ALFVEN WAVE ENERGY TRANSPORT IN SOLAR FLARES

Lyndsay Fletcher

University of Glasgow, UK.

RAS Discussion Meeting, 8 Jan 20101

Flare ‘cartoon’

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Unconnected, stressed field

Energy flux

Post-reconnection, relaxing field- shrinking and untwisting

1) Field reconfigures and magnetic energy is liberated via magnetic reconnection.

2) Energy transmitted to the chromosphere, where most of the flare energy is radiated (optical-UV).

How does the energy transport happen?

relaxed field – ‘flare loops’

It is clear that the energy for a solar flare is stored in stressed coronal magnetic field (currents).

Footpoint radiation, fast electrons, ions

Particle beams or waves?

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1) Pre-flare energy storage => twisted field, so energy release => untwisting – i.e. an Alfvenic pulse. Consequences?

2) Earth’s magnetosphere provides an example of efficient particle acceleration by Alfven waves, generated in substorms.

1) Since the (1970s) it is clear that the corona contains insufficient electrons to explain chromospheric HXRs (Hoyng et al. 1973, Brown 1976). Overall flare beam/return currents electrodynamics in a realistic geometry is far from understood.

In the ‘standard’ flare model an electron beam accelerated in the corona transports energy to the chromosphere. Here we propose a wave-based alternative, motivated by the following:

Flare energy requirements

Flare energy = 6 x 1032 ergs over ~ 1000 sec.

Woo

ds e

t al 2

005

Power directly measured in the optical can be up to 1029 erg s-1

Power in fast electrons inferred from hard X-rays is around the same.

flare

Flare energy radiated from a small area: HXR footpoints ≈1017 cm2,

(WL footpoints can be smaller.)

Power per unit area ≈ 1011-12 erg cm-2

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G-band (CH molecule)

Fe (stokes I)

Fe (Stokes V)

Isob

e et

al 2

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Source FWHM = 5 x 107 cm

Flare total irradiance

Flare electrons

Flares are very good at accelerating and heating electrons.

Radiation from non-thermal electrons is observed in the corona and chromosphere.

So a wave model must also accelerate electrons.

Kruc

ker e

t al.

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Coronal X-rays imply ≈ 1-10% of electrons are accelerated and decay approx. collisionally (e.g. Krucker et al 2008).

Chromospheric X-rays require a ‘non-thermal emission measure’(e.g. Brown et al 2009)

cm-3

Wave speed and Poynting flux

10,000 km

The flare corona is quite extreme….

Coronal |B| deduced from gyrosynchrotron:

Active region magnetic field strength at 10,000 km altitude (≈ filament height):

≈ 500 G average≈ 1kG above a sunspot

Bros

ius

& W

hite

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Coronal density ~ 109 m-3 vA ≈ 0.1 - 0.3c

Transit time through corona = 0.1 – 0.3 s

‘Poynting Flux’

So flare power ≈ 1011 erg cm-2 needs B ≈ 50 G(though note, reflection coeff ~ 0.7 initially)

Gyrosynchrotron emission (contours) above a sunspot

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€

S = va δB2 /8π

e.g. Lee et al (98) Brosius et al (02)

MHD simulations of Alfven pulse propagation

3D MHD simulations of reconnection/wave propagation

Diffusion region assumed small

Track Poynting flux and enthalpy flux.

Sheared low- coronal field, erupting

y=0 plane: ‘Poynting flux’ in x direction

y = 0 plane ‘Poynting flux’ in z direction

Photospheric projection: Temperature (grey) Poynting flux (red)

x

z

(Birn et al. 2009)

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Inwards Poynting flux

Downwards Poynting flux

Time development of energy fluxes

Wave propagation in low- plasma

In corona & upper chromosphere, vA ≈ vth,e i.e., ≈ me/mp

The wave has an EII and can damp by electron acceleration (e.g. Bian talk)

T = 4 106 KT = 3 106 KT = 2106 K

T = 106 K

Case of << me/mp (‘inertial’ regime)

requires k large - i.e. ≈ 3m to get acceleration to 10s of keV.

(McClements & Fletcher 2009)

= me/mp

VAL-C

1.0

0.5

Acc

eler

ated

fra

ctio

n

1.0 3.0 5.0

Wave propagation in ≥ me/mp plasma

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Case of ≥ me/mp (kinetic regime):Wave can damp for larger transverse scales – order of s = c/pi

Damping by Landau resonance (electron acceleration, Bian & Kontar 2010) – damping rate (s-1) is:

So, still need to generate quite small transverse scales by phase mixing/turbulent cascade

(Bian)

T ne B cross Req’d

Corona 106 K 109 cm-3 500 G 0.1s = 0.3 km

Chrom. 104 K 1011 cm-3 1 kG 1s = 0.7 km

Sample values, assuming || = 100km

Heating & acceleration in the chromosphere

Electron acceleration needs acc < e-e

• In chromosphere, electron heating first (c.f. Yohkoh SXT & EIS impulsive footpoints @ 107K, Mrozek & Tomczak 2004, Milligan & Dennis 2009)• electrons heat, scattering increases, and non-thermal tail produced.

Electron acceleration timescale is that on which large k is generated, e.g. by turbulent cascade:

Take max=10km, B/B = 10%, vA = 5000 km/s then turb ≈ 0.02s

• e.g. @107K, 1% of electrons have E > 5keV.• at 1011 cm-3 , 107K, 5keV electrons have e-e = 0.02s => acceleration.

€

acc ≈ τ turb =λ⊥,maxδ v

=λ⊥,maxB

vAδBe.g. Lazarian 04

Electron number estimates

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Look at upper/mid VAL-C chromosphere:

heating of chromosphere within 1/(kinetic) = 1s

T increases, tail becomes collisionless – within 1/turb ~ 0.02s

Non-thermal emission measure in chromosphere

Accelerated fraction f ~ 0.01 ne ~ 1011 cm-3

nh ~ 1012 cm-3 (ionisation fraction ~ 10%)So volume V = 1025 cm3 If h = 1000km, needs A = 1017cm2 - similar to HXR footpoint sizes.

A

h

Chromospheric accelerating volume

Conclusions

During a flare, magnetic energy is transported through corona and efficiently converted to KE of fast particles in chromosphere.

Proposal – do this with an Alfven wave pulse in a very low plasma

Small amount of coronal electron acceleration in wave E field

Perpendicular cascade in chromosphere & local acceleration

12RAS Discussion Meeting, 8 Jan 2010

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Overall energetics and electron numbers look plausible

Many interesting questions concerning propagation & damping of these non-ideal (dispersive) waves in ~ collisionless plasmas.