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