coronal heating
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Sept. 13, 2007
CORONAL HEATING (Space Climate School, Saariselka, March, 2009)
Eric Priest (St Andrews)
Sept. 13, 2007
1. Introduction - The Corona (Eclipse)
Sept. 13, 2007
Coronal holes -- loops -- X-ray bright points
Skylab -- X-ray telescope
Sept. 13, 2007
A dynamic magnetic
world
- subtle interactio
ns B & plasma
Yohkoh(5
arcsec)
Sept. 13, 2007
Hinode (1 arcsec)
Stunning detail on structure & dynamics
(see Tsuneta)
How is corona heated?
Sept. 13, 2007
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
Sept. 13, 2007
2. Reconnection - most likely in low corona
Many brightenings
X-ray bright points -above emerging and/or
cancelling fieldsin photosphere
[30-sec cadence, 12-hour duration]
Quiet Sun: [XRT on Hinode, Tsuneta, golub]
Sept. 13, 2007
Hinode XRT - active region(Schmeltz et al, 2009)
Observations inside white region
Differential emission measure
Normal active region emission at 3 MKPlus peak at 20 MK (?nanoflares)
Sept. 13, 2007
Parker’s classical Nanoflare Modelby braiding (1972)
Initial B uniform / motions braiding
Sept. 13, 2007
Numerical Experiment (Galsgaard)
Braiding --> Current sheets grow --> turb. recon.
Sept. 13, 2007 Magnetic sources in surface are concentrated
3. Coronal Tectonics Model (development of Parker’s model)
3.1 Effect “Magnetic Carpet”
Sept. 13, 2007
Flux Sources Highly Dynamic
Magnetogram movie (white +ve , black -ve)
Flux emerges ... cancels
Reprocessed very quickly (14 hrs !!!)
Many Sources--> Corona has
Complex Topology
In 2D -- Separatrix curves
In 3D -- Separatrix surfaces
In 3D, reconnection at
separator
In 2D, reconnection at X
In complex fields we form the
SKELETON-- set separatrices
3.3 “Simple” binary interaction of 2 photospheric sources (Haynes et al)
Separator
- and + sourcesin overlying B.
Separatrix surfaces.
Move sources& watch
Interactionflux tube
joining sources
Cross-sections of Separatrix Surfaces 2 separators
5 separators
Separatrix surfaces (positive, negative) & Separators ( )Number of separators: X
Sept. 13, 2007
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 --> 10 "network elements" (3x1018 Mx)
(c) -- move along boundary (0.1 km/s) -- cancel
Sept. 13, 2007
From observed magnetograms
- construct coronal field
lines
Time for all field lines to reconnect
only 1.5 hours(Close et al)
much more tectonicsheating low down
where field is more complex than higher up
- each source connects to 8 others
Sept. 13, 2007
Coronal Tectonics Model
(Priest, Heyvaerts & Title) Each "Loop" --> surface in many sources
Flux from each source
separated by separatrix surfaces
As sources move --> J sheets on separatrices & separators
--> Reconnect --> Heat
Corona filled w. myriads of J sheets, heating impulsively
(updated version of Parker nanoflare/topological dissipation)
Sept. 13, 2007
Fundamental Flux Units
Intense tubes (B -- 1200 G, 100 km, 3 x 1017
Mx)
100 sources
10 finer loops
not Network Elements
Each network element -- 10 intense tubes Single ephemeral region (XBP) --
Each TRACE Loop --
800 seprs, 1600 sepces
80 seprs, 160 sepces
Sept. 13, 2007
TRACE Loop
Reaches to surface in
many footpoints.
Separatrices form web in corona
Sept. 13, 2007
Corona - Myriads Different Loops
Each flux element --> many neighbours
But in practice each source has 8 connections
Sept. 13, 2007
Results Heating uniform along separatrixElementary (sub-telc) tube heated uniformly
But 95% photc. flux closes low down in carpet-- remaining 5% forms large-scale connections --> Carpet heated more than large-scale corona
So unresolved observations of coronal loops--> Enhanced heat near feet in carpet --> Upper parts large-scale loops heated uniformly & less strongly
Sept. 13, 2007
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]
Sept. 13, 2007
Magnetic field of Current Sheet in X
€
By + iBx = B' w2 − Δ2 = dΨ /dw
At large r, B = B0 + B1
€
B1φ =I0
2π r(line current),
Lots of energy far from CS
€
B0 = −B' [y ˆ x + x ˆ y ],
€
ωA =B'
4πρ
Sept. 13, 2007
Suppose sheet reconnects
Local process but has global consequences:
Decrease I --> B must change at large distances
How ??
Current (I) dissipates
Sept. 13, 2007
Model for effect of reconnection
Linearize about X-point B0 :
is “turned on” current diffuses i.e. reconnection
Assume B1 @ t=0 is due to current sheet
B0 =−B'[yx+ xy]
€
∂B1
∂t=∇ × (v1 × B0) + η∇ 2B1,
ρ 0
∂v1
∂t= j1 × B0.
Sept. 13, 2007
Combine equations:
€
rB1φ = I(r, t)Put = twice current enclosed in r
r
I
r
(r)
I0Expect:
€
∂2I
∂t 2= ωA
2 r∂
∂rr
∂I
∂r
⎛
⎝ ⎜
⎞
⎠ ⎟+ ηr
∂
∂r
1
r
∂ 2I
∂r∂t
⎛
⎝ ⎜
⎞
⎠ ⎟
wavediffusion
Sept. 13, 2007
€
∂2I
∂t 2= ωA
2 r∂
∂rr
∂I
∂r
⎛
⎝ ⎜
⎞
⎠ ⎟+ ηr
∂
∂r
1
r
∂ 2I
∂r∂t
⎛
⎝ ⎜
⎞
⎠ ⎟
(i) Large r (wave) limit: when R =ln(r / l ) ? 1>>
l =
ωA
I(R,t)=I0-F(t-R)
R
I0
(ii) Small r (diffusive) limit:
2 t
r
I0
€
j =1
r
∂I
∂rNB --> 0 at origin as t increases
wavediffusion
€
I(r, t) = I0 − I0 exp −r2
4ηt
⎛
⎝ ⎜
⎞
⎠ ⎟
Sept. 13, 2007
Numerical Solution
Diffusive solution
R = 12 lnt
I(r)
€
Location where I = 2
3I0
R
t
€
R = ωA tWave solution
Transition: diffusive towave solution
Sept. 13, 2007
EV
But flow near X does not disappear-- it slowly increases !
Sheath of Current propagates out
In wake of sheath a flow, assocd with
€
EV (r, t) ˆ z = −v1 × B0
increasing t
Sept. 13, 2007
€
∂2I
∂t 2= ωA
2 r∂
∂rr
∂I
∂r
⎛
⎝ ⎜
⎞
⎠ ⎟+ ηr
∂
∂r
1
r
∂ 2I
∂r∂t
⎛
⎝ ⎜
⎞
⎠ ⎟
Resolving the Paradox - 3rd regimeAt large t
€
(i.e., t >1/ωA )
Advectiondiffusion
=
Peak in j remains at X
and produces a steady E
(indep of ) €
j =1
r
∂I
∂r=
I0ωA
ηexp(−
ωA2 r2t
η)
€
€
I(r, t) =I0
2ωA t1− exp −
ωA2 r2t
η
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
Sept. 13, 2007
5. Summary
Response to enhanced in current sheet (CS)during coronal tectonics:
(i) Diffusion spreads CS out(ii) Wave carries current out at vA - as sheath
• Most magnetic energy is converted into kinetic energy in wave -- may later dissipate.
(iii) Peak in j at X remains --> steady E independent of i.e. fast
€
• Coronal heating -- reconnection + wave
Coronal tectonics -- updated version of Parker braiding
Sept. 13, 2007
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