Some Key Issues in Solar Plasmas(Leiden, March 21, 2005)

Eric Priest

“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”

“Principles of MHD”

- already a hit with new generation of researchers

“Milo shows signs of interest in geometry - and playing with grandpa Hans - What could be nicer ? ”

“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.

In his lab -- see meridian line

-- clock designed by C Huygens (stud. at Leiden)

James Gregory

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

Magnetic field lines expanding into corona

Similar to TRACE images

Current sheet forms High-velocity jets

Reconnection High temperatures

Amazing images at

0.1”from

Swedish telescope,La

Palma

(G Scharmer)

In close-up:

effects of B around each

granule points,

flowers,

ribbons

- half flux in supergran.

Vertical Magnetic FieldTemperature

Produce many observed features of granulation

Magnetoconvection models (e.g. Bushby)[256 x 256 x 120 points]

Results depend on B through Chandra. no

Q=10 -> points

Q=B02d2 / (μρην)

Q=100 -> ribbons

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 (Active region) - from above

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

Outer Corona

from SOHO

CME 2000 km/s

(5 times faster than

normal)

Snow -- relc

particles

Thurs Aurora in St Andrews

Overall Picture of Eruption

twisted magnetic tube- erupts

drives reconnection

(Priest and Schrijver 1999)

Reconnection heats loopsContinues:new loops

Form

Old loops cool & drain

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

Cause of Eruption ?

Magnetic Catastrophe

2.5 D Model

3D Numerical

Model

(Amari, Mikic et al)

Converging motions ->

eruption

QN. 3 -- HOW is CORONA HEATED ?

Bright Pts,

Loops,

Holes

Recon-nection possible

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

? Effect on Coronal Heating of

“Magnetic Carpet”

Magnetic sources in surface are concentrated

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

spirit & high quality example of Hans Goedbloed