MHD Coronal Seismology with SDO/AIA

UK Community Views

Len Culhane, MSSLwith inputs from

Valery Nakariakov, WarwickIneke de Moortel, St Andrews

David Williams, MSSLMihalis Mathioudakis, Queen’s University

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

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

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)

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)

Effects of transverse structuring (physical and observational).

Incorporation of a realistic TR and chromosphere in the model, including 2-D and partial ionisation effects.

Investigation of thermal over-stability of coronal plasmas.

Forward modelling of observables.

Necessary Theoretical Developments

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.

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

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)

Density Sensitive Line Ratio

Density sensitive line ratios with pairs of forbidden lines

CHIANTI is used for this estimate

Filling factor of coronal loop estimated at 2 arc sec resolution

Fe XI line ratios 182.17/188.21 and 184.80/188.21 will also be useful (Keenan et al. 2005)

Doppler Velocity and Line Width Uncertainties

Doppler velocity

Line width

Bright AR line Flare line

Photons (11 area)-1 sec Photons (11 area)-1 (10sec)-1

One- uncertainty in: - Doppler shift (v in km/s) - Non-thermal line width ( FWHM 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)

Loop Cross Section and Coronal Parameters

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 velocitiesContours: Line-of-sight velocity multiplied by ne

2

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 t = 1s in 1 arc sec slice at loop apex

Assume radial profile of azimuthal velocity amplitude (Ruderman et al.,1997)is

V (r) = 16 vo (r/a)2 (1 – r/a)2

vo is maximum azimuthal velocity, a is loop

radius and 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

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

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.

Simulated Line Profiles

Coronal Seismology Requirements SummaryObservational

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

Coronal Seismology Requirements SummaryTheoretical

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

END OF TALK

EIS Sensitivity

Ion Wavelength

(A)

logT Nphotons

AR M2-Flare

Fe X 184.54 6.00 15 36

Fe XII 186.85 / 186.88 6.11 13/21 105/130

Fe XXI 187.89 7.00 - 346

Fe XI 188.23 / 188.30 6.11 41 / 15 110/47

Fe XXIV 192.04 7.30 - 4.0104

Fe XII 192.39 6.11 46 120

Ca XVII 192.82 6.70 31 1.8103

Fe XII 193.52 6.11 135 305

Fe XII 195.12 / 195.13 6.11 241/16 538/133

Fe XIII 200.02 6.20 20 113

Fe XIII 202.04 6.20 35 82

Fe XIII 203.80 / 203.83 6.20 7/20 38/114

Detected photons per 11 area of the Sun per 1 sec exposure. Ion Wavelength

(A)

logT Nphotons

AR M2-Flare

Fe XVI 251.07 6.40 - 108

Fe XXII 253.16 7.11 - 71

Fe XVII 254.87 6.60 - 109

Fe XXVI 255.10 7.30 - 3.3103

He II 256.32 4.70 16 3.6103

Si X 258.37 6.11 14 62

Fe XVI 262.98 6.40 15 437

Fe XXIII 263.76 7.20 - 1.2103

Fe XIV 264.78 6.30 20 217

Fe XIV 270.51 6.30 17 104

Fe XIV 274.20 6.30 14 76

Fe XV 284.16 6.35 111 1.5103

Spectroscopic PerformanceLong 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

57.7 mÅ58.1 mÅ

57.9 mÅ

~ 4600

Spectroscopic PerformanceShort 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

47 mÅ 47 mÅ

~ 4000

• 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 overlap– 250 arcsec 512 arcsec slot - detecting transient events

Slit and Slot Interchange

EIS Field-of-View

360

512

EIS Slit

Maximum FOV for raster observation

512

900 900

Raster-scan range

Shift of FOV center with coarse-mirror motion

250 slot

40 slot

512

EIS Effective Area

Primary and Grating: Measured - flight model data usedFilters: 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