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Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains  

David James Pascoe   Submitted: 2017-09-28 04:32

Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.

Authors: D. J. Pascoe, C. R. Goddard, and V. M. Nakariakov
Projects: None

Publication Status: ApJL (accepted)
Last Modified: 2017-09-29 11:04
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Seismology of contracting and expanding coronal loops using damping of kink oscillations by mode coupling  

David James Pascoe   Submitted: 2017-08-22 06:01

We extend recently developed seismological methods to analyse oscillating loops which feature a large initial shift in the equilibrium position and investigate additional observational signatures related to the loop environment and oscillation driver. We model the motion of coronal loops as a kink oscillation damped by mode coupling, accounting for any change in loop length and the possible presence of parallel harmonics in addition to the fundamental mode. We apply our model to a loop which rapidly contracts due to a post-flare implosion (SOL2012-03-09) and a loop with a large lateral displacement (SOL2012-10-20). The seismological method is used to calculate plasma parameters of the oscillating loops including the transverse density profile, magnetic field strength, and phase mixing timescale. For SOL2012-03-09 the period of oscillation has a linear correlation with the contracting motion and suggests the kink speed remains constant during the oscillation. The implosion excitation mechanism is found to be associated with an absence of additional parallel harmonics. The improved Bayesian analysis of the coronal loop motion allows for accurate seismology of plasma parameters and the evolution of the period of oscillation compared with the background trend can be used to distinguish between loop motions in the plane of the loop or perpendicular to it. The seismologically inferred kink speed and density contrast imply sub-Alfvénic (MA = 0.16 ± 0.03) propagation of the magnetic reconfiguration associated with the implosion, as opposed to triggering by a wave propagating at the Alfvén speed.

Authors: D.J. Pascoe, A.J.B. Russell, S.A. Anfinogentov, P.J.A. Simões, C.R. Goddard, V.M. Nakariakov, L. Fletcher
Projects: SDO-AIA

Publication Status: A&A (in press)
Last Modified: 2017-08-23 12:50
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Coronal loop seismology using damping of standing kink oscillations by mode coupling II. additional physical effects and Bayesian analysis  

David James Pascoe   Submitted: 2017-01-19 01:29

The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling. Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.

Authors: D. J. Pascoe, S. Anfinogentov, G. Nistico, C. R. Goddard, and V. M. Nakariakov
Projects: SDO-AIA

Publication Status: A&A (accepted)
Last Modified: 2017-01-19 13:31
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Standing sausage modes in curved coronal slabs  

David James Pascoe   Submitted: 2016-08-01 04:07

Magnetohydrodynamic waveguides such as dense coronal loops can support standing modes. The ratios of the periods of oscillations for different longitudinal harmonics depend on the dispersive nature of the waveguide and so may be used as a seismological tool to determine coronal parameters. We extend models of standing sausage modes in low β coronal loops to include the effects of loop curvature. The behaviour of standing sausage modes in this geometry is used to explain the properties of observed oscillations which cannot be accounted for using straight loop models. We perform 2D numerical simulations of an oscillating coronal loop, modelled as a dense slab embedded in a potential magnetic field. The loop is field-aligned and so experiences expansion with height in addition to being curved. Standing sausage modes are excited by compressive perturbations of the loop and their properties are studied. The spatial profiles of standing sausage modes are found to be modified by the expanding loop geometry typical for flaring loops and modelled by a potential magnetic field in our simulations. Longitudinal harmonics of order n > 1 have antinodes which are shifted towards the loop apex and the amplitude of antinodes near the loop apex is smaller than those near the loop footpoints. We find that the observation of standing sausage modes by Nakariakov et al. (2003) is consistent with interpretation in terms of the global mode (n = 1) and third harmonic (n = 3). This interpretation accounts for the period ratio and spatial structure of the observed oscillations.

Authors: D. J. Pascoe and V. M. Nakariakov
Projects: Nobeyama Radioheliograph

Publication Status: A&A (in press)
Last Modified: 2016-08-02 13:36
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Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA  

David James Pascoe   Submitted: 2016-07-06 08:26

Aims. We consider a coronal loop kink oscillation observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics.
Methods. We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the detrended displacement is fitted as the sum of two damped sinusoids, having periods P1 and P2, and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs.
Results. We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P1 = 5.00 ± 0.62 minutes, P2 = 2.20 ± 0.23 minutes, P1/2P2 = 1.15 ± 0.22, and τ / P = 3.35 ± 1.45.

Authors: D. J. Pascoe, C. R. Goddard, and V. M. Nakariakov
Projects: SDO-AIA

Publication Status: A&A (in press)
Last Modified: 2016-07-06 10:35
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Numerical simulations for MHD coronal seismology  

David James Pascoe   Submitted: 2014-07-09 07:50

Magnetohydrodynamic (MHD) processes are important for the transfer of energy over large scales in plasmas and so are essential to understanding most forms of dynamical activity in the solar atmosphere. The introduction of transverse structuring into models for the corona modifies the behavior of MHD waves through processes such as dispersion and mode coupling. Exploiting our understanding of MHD waves with the diagnostic tool of coronal seismology relies upon the development of sufficiently detailed models to account for all the features in observations. The development of realistic models appropriate for highly structured and dynamical plasmas is often beyond the domain of simple mathematical analysis and so numerical methods are employed. This paper reviews recent numerical results for seismology of the solar corona using MHD.

Authors: Pascoe, D. J.
Projects: None

Publication Status: RAA (published)
Last Modified: 2014-07-09 13:41
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Fast magnetoacoustic wave trains in magnetic funnels of the solar corona  

David James Pascoe   Submitted: 2013-10-31 21:01

Fast magnetoacoustic waves are highly dispersive in waveguides and so can generate quasi-periodic wave trains if a localised, impulsive driver is applied. Such wave trains have been observed in the solar corona and may be of use as a seismological tool since they depend upon the plasma structuring perpendicular to the direction of propagation. We extend existing models of magnetoacoustic waveguides to consider the effects of an expanding magnetic field. The funnel geometry employed includes a field-aligned density structure. We perform 2D numerical simulations of impulsively generated fast magnetoacoustic perturbations. The effects of the density contrast ratio, density stratification, and spectral profile of the driver upon the excited wave trains are investigated. The density structure acts as a dispersive waveguide for fast magnetoacoustic waves and generates a quasi-periodic wave train similar to previous models. The funnel geometry leads to the generation of additional wave trains which propagate outside the density structure. These newly discovered wave trains are formed by the leakage of transverse perturbations but propagate upwards due to refraction caused by the magnetic funnel. The results of our funnel model may be applicable to wave trains observed propagating in the solar corona which demonstrate similar properties to those found in our simulations.

Authors: D. J. Pascoe, V. M. Nakariakov, and E. G. Kupriyanova
Projects: None

Publication Status: A&A (accepted)
Last Modified: 2013-11-01 09:06
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Damping of Kink Waves by Mode Coupling II. Parametric Study and Seismology  

David James Pascoe   Submitted: 2013-01-18 08:30

Context. Recent observations of the corona reveal ubiquitous transverse velocity perturbations that undergo strong damping as they propagate. These can be understood in terms of propagating kink waves that undergo mode coupling in inhomogeneous regions. Aims. The use of these propagating waves as a seismological tool for the investigation of the solar corona depends upon an accurate understanding of how the mode coupling behaviour is determined by local plasma parameters. Previous work (Pascoe et al. 2012) suggests the exponential spatial damping profile provides a poor description of the behaviour of strongly damped kink waves. We aim to investigate the spatial damping profile in detail and provide a guide to the approximations most suitable for performing seismological inversions. Methods. We propose a general spatial damping profile based on analytical results that accounts for the initial Gaussian stage of damped kink waves as well as the asymptotic exponential stage considered by previous authors. The applicability of this profile is demonstrated by a full parametric study of the relevant physical parameters. The implication of this profile for seismological inversions is investigated. Results. The Gaussian damping profile is found to be most suitable for application as a seismological tool for observations of oscillations in loops with a low density contrast. This profile also provides accurate estimates for data in which only a few wavelengths or periods are observed.

Authors: Pascoe, D.J., Hood, A.W., De Moortel, and Wright, A.N.
Projects: None

Publication Status: Accepted by A&A
Last Modified: 2013-01-18 11:59
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Damping of Kink Waves by Mode Coupling I. Analytical Treatment  

David James Pascoe   Submitted: 2013-01-18 08:27

Aims. To investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented. Methods. The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple differential-integral equation was used. Approximate analytical solutions to this equation are presented. Results. For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional to (1 + exp(-z^2/Lg^2))/2, where Lg^2 = 16/(ε κ^2 k^2). Although the actual value of 16 in Lg depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough.

Authors: Hood, A.W., Ruderman, M.S., Pascoe, D.J., De Moortel, I., Terradas, J., and Wright, A.N.
Projects: None

Publication Status: Accepted by A&A
Last Modified: 2013-01-18 12:00
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Abstracts by Author
Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains
Seismology of contracting and expanding coronal loops using damping of kink oscillations by mode coupling
Coronal loop seismology using damping of standing kink oscillations by mode coupling II. additional physical effects and Bayesian analysis
Standing sausage modes in curved coronal slabs
Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA
Numerical simulations for MHD coronal seismology
Fast magnetoacoustic wave trains in magnetic funnels of the solar corona
Damping of Kink Waves by Mode Coupling II. Parametric Study and Seismology
Damping of Kink Waves by Mode Coupling I. Analytical Treatment

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