Conclusion

Using [Yu et al.,2013] as the motivation we investigated the link between ZP ‘wig- gles’ (chapter 6) and propagating and standing fast modes in a coronal loop using analytical and numerical techniques. The results presented in this chapter clearly indicate that ZPs are strongly affected by the presence of magnetoacoustic waves, in particular the fast sausage mode. This link was first shown in the analytically de- rived ZP shown in section5.2where we derived the perturbed density and magnetic field for a fast mode in the loop context.

The ZP was constructed using the DPR mechanism and the analytically de- rived density and magnetic field perturbations. Figure5.5clearly shows the periodic

modification of the simulated zebra pattern in the presence of fast magnetoacous- tic waves. This was an indication of the manifestation of the fast mode in the ZP emission region.

With this clear result we decided to underpin the result by carrying out the same investigation using numerical techniques. We approached the problem system- atically by starting with a 1D static toy model (section5.3.1). This proved useful as we were able to recreate the 1D results for the DPR emission mechanism presented in [Chernov, 2006]. An extended source region was observed for DPR emission, thus we have shown that numerical analysis could reproduce observational results with a relatively simple model. Moreover, we demonstrated that high frequency ZP may have a low-frequency counterpart that should be looked for in the data, e.g. obtained with LOFAR or spacebourne radiospectrometers.

A 2D study was the logical next step, which came with a higher degree of complexity in balancing magnetic and thermal pressures under magnetostatic equilibrium. We were successfully able to reconstruct a magnetic field which would maintain equilibrium from an input pressure distribution. The pressure distribution was converted tofpevia (1.1), while the magnetic field was used to create the spacial

structure of fce field via (1.2) for each s harmonic. The two spatial distributions

were then cross-referenced for regions which satisfied the DPR conditions outlined by equations 5.26 and 5.27. The results showed an extended source region along the loop. ZP emission was found to be produced in the foot points and along the transverse slopes of the loop which was not observed by [Chen et al., 2011]. We speculate that radio emission from low altitude regions of the coronal loop may be reabsorbed before reaching an optically thin region. The frequency and spatial ranges of obtained simulated ZPs have been compared to [Chen et al., 2011] and [Yu et al., 2013] in table 5.2. The simple 1D static model seems to underestimate the maximum height of the ZP emission which implies that a 1D magnetic topology is not sufficient to capture the full extent of the ZP. ZP emission is seen along the entire length in all the 2D loop models. This implies the maximum emission height is limited by the loop length. If we take the loop value of 235 Mm from [Chen et al., 2011] we arrive at the same upper bound on heights where ZPs are created. The emission frequencies are scaled by electron density that has a fairly large range of values in coronal loops. We used an average value of 1011 _cm−3 _for our simulations, [Aschwanden, 2006], however this does leave some uncertainty in the frequency ranges.

Having successfully reproduced ZP emission regions and frequencies in a time independent system we moved to follow its evolution in the presence of magnetoa-

coustic fluctuations using a dynamic model. Section 5.3.2 successfully implements the use of Lare2D numerical MHD code to produce a stable 2D loop. A frame by frame approach allowed for the methodology from the section 5.3.1 to be used. A dynamic ZP spectrum was produced from the emission frequencies found using the DPR mechanism at each instant of time for both standing and propagating fast waves.

The resultant ZP by a visual inspection closely matched the observed wiggles in [Yu et al.,2013]. The standing mode produced a more closely matching spectra than propagating.

As a secondary check we compared analytical and numerical transverse ve- locity profiles, figures 5.3 and 5.14. They were in strong agreement concluding that both analytical and numerical studies yielded the manipulation of ZPs in the presence MHD disturbances such as the fast wave.

Finally we compared the oscillation periods of the reproduced ZP wiggles. We found that periodicity analysis of the simulated zebra pattern (figure 5.5) re- vealed that the wiggle period for the simulations was approximately PN = 0.3 s for

both propagating and standing fast wave disturbances. This was the same order of magnitude as that found analytically in the previous chapter withPA≈3PN where

PAis the analytical period. These periods also correspond to the 1 s experimentally

observed period for the ZP wiggles, [Yu et al.,2013].

So to conclude this chapter, we have successfully shown that a standing sausage magnetoacoustic oscillation in a coronal loop is most likely responsible for the wiggles found in ZP emission in [Yu et al., 2013]. We have confirmed this both numerically and analytically. However it is important to highlight that all the results presented in this chapter are model dependent, particularly the results outline in table5.2. Many approximations have been made to the simulations due to the complex nature of coronal loop modelling. This was manifest by the variety of magnetic field and density profiles used. We have also not accounted for the change in plasma parameters seen in the chromosphere, instead only focusing on coronal values. Thus results pertaining to this region are not physically founded. The variety in the assumptions made in these models could provide an explanation for the diversity of model predictions shown in table5.2. Which in turn is an indication that the modelling used in this thesis has not fully captured the complexity of a coronal loop. However, with new experimental techniques becoming available, a future avenue of work would be to reconcile these coronal and chromospheric models with newly available experimental data to gain a better understanding of loop geometry and ZP themselves.

Importantly, we have shown that both loop geometry and wave propagation have an equal part to play in ZP evolution. We can consider these results as a good starting point to explore more detailed and realistic simulations in the future which can then be compared to new experimental observations.