Collective Wave Modes In Transversally Nonuniform Magnetic Structures In The Sun’s Atmosphere

With the advent of SOHO, TRACE, Hinode, and SDO, a rich variety of low-frequency waves and oscillations have been identified in the highly structured solar atmosphere. When combined with a refined theoretical understanding of the collective Magnetohydrodynamic waves hosted by magnetized structures, the measurements of these waves and oscillations then enable the inference of some key physical parameters that prove difficult to measure directly. Among these parameters, the Alfven speeds and the information on the transverse density in-homogeneity have received much attention. However, as the starting point of the theories on collective waves, coronal structures are usually assumed to be stat-ic, their density often assumed to be transversally structured in a step-function fashion. This thesis examines, in a rather systematic manner, the effects of flow shear and continuous density structuring between coronal structures and their surroundings on a number of techniques in coronal seismology. The main result-s can be summarized as follows.1. We present the first systematic study on the effects of a flow shear on standing modes in magnetized loops, finding that a strong flow shear can significantly alter the period ratios of the fundamental kink mode to its harmonics, and it can substantially restrict the geometric sizes of the magnetic loops that can support trapped sausage modes.2. We present the first analytical description of fast collective waves in magnetic slabs with es-sentially arbitrary transverse density structuring. We find that the lowest-order kink modes are not significantly altered by the details of the transverse structur-ing, thereby lending support to their seismological applications based on simple theories with discontinuous transverse density profiles. However, sausage modes and higher-order kink modes are found to depend sensitively on how the density structuring is described.3. We present the first study on impulsively generated sausage waves in magnetic loops with arbitrary transverse density structuring. In contrast to the classical results, we find that some active region loops with diffuse boundaries may not support the existence of a quasi-periodic phase in wave signals. This has important implications on the observability of impulsive-ly generated waves. These findings are detailed as follows.Standing oscillations with multiple periods interpreted as the fundamental mode and its overtones were found in a number of magnetic loops in the solar at-mosphere. The ratio of the period of the fundamental to twice the one of its first overtone, P1/2P2, plays an important role in the applications of solar magneto-seismology. Chapter 2 presents a study on the effects of field-aligned flows on the period ratios of standing modes supported by solar magnetic cylinders. For coro-nal loops, the flow effects are significant for both fast kink and sausage modes. For kink ones, flows lead to a reduction in P1/2P2 by up to 17% relative to the static case even in the limit where the density contrast between the loop and its surroundings approaches infinity. For sausage modes, the reduction in P1/2P2 due to flow is typically ≤5.5% compared with the static case. However, the threshold aspect ratio, only above which can trapped sausage modes be support-ed, may increase dramatically with flow magnitude, leading to a new diagnostic tool for deducing the internal Alfven Mach number. For photospheric loops, the flow effect on P1/2P2 is not as strong. However, as applied to sausage modes, in-troducing field-aligned flows offers more possibilities in interpreting the multiple periods recently measured using imaging instruments. We conclude that the role of field-aligned flows should be taken into account for one to better understand multiple periodicities in oscillating signals in solar atmospheric structures.Compared with the cylindrical geometry, a slab one is more appropriate for describing a substantial number of waves and oscillations observed in some coro-nal structures. We examine in Chapter 3 the influence of a continuous density structuring transverse to coronal slabs on the dispersive properties of funda-mental standing kink and sausage modes supported therein. We derive generic dispersion relations (DRs) governing linear fast waves in pressureless straight s-labs with general transverse density distributions, and focus on the cases where the density inhomogeneity takes place in a layer of arbitrary width and in arbi-trary form. The physical relevance of the solutions to the DRs is demonstrated by the corresponding time-dependent computations. For all profiles examined, the lowest-order kink modes are trapped regardless of longitudinal wavenumber k. A continuous density distribution introduces a difference to their periods of ≤13% when k is in the observed range, relative to the case where the density profile takes a step-function form. Sausage modes and other branches of kink modes are leaky at small k, and their periods and damping times are heavily influenced by how the transverse density profile is prescribed, the lengthscale in particular. These modes have sufficiently high quality to be observable only for physical parameters representative of flare loops. We conclude that while the simpler DR pertinent to a step-function profile can be used for the lowest-order kink modes, the detailed information on the transverse density structuring needs to be incorporated into studies of sausage modes and higher-order kink modes.Quasi-periodic propagating disturbances have been seen in a considerable number of coronal structures as indicated by recent Extreme Ultra-violet, white-light, and radio observations. While intuitively speaking this quasi-periodicity has to do with quasi-periodicities in the wave sources, it is equally possible to be caused by an impulsive driver. In this latter scenario, the frequency dependence of the longitudinal group speed vgr is crucial for determining the temporal and spectral signatures of impulsively generated disturbances. Due to their strong dispersion, trapped sausage waves have received much attention. Previous stud-ies, in which density profiles transverse to coronal loops are in a step-function fashion, indicate that vgr always first decreases and then increases with angular frequency ω. This non-monotonical behavior in the vgr-ω curves is the physical cause of the quasi-periodic phase in the signals of impulsively generated sausage waves. However, little is known on how other density distributions may impact the group speed diagrams. To address this issue, Chapter 4 contrasts two contin-uous profiles, labeled "parabolic" and "linear", by capitalizing on our previous theoretical study on sausage waves in coronal tubes with general transverse den-sity profiles. Here two parameters are relevant, one being the density contrast between loops and their surroundings, the other being the transverse density lengthscale. For parabolic profiles, the group speed vgr shows a behavior similar to the step-function case, regardless of the density contrast and transverse length-scale. For linear profiles,vgr shows a much richer variety of ω dependence. For relatively short transverse lengthscales, the vgr-ω curves are qualitatively similar to the step-function case. However, for longer lengthscales (or equivalently, more diffuse coronal loops), the vgr-ω curves vary in a monotonic manner for density contrasts representative of active region loops, meaning that the quasi-periodic phase will no longer exist. For higher density contrasts, the ugr-ω curves may posses more than one extrema. Focusing on the cases where a local maximum exists in addition to a local minimum, we show that the temporal and spectral properties as well as the duration of the quasi-periodic phase are different from the step-function case. We conclude that our study offers a possible seismological technique of using the measured temporal and spectral variation of impulsively generated waves to distinguish between different density profiles and to deduce the transverse density lengthscale.