“I have my calculations, teaching & students - and I love it”“My ‘retirement’ approaches this summer - but is not to be taken too literally as far as I am concerned”
“Some Key Issues in Solar Plasmas”CONTENT:
1. Introduction 2. Structure of the Sun 3. Sunspots
4. Corona5. MHD - Reconnection
6. Key advances - SOHO satellite* Interior
* Solar Flares and CME's * Heating Atmosphere
Conclusions
1. INTRODUCTION
Our Sun
1. Of great scientific interest in own right
2. Influence on Earth
3. Important for Astronomy
-- fundamental cosmic processes
4. Many basic properties of Sun
a mystery
B generated ? Solar wind acceld ?
Corona heated ? Nature sunspots ?
Eruptions occur ? Flare particles acceld ?
Today some of progress
James Gregory 1st regius prof maths at St
Andrews (1668) age 30
Co-founder of Calculus
Invented Reflecting Telescope
Traditionallyclose link St Andrews - Holland
St Andrews founded 1411Many students came from Low Countries (16/17 C)
Dutch stone masons.
Discovered:
-- General binomial theorem
-- Taylor expansions
-- Ratio test for convergence of a series
-- Series for sin x and tan x
-- Integral of log x and sec x
-- Differentiation is inverse of integration
-- How to use change of variable in integration
James Gregory - died 1675 (37)
Interior:Core (< 0.25 R0),
[R0 = 700 Mm]
Radiative zone,
Convection zone (> 0.7 R0)
Atmosphere: Photosphere (6000K), Chromosphere (104K), Corona (106K)
2. Overall Structure of Sun
Classical Picture:
So need analytical / computl MHD (e.g., Keppens) - idealised 1D models + physical insight- sophisticated 2D & 3D- both -> understanding
static plane-parallel atmosphere - rise in T
But - highly nonuniform - multi-T - strongly t-dept
- plasma heating/cooling dynamically
Even 1D model of Chromosphere (B=0) tough
• Start with 1D atmosphere T(h)
• Impose small oscn at photo
(Carlsson & Stein)
Similar process in flux tubes -> spicules (De Pontieu, Erdelyi)
• Need high-resolution adaptive grid to resolve shocks
Covered with turbulent
convection cells: “Granulation”
(1 Mm)“Supergranulation”
(15 Mm)
Photosphere
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2. Tiny intense magnetic fields over whole Sun
Map of Photospheric Magnetic Field
B carried to edges of supergran. cells
White -- towardsBlack -- away from
1. around spots -- bipolar
"Active Regions"
3. Diffl. rotation
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Model of Flux Emergence from Interior to Corona V Archontis, F Moreno-Insertis, K Galsgaard, A Hood
3D compressible MHD, through 108 in density
Model of Flux Emergence from Interior to Corona V Archontis, F Moreno-Insertis, K Galsgaard, A Hood
3D compressible MHD, through 108 in density
Vertical Magnetic FieldTemperature
Produce many observed features of granulation
Magnetoconvection models (e.g. Bushby)[256 x 256 x 120 points]
Photosphere --> Sunspots
Dark because cool3. SUNSPOTS
- magnetic field (B) stops
granulation
Vertical magnetic flux tubes
“Not so simple !”
Vary with 11-year cycle
Stunning Image(Swedish telescope)
[Scharmer & van der Voort]
Close-up of penumbral structure
(created by B) -> new surprises:
Points moving along lanes; Bright flows in/out;
Strange dark cores
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New Model (Weiss, Thomas et al)
Dark filaments-(low)
held down by granule flux
pumping
Bright filaments-
(high)
Penumbra - a mixture of interlocked field lines
See below sunspot by t-
distance seismology(eg Bogdan)
Wave speed slower - cooler
Wave speed higher - B
-- See at ECLIPSE of Sun
Temperature is million degrees
4. CORONA
Iran (1999) - Koutchmy
Magnetic field dominates plasma -> magnetic world
-- heats corona
But how ??
Can observe corona direct in x-rays/euv
Early image from
Skylab -
bright pts, holes, loops,
act. reg.
TRACE - from side - intricate structure
Not isolated coronal loops -
plasma that is at one temp.
[1.5 MK]
Key Discovery from SOHO/TRACE
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MHD WAVES in CORONA (eg Nakariakov)
Periods 2-20 min, amplitudes 2-5% -> insuff. to heat corona
But Coronal Seismology:
B, structure, transp coeffs.
1D slabs/tubes - basis (Hans G)
2 & 3D modelling
(Andries, Bogdan, Erdelyi, Goossens, Poedts, Young ….)
5. Eqns of Magnetohydrodynamics
But - in corona: ? H
- in photosphere: optically thick
? Correct forms for transport coeffs.
need collisionless effects when l < 30 km
Induction Equation
€
∂B∂ t
= ∇× (v × B) + η∇2B
[B changes due to transport + diffusion]
In most of Universe Rm>>1, B frozen to plasma
Except SINGULARITIES -- & large j =∇×B / μ
∇B
Reconnecting current sheets
Resonant absorption layers
Shock waves
In 2D, reconnecting sheets form at NULL POINTS, B = 0
(e.g., Baty)
In 3D reconnection can take place at
nulls or at non-null points (eg Galsgaard)
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5.1 3D RECONNECTION
Simplest B = (x, y, -2z)
Spine Field LineFan Surface
(i) Structure of Null Point
Many New Features
2 families of field lines through null point:
(ii) Topology of Fields - Complex
In 2D -- Separatrix curves
In 3D -- Separatrix surfaces
-- intersect in Separator
Note
Coronal magnetic field - highly complex - many sources.
1. When constructing coronal field/ numerical expts -
useful to construct skeleton (web of separatrix surfaces).
2. Understand nature bifurcations
[3. For continuous sources:quasi-separatrix surfaces, quasi-separator,
- no discont., but steep change in mapping grad]
(iii)Numerical Experiment(Linton & Priest)
[3D pseudo-spectral code, 2563 modes.]
Impose initial stagn-pt flow
v = vA/30
Rm = 5600
Isosurfaces of B2:
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B-Lines for 1 Tube
Colour shows
locations of strong Ep
stronger Ep
Final twist
€
π
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6. SOHO (Solar & Heliospheric Observatory)
Observing Sun continuously for 1st time (ESA/NASA)
Launched 1995. Orbiting Sun at point in phase
with Earth
MANY NEW ADVANCES - only 3 today
--> 1st comprehensive view of Sun
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QN. 1 -- ? Structure of Solar Interior
Measures velocity of Sun's surface at
million pts/min
-> frequencies: -> T(r)
[agrees with model to < 1%]
SOHO (MDI) detected several million normal modes
Deduce Internal Rotation
Observe: * Faster at equator --
Expect: * const. on cylinders * B generated throughout conv. zone
Surprise: -- const on radial lines -- intense shear layer
? site dynamo
Need build models for tacocline (see Rosner)
Photosphere
QN. 2 -- ? How Do Flares & CME’s Occur
Oct-Nov, 2003- v. complex
sunspot group
-> largest flares + mass ejections
Example from TRACE (171 A)
20 MK [Fe
XVI]
+ 1 MK
[Fe IX]
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RHESSI Overlay of TRACE• Red contours: 12 – 25
keV X-ray flux.
• Blue contours: 50 – 100 keV X-ray flux.
• Particle acceleration: DC acceleration in sheet + Fermi in collapsing trap
Numerical 3D MHD Experiment
171
195
(Gudiksen and Nordlund)
- start with “realistic” potential active region field
- impose “realistic” photoc velocity
- find Poynting flux maintains a corona at 1 MK
- assume that somehow at realistic Rm energy would cascade down
- but ? details of energy dissipation
- deduce TRACE images
Reconnection can heat low corona: (i) Drive Simple Recon. by photc. motions --> X-ray bright point (Parnell)
(ii) Separator Reconnection -- complex B (Galsgaard)
(iii) Coronal Tectonics -- modern version of Parker braiding
From observed magnetograms -
construct coronal field lines
- statistical properties: most close low down
Time for all field lines to reconnect
only 1.5 hours
Coronal Tectonics Model Each "Loop" --> surface in many sources
Flux from each source separated by (separatrix) surfaces
As sources move --> J sheets on surfaces --> Reconnect --> Heat Corona filled w. myriads of J sheets,
heating impulsively
7. CONCLUSIONS Solar Physics - golden age - observations
Sense of vitality will continue
Computational plasma expts. playing a key role
- present missions(SOHO 1995 -, TRACE 1998 -, RHESSI 2002) -->
Stereo 2006, Solar B 2006, SDO 2008, Orbiter 2013
Need- numerical expts in 1,2,3D + analytical theory- link macro / micro physics- link with astro- and lab plasma community