CORONAL HEATING

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CORONAL HEATING
(Space Climate School, Saariselka, March,
2009)Eric Priest (St Andrews)
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1. Introduction - The Corona (Eclipse)
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Skylab -- X-ray telescope
Coronal holes -- loops -- X-ray bright points
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Yohkoh(5 arcsec)
A dynamic magnetic world - subtle interactions B
plasma
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Hinode (1 arcsec)
Stunning detail on structure dynamics (see
Tsuneta)
How is corona heated?
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Waves or reconnection? - Space Obsns

• Low-freq. waves in loops TRACE-too weak to
  heat
• High-freq. waves UVCS -- ?? heat outer corona
• Hinode --
• Chromospheric
• Spicules
• swaying
• (straw, prairy)
• Hansteen, Suematsu

--?? Solar wind/ coronal heating
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2. Reconnection - most likely in low corona
Quiet Sun XRT on Hinode, Tsuneta, golub
Many brightenings X-ray bright points - above
emerging and/or cancelling fields in photosphere
30-sec cadence, 12-hour duration
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Hinode XRT - active region
(Schmeltz et al, 2009)
Observations inside white region
Differential emission measure
Normal active region emission at 3 MK
Plus peak at 20 MK (?nanoflares)
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Parkers classical Nanoflare Model
by braiding (1972)
Initial B uniform / motions braiding
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Numerical Experiment (Galsgaard)
Braiding --gt Current sheets grow --gt turb. recon.
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3. Coronal Tectonics Model (development of
Parkers model)
3.1 Effect Magnetic Carpet
Magnetic sources in surface are concentrated
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Flux Sources Highly Dynamic
Magnetogram movie (white ve , black -ve)

• Flux emerges ... cancels

• Reprocessed very quickly (14 hrs !!!)

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Many Sources--gt Corona has Complex Topology
In 2D -- Separatrix curves
In 3D -- Separatrix surfaces
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In 2D, reconnection at X
In 3D, reconnection at separator
In complex fields we form the SKELETON-- set
separatrices
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3.3 Simple binary interaction of 2 photospheric
sources (Haynes et al)
- and sources in overlying B.

• Separatrix
• surfaces.

• Move sources
• watch
• Interaction
• flux tube
• joining sources

Separator
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Cross-sections of Separatrix Surfaces
Separatrix surfaces (positive, negative)
Separators ( ) Number of separators X
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Life of Magnetic Flux in Surface

• (a) 50? flux in Quiet Sun emerges as ephemeral
  regions
• 1 per 8 hrs per supergran, 3 x 1019 Mx

• (b) Each pole migrates to boundary (4 hours),
  fragments --gt 10 "network elements" (3x1018 Mx)

• (c) -- move along boundary (0.1 km/s) -- cancel

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From observed magnetograms - construct coronal
field lines

• each source
• connects to 8 others

Time for all field lines to reconnect
only 1.5 hours
(Close et al)

• much more tectonics
• heating low down
• where field is more
• complex than higher up

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Coronal Tectonics Model
(updated version of Parker nanoflare/topological
dissipation)

• (Priest, Heyvaerts Title)
• Each "Loop" --gt surface in many sources

• Flux from each
• source
• separated by
• separatrix surfaces

• As sources move
• --gt J sheets on separatrices separators
  --gt Reconnect --gt Heat

• Corona filled w. myriads of J sheets, heating
  impulsively

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Fundamental Flux Units
not Network Elements

• Intense tubes (B -- 1200 G, 100 km, 3 x 1017
  Mx)

• Each network element -- 10 intense tubes

• Single ephemeral
• region (XBP) --

100 sources
800 seprs, 1600 sepces

• Each TRACE
• Loop --

10 finer loops
80 seprs, 160 sepces
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TRACE Loop
Reaches to surface in many footpoints.
Separatrices form web in corona
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Corona - Myriads Different Loops
Each flux element --gt many neighbours
But in practice each source has 8 connections
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Results

• Heating uniform along separatrix
• Elementary (sub-telc) tube heated uniformly

• But 95 photc. flux closes low down in carpet
• -- remaining 5 forms large-scale connections
• --gt Carpet heated more than large-scale corona

• So unresolved observations of coronal loops
• --gt Enhanced heat near feet in carpet
• --gt Upper parts large-scale loops heated
  uniformly less strongly

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4. If reconnection heats coronaat many sheets,
1. How does energy spread out ?
-- conduction along B -- reconnection jets --
waves across B
2. If reconnection time-dependent, how much
energy liberated locally/globally?
Simple model problem Longcope Priest
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Magnetic field of Current Sheet in X
At large r, B B0 B1
(line current),
Lots of energy far from CS
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Suppose sheet reconnects
Current (I) dissipates
Local process but has global consequences
Decrease I --gt B must change at large distances
How ??
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Model for effect of reconnection
Linearize about X-point B0
Assume B1 _at_ t0 is due to current sheet
current diffuses i.e. reconnection
? is turned on

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Combine equations
Put twice current enclosed in r
wave diffusion
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wave diffusion
(i) Large r (wave) limit when
gtgt
I(R,t)I0-F(t-R)
(ii) Small r (diffusive) limit
NB --gt 0 at origin as t increases
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Numerical Solution
I(r)
Wave solution
R
Transition diffusive to wave solution
Diffusive solution
t
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Sheath of Current propagates out
In wake of sheath a flow, assocd with
But flow near X does not disappear -- it slowly
increases !
EV
increasing t
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Resolving the Paradox - 3rd regime
At large t

Advection diffusion
Peak in j remains at X and produces a steady
E (indep of )
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5. Summary
Coronal tectonics -- updated version of Parker
braiding

• Response to enhanced ? in current sheet (CS)
• during coronal tectonics
• (i) Diffusion spreads CS out
• (ii) Wave carries current out at vA - as sheath

(iii) Peak in j at X remains --gt steady E
independent of i.e. fast

• Most magnetic energy is converted into
• kinetic energy in wave --

may later dissipate.

• Coronal heating -- reconnection wave

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