Transcript RAS_waves - University of Glasgow

ALFVEN WAVE ENERGY TRANSPORT
IN SOLAR FLARES
Lyndsay Fletcher
University of Glasgow, UK.
RAS Discussion Meeting, 8 Jan 2010
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Flare ‘cartoon’
It is clear that the energy for a solar flare is stored in stressed
coronal magnetic field (currents).
Unconnected,
stressed field
Post-reconnection,
relaxing field
- shrinking and
untwisting
Energy
flux
relaxed field –
‘flare loops’
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?
Footpoint radiation, fast electrons, ions
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Particle beams or waves?
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:
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.
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Flare energy requirements
Power directly measured in the
optical can be up to 1029 erg s-1
flare
Power in fast electrons inferred from
hard X-rays is around the same.
Woods et al 2005
Flare total irradiance
Flare energy = 6 x 1032 ergs over ~ 1000 sec.
Isobe et al 2007
G-band (CH
molecule)
Flare energy radiated from a small
area: HXR footpoints ≈1017 cm2,
Fe (stokes I)
(WL footpoints can be smaller.)
Fe (Stokes V)
Source FWHM = 5 x
107
cm
Power per unit area ≈ 1011-12 erg cm-2
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Krucker et al. 2008
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.
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’
cm-3
(e.g. Brown et al
2009)
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Wave speed and Poynting flux
Brosius & White 2006
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
e.g. Lee et al
(98) Brosius et
al (02)
Gyrosynchrotron emission
(contours) above a sunspot
Coronal density ~ 109 m-3  vA ≈ 0.1 - 0.3c
Transit time through corona = 0.1 – 0.3 s
‘Poynting Flux’
S  v a B 2 /8
10,000 km
So flare power ≈ 1011 erg cm-2 needs B ≈ 50 G
(though note, reflection coeff ~ 0.7 initially)
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MHD simulations of Alfven pulse propagation
3D MHD simulations of reconnection/wave propagation
Diffusion region assumed small
Track Poynting flux and enthalpy flux.
(Birn et al. 2009)
Sheared low-b coronal
field, erupting
x
Inwards
Poynting
flux
z
Downwards
Poynting flux
y=0 plane:
y = 0 plane
‘Poynting flux’ ‘Poynting flux’
in x direction in z direction
Time
development of
energy fluxes
Photospheric
projection:
Temperature (grey)
Poynting flux (red)
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Wave propagation in low-b plasma
In corona & upper chromosphere,
vA ≈ vth,e i.e., b ≈ me/mp
b = me/mp
Case of b << me/mp (‘inertial’ regime)
0.5
Accelerated fraction
1.0
The wave has an EII and can damp
by electron acceleration (e.g. Bian
talk)
VAL-C
1.0
T = 4 106 K
T = 3 106 K
T = 2106 K
T = 106 K
3.0
l
5.0
requires k large - i.e. l ≈ 3m to get
acceleration to 10s of keV.
(McClements & Fletcher 2009)
Wave propagation in b ≥ me/mp plasma
Case of b ≥ me/mp (kinetic regime):
Wave can damp for larger transverse scales – order of rs = c/wpi
Damping by Landau resonance (electron acceleration, Bian & Kontar
2010) – damping rate (s-1) is:
(Bian)
Sample values, assuming l|| = 100km
Corona
Chrom.
T
106 K
ne
109 cm-3
B
500 G
tcross
0.1s
Req’d l
l = 0.3 km
104 K
1011 cm-3
1 kG
1s
l = 0.7 km
So, still need to generate quite small transverse scales by phase
mixing/turbulent cascade
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Heating & acceleration in the chromosphere
Electron acceleration needs tacc < te-e
• In chromosphere, electron heating first (c.f. Yohkoh SXT & EIS
impulsive footpoints @ 107K, Mrozek & Tomczak 2004, Milligan &
Dennis 2009)
• electrons heat, tscattering increases, and non-thermal tail produced.
Electron acceleration timescale is that on which large k is generated,
e.g. by turbulent cascade:
t acc  t turb 
l,max l,max B

v
vA B
e.g. Lazarian 04
Take lmax=10km, B/B = 10%, vA = 5000 km/s then tturb ≈ 0.02s

• e.g. @107K, 1% of electrons have E > 5keV.
• at 1011 cm-3 , 107K, 5keV electrons have te-e = 0.02s => acceleration.
Electron number estimates
Look at upper/mid VAL-C chromosphere:
heating of chromosphere within 1/g(kinetic) = 1s
T increases, tail becomes collisionless – within 1/tturb ~ 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
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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 b plasma
Small amount of coronal electron
acceleration in wave E field
Perpendicular cascade in
chromosphere & local acceleration
Overall energetics and electron numbers look plausible
Many interesting questions concerning propagation & damping of
these non-ideal (dispersive) waves in ~ collisionless plasmas.
RAS Discussion Meeting, 8 Jan 2010
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