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Statistical seismology of transverse waves in the solar corona  

Erwin Verwichte   Submitted: 2013-02-28 01:37

Observations show that transverse oscillations occur commonly in solar coronal loops. The rapid damping of these waves has been attributed to resonant absorption. The oscillation characteristics carries information of the structuring of the corona. However, self-consistent seismological methods to extract information from individual oscillations is limited because there are less observables than model unknown parameters and the problem is underdetermined. Furthermore, it has been shown that one-to-one comparisons of the observed scaling of period and damping times with wave damping theories is misleading. We aim to investigate if seismological information can be gained from the observed scaling laws in a statistical sense. A statistical approach is used whereby scaling-laws are produced by forward modelling using distributions of values for key loop cross-sectional structuring parameters. We study two types of observations: 1) transverse loops oscillations as seen mainly with TRACE and SDO and 2) running transverse waves seen with CoMP. We demonstrate that the observed period-damping time scaling law does provide information about the physical damping mechanism, if observations are collected from as wide as possible range of periods and a comparison with theory is performed in a statistical sense. The distribution of the ratio of damping time over period, i.e. the quality factor, has been derived analytically and fitted to the observations. A minimum value for the quality factor of 0.65 has been found. From this, a constraint linking the ranges of possible values for the density contrast and inhomogeneity layer thickness is obtained for transverse loop oscillations. If the layer thickness is not constrained, then the density contrast is maximally equal to 3. For transverse waves seen by CoMP, it is found that the ratio of maximum to minimum values for these two parameters has to be less than 2.06. i.e. the sampled values for the layer thickness and Alfvén travel time comes from a relatively narrow distribution. Now that more and more transverse loop oscillations have been analysed, a statistical approach to coronal seismology becomes possible. Using the observed data cloud restrictions in the loop parameter space of density contrast and inhomogeneity layer thickness are found and surprisingly for the running waves narrow distributions for loop parameters have been found.

Authors: Verwichte, E., Van Doorsselaere, T., White, R.S. & Antolin, P.
Projects: SDO-AIA

Publication Status: accepted for publication in A&A
Last Modified: 2013-02-28 12:33
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Coronal Alfvén speed determination: consistency between seismology using AIA/SDO transverse loop oscillations and magnetic extrapolation  

Erwin Verwichte   Submitted: 2013-02-10 11:58

Two transversely oscillating coronal loops are investigated in detail during a flare on the 6th September 2011 using data from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We compare two independent methods to determine the Alfvén speed inside these loops. Through the period of oscillation and loop length information about the Alfvén speed inside each loop is deduced seismologically. This is compared with the Alfvén speed profiles deduced from magnetic extrapolation and spectral methods using AIA bandpass. We find that for both loops the two methods are consistent. Also, we find that the average Alfvén speed based on loop travel time is not necessarily a good measure to compare with the seismological result, which explains earlier reported discrepancies. Instead, the effect of density and magnetic stratification on the wave mode has to be taken into account. We discuss the implications of combining seismological, extrapolation and spectral methods in deducing the physical properties of coronal loops.

Authors: Verwichte, E., Van Doorsselaere, T., Foullon, C. & White R.S.
Projects: SDO-AIA

Publication Status: Accepted for publication in ApJ
Last Modified: 2013-02-10 11:58
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Periodic spectral line asymmetries in solar coronal structures from slow magnetoacoustic waves  

Erwin Verwichte   Submitted: 2010-09-17 11:24

Recent spectral observations of upward moving quasi-periodic intensity perturbations in solar coronal structures have shown evidence of periodic line asymmetries near their footpoints. These observations challenge the established interpretation of the intensity perturbations in terms of propagating slow magnetoacoustic waves. We show that slow waves inherently have a bias towards enhancement of emission in the blue wing of the emission line due to in-phase behaviour of velocity and density perturbations. We demonstrate that slow waves cause line asymmetries when the emission line is averaged over an oscillation period or when a quasi-static plasma component in the line-of-sight is included. Therefore, we conclude that slow magnetoacoustic waves remain a valid explanation for the observed quasi-periodic intensity perturbations.

Authors: Verwichte, E., Marsh, M., Foullon, C., Van Doorsselaere, T., De Moortel, I., Hood, A.W. and Nakariakov, V.M.
Projects: Hinode/EIS

Publication Status: accepted for publication in ApJL
Last Modified: 2010-09-18 13:46
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Spatial seismology of a large coronal loop arcade from TRACE & EIT observations of its transverse oscillations  

Erwin Verwichte   Submitted: 2010-05-10 12:54

We present a study of transverse loop oscillations in a large coronal loop arcade, using observations from the Transition Region And Coronal Explorer (TRACE) and Extreme-ultraviolet Imaging Telescope (EIT). For the first time we reveal the presence of long-period transverse oscillations with periods between 24 minutes and 3 hours. One loop bundle, 690 Mm long and with an oscillation period of 40 min., is analysed in detail and its oscillation characteristics are determined in an automated manner. The oscillation quality factor is similar to what has been found earlier for oscillations in much shorter loops. This indicates that the damping mechanism of transverse loop oscillations is independent of loop length or period. The displacement profile along the whole length of the oscillating loop is determined for the first time and consistently between TRACE and EIT. By comparing the observed profile with models of the three-dimensional geometry of the equilibrium and perturbed loop, we test the effect of longitudinal structuring (spatial seismology) and find that the observations cannot unambigiously distinguish between structuring and non-planarity of the equilibrium loop. Associated intensity variations with a similar periodicity are explained in terms of variations in the line of sight column depth. Also, we report intensity oscillations at the loop foot point, which are in anti-phase with respect to the intensity oscillations in the loop body. Lastly, this observation offers the first opportunity to use the transverse oscillations of the arcade to model the Alfvén speed profile in the global corona.

Authors: E. Verwichte, C. Foullon & T. Van Doorsselaere
Projects: SoHO-EIT,TRACE

Publication Status: ApJ, in press
Last Modified: 2010-05-11 07:11
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Self-Organisation of magnetoacoustic waves in a thermally unstable environment  

Erwin Verwichte   Submitted: 2010-02-22 05:35

The nonlinear evolution of magnetoacoustic waves in a nonadiabatic plasma are investigated analytically. The effect of plasma activity due to linear and quadratic heating and radiative cooling on propagating magnetoacoustic waves in a uniform plasma are considered. A nonlinear evolution equation is derived and stationary solutions are looked for the various combination of signs of the linear and quadratic heating-cooling terms, which determine the thermal activity of the plasma. It is shown that self-organizing magnetoacoustic waves (autowaves) exist in an active plasma. These wave have amplitudes that are independent from the initial conditions and function of plasma properties only. Their potential diagnostic purposes are discussed. Furthermore, magnetoacoustic auto-solitary waves are shown to exist. They have been modeled using a novel perturbative technique which allows to determine their propagation speed and shape.

Authors: Robert Chin, Erwin Verwichte, George Rowlands and Valery M. Nakariakov
Projects: None

Publication Status: in press
Last Modified: 2010-02-22 09:07
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Seismology of a large solar coronal loop from EUVI/STEREO observations of its transverse oscillation  

Erwin Verwichte   Submitted: 2009-03-24 13:50

The first analysis of a transverse loop oscillation observed by both STEREO spacecraft is presented, for an event on the 27th of June, 2007 as seen by the Extreme UltraViolet Imager (EUVI). The three-dimensional loop geometry is determined using a three-dimensional reconstruction with a semi-circular loop model, which allows for an accurate measurement of the loop length. The plane of wave polarisation is found from comparison with a simulated loop model and shows that the oscillation is a fundamental horizontally polarised fast magnetoacoustic kink mode. The oscillation is characterised using an automated method and the results from both spacecraft are found to match closely. The oscillation period is 630+-30 s and the damping time is 1000+-300 s. Also, clear intensity variations associated with the transverse loop oscillations are reported for the first time. They are shown to be caused by the effect of line-of-sight integration. The Alfvén speed and coronal magnetic field derived using coronal seismology are discussed. This study shows that EUVI/STEREO observations achieve an adequate accuracy for studying long-period, large amplitude transverse loop oscillations.

Authors: Verwichte, E., Aschwanden, M.J., Van Doorsselaere, T., Foullon, C. and Nakariakov, V.M.
Projects: STEREO

Publication Status: accepted for publication in ApJ
Last Modified: 2009-03-25 10:04
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Subject will be restored when possible  

Erwin Verwichte   Submitted: 2008-06-07 08:36

he damping of slow magnetoacoustic coronal loop oscillations by shock dissipation is investigated. Observations of large amplitude slow mode observations by SUMER show a clear dependency of the damping rate on the oscillation amplitude. Fully nonlinear MHD simulations of slow mode oscillations in the presence of thermal conduction are performed that show that shock dissipation is an important damping mechanism at large amplitudes, which enhances the damping rate by up to 50% above the rate given by thermal conduction alone. A comparison between the numerical simulations and the SUMER observations shows that, although the shock dissipation model can indeed produce an enhanced damping rate that is function of the oscillation amplitude, the found dependency is not as strong as that for the observations, even after considering observational corrections and the inclusion of enhanced linear dissipation.

Authors: Verwichte, E., Haynes, M., Arber, T.D. and Brady, C.S
Projects: SoHO-SUMER

Publication Status: Accepted for publication in ApJ
Last Modified: 2008-09-23 21:00
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Subject will be restored when possible  

Erwin Verwichte   Submitted: 2008-06-07 08:36

The damping of slow magnetoacoustic coronal loop oscillations by shock dissipation is investigated. Observations of large amplitude slow mode observations by SUMER show a clear dependency of the damping rate on the oscillation amplitude. Fully nonlinear MHD simulations of slow mode oscillations in the presence of thermal conduction are performed that show that shock dissipation is an important damping mechanism at large amplitudes, which enhances the damping rate by up to 50% above the rate given by thermal conduction alone. A comparison between the numerical simulations and the SUMER observations shows that, although the shock dissipation model can indeed produce an enhanced damping rate that is function of the oscillation amplitude, the found dependency is not as strong as that for the observations, even after considering observational corrections and the inclusion of enhanced linear dissipation.

Authors: Verwichte, E., Haynes, M., Arber, T.D. and Brady, C.S
Projects: SoHO-SUMER

Publication Status: Accepted for publication in ApJ
Last Modified: 2008-09-23 21:00
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Damping of slow MHD coronal loop oscillations by shocks  

Erwin Verwichte   Submitted: 2008-06-07 08:36

The damping of slow magnetoacoustic coronal loop oscillations by shock dissipation is investigated. Observations of large amplitude slow mode observations by SUMER show a clear dependency of the damping rate on the oscillation amplitude. Fully nonlinear MHD simulations of slow mode oscillations in the presence of thermal conduction are performed that show that shock dissipation is an important damping mechanism at large amplitudes, which enhances the damping rate by up to 50% above the rate given by thermal conduction alone. A comparison between the numerical simulations and the SUMER observations shows that, although the shock dissipation model can indeed produce an enhanced damping rate that is function of the oscillation amplitude, the found dependency is not as strong as that for the observations, even after considering observational corrections and the inclusion of enhanced linear dissipation.

Authors: Verwichte, E., Haynes, M., Arber, T.D. and Brady, C.S
Projects: SoHO-SUMER

Publication Status: Accepted for publication in ApJ
Last Modified: 2008-09-23 21:00
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Subject will be restored when possible  

Erwin Verwichte   Submitted: 2007-12-07 07:54

Aims. To establish the dominant wave modes generated by an internal, m = 1 kink instability in a short coronal flux tube . Methods. 3D MHD numerical simulations are performed using Lare3d to model the kink instability and the subsequent wave generation. The initial conditions are a straight, zero net current flux tube containing a twist higher than the kink instability threshold. Results. It is shown that the kink instability initially sets up a 1st harmonic (1st overtone) which is converted through the rearrangement of the magnetic field into two out of phase fundamental slow modes. These slow modes are in the two entwined flux tubes created during the kink instability. Conclusions. The long lived oscillations established after a kink instability provide a possible way to identify whether sudden short coronal loop brightenings may have resulted from a confined kink instability. The mode oscillation structure changes from 1st harmonic to fundamental due to field line relaxation. The subsequent decay of the fundamental mode is comparable with observations and is caused by shock dissipation. This result has important consequences for the damping of slow mode oscillations observed by SUMER

Authors: M. Haynes. T.D. Arber and E. Verwichte
Projects: None

Publication Status: accepted for publication in A&A
Last Modified: 2007-12-08 08:06
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Seismology of curved coronal loops with vertically polarised transverse oscillations  

Erwin Verwichte   Submitted: 2006-03-03 05:06

Using a model of vertically polarised fast magnetoacoustic waves in curved coronal loops, the method of coronal seismology is applied to observations of transverse loop oscillations. A coronal loop is modeled as a curved magnetic slab in the zero plasma-beta limit. For an arbitrary piece-wise continuous power law equilibrium density profile, the dispersion relation governing linear vertically polarised fast magnetoacoustic kink waves is derived. The ways in which this model can be used for coronal seismology are explored and applied to two observational examples. The Alfvén speed and equilibrium density profile are determined from observations. It is shown that the mechanism of lateral leakage of fast magnetoacoustic kink oscillations described in this model is efficient. In fact, the damping is so efficient that in order to match predicted values with observational ones, either the loop needs to be highly contrasted or the transverse Alfvén speed profile needs to be close to linear. Possible improvements to make the modeling of lateral wave leakage in loops more realistic, allowing a lower damping efficiency, are discussed.

Authors: E. Verwichte, C. Foullon and V.M. Nakariakov
Projects: TRACE

Publication Status: A&A, accepted
Last Modified: 2006-03-03 06:07
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Fast magnetoacoustic waves in curved coronal loops II. Tunneling modes  

Erwin Verwichte   Submitted: 2005-12-09 07:36

Fast magnetoacoustic waves in curved coronal loops are investigated and the role of lateral leakage in wave damping, which includes the mechanism of wave tunneling, is explored. A coronal loop is modeled as a curved, magnetic slab in the zero plasma-beta limit. In this model and for an arbitrary piece-wise continuous power law equilibrium density profile, the wave equation governing linear vertically polarised fast magnetoacoustic waves is solved analytically. An associated dispersion relation is derived and the frequencies and eigenfunctions of the wave modes are characterised. For some equilibria, the waves are shown to be all damped due to lateral leakage. It is demonstrated that waves either leak straight out into the external medium or have to overcome an evanescent barrier, which is linked to wave tunneling. The wave solutions consist of alternating vertically polarised kink and sausage branches. Fast kink oscillations may have a non-zero density perturbation when averaged across the loop. The calculated damping rate of fast magnetoacoustic kink oscillations is shown to be consistent with related numerical simulations and show that lateral leakage may explain the observed damping of (vertically polarised) fast magnetoacoustic kink oscillations.

Authors: E. Verwichte, C. Foullon and V.M. Nakariakov
Projects: None

Publication Status: A&A, accepted
Last Modified: 2005-12-09 07:36
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Fast magnetoacoustic waves in curved coronal loops I. Trapped and leaky modes  

Erwin Verwichte   Submitted: 2005-10-02 08:24

A study of vertically polarised fast magnetoacoustic waves in a curved coronal loop is presented. The loop is modeled as a semi-circular magnetic slab in the zero plasma-beta limit. The governing equations for linear waves are derived. We show that the wave mode behaviour depends on the slope of the equilibrium density profile, which is modeled as a piece-wise continuous power law curve of index α For all profiles, except for α -4, wave modes are not trapped in the loop and leak out into the external medium through wave tunneling. The behaviour of the density perturbation depends on α which provides a seismological tool to infer information about the equilibrium density profile from observational signatures of vertically polarised fast magnetoacoustic kink oscillations. The particular case of α -4, which corresponds to a linearly increasing Alfvén speed profile, is examined in more detail as this is the only model that can support trapped wave modes. We compare the results with a straight slab model and find similar behaviour. Coupling between sausage and kink wave modes has not been found in the model.

Authors: Verwichte, E., Foullon, C. and Nakariakov, V.M.
Projects:

Publication Status: A&A 446, 1139-1149
Last Modified: 2006-03-01 10:17
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Transverse waves in a post-flare supra-arcade  

Erwin Verwichte   Submitted: 2004-12-13 09:24

Observations of propagating transverse waves in an open magnetic field structure with the Transition Region And Coronal Explorer (TRACE) are presented. Waves associated with dark tadpole-like sunward moving structures in the post-flare supra-arcade of NOAA active region 9906 on the 21st of April 2002 are analysed. They are seen as quasi-periodic transverse displacements of the dark tadpole tails, with periods in the range of 90-220 s. Their phase speeds and displacement amplitudes decrease as they propagate sunwards. At heights of 90 and 60 Mm above the post-flare loop footpoints the phase speeds are in the ranges 200-700 km s-1 and 90-200 km s-1 respectively. Furthermore, for consecutive tadpoles the phase speeds decrease and periods increase as a function of time. The waves are interpreted as propagating fast magnetoacoustic kink waves guided by a vertical, evolving, open structure.

Authors: Verwichte, E., Nakariakov, V.M. and Cooper, F.C.
Projects: TRACE

Publication Status: A&A 430, L65-L68
Last Modified: 2006-03-01 10:19
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Characteristics of Transverse Oscillations in a Coronal Loop Arcade  

Erwin Verwichte   Submitted: 2004-06-16 05:25

TRACE observations from April 15th, 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations.Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic.The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies.The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived.

Authors: E. Verwichte, V.M. Nakariakov, L. Ofman, E.E. DeLuca
Projects: TRACE

Publication Status: Solar Phys. 223, 77-94.
Last Modified: 2006-03-01 10:16
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Abstracts by Author
Statistical seismology of transverse waves in the solar corona
Coronal Alfven speed determination: consistency between seismology using AIA/SDO transverse loop oscillations and magnetic extrapolation
Periodic spectral line asymmetries in solar coronal structures from slow magnetoacoustic waves
Spatial seismology of a large coronal loop arcade from TRACE & EIT observations of its transverse oscillations
Self-Organisation of magnetoacoustic waves in a thermally unstable environment
Seismology of a large solar coronal loop from EUVI/STEREO observations of its transverse oscillation
Subject will be restored when possible
Subject will be restored when possible
Damping of slow MHD coronal loop oscillations by shocks
Subject will be restored when possible
Seismology of curved coronal loops with vertically polarised transverse oscillations
Fast magnetoacoustic waves in curved coronal loops II. Tunneling modes
Fast magnetoacoustic waves in curved coronal loops I. Trapped and leaky modes
Transverse waves in a post-flare supra-arcade
Characteristics of Transverse Oscillations in a Coronal Loop Arcade

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