1. Transverse (Kink) Oscillations

1. MHD Coronal Seismology with SDO/AIAUK Community ViewsLen Culhane, MSSLwith inputs fromValery Nakariakov, WarwickIneke de Moortel, St AndrewsDavid Williams, MSSLMihalis Mathioudakis, Queen’s University

2. 1. Transverse (Kink) Oscillations Commonly accepted interpretation • Standing fast magnetoacoustic m=1 modes of coronal loops Seismological applications • Estimation of the mean value of the magnetic field strength (Nakariakov and Ofman, 2001) • Estimation of the density stratification in the loop (Andries et al. 2005) Open questions • Excitation Mechanisms • Decay Mechanisms • Selectivity of the Excitation • Role of Nonlinear Effects • Use of Observations for Seismology

3. Necessary Theoretical Developments • 3- D MHD modelling • Incorporation of fine structuring effects • - stratification, curvature, nonlinearity in simple • magnetic geometries (isolated loop, arcade, • parallel loops bundle) • Parametric numerical study of the dependence of • observables on model parameters (period, decay • time, time dependence, scaling laws) • Derivation of simple analytical expressions • Linking the observables with physical parameters in the loop (e.g. magnetic • field strength) • 3- D MHD numerical modelling in extrapolated magnetic geometry • Linking the outcomes with analytical theory • Testing the robustness of the modelling, in particular to the errors in extrapolation • and to computational constraints • Creation of seismological methods for the determination of coronal currents by • MHD waves

4. 2. Longitudinal (Slow) Waves Commonly Accepted Interpretation: • Slow magnetoacoustic perturbations, guided by magnetic field lines. Seismological Applications: • Observables (periods, wave lengths, height evolution) depend strongly upon thermal effects - information about the heating function. • Modes are natural probes of coronal thermal structure - simultaneous detection of mode in TRACE 171A and 195A suggested as a probe of sub-resolution structuring of the corona (King et al., 2003) Open Questions: • What is their origin and driver? • What determines the periodicity and coherence of propagating waves? • What is the physical mechanism for the abrupt disappearance of the waves at a certain height • Are the waves connected with the running penumbra waves? (King et al., 2003)

5. Necessary Theoretical Developments • Effects of transverse structuring (physical and observational). • Incorporation of a realistic TR and chromosphere in the model, including 2-D and partial ionisationeffects. • Investigation of thermal over-stability of coronal plasmas. • Forward modelling of observables.

6. Novel Data Analysis Techniques - Periodogram Mapping • Periodograms of the time signals from each pixel of analysed data cube are calculated. • Determine whether there is a spectral peak with an amplitude over a prescribed confidence level. • There are two types of maps: • - Periodomaps: pixel colour corresponds to the • detected period if its amplitude exceeds a certain • threshold • - Filtermaps: pixel colour corresponds to the • amplitude of the detected signal, if the period • is in a certain prescribed range. • Reduce a 3-D data cube to a 2-D periodogram map • Current desktop computing for 4k x 4k datacube takes 150 hours; sample duration was ~ 83 minutes at 30 sec cadence - code in IDL - using regular Fourier transform - gain at least x 10 with FFT and better code Periodomap of a TRACE data cube from the 2nd of July 1998. The period detection level is 95%. The period range is 2.9-3.2 mHz.

7. Solar-B – Role of EUV Imaging Spectrometer • Solar-B launched two years before SDO • Observations will focus on individual Active Regions and Photospheric Dynamics • Spectral line wave observations with EIS will be challenging • Identify target structures for joint observations • Measure ne (ratios), vplasma (peak shifts) and vnon-thermal (line widths) • Undertake Doppler shift and broadening observations related to wave phenomena (e.g. torsional Alfven modes) • Before SDO launch, rehearse using EIS observations of structures in campaigns with TRACE • Establish links between Solar-B observation planning and SDO operational modes for joint study of targets of interest for coronal seismology

8. EIS Instrument Features • Large Effective Area in 2 EUV bands: 170-210 Å and 250-290 Å • Multi-layer Mirror (15 cm dia ) and Grating • both with optimized Mo/Si Coatings • CCD camera • two 2048 x 1024 high QE back-illuminated CCDs • Spatial resolution → 1 arc sec pixels/2 arc sec resolution • Line spectroscopy with ~ 25 km/s per pixel sampling • Field of View： • Raster: 6 arc min×8.5 arc min • FOV centre moveable E – W by ± 15 arc min • Wide temperature coverage: log T = 4.7, 5.4, 6.0 - 7.3 K • Simultaneous observation of up to 25 lines (spectral windows)

9. Density Sensitive Line Ratio • Density sensitive line ratios with pairs of forbidden lines • Filling factor of coronal loop estimated at 2 arc sec resolution • CHIANTI is used for this estimate • Fe XI line ratios 182.17/188.21 and 184.80/188.21 will also be • useful (Keenan et al. 2005)

10. Doppler Velocity and Line Width Uncertainties Flare line Bright AR line Doppler velocity Line width Photons (11 area)-1 sec Photons (11 area)-1 (10sec)-1 • One-s uncertainty in: - Doppler shift (dv in km/s) - Non-thermal line width (dFWHM in km/s) • Values are plotted against number of detected photons in the line for: - Bright AR line (Fe XV/284 Å) - Flare line (Fe XXIV/255 Å)

11. Simulated cross-section of a loop with radius 720 km (1” Earth view). Horizontal axis is perpendicular to the observer’s line-of-sight, whilst the vertical axis extends parallel to the line-of-sight. Coloured areas: Simulated line-of-sight velocities Contours: Line-of-sight velocity multiplied by ne2 • Williams et al. simulated effect on line profile of a torsional wave passing through a coronal AR loop – effects invisible in e.g. TRACE-like passband unless high velocities Loop Cross Section and Coronal Parameters • Calculated emission from a flux tube imaged by Solar-B EIS assuming: • 1 arc sec spatial pixel • 23 mÅ spectral pixel • Fe XII 195 Å line registered in EIS • possible periods ~ 10 – 100 s • assume Dt = 1s in 1 arc sec slice at loop apex • Assume radial profile of azimuthal velocity • amplitude (Ruderman et al.,1997)is • Vf (r) = 16 vo (r/a)2 (1 – r/a)2 • vo is maximum azimuthal velocity, a is loop • radius and f is measured clockwise from • line-of-sight about loop axis • Also assume Bo = 50 G, ne, max = 2.109, • Te = 1.5.106 K, ne, core is x10 external • density (r > a) and loop length L = 10a

12. Simulated Line Profiles Simulated profile of the Fe XII 195 Å line in EIS B AR loop of radius a = 350km (0.5”) Loop cross-section is contained in a single 1” pixel Torsional velocity amplitude maximum of 25 km.s-1. Rest profile centre shown by vertical dotted line. Spatially averaged, optically thin torsional broadening mimics a non-thermal velocity of approximately half the maximum amplitude of the actual azimuthal velocity. Simulated profile of the Fe XII 195 Å line in EIS B AR loop of radius a=720km (1.0”) Loop cross-section straddles two pixels, each of which detects a profile with a different centroid For receding right-hand side (x > 0), profile has spatially averaged red-shift of ~ 12 km.s-1 Approaching left-hand side of loop shows apparent blue-shift of ~ 5 km.s-1 Discrepancy is largely due to the photon noise in these simulated lines.

13. Coronal Seismology Requirements Summary • Observational • Observe transverse “kink” modes in coronal loops to enable seismology applications • e.g. magnetic field estimates, damping scaling laws • - search for higher harmonics for density stratification information • Study propagating longitudinal waves throughout the solar atmosphere to investigate • coupling of different regions of solar atmosphere and probe thermal structure • - high-cadence observations of quiescent coronal loops in a wide Te range • Observe EIT waves to check evolution of wave amplitude and speed with distance • study wave front interaction with active regions • establish height structure of disturbances • - clarify role of global magnetic topology • Search for torsional Alfven modes • - observe line shifts and broadenings with Solar-B EIS and target structures • at high cadence with AIA

14. Coronal Seismology Requirements Summary • Theoretical • Incorporate effects of e.g fine structure, stratification, curvature, in analytical theory • and numerical simulations for propagation in simple loop geometries • Incorporate transverse structure and realistic transition region and chromosphere in analytical theory and numerical simulations for propagation throughout atmosphere • Examine role of magnetic topology in wave propagation – EIT waves? • Techniques and Tools • Automated detection of wave modes and oscillations • periodogram mapping search for significant periods • amplitude search within specified frequency ranges • Develop robust and automated (?) wavelet analysis techniques • Relate NLFF extrapolated magnetic fields (HMI) with AIA wave observations • Joint spectral (Solar-B) and imaging (AIA) observations → ne, vplasma, vnon-thermal

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16. EIS Sensitivity Detected photons per 11 area of the Sun per 1 sec exposure.

17. l/Dl ~ 4600 57.7 mÅ 58.1 mÅ 57.9 mÅ Spectroscopic Performance Long Wavelength Band • Ne III lines near 267 Å from the NRL Ne–Mg Penning discharge source • Gaussian profile fitting gives the FWHM values shown in the right-hand panel

18. l/Dl ~ 4000 47 mÅ 47 mÅ Spectroscopic Performance Short Wavelength Band • Mg III lines near 187 Å from the NRL Ne–Mg Penning discharge source • Gaussian profile fitting gives the FWHM values shown in the right-hand panel

19. Slit and Slot Interchange • Four slit/slot selections available • EUV line spectroscopy - Slits - 1 arcsec  512 arcsec slit - best spectral resolution - 2 arcsec  512 arcsec slit - higher throughput • EUV Imaging – Slots • Overlappogram; velocity information overlapped • 40 arcsec  512 arcsec slot - imaging with little l overlap • 250 arcsec  512 arcsec slot - detecting transient events

20. Shift of FOV center with coarse-mirror motion Maximum FOV for raster observation 360  900  900  512  512  512  Raster-scan range 250  slot 40  slot EIS Slit EIS Field-of-View

21. EIS Effective Area Primary and Grating: Measured - flight model data used Filters: Measured - flight entrance and rear filters CCD QE: Measured - engineering model data used Following the instrument end-to-end calibration, analysis suggests that the above data are representative of the flight instrument