 0.488+1.018 3.223+0.437_−0.652 0.815+0.188_−0.286 Both lobes 0.604 2.00 0.245+1.207 3.393+0.292_−0.260 0.885+0.123_−0.314 Eastern 0.915 1.50 0.000204+0.291 2.915+0.315_−0.795 0.449+0.0593_−0.0838 Eastern 0.915 1.75 0.00+0.445 2.912+0.332_−0.715 0.448+0.0590_−0.123 Eastern 0.915 2.00 0.00+0.557 2.911+0.361_0.451 0.448+0.0585_−0.157 Western 0.511 1.50 0.644+0.297 2.769+1.442_0.652 0.289+0.170_−0.107 Western 0.505 1.75 0.976+0.559_−0.931 3.317+0.931_−1.01 0.178+0.255_−0.134 Western 0.512 2.00 0.929+0.553 4.393+0.880_−0.771 0.178+0.282_−0.0900

TABLE 2.7: Statistics and fitted parameters for the east and west lobe regions fitted with an absorbed power-law plus thermal APEC model with fixed values of γ = 1.75, thermal abundance at 0.3× solar and the temperature at the shocked temperature of 3.560 keV from Table 2.3. γ is defined in the sense A(E) ∼ E−γ. Note that the power-law normalisation was set such that it returns the 1 keV flux density

in units of µJy.

Region χ_red2 PL norm (µ Jy) Therm norm (×10−4) Eastern 0.973 0.000+0.0022681 0.420+0.050_−0.176 Western 0.653 0.000771+0.00522 0.531+0.113_−0.531