AYA2003-00123 Oscillations in Solar Coronal Magnetic Structures P. I.: J. L. Ballester (Staff) R. Oliver (Staff) Department of Physics M. Carbonell (Staff) University of the J. Terradas (J. De la Cierva) Balearic Islands T. Zaqarashvili (Postdoc) P. Forteza (Ph. D. Student, FPU) M. Luna (Ph. D. Student, FPI) I. Arregui (Now Postdoc Leuven) A. Díaz (Now Postdoc St Andrews) 1
Outline Motivation of the Research Grant MHD Coronal Seismology Research Grant: Progress Report Ongoing and Future Research 2
Motivation: Oscillations in Coronal Loops T = 256 s,τd = 870 s Damped Oscillations understood as Standing Fast Kink MHD wave TRACE > 20 events Aschwanden et al. ApJ, 520, 3880, 1999
Motivation: Oscillations in Prominences and.. Doppler velocity movie T=80 min, τ=170 min, V 0 =2 km/s T=85 min, τ=367 min, V 0 =1.7 km/s (Terradas et al., A+A, 393, 2002) 4
Filaments Significant periodicity at 26 min. strongly damped after 4 periods Same phase maintained over a large filament area (Lin, 2004) Evidence for Coronal waves has grown 5 dramatically during last years
MHD Coronal Seismology MHD waves have been intensively investigated for more than two decades in the context of coronal heating and acceleration of fast solar wind We need to know physical conditions and parameters in the Corona which are difficult to measure accurately [coronal magnetic field, transport coefficients (viscosity, resistivity, thermal conductivity, etc.), heating function, filling factors] Coronal waves provide with an indirect path to determine unknown physical parameters of the Solar Corona 6
MHD coronal seismology Observations (imaging, spectral) MHD wave theory (dispersion relations, evolutionary equations) Properties of waves (Speeds, amplitudes, spectra, signatures) Physical parameters of the corona (density, temperature, structuring ) MHD Seismology Physical parameters of the corona: (magnetic field, subresolution structuring, transport coefficients, 7
Research Grant: Progress Report 8
1.- MHD waves in sheared coronal arcades Effects of magnetic field shear (B y 0) and longitudinal propagation of perturbations (k y 0) on the normal modes of oscillation of a potential coronal arcade Finite differences code with staggered mesh Linear coupling of discrete fast modes and Alfvén continuum modes. Modes with mixed properties 9arise
1.- MHD waves in sheared coronal arcades No B y Only B y Coupling rules. With k y and B y, no evanescent modes 10 (Arregui et al., A+A, 425, 729, 2004)
We have studied: 2.- Time Damping of Oscillations in the Solar Corona Time damping of oscillations in a homogeneous, isothermal, unbounded medium with uniform magnetic field, with Prominence, PCTR and Corona physical properties. Heat - loss function including optically thin radiation, different heating mechanisms and parallel thermal conduction (Carbonell et al., A+A, 415, 739, 2004) Time damping of oscillations in a bounded slab Prominence 11
2.- Time Damping of oscillations in a bounded Slab prominence Bounded slab prominence Thermal conduction and a heat - loss function: L(ρ, T) = χ * ρt α - hρ a T b Damping of the slow mode (Terradas et al., A+A, 434, 741, 2005) 12
3.- MHD Modes in Multifibril filaments Remember Lin s Observations: Oscillations in phase over a large part of the filament!! (Díaz et al., A+A, 440, 1167, 2005) 13
4.- Application of Statistical Techniques to the Analysis of Coronal Oscillations To apply methods, borrowed from other disciplines of physics, to the analysis of coronal oscillations data Empirical Mode Decomposition (EMD): Allows to separate a signal into its intrinsic modes of oscillation Complex Empirical Orthogonal Function analysis: Allows to extract oscillatory features (such as standing or propagating waves) contained in a spatially distributed data set Application to Coronal Loop Oscillations: TRACE 171 Å observation of AR 8496 taken on March 23, 1999 14
4.- EMD + CEOF Analysis EMD analysis of the time series at each spatial point. Obtain a filtered time series without noise and trend CEOF analysis of the filtered data set. Spatial and Temporal Amplitude and phase Five modes account for 71% variance of the signal. Oscillations with different properties 15
4.- CEOF analysis: Short periods Reconstruction of the field with two modes (5.3 and 4.3 min) Period of propagating disturbance is around 5 min 16
4.- CEOF analysis: Long periods Reconstruction of the field with one mode (~ 10 min) 17
4.- Interpretation Propagating disturbance (with T 5 min) seems to be a propagating slow mode, since v ph 100 km s -1 (exciter: p-mode?) Standing wave (with T 11 min) can be a normal mode of the structure: Length of loop L 120 Mm Fundamental mode (nodes at the feet only) c 364 km s -1 18 First harmonic (additional node at the top) c 182 (Terradas et al. ApJ, 614, 435, 2004) T 1.2 MK
5.- Coronal Loop Oscillations 5.1 Numerical Simulations Aim: To study the temporal evolution of oscillations in coronal structures, such as coronal loops, in order to gain a more in-depth knowledge of the damping of oscillations Suitable codes for temporal evolution and parallel computations like PDE2D (Finite elements (Sewell, ); CLAWPACK (Leveque, 2002)) We have studied: The excitation and damping of transversal coronal loop oscillations (Terradas et al., Ap. J. L., 618, 2005) The excitation of Trapped and Leaky modes in coronal slabs (Terradas et al., A+A, 2005, In press) The excitation and damping of Transversal oscillations in 19 a cylindrical loop with an inhomogeneous layer (Terradas
5.- Coronal Loop Oscillations 5.1 Numerical Simulations Excitation and Damping of Transversal coronal loop oscillations using a 2D line-tied cylindrical loop with an inhomogeneous layer First temporal evolution simulation of Flare induced Kink oscillations Initial disturbance in the solar corona induces kink mode oscillations Resonant absorption damps the oscillation almost inmediately after excitation 20
5.- Coronal Loop Oscillations 5.2 Analytical Studies Fast MHD oscillations in line-tied homogeneous coronal loops with chromospheric layers: High-frequency modes in a homogeneous loop are trapped and should be detected in regular observations. The inclusion of a chromospheric layer produces that these modes become leaky, so, could be undetectable and damp the oscillations (Díaz et al., A+A, 424, 1055, 2004) Nightingale et al. (1999): Propagating compressing disturbances in a short loop system (~30 Mm). Periodic footpoint motions in the photosphere may resonantly amplify slow magnetoacoustic waves in the corona, at least in short coronal magnetic structures (with length < 21 50-70 Mm). Zaqarashvili et al., A+A, 433, 357, 2005)
Part of this research has been summarized in three Invited reviews: Ballester, J. L.: Recent Progress in Prominence Seismology. Royal Society Discussion Meeting on MHD waves in the Solar Atmosphere March 2005, London. (In press in Phil. Trans. Royal Soc. A) Ballester, J. L.: Theoretical Advances in Prominence Seismology. WISER Workshop on High Performance Computing in Plasmas. April, 2005, Leuven (In press in Space Science Reviews) Ballester, J. L.: Seismology of Prominence Fine Structures: Observations and Theory. WSEF Workshop. May 2005, Graz (To be published) Publications: 7 A+A, 1 Ap.J. + 2 submitted, 1 Ap. J. Let., 1 SSR, 1 Phil. Trans.) + ~ 20 Contributions 22 to
Ongoing and Future Research Time damping Prominence-PCTR-Corona bounded medium Ion-neutral collisional damping in prominences Fast MHD waves in Multifibril cylindrical systems: Time evolution Fast MHD waves in coronal loops with temperature profiles Numerical Simulations of collective oscillations in coronal loop systems 23