Download 6. Solar wind acceleration

Solar wind acceleration
o The acceleration of the solar wind is considered with
emphasis on the fast solar wind that is known to
originate on open field lines in coronal holes, and in
the smaller-scale coronal funnels.
o Acceleration processes leading to slow solar wind and
to transient flows driven by solar eruptions such as
coronal mass ejections will only be shortly addressed.
o The acceleration by the pressure gradient exerted on
the ambient flow by waves and turbulence will be
discussed, and some recent developments in theory
and multi-fluid modeling be addressed.
o Particular attention is given to wave dissipation via
kinetic effects and wave particle interactions, which
lead to plasma heating and wave damping.
Solar corona and solar wind
23 December 1996
•
Composite image: Innermost region in Fe XV 28.4 nm showing the corona above the disk
at a temperature of about 2 M K, middle region showing the Sun's outer atmosphere as it
appears in ultraviolet light in O VI 103.2 nm of oxygen ions flowing away from the Sun to
form the solar wind, and extended white-light corona as recorded by the coronagraph.
Solar wind types I
1. Fast wind near activity minimum
High speed
Low density
Low particle flux
Helium content
Source
Signatures
400 - 800 kms-1
3 cm-3
2 x 108 cm-2 s-1
3.6%, stationary
coronal holes (magnetically open)
stationary for long times (weeks)
2. Slow wind near activity minimum
Low speed
High density
High particle flux
Helium content
Source
Signatures
Schwenn, 1990
250 - 400 km s-1
10 cm-3
3.7 x 108 cm-2 s-1
below 2%, highly variable
helmet streamers (closed) and current sheet
sector boundaries embedded
Solar wind types II
3. Slow wind near activity maximum
Similar characteristics as 2., except for
Helium content
Source
Signatures
4.
4%, highly variable
active regions (magnetically closed) and small CHs
shock waves, often embedded
Solar ejecta (CMEs), often associated with shocks
High speed
Helium content
Other heavy ions
Signatures
Schwenn, 1990
400 - 2000 kms-1
high, up to 30%
often Fel6+ ions, in rare cases He+
often magnetic clouds, about 30% of the cases
related with erupting prominences
Coronal mass ejections
- magnetically driven
- origin and acceleration
- Lorentz force essential
- longitudinal-latitudinal spreading
- interplanetary propagation
Light bulb CME
LASCO/SOHO
Helical CME
W (103 erg cm-2s-1)
The solar wind energy flux I
Le Chat et al., Solar Phys. 2012
27.2-day
averages
scaled to
1AU
The solar wind energy flux II
Ulysses
fluxes are
scaled to
1AU
Le Chat et al., Solar Phys. 2012
(x 1 erg cm-2s-1)
Solar wind scaling law
Schwadron and McComas, ApJ 2003
Energetics of the fast solar wind
• Energy flux density at 1 RS:
F = 5 105 erg cm-2 s-1
• Power ( A(Rs) = 1m2 ):
P = 500 W
• Speed beyond 10 RS:
Vp = (700 - 800) km s-1
• Temperatures at
1.1 Rs:
Te ≈ Tp ≈ 1-2 106 K
1 AU: Tp = 3 105 K ; Tα = 106 K ; Te = 1.5 105 K
• Heavy ions:
Ti ≅ mi / mp Tp ;
Vi - Vp = VA
γ/(γ-1) 2kBTS = 1/2mp(V∞2 + V2)
γ=5/3, V∞=618 kms-1, TS=107 K for Vp=700 kms-1
--> 5 keV
Lorentz force (in 2-order of the fluctuations) -> wave pressure
Solar wind acceleration
Cranmer, Liv. Rev. Solar Phys., 2009
UVCS Doppler dimming determinations for protons (red; Kohl et al., 2006) and O5+ ions (green; Cranmer et al., 2008)
are shown for polar coronal holes, and are compared with theoretical models of the solar wind at solar minimum (black
curves; Cranmer et al., 2007) and the speeds of blobs above equatorial streamers (open circles; Sheeley Jr et al., 1997).
Solar coronal-hole and wind temperature
Helios
Cranmer, Liv. Rev. Solar Phys., 2009
Black: Turbulence driven coronal heating model (Cranmer et al., ApJ 2007)
Empirical constraints on solar wind heating
Combined data from Helios and Ulysses, 0.29-5.4 AU
Cranmer et al., ApJ, 2009
Funnels merging in coronal hole
Cranmer and van Ballegoijen, ApJS, 2005
Field lines in (c) are plotted
at 2.1° intervals at the solar
surface, and thus each pair
encompasses 1–2 funnels.
Byhring et al., ApJ, 2008
One-dimensional fluid equations
• Mass flux:
• Magnetic flux:
FM = ρ V A
ρ = npmp+nimi
FB = B A
• Stream/flux-tube cross section: A(r)
• Total momentum equation:
ρ V d/dr V = - d/dr (p + pw) - ρ GMS/r2 + aw
• Thermal pressure:
p = npkBTp + nekBTe + nikBTi
• Alfvén wave pressure:
pw = (δB)2/(8π)
• Kinetic wave acceleration:
aw = ρpap + ρiai
MHD equations for
the 3-D solar wind
The dependent variables are
ρ, v, B, P, and Є, which is
the plasma density, flow
velocity in the frame rotating
with the Sun, magnetic field,
thermal pressure, and the
Alfvén wave energy density,
respectively. M⊙ is the solar
mass, Ω the solar angular
velocity vector, γ the
polytropic index, t the time,
and r the radial distance. We
use P ∼ n-γ. L is the wave
damping length, and VA the
Alfvén velocity.
Usmanov et al., JGR
105, 12675, 2000
Radial model profiles of the solar wind
poles
-
equator
-
wind speed
proton density
thermal pressure
wave energy
Usmanov et al., JGR 105, 12675, 2000
Gyrokinetic transport equations I
Density
Flux tube area A(r)
Speed
Collisional friction, thermal force
Parallel
temperature
Parallel heating Q║(r),
Perpendicular
temperature
Perpendicular heating Q┴(r)
Heat flux
Heat exchange q(r)
Killie et al. ApJ, 2004; Janse et al., J. Plasma Phys., 2005
No waves!
Gyrokinetic transport equations II
Multi-fluid,
species index s
Echim, Lemaire, and Lie-Svendsen, Surv Geophys, 32, 1-70, 2011
Magnetic funnels as solar wind source
polar
hole
funnel
Tu, Zhou, Marsch, et al., Science and SW11, 2005
Constraints on funnel geometry
Normalized
line emissivity
• Area factor 4
• Expansion
occurs above
emission height
of Ne VIII
Byhring et al., ApJL, 673, 2008
Effects of helium on funnel flow
Two states
Fms0 = 390 W; r1i = 1.03 Rs
Hmi = 0.4 Rs
Slow flow: High
coronal He abundance
slow flow: 20% He
heating
fast flow:
heating
5 % He
Janse et al., A&A, 2007
Lateral mass and energy supply
Sketch to illustrate the scenario of the solar wind origin and mass supply through
reconnection. The supergranular convection is the driver of solar wind outflow in
coronal funnels. Sizes and shapes of funnels and loops shown are drawn to scale.
He, Tu and Marsch, Solar Phys., 2008
Chromospheric Alfvén waves
FW = 100 W/m2
T = 150 – 350 s
Hinode SOT CaII H 396.8 nm
1
Spicular transverse motion
δv = 20 km/s
Numerical simulation
2
VA = 200 km/s
DePontieu et al. Science, 2007
Alfvén waves from reconnection in
magnetic network
Simulations of Alfvén waves:
• Self-consistent 3D radiative
MHD simulation, ranging from
the convection zone up to the
corona. The field lines (red) are
continuously shaken and carry
Alfvén waves (movie). Periods
are 100-500 s. Wave energy flux
is about 100 Wm-2.
De Pontieu et al. Science, 2007
• The coloring shows the plasma
temperature from lower
chromospheric (red) to higher
transition-region values (green).
Fast solar wind
acceleration by
magnetic flux
emergence
Fisk et al., JGR 104, 19765, 1999
Connecting photosphere and solar wind I
Nonuniform magnetic field
- photosphere: B= 2.8 kG
- corona: B= 4 G at 4 Mm
- radiative losses
- nonlinear wave coupling
- injection of white noise
with V=1km/s
- frequency 2(10-4 – 10-5) Hz
Comparison between direct
numerical MHD simulation and
observations; averages over space
and time (30 min.);
steady state after ½ hour
Matsumoto and Suzuki, 2012
Connecting photosphere and solar wind II
Some results:
- Alfven (A), fast (T) and slow
(L) wave coupling
- Mode conversion and decay
with compressibility
- Dissipation via shocks
Matsumoto and Suzuki, 2012
Acceleration of solar wind ions
Three-fluid model
Preferential heavy ion heating
Ofman, LRSP, 2010
Equal heating
Wave driven wind
Coronal model ion temperature profiles
He
H
Wave-driven wind with wave dissipation by strongly
enhanced (numerical hyper-) resistivity and viscosity
Ofman, JGR, 2004
Three-fluid model
Radial profile of Alfvén wave amplitude
± 3 km/s
Cranmer and van
Ballegooijen, ApJS, 2005
Sources: (1) VAL Model, (2),(3) SUMER, (4) UVCS,
(5), (6) Radio scintillations, (7) Helios, Ulysses
Model magnetic field fluctuations
Calculated model spectrum at
18 Rs obtained in 3-fluid model
Ofman, JGR, 2004
Alfvén-cyclotron-wave turbulence
5/3
α
1
Ulysses
Turbulence spectrum:
Horbury et al., JGR 101, 405, 1996
e±(f) = 1/2 (δZ±)2 ∼ (f/f0)-α
Empirical in situ correlations
Scatter plot of the mean
(0.008- 0.1 Hz) wave
amplitude versus proton
(radial) temperature
4 years of ACE
data at 1 AU
Scatter plot of the proton
temperature versus speed
Vasquez et al., JGR, 2007
Heating rate for turbulent cascade
ACE data
at 1 AU
Vsw [km/s]
Expected heating
rate accounting
for in situ proton
temperature
Vasquez et al.,
JGR, 2007
Kinetic damping of plasma waves
Marsch, Liv. Rev. Solar Phys. 2004
Free
energy
source
Kinetic
wave mode
Proton
anisotropy
Ion cyclotron
wave
Proton beam
Ion acoustic
wave
Ion
differential
streaming
Magnetosonic wave
Pitch-angle diffusion plateau
VA=109 km/s
Helios
core
beam
vy
vy
Protons
0.9, 0.7, 0.5, 0.3, 0.1, 0.03, 0.01, 0.003
vx (km/s)
V=614 km/s
vx (km/s)
Heuer and Marsch, JGR, 2007
Ωp= 1.1 Hz
Parametric decay of Alfvén wave
• Linear Vlasov theory and 1-D
hybrid simulations to study
the parametric instabilities of
a circularly polarized parallelpropagating Alfvén wave.
• Linear and weakly nonlinear
instabilities of the Alfvén
wave drive ion acoustic-like
and cyclotron waves, leading
to beam and anisotropic core.
Pitch-angle scattering
and energy diffusion
in micro-turbulent
wave fields
Araneda, Marsch, and Viñas, PRL, 2008
Resonant diffusion and ion heating
Isenberg and Vasquez, ApJ, 668, 2007
T┴ = 4 T║
Resonant diffusion of O5+ ions, exhibiting perpendicular cyclotron heating. These results are
for equal sunward and anti-sunward wave intensities, and a power spectrum index of - 5/3.
Color contours show the velocity-space density, normalized in each panel to the maximum
value at the origin. At left is the initial, isotropic distribution. Adjacent panels show the time
development for three later times, where τ is proportional to the normalized wave intensity.
Some conclusions
• Fast solar wind is mainly driven by wave forces.
• Waves are responsible for ion acceleration and heating.
• Parametric decay of Alfvén waves produces cyclotron and
acoustic waves shaping the protons (beam, core).
• Heavy ions are driven by the mirror force stemming from
preferential (resonant) perpendicular heating.
• Mass and energy are supplied through reconnection
between funnels and adjacent small loops in the network.
• Origin and acceleration of the slow wind (may involve
reconnection) remains less clear (compositional
signatures: Helium depletion and FIP fractionation).
• Transients and CMEs are driven by large-scale Lorentz
forces arising from magnetic flux emergence and eruption.