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MHD Waves and Oscillations in Solar Magnetic Structures

Programme and Abstract Book

Mallorca, 29 May - 1 June, 2006

Sponsored by: Ministerio de Ciencia y Tecnologia,

Conselleria d’Economia, Hisenda i Innovació (CAIB), Universitat de les Illes Balears

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Scientific and Social Programme

Sunday, May 28, 2006 19.30 Registration and Welcome Reception

Monday, May 29, 2006 08.30–13.00 Registration 08.55–09.00 Welcome Address 09.00–09.30 Opening Lecture. A. Hood

Session 1: Theory of MHD modes of magnetic structures Chairman: A. Hood

09.30–10.00 Theory of MHD waves for simple equilibrium configurations. M. Goossens 10.00–10.30 Nonlinear MHD waves in magnetically structured plasmas. M. Ruderman 10.30–10.50 On the continuous spectrum of leaky MHD modes. J. Andries 10.50–11.10 A mechanism for parallel electric field generation in the MHD limit: possible implications for coronal heating problem in the two stage mechanism. D. Tsiklauri 11.10–11.45 Coffee Break and Poster Viewing 11.45–12.15 Solitons in Flux Tubes: from Shaping Sunspots to Coronal Structure Formation. R. Ryutova 12.15–12.35 Finite beta wave propagation near magnetic null points. A. Hood 12.35–12.55 Interaction of MHD Waves with Corona Magnetic Null-Points. N. P. Young 12.55–13.15 Swing Absorption of compressional waves in

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inhomogeneous magnetized plasma. B.M. Shergelashvili

Session 2: Magnetic Helioseismology and Waves in sunspots Chairman: M. Goossens

15.30–16.00 Magnetic helioseismology and waves in sunspots. R. Rutten 16.00–16.20 Responses of helioseismic f modes on atmospheric effects in analytical MHD. B. Pinter 16.20–16.40 Local Helioseismology of Small Magnetic Elements. A. C. Birch 16.40–17.15 Coffee Break and Poster Viewing 17.15–17.45 Effects of surface magnetic field on Helioseismology. R. Jain 17.45–18.05 MHD waves in sunspot regions, excited by solar flares. A. G. Kosovichev 18.05–18.25 Multi-wavelength detection of 3 minute oscillations in and around sunspot. D. Banerjee

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Tuesday, May 30, 2006

Session 3: MHD Waves in the Lower Atmosphere Chairman: R. Rutten

09.00–09.30 Dynamics and magnetic coupling in the lower solar atmosphere. R. Erdélyi 09.30–09.50 Waveguiding of P-modes Into The Solar Corona. M. Marsh 09.50–10.10 MHD waves in magnetically twisted vertical solar flux tubes. V. Fedun 10.10–10.45 Coffee Break and Poster Viewing 10.45–11.05 Dynamics of the lower atmosphere in internetwork regions. S. Wedemeyer-Böhm 11.05–11.25 Chromospheric oscillations from quiet Sun millimeter observations. M. A. Loukitcheva

Session 4: Waves and Oscillations in Prominences Chairman: R. Ryutova

15.00–15.30 Prominence Oscillations (Observations). R. Oliver 15.30–15.50 Evidence for propagating waves in a quiescent filament. Y. Lin 15.50–16.10 Oscillations in a filament with CDS(SOHO): first observation of long periods in the HeI 584.33 line, modelling and diagnostic. G. Pouget 16.10–16.45 Coffee Break and Poster Viewing 16.45–17.15 Theory of small-amplitude prominence oscillations: Historical Review. J. L. Ballester 17.15–17.35 Filling factor on prominence oscillations. A. J. Díaz 19.00 Seven a side Football Match

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Wednesday, May 31, 2006

Session 5: Waves in the Corona. MHD Coronal Seismology Chairman: B. Roberts

09.00–09.30 Current trends in MHD Coronal Seismology. V. M. Nakariakov 09.30–09.50 Slow magnetoacoustic waves in curved hot coronal loops.T. Zaqarashvili 09.50–10.10 Transverse oscillations in coronal loops: the effects of curvature and transverse structuring. E. Verwichte 10.10–10.45 Coffee Break and Poster Viewing 10.45–11.15 Global coronal seismology. I. Ballai 11.15–11.35 Coronal loop oscillations: Collective behaviour and damping in a system of two coronal slabs. I. Arregui 11.35–11.55 Random heating excitation of waves in solar coronal loops. C. Mendoza 11.55–12.15 Possible methods to determine if a magnetic field is constant or varying along a coronal loop by direct observation of fast kink standing mode oscillations. G. Verth

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Session 5: Waves in the Corona. MHD Coronal Seismology Chairman: V. Nakariakov

15.30–16.00 Numerical simulations of impulsively generated waves in solar coronal loops. K. Murawski 16.00–16.20 Detection of slow magnetoacoustic waves in open field regions. E. O’Shea 16.20–16.40 Global Sausage Modes of Coronal Loops D. J. Pascoe 16.40–17.15 Coffee Break and Poster Viewing 17.15–17.35 On The Period Ratio P1/2P2 in the Oscillations of Coronal Loops. M. P. McEwan 17.35–17.55 Seismology of Dynamically Heated Quiescent Coronal Loops. Y. Taroyan 17.55–18.15 Oscillations of solar coronal magnetic loops in microwaves. M. Khodachenko 19.30 Conference Dinner

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Thursday, June 1, 2006

Session 6: MHD waves in Astrophysical Structures Chairman: R. Erdélyi

09.00–09.30 Magnetoseismology of accretion disks. R. Keppens 09.30–09.50 The periodic variations of stellar flares M. Mathioudakis 09.50-10.10 Damping of hydromagnetic waves by bulk viscosity. M. H. Ibañez 10.10-10.30 Slow nonlinear and shock waves in flux tubes. Y.D.Zhugzhda 10.30–11.00 Coffee Break

Session 7: Modern Data Analysis Methods for Wave and Oscillation Phenomena

Chairman: R. Oliver 11.00–11.30 Modern Data Analysis Methods for Wave and Oscillation Phenomena. B. Fleck 11.30–11.50 Application of statistical techniques to the analysis of solar coronal oscillations. J. Terradas 11.50–12.10 High frequency oscillations in active regions and sunspots. K. Muglach 12.10–12.30 Application of the POD in the study of the solar atmospheric dynamics. A. Vecchio 12.30–13.00 Closing Summary Review. B. Roberts

End of the Scientific Programme

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Friday, June 2, 2006 09.30 Excursion

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Session 1: Theory of MHD Modes of Magnetic Structures

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Invited Review: Theory of MHD waves for simple equilibrium configurations

M. Goossens

Centrum Plasma Astrofysica, K.U.Leuven

Abstract

The magnetic field in the solar atmosphere is not uniformly distributed but organized in typical configurations. Each of these magnetic configurations can support MHD waves and observations show that this is indeed the case. The solar magnetic plasma configurations are often characterized by non-uniformity. In addition, they are not bounded by rigid walls but embedded in a surrounding plasma environment. This review concentrates on basic properties that are independent of specific equilibrium models but are rather related to non-uniformity of the plasma and the fact that the equilibrium configuration is embedded in a surrounding plasma environment. The discussion is confined to MHD waves in 1-d equilibrium models. These models contain sufficient physics for understanding basic properties of MHD waves and still allow for a relatively straightforward mathematical analysis. The non-uniformity enables local slow and Alfvén waves to exist on individual magnetic surfaces. In ideal MHD these local slow and Alfvén waves are confined to their resonant magnetic surfaces on which their dispersion relations are satisfied locally. Dissipative effects produce coupling to the neighbouring surfaces, but the local slow and Alfvén waves still have steep gradients across the magnetic surfaces. These local resonant MHD modes exist in addition to the discrete MHD modes. Non-uniformity can produce discrete modes with mixed character and can couple discrete eigenmodes to local slow or Alfvén waves producing quasi-modes. These quasi-modes are the natural wave modes of

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the system. They are important for wave damping and wave heating. The fact that the magnetic plasma configuration is not bounded means that the system can support both non-leaky and leaky modes. In turn both non-leaky and leaky modes can have a non-resonant or resonant behaviour. These various cases and possible applications are discussed for 1-d equilibrium configurations.

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Invited Review: Nonlinear MHD waves in magnetically structured plasmas

M. Ruderman

Solar Physics and Upper-Atmosphere Research Group, Department of Applied Mathematics, University of Sheffield,

Hicks Building, Hounsfield Road, S3 7RH, England, UK,

Abstract It is well known that the solar atmosphere is strongly magnetically structured. The simples examples of magnetic structures are single magnetic interfaces, magnetic slabs and magnetic tubes. We consider the nonlinear waves propagation in magnetically structured plasmas. We start from studying nonlinear surface waves on magnetic interfaces and discuss the equation governing the propagation of these waves. We present the results of a numerical solution of this equation. Then we discuss various generalizations of the governing equation. We proceed to studying slow nonlinear waves in magnetic slabs. We present the Benjamin-Ono equation describing nonlinear slow sausage surface waves in magnetic slabs, and discuss its solutions in the form of algebraic solitons. We also briefly describe the extension of the Benjamin-Ono equation for more complicated slab-like magnetic structures. Finally, we consider nonlinear slow sausage waves in magnetic tubes. We briefly discuss the derivation of the Leibovich-Roberts equation for slow sausage waves and present the results of its numerical study. We complete the review with presenting the governing equation for non-axisymmetric surface waves in a thin magnetic tube in an incompressible plasma.

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mOn the continuous spectrum of leaky MHD modes

Jesse Andries* and Marcel Goossens Centrum voor Plasma Astrofysica, KULeuven, Belgium

Abstract

When the MHD operator is considered on an unbounded spatial domain the self-adjointness of the operator can still be established, resulting in the fact that eigenfrequencies are necessarily either real or imaginary, and that a complete spectral representation can be constructed. Nevertheless, considering an unbounded domain removes one of the boundary conditions (at the boundary which is moved to infinity) resulting in the appearance of additional continuous spectra as infinity becomes a singular point in the equations. These additional leaky continuous spectra are the MHD analog of the free electrons in the quantum mechanical model of the hydrogen atom. As soon as the spatial domain is unbounded the continuous spectrum does not only consist of the classical Alfvén and slow continuous spectrum, but is to be extended with a fast and slow leaky continuous spectrum. The eigenmodes that are associated with the leaky MHD continuum are shown to be improper in the sense that they carry an infinite amount of energy (just like the Alfv´en continuum modes, or the Case – van Kampen modes in Vlasov plasmas), and are therefor not contained in the Hilbert space of square integrable functions. The unstable leaky modes found by Wilson (1981), Spruit(1982) and Cally (1986) are quasi-modes and are found by continuation of the Green’s function into the lower half of the complex frequency plane. The physical relevance of these modes in the context of the observed damping of oscillations in the solar corona is subject of a debate by Ruderman and Roberts (2006) and Cally (2006). The present discussion is intended to shed light on the debate and to

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clarify at least the mathematical status of the unstable leaky quasi-modes in terms of the mathematical process of continuum damping. *Postdoctoral Fellow of the National Fund for Scientific Research - Flanders (Belgium) (F.W.O.-Vlaanderen)

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A mechanism for parallel electric field generation in the MHD limit: possible implications for coronal heating

problem in the two stage mechanism

David Tsiklauri Institute for Materials Research, University of Salford,

Greater Manchester, M5 4WT, United Kingdom

Abstract

Using Particle-In-Cell simulations i.e. in the kinetic plasma description Tsiklauri et al. and Genot et al. recently reported on a discovery of a new mechanism of parallel (to the ambient uniform magnetic field) electric field generation, which results in electron acceleration. This new effect takes place when an Alfvén wave moves along the field in the plasma which has transverse density inhomogeneity. The progressive distortion of the Alfvén wave front due to differences of local Alfvén speed then generates the parallel electric field. In this work we show that the parallel (to the uniform unperturbed magnetic field) electric field generation can be obtained in much simpler framework using ideal MHD description, i.e. without resorting to complicated wave particle interaction effects such as ion polarisation drift and resulting space charge separation which is the ultimate cause of electron acceleration. Within ideal MHD the parallel electric field appears due to fast magnetosonic waves which are generated by the interaction of weakly non-linear Alfvén waves with the transverse density inhomogeneity. Further, in the context of the coronal heating problem a new two stage mechanism of the plasma heating is presented by putting emphasis, fi rst, on the generation of parallel electric fields within ideal MHD description directly, rather than focusing on the enhanced dissipation mechanisms of the Alfvén waves and, second, dissipation of these parallel electric

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fields via kinetic effects. It is shown that a single Alfvén wave harmonic with frequency (υ = 7 Hz), (which has longitudinal wavelength λA= 0.63 Mm for putative Alfvén speed of 4328 km/s) the generated parallel electric field could account for the 10% of the necessary coronal heating requirement. We conjecture that wide spectrum (10-4 – 103 Hz) Alfvén waves, based on observationally constrained spectrum, could provide necessary coronal heating requirement. Exact amount of energy that could be deposited by such waves under our mechanism of parallel electric field generation could only be calculated once fuller parametric study is done. In other words "theoretical spectrum" of the energy stored in parallel electric fields versus frequency needs to be yet obtained. It is also shown that the amplitude of generated parallel electric field exceeds the Dreicer electric field by about four orders of magnitude, which implies realisation of the run-away regime with the associated electron acceleration.

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� Invited Review: Solitons in Flux Tubes: from Shaping Sunspots to Coronal Structure Formation

M. Ryutova

Lawrence Livermore National Laboratory/IGPP L-413, CA 94550, USA

Abstract

Flux tubes in highly dynamic environment with source and sink of energy do not obey the local conservation laws; far less the ensembles of flux tubes that exhibit collective wave phenomena. Seemingly complex approach of energetically open nonlinear dissipative systems makes the explanation of many observed phenomena simple and easy. I'll discuss two problems associated with nonlinear waves in flux tubes: (1) the origin of moving magnetic features (MMFs) around sunspots and their impact on dynamics of overlying atmosphere, and (2) soliton gas above the ``unipolar'' plages providing generation of the amorphous emission at coronal temperatures. In the first part I'll describe all types of MMFs (for now at least 5 different types of MMFs are discussed in literature) on basis of evolutionary soliton- and shock-like formations, and corresponding response of overlying atmosphere that depends on their type. Several multi-wavelength datasets allowed us to study hundreds of MMFs and their signatures in the overlying atmosphere, and bring the theory to numbers. I'll also mention a new phenomenon discovered during these observations, consisting in fact that as an ensemble, MMFs seem to suppress the formation of large scale ``stable'' coronal loops; in other words, such loops avoid regions of penumbra highly populated by MMFs. This fact still needs to be explained, although some hypothesis have been proposed. In the second part I'll describe the observed properties of the amorphous coronal

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emission evolving in space and time, and show how well these properties fit the behavior of a soliton gas produced by the ensemble of non-collinear oscillating flux tubes distributed over the space with the filling factor corresponding to plage regions.

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> A @: Finite beta wave propagation near magnetic null points

James Mclaughlin and Alan Hood

Mathematical Institute, University of St Andrews, St. Andrews (Scotland)

Abstract

Previous work has looked at the propagation of fast waves near a magnetic null point in the cold plasma limit. The inclusion of a small uniform gas pressure means that the plasma beta varies from smaller than unity away from the null point to extremely large at the null point. There is a circle (defined by beta approximately unity) at which the small beta fast wave is converted into a high beta fast and slow wave. The implications for wave dissipation are considered.

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Interaction of MHD Waves with Corona Magnetic Null-Points

N.P. Young (1), V.M. Nakariakov (1), C. Foullon (2), E. Verwichte(1)

(1) University of Warwick, Coventry, UK (2) MSSL, University College London, UK

Abstract

In recent work we have proposed a model for production of quasiperiodic pulsations in flaring light curves through the triggering of reconnection by small-amplitude fast magnetoacoustic waves via current driven microinstabilities (Nakariakov et al. 2006). Using a 2D numerical simulation (the Lare2d code) with finite plasma-beta and resistivity, we model the interaction of a periodic fast wave with a coronal magnetic null point. We observe the incoming wavefront wrap around the neutral point (similar to the zero-beta simulations of McLauglin& Hood 2004), producing a current density spike at the null point and current sheets along the separatrices. Finite plasma-beta and resistivity allow the wavefront to both pass through the null point and to dissipate. As a result, if the wave period is sufficiently long, each incoming wavefront results in a distinct peak in the maximum current density. A sufficiently long-period harmonic fast wave produces quasi-periodic aharmonic variation of the current in the vicinity of the null point. The modelling demonstrates that the modulation depth of the current is much greater than the initial amplitude of the wave and could be sufficiently large to trigger microinstabilities and hence anomalous resistivity. This would result in periodic triggering of magnetic reconnection and thus the observed quasi-periodic pulsations in flaring light curves. This effect can easily explain the observed patchy spatial structure of the quasi-periodic energy

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releases in two-ribbon solar flares.

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Swing Absorption of compressional waves in inhomogeneous magnetized plasma

B.M. Shergelashvili, T.V. Zaqarashvili, S. Poedts and B. Roberts

Abstract

The recently suggested swing interaction between fast magnetosonic and Alfvén waves is generalized to inhomogeneous media. We show that the fast magnetosonic waves propagating across an applied non-uniform magnetic field can parametrically amplify the Alfvén waves propagating along the field through the periodical variation of the Alfvén speed. The resonant Alfvén waves have half the frequency and the perpendicular velocity polarization of the fast waves. The wavelengths of the resonant waves have different values across the magnetic field, due to the inhomogeneity in the Alfvén speed. Therefore, if the medium is bounded along the magnetic field, then the harmonics of the Alfvén waves, which satisfy the condition for onset of a standing pattern, have stronger growth rates. In these regions the fast magnetosonic waves can be strongly absorbed, their energy going in transversal Alfvén waves. We refer to this phenomenon as Swing Absorption. This mechanism can be of importance in various astrophysical situations.

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Session 2: Magnetic Helioseismology and Waves in Sunspots

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Invited Review: Magnetic helioseismology and waves in sunspots

R. J. Rutten

Sterrenkundig Instituut, Universiteit Utrecht, P.O. Box 80000, NL-3508 TA Utrecht, The Netherlands.

Abstract

I will review sunspot waves emphasizing observations of umbral flashes and running penumbral waves. I believe these to be closely similar to acoustic internetwork waves, but field guided, and ripe for full explanation through MHD simulation.

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Responses of helioseismic f modes on atmospheric effects in analytical MHD models

Balázs Pintér and Róbert Erdélyi

Department of Applied Mathematics, The University of Sheffield

Abstract

The helioseismic fundamental (f) mode is investigated in plane parallel hydrodynamic (HD) and magnetohydrodynamic (MHD) solar models, which consist of three layers of incompressible plasma. The lower, semi-infinite layer is the solar interior with constant density and plasma pressure decaying linearly with height. Two overlaying upper layers, representing the solar atmosphere, are embedded in a horizontal canopy-like magnetic field. The top semi-infinite layer is the corona with exponentially decaying density, plasma pressure and magnetic field strength. In the intermediate (transitional) layer, the plasma density is constant while the magnetic field increases with height continuously from zero to its maximum value. It is shown, that the f mode can be coupled resonantly to a local incompressible Alfvén wave in the transitional layer, which results in damping of the f mode, due to resonant absorption. Solutions (both analytic and numerical) of the dispersion relation are obtained for a magnetic-field-free (HD) model with a transitional layer of non-zero thickness and also for a magnetic (MHD) model in the thin-transitional-layer approximation. We focus on the shifts of the f mode frequency caused by the atmospheric magnetic field and the line width variation due to resonant absorption.

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Local Helioseismology of Small Magnetic Elements

A.C. Birch (1), T.L. Duvall, Jr. (2), L. Gizon (3), S. Hanasoge (4)

(1) NWRA/CoRA, Boulder, CO USA (2) Laboratory for Solar and Space Physics NASA/Goddard Space

Flight Center Greenbelt, MD USA (3) Max-Planck-Institut fuer Sonnensystemforschung

Katlenburg-Lindau, Germany (4) W.W. Hansen Experimental Physics Laboratory

Stanford University USA

Abstract

We show helioseismic observations of the scattering of f modes from small quiet-Sun magnetic elements. These measurements are approximately consistent with a toy model in which small magnetic elements act as monopole and dipole scatterers. We show that in a simple model for the scattering of acoustic waves by a magnetic cylinder the Born approximation can be used when the magnetic field strength is sufficiently weak, but is not always valid in the limit of small tube radius. We discuss progress in modeling the scattering of waves by thin flux tubes.

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Invited Review: Effects of surface magnetic field on Helioseismology

Rekha Jain

Applied Mathematics, University of Sheffield

Abstract

In this talk, the effect of surface magnetic fields on helioseismology will be discussed. The amplitudes, frequencies and the travel times of p-modes are altered by the presence of magnetic fields. Amplitudes are suppressed in the p-band frequencies. The global frequency shift in p-modes is induced by solar magnetic activity and the local frequency shifts are induced by the movement of magnetic region. The travel times of the acoustic waves are also affected due to the change in the acoustic cut-off frequencies in the presence of a horizontal field. In this talk, I will discuss these issues using relevant data analysis and theoretical work.

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Invited Review: MHD waves in sunspot regions, excited by solar flares

A. G. Kosovichev

Stanford University

Abstract

Helioseismic response to solar flares ("sunquakes") provides unique opportunity for direct observations of the interaction of magnetoacoustic waves with sunspots. These waves are excited by strong hydrodynamic impact caused by shocks generated by high-energy particles, and are observed as expanding circular-shape ripples on the surface. The waves propagate through surrounding sunspots regions, allowing us to observe changes in their properties, wave speed, amplitude and travel times. I present the results for several cases, obtained from the MDI instrument on SOHO, showing new unexpected properties of sunquakes, such as small distortion of wavefronts in sunspots, large variations of the decay time, and very strong anisotropy. These results challenge the current theories of MHD waves in sunspots. Sunquake observations provide new means for helioseismic diagnostics of magnetic regions.

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Multi-wavelength detection of 3 minute oscillations in and around sunspot

D. Banerjee (1), Chia-Hsien Lin(2), E. O’Shea(3), J.G. Doyle(3)

(1) Indian Institute of Astrophysics, Koramangala, bangalore 560034, (2) Astronomy Department, Yale University, 260

Whitney Ave., New Haven, CT06511, (3) Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland

Abstract

We use CDS/NIS time series and images from MDI, CDS, TRACE and EIT to investigate the chromospheric and transition region dynamics above the active region AR0554. We examine the extent and range of 3-min oscillations from a range of features. Among all the NIS spectral lines analysed, significant oscillations were found in Si xii 520 °A, Mg x 625 °A, O v 629 °A and He i 522 °A. We found that weak but significant 3-min oscillations are not confined to the umbra/plume but can be seen in many bright locations. To find the possible sources of these 3-min oscillations outside the umbra, we compared the oscillations of single pixels in different regions. The results of our comparison indicate a possible connection between the magnetic fields and the oscillations. Therefore, we suggest that 3-min oscillations may exist in many magnetic structures. We also detected signatures of a moving magnetic monopole up to the transition region, suggesting that the monopole, despite being small, can influence the dynamics in the upper atmosphere layers.

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Session 3: MHD Waves in the Lower Atmosphere

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Invited Review: Dynamics and magnetic coupling in the lower solar atmosphere

Robert Erdélyi

Solar Physics and Upper-Atmosphere Research Group, Department of Applied Mathematics, University of Sheffield,

Hicks Building, Hounsfield Road, S3 7RH, England, UK, email: robertus@sheffield.ac.uk

Abstract

The interaction between solar photospheric coherent motions, e.g. acoustic or p-modes have important implications for the dynamics of the solar atmosphere ranging from the low chromosphere even deeply into corona. Combined high spatial and time resolution observations (SOHO, TRACE, SVT in La Palma) supplemented with MHD modelling demonstrated the p-mode leakage into the chromosphere, transition region and low corona. In my talk I review the latest results available in the literature on how photospheric motions interact with the magnetic structures of the transitional layer between the photosphere and the corona. A comprehensive study of this transitional layer, also called solar atmospheric boundary layer, allows us to perform lower atmospheric magneto-seismology. Theoretical and observational efforts on the coupling mechanism(s) of coherent and random motions and fields to the low atmosphere will be discussed. Key issues will be addressed, including what dynamic impact the photosphere has on the overlaying magnetic atmosphere; what is the role of magnetic wave guides in the photosphere - chromosphere - transition region dynamics; what are the possible scenarios and physical details of the boundary layer coupling mechanism(s); how p/f-modes resonantly interact to lower atmospheric MHD slow and Alfvén waves; how the coupling

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could be used for diagnostics, lower atmospheric magnetic seismology and connectivity studies.

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Waveguiding of P-modes Into The Solar Corona

M. S. Marsh NASA Goddard Space Flight Center, USA

Abstract

Magneto-hydrodynamic (MHD) wave modes propagating from the photosphere into the corona may be exploited as an observational tool in an analogous way to the use of acoustic waves in helio/terrestrial seismology. P-modes are thought to undergo mode conversion to slow magneto-acoustic waves in regions of strong magnetic field. Using new spectroscopic imaging data at transition region temperatures, combined with coronal imaging, observations are presented of the propagation of these slow magneto-acoustic p-modes through the transition region and into the solar corona along active region magnetic eld. The prospects for new observations with STEREO and Solar-B are also discussed.

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MHD waves in magnetically twisted vertical solar flux tubes

Robert Erdélyi (1), Viktor Fedun (2) (1,2) Solar Physics and upper-Atmosphere Research Group, Department of Applied Mathematics University of Sheffield,

Hounsfield Road, Hicks Building, Sheffield, S3 7RH, UK

Abstract

Recent high-resolution satellites clearly prove the existence of wide range of theoretically predicted MHD waves in solar atmospheric magnetic structures. A detailed analysis of these ways provides us excellent diagnostic tools of the magnetic waveguide structure (loops, arcades) they propagate in. In this work we elaborate on effects due to the presence of magnetic twist in cylindrical magnetic waveguides. The propagation of surface and body linear MHD modes in a twisted magnetic flux tube embedded in a magnetically twisted plasma environment is considered. Two distinct cases are considered: (i) incompressible twisted flux tube and magnetised plasma environment, and, (ii) compressible twisted flux tube with an unmagnetised plasma environment. The dispersion relation for surface and body modes are derived assuming constant external twisted field for case (i). For the compressible case (i.e. more directly relevant for and applicable to coronal waveguides) the external twisted field is zero. Analytic approximate solutions to the dispersion equations are found for the long and short wave limits, respectively. Solutions of linear the dispersion relations are obtained numerically for intermediate wavelengths. It was found, that in case the twisted component of the external magnetic field in the environmet is constant, the index of Bessel functions in the corresponding dispersion relation is not integer any more in a general incompressible plasma. This new feature gives rise to a

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reach mode-structure of denegerated magneto-acoustic waves in the flux tubes. In the particular case of homogen magnetic twist, the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is also estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few per cent when compared to their untwisted counterparts. Further detailed analysis is necessary in order to find the dispersion relation for more realistic cases, where the magnetic twist diminishes with distance from the tube. Finally, observational relevances will be discussed in light of the resolution capabilities of Solar-B and SDO.

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Dynamics of the lower atmosphere in internetwork regions

Sven Wedemeyer-Böhm, Oskar Steiner Kiepenheuer-Institut für Sonnenphysik, Freiburg, Germany

Abstract

For a long time the chromosphere in internetwork regions of the quiet Sun was regarded as a static and homogeneous layer. Thanks to the pioneering work by Carlsson & Stein but also due to advances on the observational side, the wave nature of these atmospheric regions received increasing attention during the last decade. We present results of recent three-dimensional radiation magnetohydrodynamic simulations with CO5BOLD that show the chromosphere of internetwork regions as a dynamic and intermittent phenomenon. It is a direct product of interacting waves that form a mesh-like pattern of hot shock fronts and cool post-shock regions. The waves are excited self-consistently in the lower layers of the model and provide enough acoustic power to counterbalance radiative losses in the (low) chromosphere. We also find that the average power spectrum based on synthetic UV intensity maps can match power spectra derived from the 160 nm channel of TRACE. However, in the middle chromosphere above an average height of 1000 km, plasma beta gets larger than one and magnetic fields become more important. The model chromosphere exhibits a magnetic field that is much more homogeneous than in the layers below and evolves much faster. That includes fast propagating (MHD) waves. We will discuss the consequences for atmospheric structure of the lower atmosphere, including the capability of explaining apparently contradicting diagnostics such as carbon monoxide and UV emission at the same time. We consider this class of models as a fundament for a comprehensive, dynamic model of the lower solar atmosphere.

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Chromospheric oscillations from quiet Sun millimeter observations

M. A. Loukitcheva (1), (2), S. K. Solanki (2), S. White (3)

(1) Astronomical Institute of St. Petersburg University, Russia (2) Max-Planck-Institut fuer Sonnensystemforschung, Germany

(3) Astronomy Department, University of Maryland, United States

Abstract

In this contribution we analyze the millimeter intensity spectrum, expected from the radiation-hydrodynamic simulations of the solar non-magnetic atmosphere of Carlsson & Stein, together with the interferometric observations of the quiet Sun, obtained at a wavelength of 3.5 mm with the Berkeley-Illinois-Maryland Array. Model radio emission at millimeter wavelengths is found to be extremely sensitive to dynamic processes in the chromosphere, if these are spatially and temporally resolved. The estimated millimeter brightness temperatures are time-dependent, following changes in the atmospheric parameters, and clear signatures of waves with a period of 180 s (corresponding frequency of 5.5 mHz) are seen in the radio intensity as a function of time. With BIMA data we have constructed two-dimensional maps of the solar chromosphere with a resolution of 1000, which represents the highest spatial resolution achieved so far at this wavelength for non-flare solar observations. Intensity oscillations with RMS brightness temperature amplitudes of 50-150 K in the frequency range 1.5-8 mHz are found to be significant in the data. There is a tendency toward short period oscillations in the quiet Sun internetwork and longer periods in active regions and the network. Most of the oscillations are short wave trains lasting for typically 1-3 wave periods. A correspondence between the model

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predictions based on the RHD simulations of Carlsson and Stein and the observational data can be established under assumptions on the horizontal coherence length of the oscillations (of order of 100). We also give estimates of the influence of the limited available spatial and temporal resolution of observations on the comparison with the model predictions. We argue that millimeter continuum observations promise to be an important diagnostic of the chromospheric dynamics and the appropriate wavelengths to look for dynamic signatures are in the range 0.8-5.0 mm.

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Session 4: Prominence Oscillations

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Prominence oscillations (observations)

Ramón Oliver Departament de Física, Universitat de les Illes Balears,

07122 Palma de Mallorca, Spain

Abstract

The evolution of our observational knowledge of prominence oscillations is reviewed, from the very first detections of this kind of phenomenon to the most recent developments, acquired from ground- and space-based observations. A discussion of future research trends in this area is given.

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Evidence for propagating waves in a quiescent filament

Yong Lin(1), Oddbjorn Engvold (1), Luc Rouppe van der Voort (1 ; 2), Michiel van Noort (1;3)

(1) Institute of Theoretical Astrophysics, University of Oslo PO Box 1029, Blindern, N-0315 Oslo, Norway

(2) Center of Mathematics for Applications, University of Oslo PO Box 1053 Blindern, N-0316 Oslo, Norway

(3) The Institute for Solar Physics of the Royal Swedish Academy of Sciences

AlbaNova University Center, SE-106 91 Stockholm, Sweden

Abstract

The high resolution Hα filtergrams (0.2 arc sec) used in this study were recently obtained with the Swedish 1-m Solar Telescope (SST). These images resolve numerous very thin, thread-like structures in solar filaments. The threads are thought to represent sections of thin magnetic flux tubes longer than the observable threads. Time series of Hα filtergrams and derived Dopplergrams both revealed counterstreaming with typical speeds of 5-10 km/s in opposite directions along adjacent threads as previously shown. We hereby report our new finding of small amplitude (-3 to 3 km/s) waves propagating along a number of the thin threads with vph ≈ 12 km/s and wavelength ≈ 6 arc sec. Also, the temporal variation of the Doppler velocities averaged over a small area (3.4 x 10 arc sec) where filament threads are closely packed, shows a short period (3.6 min) wave pattern. These short period oscillations could possibly represent so-called string and internal Love modes in accordance with numerical fibril models derived by Joarder, Nakariakov and Roberts (1997). In some cases, it is clear that the propagating waves are moving in the same direction as the mass flows.We suggest that the flows in filaments may be

44

accelerated by weakly damped waves.

45

Oscillations in a filament with CDS(SOHO): first observation of long periods in the HeI 584.33 line,

modelling and diagnostic

Guillaume Pouget, Karine Bocchialini, Jacques Solomon Institut d'Astrophysique Spatiale

Abstract

Three long observations of filaments were carried out, in the 584.33 He1 line, during MEDOC campaigns in 2003 and 2004, by CDS (Coronal Diagnostic Spectrometer) onboard SOHO. Their duration is of the order of 15-16 hours. The Fourier analysis of the Doppler velocities in the filament allows us to detect very slow (5-7 h) velocity oscillations; faster oscillations are also detected, at a smaller level. We discuss the possibility of an interpretation of these velocity oscillations considering the prominence model of Joarder and Roberts (1993), which treats the prominence as a whole plasma slab. We use a systematic method to identify, among the frequencies detected, the six fundamental modes predicted by the model. If the identification is successful, it provides a complete diagnostic of the filament, in terms of Alfven speed, temperature, and angle between the magnetic field and the main axis of the filament.

46

Theory of small-amplitude prominence oscillations: Historical review

J. L. Ballester

Dept. Física. Univ. Illes Balears. E-07122 Palma de Mallorca (Spain)

Abstract

Nowadays, an extense observational background about small-amplitude oscillations in solar prominences has been gathered. From the beginning of nineties, simple theoretical models to explain these oscillations have been developed, but they are still far from the complexity needed to reproduce the reality. Here, I plan to review, in a historical way, theoretical developments about small-amplitude prominence oscillations.

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Filling factor on prominence oscillations

A. J. Díaz & B. Roberts Mathematical Institute, University of St Andrews,

St Andrews, KY16 9SS, Scotland (UK)

Abstract

During recent years a number of observations of prominence oscillations have been reported. These data is used for prominence seismology with the help of theoretical oscillatory models of prominences as homogeneous slabs. However, it is well known that there is a fine structure, whose effect in the global oscillations has been neglected. Here we discuss the role of this fine structure and show that the homogeneous model should take into account at least the filling factor, since it may lead to important shifts in the measured periods of certain modes.

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49

Session 5: Waves in the Corona. MHD Coronal Seismology

50

Invited Review: Current trends in MHD Coronal Seismology

V.M. Nakariakov Centre for Fusion, Space & Astrophysics,

University of Warwick, Coventry CV4 7AL, United Kingdom

Abstract

The review presents the current trends in the observational and theoretical aspects of remote diagnostics of the solar coronal plasma by magnetohydrodynamic waves and oscillations. Physical mechanisms responsible for the observed periodicities and wave signatures are discussed. Coronal seismological methods for the estimation of the magnetic field in active regions, for probing the transverse sub-resolution structure of coronal loops and for the study of the coronal heating function are presented.

51

Slow magnetoacoustic waves in curved hot coronal loops

Zaqarashvili, T.V., Oliver, R., Ballester, J. L., Terradas, J. Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain

Abstract

Recent observations by SUMER spectrometer on SOHO show the rapidly damped standing slow magnetoacoustic waves in hot coronal loops. Several different mechanisms can be responsible for the damping of the oscillations but, so far, only straight magnetic tube has been used for modelling the oscillations. However the loop curvature can be of importance in the dynamics of lower order harmonics. Here we study the infuence of curvature on the standing slow magnetoacoustic waves in hot coronal loops embedded in the cool environment. It is shown that the first harmonic of the slow magnetoacoustic standing waves is rapidly damped due to the energy leakage by fast waves from the loop outer boundary. The damping time is shorter for wider loops. Theoretically estimated damping rate seems to be in perfect agreement to the observations (Wang et al. 2003).

52

Transverse oscillations in coronal loops: the effects of curvature and transverse structuring

E. Verwichte (1), C. Foullon (2), V. M. Nakariakov (1),

C. S. Brady (3) & T. D. Arber (1) (1) Department of Physics, University of Warwick,

Coventry CV4 7AL, UK (2) Mullard Space Science Laboratory, University College

London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK (3) School of Mathematics and Statistics, University of St

Andrews, St Andrews, Fife KY16 9SS, UK

Abstract

Transverse loop oscillations have first been reported in 1999 using EUV image sequences and are interpreted as fast magnetoacoustic kink modes, impulsively excited by a nearby flare or eruption. Such modes offer a unique seismological tool for determining the strength of the local coronal magnetic field. Moreover, the observed rapid decay of these modes has received much interest as it cannot be explained by straightforward dissipation. Stock is taken of the achievements and current developments. In particular, the effects of curvature and transverse structuring on the behaviour of transverse loop oscillations are modelled. It is shown that for a range of realistic loop structures, wave energy naturally leaks out of the loop through the mechanism of wave tunneling. The efficiency of this damping mechanism is discussed. Furthermore, the potential of this model for coronal seismology is explored and a few examples of comparisons with observations are given.

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Invited Review: Global coronal seismology

Istvan Ballai SPARG, Dept. of Applied Mathematics, University of Sheffield,

Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK

Abstract

Large scale eruption events in the solar atmosphere can generate global waves, i.e. waves which propagate over distances comparable to the solar radius. In the low solar corona, global waves observed by SOHO/EIT, generated by coronal mass ejections or flares are usually referred to as EIT waves. Since EIT waves carry information about their environment, they can be used for diagnostics of, e.g. the local and global magnetic field. This contribution presents theoretical models for finding values of magnetic field in the quiet Sun and coronal loops based on the interaction of global waves and coronal loops. We will also explore the physical connection between local and global solar coronal events (e.g. flares, EIT waves and coronal loop oscillations).

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Coronal loop oscillations: Collective behaviour and damping in a system of two coronal slabs

I. Arregui, J. Terradas, R. Oliver, & J. L. Ballester

Departament de Física, Universitat de les Illes Balears E-07122 Palma de Mallorca, Spain

Abstract

The magnetohydrodynamic normal modes of oscillation of a sys tem of two coronal slabs including longitudinal propagation is studied. The period and damping rate of the collective resonantly damped mode is computed for different values of the longitudinal propagation and of several equilibrium parameters such as the width of the inhomogeneous layers, the distance between the slabs and their density contrasts. The obtained results are then compared with the oscillatory properties of single-loop equilibrium models.

55

Random heating excitation of waves in solar coronal loops

César A. Mendoza-Briceño (1), Robert Erdélyi (2) (1) Centro de Física Fundamental, CFF, Facultad de Ciencias, Universidad de Los Andes, Apartado Postal 26, La Hechicera,

Mérida 5251, Venezuela, cesar@ula.ve (2) Solar Physics & Upper-Atmosphere Research Group,

Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, England, UK,

robertus@sheffield.ac.uk

Abstract

In a recent work by Mendoza-Briceño et al. (2005) ApJ, 625, 1080 the dynamic response and heating efficiency of coronal plasma to a series of random impulsive heating was studied in coronal loops. In the present work we focus on the nature of oscillatory patterns that appear during the evolution of coronal loops undergoing impulsive heating through the release of localized energy pulses near the loop's footpoints. We investigate these oscillatory patterns by using wavelet analysis technique. We found periodic features, like wave packets, with periods of 150-220, 500-600 and 800-1000 s. These periods are also found to scale (increase) with the loop length and decrease with the length of the loop segments along which the pulses are injected. Implications of our results upon the latest coronal observations are also briefly discussed.

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Possible methods to determine if a magnetic field is constant or varying along a coronal loop by direct observation of fast

kink standing mode oscillations

G.Verth and R. Erdélyi Department of Applied Mathematics

University of Sheffield, Sheffield, S3 7RH, UK

Abstract

One of the mysteries of coronal loops is that they do not appear to vary in width with increasing height in the corona. A flux tube of constant width suggests that the magnetic field strength is constant along a loop. This is in contradiction with potential extrapolation models based on magnetogram data that always produce B fields decreasing in strength with distance from photospheric magnetic sources. Our recently developed MHD theory may be used to determine if a magnetic field is constant or varying along a coronal loop by direct observation of standing fast kink mode oscillations.

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Invited Review: Numerical simulations of impulsively generated waves in solar coronal loops

K. Murawski

Group of Astrophysics and Gravity Theory, Institute of Physics, UMCS, 20-031 Lublin, Poland

Abstract

We present numerical results of a temporal evolution of impul sively triggered magnetosonic waves in solar coronal loops that are approximated by mass density enhancement regions. We discuss both monolithic and multi-stranded slabs and loops. In particular, in a case of a monolithic slab we show a simultaneous presence of standing slow and fast magnetosonic waves. We show that standing slow waves in an arcade loop can be excited by a pulse launched at a foot-point. Such pulse is able to trigger a distortion mode, leading to asymmetric oscillations which are distinct from the vertical or horizontal kink oscillations. We show that these oscillations are affected by a constant gravity which alters their excitation and attenuation times. As examples of multi-stranded structures we discuss propagating waves in two parallel identical slabs and standing fast magnetosonic kink waves in a two-stranded arcade loop. The results of the numerical simulations reveal wave signatures which are reminiscent of recent TRACE observations.

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Detection of slow magnetoacoustic waves in open field regions

E. O'Shea, D. Banerjee, J. G. Doyle Armagh Observatory

Northern Ireland

Abstract Using time series data obtained from the CDS instrument on SOHO, we will present results of a statistical study of phase delays measured between oscillations in intensity (flux) and between oscillations in line-of-sight velocity. These measurements allow for the identification of compressional MHD waves present in the open field regions being studied, that is, in off-limb polar regions and in on-disk coronal holes, which may be responsible for the (fast) solar wind acceleration. From a calculation of propagation speeds, we show that it is slow magnetoacoustic waves that produce the observed time delays between the oscillations of the transition region and coronal spectral lines. The evidence for a change in the propagation speeds of the observed waves in open field locations off-limb at the poles as opposed to similar open field regions in equatorial and polar coronal holes on the disk of the Sun will be discussed as will the evidence for a resonant cavity effect to be present at coronal temperatures.

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Global Sausage Modes of Coronal Loops

D. J. Pascoe (1), V. M. Nakariakov (1), T. D. Arber (1) (1) University of Warwick, Coventry, CV4 7AL, UK

Abstract

Symmetric fast magnetoacoustic perturbations of solar coronal loops (sausage, or m = 0 modes) are modelled using the Lare2d code. Analytical theory predicts the existence of trapped global modes of this kind in sufficiently thick and dense loops only, with the periods estimated as the ratio of double the loop length and the Alfvén speed outside the loop. Our numerical modelling generalises this study to the case of long loops with sufficiently small density contrast. It was found that these loops can support global sausage leaky modes of detectable quality and with the wave numbers smaller than the theoretical cut-off for trapped modes. The periods of the leaky modes are found to be approximately determined by the loop length and the external Alfvén speed. When the loop length can be estimated from imaging observations, the observed period of this mode provides us with the seismological information about the Alfv´en speed outside the loop. For typical flaring loops, the estimated periods of the global sausage modes are about 10-60 s.

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On The Period Ratio P1/2P2 in the Oscillations of Coronal Loops

M. P. McEwan, G. R. Donnelly, A. J. Diaz and B. Roberts

Mathematical Institute, University of St Andrews, St. Andrews (Scotland)

Abstract

With strong evidence of fast and slow magnetoacoustic modes arising in the solar atmosphere there is scope for improved determinations of coronal parameters through coronal seismology. Of particular interest is the ratio P1/2P2 between the period P1 of the fundamental mode and the period P2 of its first harmonic. In an homogeneous medium this ratio is one, but in more complex configurations P1/2P2 is shifted from unity. We consider analytically the effects on various MHD modes of structuring and stratification, pointing out that transverse or longitudinal structuring or gravitational stratification modifies the ratio P1/2P2. The departure of P1/2P2 from unity can be used as a seismological tool in the corona. We illustrate our method by reference to observations by Verwichte et al. (2004).

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Seismology of Dynamically Heated Quiescent Coronal Loops

Y. Taroyan (1), R. Erdélyi (1) (1) Solar Physics and upper-Atmosphere Research Group,

Department of Applied Mathematics University of Sheffield, Sheffield, S3 7RH, UK

Abstract

The determination of the physical parameters of coronal loops remains both an observational and a theoretical challenge. A new diagnostic technique for quiescent dynamically heated coronal loops, based on the analysis of the power spectra of the Doppler shift time series, is proposed. It is assumed that a given loop is heated randomly both in space and time by small-scale discrete impulsive events of unspecified nature. The results show that depending on the heliographic position of the loop and the orientation of the observing instrument various harmonics can be identified in the power spectra of the line shift time series. The highest power peak corresponds to the fundamental mode. The peaks become smaller as the frequency of harmonics increases. The frequency peaks are sensitive to changes in the average loop temperature and thus could be used as temperature diagnostic tool. The analysis of the power spectra also allows to distinguish uniformly heated loops from loops heated near their footpoints. The proposed method could, in principle, be used to study the multi-thermal structure of the loops.

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Oscillations of solar coronal magnetic loops in microwaves

M. L. Khodachenko 1, A.G. Kislyakov 2, H.O. Rucker 1, V.V. Zaitsev 3, S. Urpo 4

1 Space Research Institute, Austrian Academy of Sciences,

Schmiedlstr. 6, A-8042 Graz, Austria (maxim.kodachenko@oeaw.ac.at; helmut.rucker@oeaw.ac.at)

2 Lobachevsky State University, Nizhny Novgorod, Gagarin av., 23, 603950, Nizhny Novgorod, Russia

(agkis@appl.sci-nnov.ru)

3 Institute of Applied Physics, Russian Academy of Sciences, Ulyanov str. 46, 603950, Nizhny Novgorod, Russia

(za130@appl.sci-nnov.ru;)

4 Metsaehovi Radio Observatory, Metsaehovintie 114, 02540, Kylmaelae, Finland

(Seppo.Urpo@hut.fi)

Abstract Analysis of the Low-Frequency fluctuations of solar microwave radiation (37 GHz and 11.7 GHz) appears as a relatively new direction of investigations in the traditional branch of the microwave radio astronomy. For this purpose a "sliding window" Fourier transform combined with the Wigner-Ville technique is applied. It has been shown that slow variations of the electric current and associated magnetic field in a source of solar microwave emission, as well as a large-scale motion of the source, can modulate the intensity of the received signal. Special attention in the present study is paid to the analysis of modulations of

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microwave emission recorded at the same time when TRACE EUV telescope observed large scale oscillations of coronal loops. For some events the spatial resolution of the radio telescope at 37 GHz allows also to localize an active region containing the oscillating loops. The applied data analysis technique, besides of the modulations probably connected with loop oscillations detected by TRACE, makes possible to detect additional modulations, which may be associated with oscillations of smaller (invisible for TRACE) loops. These modulations can be connected as well with specific wave modes (sausage mode) excited in solar coronal structures. Comparative analysis of phases of oscillations of TRACE loops and the microwave emission modulation allows deeper insight into the global dynamics and structure of solar active regions. This makes the analysis of LF modulations of microwave radiation intensity to be an important and useful tool for diagnostics of the solar corona.

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65

Session 6: MHD Waves in Astrophysical Magnetic Structures

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Invited Review: Magnetoseismology of accretion disks

Rony Keppens (1,2,3), Jan-Willem Blokland (2), Hans Goedbloed(2,3)

(1) Centre for Plasma-Astrophysics, K.U.Leuven (2) FOM-Institute for Plasma Physics Rijnhuizen

(3) Astronomical Institute, Utrecht University

Abstract

We review recent insights on magnetohydrodynamic waves and instabilities in accretion disk models. We apply MHD spectroscopy, i.e. the ability to compute all waves and instabilities for a given equilibrium configuration, and use the knowledge that the continuous parts (Alfvén and slow) in the spectrum form the basic organizing structure for categorizing the various wave types. The application of MHD spectroscopy to magnetized accretion disks is challenging due to the presence of a stationary (i.e. flowing), gravitationally stratified equilibrium state. In particular, we point out how: • the transition from static to stationary equilibria introduces forward and backward Doppler shifted continua and how the familiar MHD Alfvén and slow continua reduce to the flow continuum of a stationary hydrodynamic equilibrium; • the application of the Frieman-Rotenberg formalism to radially stratified accretion disks has provided new insights into the nature and relative importance of the magneto-rotational instability in accretion flows; • a fully self-consistent computation of axisymmetric accretion disk tori and their MHD spectra demonstrated the existence of a novel class of violently unstable Alfvén continuum modes when crosssectional poloidal flows exceed the slow magnetosonic speed. These ‘trans-slow’ Alfvén continuum modes are

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intrinsically localized to individual flux surfaces, and thus form ideal candidates to explain the observationally inferred highly turbulent nature of accretion disks.

68

The periodic variations of stellar flares

M. Mathioudakis (1), S. Bloomfield (1,2), D.B.Jess (1) (1) Physics and Astronomy, Queens University Belfast, Northern

Ireland (2) currently at : Max Planck Institute, Katlenburg-Lindau,

Germany

Abstract

The white-light flares observed in cool stars can be as much as 104 times more energetic than their solar counterparts. Multi-wavelength observations of stellar flares have revealed the existence of periodic signatures on the flare light-curves. I will review some recent observations on the subject and discuss the application of solar atmospheric seismology techniques to stellar studies.

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Damping of hydromagnetic waves by bulk viscosity

Miguel H. Ibáñez S.

Centro de Física Fundamental, Universidad de los Andes, Apartado 26, Ipostel, La Hechicera, Mérida, Venezuela

Abstract

As it was shown in a previous paper (2004) for certain kind of plasmas the coefficient of second (bulk) viscosity can be orders of magnitude larger than the coefficient of the dynamical viscosity and the thermometric conductivity. At the present paper the damping effects of the second viscosity on the hydromagnetic waves propagating in optically thin plasmas is analyzed. In particular, mhd waves propagating in a photoionized gas of arbitrary metallicity Z and mean photon energy of the ionizing photons E where an initial steady magnetic field H is present.

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Slow nonlinear and shock waves in flux tubes

Y.D.Zhugzhda IZMIRAN, Troitsk, Moscow Region, 142190 Russia

Abstract

The theory of weakly nonlinear waves in flux tubes is described. It is pointed out that it is not possible to make a choice between different model equations obtained in the long-wavelength approximation. The only way to obtain an adequate description of slow waves is to use the model equation based on the dispersion law which has correct limits for short and long waves. Such kind of model equations for slow surface and body waves are presented. The model equation for slow shock waves in flux tubes is presented. This model equation is the extension of KdV-Burgers equation. It is revealed that along with shock waves the slow body bore wave occurs in flux tubes. The bore waves are well-known in hydrodynamics.

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Session 7: Modern Data Analysis Methods for Wave and Oscillation Phenomena

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Invited Review: Modern Data Analysis Methods for Wave and Oscillation Phenomena

Bernhard Fleck (1), Jack Ireland (2)

(1) European Space Agency, c/o NASA/GSFC (2) L3Com/GSI, c/o NASA/GSFC

Abstract

Waves and oscillations in the Sun’s atmosphere have been studied in great detail since the discovery of the 5-min oscillations in the early sixties. The recent discoveries of oscillations in coronal structures by SOHO and TRACE have opened new prospects for ”coronal seismology”. In many cases the characterization of the waves and oscillations is difficult because of a number of compounding factors. The waves usually have low amplitudes and thus low signal to noise in the observations, and their non-stationary behaviour in the dynamic, ever-changing atmosphere of the Sun adds to the complexity. Various methods have been developed to characterize and analyze waves and oscillations observed in the Sun’s atmosphere. Most prominent among them are Fourier methods (power, phase, coherence spectra) and Wavelet techniques, which have become en vogue in recent years after their implementation in IDL by Torrence & Compo. Other techniques have been somewhat overlooked. In this talk we will review a number of analysis techniques and highlight both their strengths as well as shortcomings.

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Application of statistical techniques to the analysis of solar coronal oscillations

J. Terradas, R. Oliver, J. L. Ballester

Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

Abstract

In this work, the application of two different techniques to the analysis of coronal time series is investigated. The first technique, called Empirical Mode Decomposition (EMD) can be used to decompose a signal in its characteristic time scales, allowing, among other applications, to filter the signal efficiently. The second technique, called Complex Empirical Orthogonal Function (CEOF) analysis, is an extension of the well-known Principal Component analysis. The CEOF analysis allows to identify the dominant spatial and temporal structures in a multivariate data set and is thus ideally suited for the study of propagating and standing features that can be associated with waves or oscillations. The application of both methods to time series obtained from a coronal loop are presented here. Detailed two-dimensional information of a propagating and a standing wave with periods around 5 and 10 min, respectively, is obtained.

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High frequency oscillations in active regions and sunspots

K. Muglach Naval Research Laboratory

Washington, (USA)

Abstract

High frequency waves are supposed to play an important role in the heating of the solar chromosphere according to various models. Recent oscillation simulations studied the propagation of waves in a magnetized solar atmosphere. This contribution presents the results of an observational study of the presence of high frequency oscillations (υ > 15mHz) in active regions and sunspots. In addition to standard Fourier techniques we will also use wavelet transforms to identify the high frequency waves and test the presence of significant oscillation power statistically.

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Application of the POD in the study of the solar atmospheric dynamics

A. Vecchio, G. Cauzzi, K. Janssen

INAF-Osservatorio Astro sico di Arcetri Largo Enrico Fermi 5, 50125

Firenze, Italy

Abstract

The POD has been traditionally employed to study coherent struc- tures in laboratory turbulent flow and was recently successfully applied to analyze oscillations (Vecchio et al. (2005)) and magnetic fields (Cadavid et al.(2005)) in the solar atmosphere We present here some applications of the POD for the analysis of periodic signals in the lower solar atmosphere, using both intensity and velocity data obtained with the imaging interferometer IBIS (mounted at the DST of NSO). In particular we show how the technique can isolate the contribution of spatially coherent phenomena (e.g. magnetic network) maintaining the resolution a orded by the full eld of view. Cadavid, A. C.; Lawrence, J. K.; McDonald, D. P.; Ruzmaikin, A., Solar Physics, Volume 226, Issue 2, pp.359 Vecchio A. et al., Physical Review Letters, vol. 95, Issue 6, id. 061102

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Closing Summary: B. Roberts

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Posters

78

Wave-like magnetic disturbances within solar flux ropes

E. Romashets and S. Poedts Centre for Plasma Astrophysics, KU Leuven

Abstract

To treat local disturbances in a solar flux rope we consider the magnetic field in its interior as a superposition of two linear (alpha=const.) force-free distributions: first a global one, which is locally similar to a part of a cylinder, and next local toroidal distribution. The axes of the toroid and the cylinder coincide. The large and small radii of the toroid are set equal to the cylinder’s radius. Depending on the field magnitude and the handedness there is a local decrease or increase of the flux tube diameter. The different physical nature of processes caused by this inhomogeneity can lead to motions along the tube or to oscillations at a given point in the tube. We are going to use this approach for the interpretation of limb observations. The newly derived solution for a toroid with an aspect ratio close to unity is applied, in terms of full elliptical integrals. Force-free toroidal distributions that are available in the literature (for example Miller and Turner, 1981) can be applied only to the case of small inverse aspect ratios.

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Coronal seismology using periods and damping rates of oscillating loops

I. Arregui (1), J. Andries (2), T. Van Doorsselaere (2),

M. Goossens (2), & S. Poedts (2) (1) Departament de Física, Universitat de les Illes Balears

E-07122 Palma de Mallorca, Spain (2) Centrum voor Plasma Astrofysica, KULeuven, Celestijnenlaan 200B, B-3001 Heverlee, Belgium

Abstract

We report on how the combination of observational values of the period and the damping rate of transverse loop oscillations and theoretical and numerical results for resonantly damped quasi-mode kink oscillations in non-uniform flux tubes can be used to extract information on physical parameters in oscillating coronal loops. Observationally estimated periods and damping rates of coronal loops are used together with parametric studies of the period and damping of quasi-mode kink oscillations to calculate equilibrium models that have the same period and damping rate as observed through the assumed damping mechanism. The use of both the observed periods and damping rates allows us to obtain the valid equilibrium models in the form of a one-dimensional curve in the three-dimensional parameter space (density contrast; Alfvén speed; inhomogeneity length-scale). The possible values for the internal Alfvén speed are found to be restricted to a rather narrow range, showing also an upper limit. The present method not only allows the estimation of unknown physical parameters of coronal loops, but is also a test of the assumed physical damping mechanism.

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Fast magnetohydrodynamic oscillations in two cylindrical coronal loops: Collective behaviour

M. Luna, J. Terradas, R. Oliver, J.L. Ballester

Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

Abstract

We study fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma cylindrical flux tubes in a uniform magnetic field. The time-dependent problem of the excitation of loop oscillations is analysed by numerically solving the initial value problem. We investigate the behaviour of the system for several shapes of planar pulses. This allows us to study in a simple configuration the collective behaviour of the structure due to the interaction between the two cylinders. We nd that for any initial disturbance the loops oscillate with the normal modes of the coupled system, which are different from the modes of the individual loops. In addition, we show that for some initial conditions there is a continuous exchange of energy between the individual magnetic flux tubes.

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Time dependent simulations of sideways driven coronal loop oscillations

Tom Van Doorsselaere (1), Stefaan Poedts (1),

Inigo Arregui (2), Jesse Andries (1) (1) Centrum voor Plasma-Astrofysica, KULeuven,

Celestijnenlaan 200B, B-3001 Leuven, Belgium (2) Departament de Física, Universitat de les Illes Balears,

E-07122 Palma de Mallorca, Spain

Abstract

We use the computer code PET to study the time evolution of a two dimensional cylindrical coronal loop. The coronal loop is driven monoperiodically from the side in the framework of linear MHD. When the driver period matches the kink quasi-mode frequency closely, a resonant layer is formed and damping occurs. As a result of the resonance, three phases in the time evolution can be distinguished. Initially, we have a build-up phase when the resonant layer is set up. In this phase the amplitude of the global oscillation increases linearly. Secondly, a steady state is obtained. In this state, the driver energy is exactly dissipated in the resonant layer. Consequently, the amplitude of the oscillations is constant. As a last phase, we distinguish the time interval when the driver is stopped. As expected, in this phase, the global kink oscillation damps out exponentially. The measured damping times correspond very closely to the values obtained in the eigenvalue problem (Arregui et al. 2005). When considering a radially highly inhomogeneous coronal loop and a large density contrast between the interior of the loop and the surroundings, the oscillations are heavily damped. As a result, the build-up phase is very short (only a few periods) and the amplitude in the steady state is small. Consequently, after a few cycles, much more driver energy than

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the energy in the global oscillation is dissipated. The classical argument that not enough oscillatory energy is observed in the solar corona to sustain the heating, is therefore invalid. The fact that little oscillations are observed, does not mean that no oscillation energy is dissipated. The amount of observed oscillatory energy is not related to the total energy dissipated by waves.

83

Time damping of non-adiabatic MHD waves in a multilayer slab model

R. Soler, R. Oliver, and J. L. Ballester

Departament de Física. Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.

Abstract

We study the time damping of non-adiabatic MHD waves in a multilayer slab model made of a prominence region, a prominence-corona transition region and a coronal region.

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X-ray quasi-periodic pulsations in solar flares driven by magnetohydrodynamic oscillations in a nearby loop

C. Foullon (1,2), V. M. Nakariakov (1), E. Verwichte (1),

L. Fletcher (3) & N. P. Young (1) (1) Centre for Fusion, Space and Astrophysics, Department of

Physics, University of Warwick, Coventry CV4 7AL, UK (2) Mullard Space Science Laboratory, University College London

Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK (3) Department of Physics and Astronomy, University of Glasgow

Glasgow G12 8QQ, UK

Abstract

In Foullon et al. (2005), we analysed long-period (8-12 min) quasiperiodic pulsations (QPP) of X-ray radiation during solar flares, made possible with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), supported by complementary data at other wavelengths from space-based and ground-based telescopes. Evidence for the presence of a transequatorial loop possibly responsible for the detected periodicity connected with its kink mode was found. Our findings suggested that QPP can be interpreted as a periodic pumping of electrons in a compact flaring loop, modulated by oscillations in a magnetically linked and larger loop acting as a long-period magnetohydrodynamic resonator. Our new model for quasi-periodic modulation of solar and stellar flaring emission (Nakariakov et al., 2006) can explain the coupling of oscillations in nearby loops with QPP of flaring energy release. The interaction between fast magnetoacoustic oscillations of a non-flaring loop and a nearby flaring active region occurs when part of the oscillation situated outside the loop reaches the regions of steep gradients in magnetic field within an active region and produce periodic variations of electric current

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density. The modulation depth of these variations is a few orders of magnitude greater than the amplitude of the driving oscillation. The variations of the current can induce current-driven plasma micro-instabilities and thus anomalous resistivity. This can periodically trigger magnetic reconnection, and hence acceleration of charged particles, producing quasiperiodic pulsations of X-ray, optical and radio emission at the arcade footpoints.

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Fast and Slow MHD Waves in a Gravitationally Stratified Corona

A. M. D. McDougall, A. W. Hood and I. De Moortel

School of Mathematics and Statistics. St Andrews University, St Andrews,

Fife KY16 9SS (Scotland)

Abstract We wish to investigate the coupling between fast and slow wave modes in a gravitationally stratified magnetic field. The investigation has taken the form of a numerical study backed up by analytical work using, for example, the WKB method. Having verified the code results, a number of simulations have been run in order to examine the behaviour and interaction of the different wave modes across the region where the sound and Alfven speeds are of comparible size.

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Resonantly damped oscillations of longitudinally stratified coronal loops

Maria V. Dymova, Michael S. Ruderman

Department of Applied Mathematics, University of She eld, Hicks Building, Hounsfield Road, She eld S3 7RH, UK

e-mail: M.S.Ruderman@sheffield.ac.uk

Abstract

Soon after coronal loop oscillations were observed by TRACE spacecraft for the first time in 1999, various theoretical models have been put forward to explain the rapid damping of the oscillations of these intriguing objects. Coronal loop oscillations are often interpreted as fast kink modes of a straight cylindrical magnetic flux tube with immovable edges modelling dense photospheric plasma at the ends of the loop. Taking this model as a basis we use cold plasma approximation and consider the tube to be thin to simplify the problem and be able to deal with it analytically. In its equilibrium state the tube is permeated by a homogeneous magnetic field directed along the tube axis. We include the effect of stratification in our model supposing that plasma density varies along the tube. There is also density inhomogeneity in the radial direction confined in a layer with thickness much smaller than the radius of the tube. Considering the system of linearized MHD equations we study the dependence of the spectrum of tube oscillations and its damping due to resonant absorption on the parameters of the unperturbed state. The implication of the obtained result on coronal seismology is discussed.

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Anomalous dissipation of torsional flux-tube waves

T.Siversky, Y.Voitenko, M.Goossens Centre for Plasma Astrophysics, K.U.Leuven,

Celestijnenlaan 200B, B-3001 Heverlee, Belgium e-mail: taras.siversky@wis.kuleuven.be

Abstract

Torsional waves and perturbations in magnetic flux-tubes are efficient agents for transporting energy in the solar corona. We study a mechanism for the damping of these waves and its possible role in coronal heating. There is a field-aligned electric current inside the magnetic flux-tube when the torsional wave propagates along it. This current is a subject to anomalous dissipation due to current-driven instability of kinetic Alfvén waves. We use the kinetic electro-magnetic approach to study this micro-instability. We found that the cross-field gradient of the electron current reduces the threshold current velocity for the instability well bellow the Alfvén velocity.

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Spatial damping of MHD waves in a prominence medium

M. Carbonell (1), J. Terradas(2), R. Oliver(2) & J. L. Ballester (2)

(1) Dept. Matemàtiques. Univ. Illes Balears. E-07122 Palma de Mallorca, (Spain)

(2) Dept. Física. Univ. Illes Balears. E-07122. Palma de Mallorca, (Spain)

Abstract

Using an energy equation with optically thin radiative losses, thermal conduction and heating, we have studied the spatial damping of MHD waves in a prominence medium. The results point out that at long and intermediate periods, the spatial damping of magnetoacoustic waves is dominated by radiation, while at short periods thermal conduction dominates. Then, for the interval of periods detected in prominence oscillations, radiation is responsible for the spatial damping of magnetoacoustic waves and, while the fast wave displays a very long damping length, the slow wave shows that for typical periods of prominence oscillations between 5 and 15 minutes, the damping length is order 104 – 105 km. On the other hand, the thermal wave, which in this case of spatial damping is a propagating wave, displays, when compared with the magnetoacoustic waves, the shortest damping length and damping length per wavelength.

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The damping of prominence oscillations by ion-neutral collisions

P. Forteza (1), R. Oliver (1), J. L. Ballester (1),

M. L. Khodachenko (2) (1) Departament de Física, Universitat de les Illes Balears, E-

07122 Palma de Mallorca, Spain (2) Space Research Institute, Austrian Academy of Sciences,

A-8042 Graz, Austria

Abstract Small-amplitude oscillations in quiescent prominences have been known for long time. Often, these oscillations have been interpreted in terms of MHD waves and the observations show that one of the typical features of those oscillations is that they are damped with time. Since solar prominences are partially ionised plasmas, one can consider the ion-neutral collisions as one of the potential mechanisms to explain this damping. Here, we report the results obtained about the time damping of fast and slow waves by means of ion-neutral collisions.

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Sunspot oscillations: theory and comparison with observations

Y.D.Zhugzhda

IZMIRAN, Troitsk, Moscow Region, 142190 Russia

Abstract

The exploration of sunspot oscillations lasts for long time but there is no generally accepted theory of the phenomenon. An adequacy of different mathematical approaches to the problem and real physical problem is discussed. Wealth of observational evidence and analysis of sunspot models testify against eigenoscillations of sunspots. In contrast with p-modes, the eigenvalue approach is not suitable for sunspot oscillations since oscillations are not captured by sunspots. The exploration of filtering properties of sunspot atmosphere is the correct way to develop the theory. The filtering through temperature minimum and chromosphere is considered. The possibility of the seismology of sunspot atmosphere is considered. The theory is compared with observations. The effects of inhomogeneity of the atmosphere is discussed. The nonlinear 3-min oscillations are discussed.

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Analytical signal as a new tool for helioseismology

Y. D. Zhugzhda IZMIRAN, Troitsk, Moscow Region, 142190 Russia

Abstract

A new method of treatment for narrow band oscillatory processes is described. The method is based on the concept of analytical signal. It makes possible to obtain instant frequency, amplitude and phase of oscillations. The resolution of rather closed lines in spectrum is possible. It makes possible to separate the effects of amplitude and frequency fluctuations on line broadening. The method is applied to the treatment of brightness oscillations of the Sun observed by the multichannel photometer on the board of CORONAS satellite. It is revealed that the line width of p-modes appears mostly due to amplitude fluctuations while frequency fluctuations are very low. The exploration of phase relations between different channels of the photometer discovers that p-modes from deep and upper layers of photosphere are running to the middle layers. This effect is possible only for nonadiabatic evanescent p-modes.

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List of Participants

J. Andries Centre for Plasma Astrophysics

K. U. Leuven (Belgium)

I. Arregui Departament de Física, Universitat

de les Illes Balears, Palma de Mallorca (Spain)

I. Ballai Space and Atmosphere Research Centre

Department of Applied Mathematics University of Sheffield (UK)

J. L. Ballester

Departament de Física, Universitat de les Illes Balears, Palma de Mallorca (Spain)

D. Banerjee

Indian Institute of Astrophysics Koramangala, Bangalore (India)

A. Birch

NWRA/CoRA, Boulder, CO, (USA)

M. Carbonell Departament de Matemátiques i Informática, Universitat

de les Illes Balears, Palma de Mallorca (Spain)

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A. Díaz School of Mathematics and Statistics

St Andrews University (Scotland)

G. Doyle Armagh Observatory,

Armagh (Northern Ireland)

M. Dymova Dept. of Applied Mathematics, University of Sheffield (UK)

R. Erdélyi

Space & Atmosphere Research Center, Dept. of Applied Mathematics, University of Sheffield (UK)

V. Fedun

Space & Atmosphere Research Center, Dept. of Applied Mathematics, University of Sheffield (UK)

B. Fleck

European Space Agency NASA/GSFC 20771 (USA)

P. Forteza

Departament de Física, Universitat de les Illes Balears, Palma de Mallorca (Spain)

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M. Goossens Centre for Plasma Astrophysics

K. U. Leuven (Belgium)

A. W. Hood School of Mathematics and Statistics.

St Andrews University (Scotland)

M. H. Ibañez Centro de Física Fundamental

Universidad de los Andes Merida (Venezuela)

R. Jain

Space & Atmosphere Research Center, Dept. of Applied Mathematics, University of Sheffield (UK)

R. Keppens

Centre for Plasma Astrophysics K. U. Leuven (Belgium)

M. L. Khodachenko

Space Research Institute Austrian Academy of Sciences,

(Austria)

A. Kosovichev HEPL A204, Stanford University

Stanford (USA)

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Y. Lin Institute of Theoretical Astrophysics

University of Oslo (Norway)

M. A. Loukitcheva

Astronomical Institute, St Petersburg (Russia)

M. Luna

Departament de Física, Universitat de les Illes Balears, Palma de Mallorca (Spain)

M. S. Marsh

NASA/GSFC (USA)

M. Mathioudakis

Physics and Astronomy Queens University

Belfast (Northern Ireland)

A. M. D. McDougall School of Mathematics and Statistics. St Andrews University, St Andrews,

(Scotland)

M. P. McEwan Mathematical Institute, University of St

Andrews, St. Andrews (Scotland)

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C. A. Mendoza-Briceño Centro de Astrofisica Teorica, CAT

Universidad de los Andes Merida (Venezuela)

K. Muglach

Naval Research Laboratory Washington (USA)

K. Murawski

Institute of Physics UMCS, Lublin (Poland)

V. Nakariakov

Centre for Fusion, Space & Astrophysics University of Warwick (UK)

R. Oliver

Departament de Física, Universitat de les Illes Balears, Palma de Mallorca (Spain)

E. O’Shea

Armagh Observatory, Armagh (Northern Ireland)

D. J. Pascoe

University of Warwick (UK)

B. Pinter Space & Atmosphere Research Center,

Dept. of Applied Mathematics, University of Sheffield (UK)

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G. Pouget Institute d’Astrophysique Spatiale

(France)

A. Roberts Mathematical Institute

University of St Andrews (Scotland)

M. Ruderman Space & Atmosphere Research Center,

Dept. of Applied Mathematics, University of Sheffield (UK)

R. J. Rutten

Sterrenkundig Instituut, Universiteit Utrecht, Utrecht (The Netherlands)

M. Ryutova

LLNL, California (USA)

B. Shegerlasvili Centre for Plasma Astrophysics

K. U. Leuven (Belgium)

R. Soler Departament de Física, Universitat

de les Illes Balears, Palma de Mallorca (Spain)

Y. Taroyan Space & Atmosphere Research Center,

Dept. of Applied Mathematics, University of Sheffield (UK)

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J. Terradas Departament de Física, Universitat

de les Illes Balears, Palma de Mallorca (Spain)

D. Tsiklauri Institute for Materials Research, University of Salford,

Greater Manchester (UK)

T. Van Doorsselaere Centre for Plasma Astrophysics Katholieke Universiteit Leuven

(Belgium)

A. Vecchio Osservatorio Astrofisico Arcetri

Firenze (Italy)

G. Verth Space & Atmosphere Research Center,

Dept. of Applied Mathematics, University of Sheffield (UK)

E. Verwichte

Departament of Physics University of Warwick (UK)

S. Wedemeyer-Böhm

Kiepenheuer-Institut für Sonnenphysik Freiburg (Germany)

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N. P. Young Physics Department,

University of Warwick Coventry (UK)

T. Zaqarashvili

Abastumani Astrophysical Observatory (Georgia)

Y. D. Zhugzhda

IZMIRAN, Troitsk Moscow region (Russia)