The Standing Kink And Sausage Modes In Coronal Magnetic Slabs: The Effect Of Flow

Traditionally the primary means to measure the parameters of the solar atmosphere is via spectroscopic observations. However, with low-frequency oscillations and propagating waves abundantly observed, these parameters can also be inferred by interpreting measured wave parameters in the framework of Magnetohydrodynamic (MHD) theory. This practice constitutes the so-called "magneto-seismology", which has seen increasingly more interest in the solar physics community. On the other hand, multiple periodicities have been found in a number of oscillations, and their application to the inference of the longitudinal structuring of the solar atmosphere is becoming increasingly popular. Moreover, field-aligned flows abound in oscillating structures and they may reach the Alfvenic regime. It has been that shown these Alfvenic flows may substantially alter the magnetic field strength inferred seismologically. Will they also influence multiple periodicities, the period ratios between the fundamental and its overtones in particular? This is the focus of this thesis.We adopt a magnetized slab as our model of coronal loops. On the one hand, the results hence derived serve as a nice reference for the results derived for magnetized cylinders, as has been routinely seen in the literature. On the other hand, this allows us to directly deduce the flow effects by comparing our results with the only theoretical study on standing modes supported by slabs (Macnamara&Roberts2011, hereafter MR11) where the slabs are static. We examine the dispersion properties of propagating waves in an MHD system where a flowing slab is embedded in an otherwise uniform background, and present a simple graphical means to construct standing modes. By doing so we are able to systematically examine how the flow affects the period ratios for standing kink and sausage modes, the one between the fundamental and its first overtone P1/2P2in particular.Considering a general MHD environment with finite beta, we find that while the siphon flow enhances the dispersion of fast modes in general, it affects the kink and sausage modes to different extent. For standing kink modes, relative to the static case, P1/2P2may be reduced by up to23%due to the background flow. The minimum P1/2P2attains for significant flows may drop below the lower limit established analytically by MR11for static slabs. It is noteworthy that the effect of flow on P1/2P2may not be negligible even for thin slabs. For standing sausage modes, the changes to P1/2P2introduced by flow are not as significant. However, the flow does substantial influence the cutoff aspect ratio (d/L)cutoff below which no standing sausage modes are allowed:(d/L)cutoff may be several time larger than its static counterpart, thereby limiting detectable sausage modes to even wider slabs.Even though our approach applies to an MHD environment with an arbitrary beta, the effects of a finite temperature are found to be minimal for fast modes in a realistic solar corona. Hence we adopt a zero-beta MUD approach to climinate slow modes. and extend the previous results by examining even higher-order overtones, namely P1/nPn with n up to4. With beta being zero, the dispersion behavior of fast modes is determined by only two factors:the density contrast pe/po and Alfvenic Mach number Ma (measuring the internal flow speed in units of the internal Alfven speed). Similar to what we found for a finite-beta case, even when pe/po is large, the flow has a substantial effect on the period ratios. For the kink modes, the background flow may lower the period ratios by up to30%, and these ratios may readily fall below the analytically lower limits expected for static slabs. For sausage modes, once again the changes to the period ratios brought forth by the flow are not as significant. However, its presence may render the cutoff aspect ratio an order-of-magnitude larger than in the static case.We conclude that when substantial flow exists in an oscillating coronal structure, care has to be taken when one tries to exploit multiple periodicities, the period ratios between the fundamental and its overtones in particular, to infer the structuring information along or across magnetic structures.