Turbulent Origins of the Solar Wind

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Turbulent Origins of the Solar Wind
Steven R. CranmerHarvard-Smithsonian Center for
Astrophysics
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Turbulent Origins of the Solar Wind
Steven R. CranmerHarvard-Smithsonian Center for
Astrophysics
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Overview the solar atmosphere
Heating is everywhere!
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In situ solar wind properties

• Mariner 2 (1962) first direct confirmation of
  continuous fast slow solar wind.

• Uncertainties about which type is ambient
  persisted because measurements were limited to
  the ecliptic plane . . .
• Ulysses left the ecliptic provided 3D view of
  the winds source regions.

By 1990, it was clear the fast wind needs
something besides gas pressure to accelerate so
fast!
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In situ solar wind connectivity

• High-speed wind strong connections to the
  largest coronal holes

hole/streamer boundary (streamer edge) streamer
plasma sheet (cusp/stalk) small coronal
holes active regions

• Low-speed wind still no agreement on the full
  range of coronal sources

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Coronal magnetic fields

• Coronal B is notoriously difficult to measure . .
  .
• Potential field source surface (PFSS) models have
  been successful in reproducing observed
  structures and mapping between Sun in situ.
• Wang Sheeley (1990) flux-tube expansion
  correlation, modified by, e.g., Arge Pizzo
  (2000).

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Coronal magnetic fields solar minimum
A(r) B(r)1 r2 f(r) Banaszkiewicz et al.
(1998)
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Why is the fast/slow wind fast/slow?

• Several ideas exist one powerful one relates the
  spatial dependence of the heating to the location
  of the Parker critical point this determines how
  the available heating affects the plasma
  (e.g., Leer Holzer 1980)

Banaszkiewicz et al. (1998)
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Wind origins in open magnetic regions

• UV spectroscopy shows blueshifts in supergranular
  network (e.g., Hassler et al. 1999)

Leighton (1963)
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Supergranular funnels
Peter (2001)
Fisk (2005)
Tu et al. (2005)
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Granules Supergranules
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Inter-granular bright points (close-up)

• Its widely believed that the G-band bright
  points are strong-field (1500 G) flux tubes
  surrounded by much weaker-field plasma.

100200 km
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Waves in thin flux tubes

• Statistics of horizontal BP motions gives power
  spectrum of kink-mode waves.
• BPs undergo both random walks intermittent
  (reconnection?) jumps

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Waves in thin flux tubes

• Statistics of horizontal BP motions gives power
  spectrum of kink-mode waves.
• BPs undergo both random walks intermittent
  (reconnection?) jumps

In reality, its not just the pure kink mode. .
. (Hasan et al. 2005)
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Global magnetic field connectivity

• Cranmer van Ballegooijen (2005) built a model
  of the global properties of incompressible
  non-WKB Alfvenic turbulence along an open flux
  tube.
• Lower boundary condition observed horizontal
  motions of G-band bright points.
• Along the flux tube, wave/turbulence properties
  should be computed consistently.

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How is magnetic energy dissipated along these
open flux tubes? How does this energy get into
the corona to heat accelerate the solar wind?
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Coronal heating location location location

• The basal coronal heating problem is well known

• Above 2 Rs , additional energy deposition is
  required in order to . . .

• accelerate the fast solar wind (without
  artificially boosting mass loss and peak Te ),
• produce the proton/electron temperatures seen in
  situ (also the varying magnetic moment!),
• produce the strong preferential heating and
  temperature anisotropy of heavy ions (in the
  winds acceleration region) seen with UV
  spectroscopy.

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UVCS/SOHO fast solar wind

• In coronal holes, heavy ions (e.g., O5) both
  flow faster and are heated hundreds of times more
  strongly than protons and electrons, and have
  anisotropic temperatures. (e.g., Kohl et al.
  1997, 1998, 2006)

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Heating mechanisms

• A surplus of proposed ideas? (Mandrini et al.
  2000 Aschwanden et al. 2001)

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Heating mechanisms

• A surplus of proposed ideas? (Mandrini et al.
  2000 Aschwanden et al. 2001)

• Where does the mechanical energy come from?

vs.
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Heating mechanisms

• A surplus of proposed ideas? (Mandrini et al.
  2000 Aschwanden et al. 2001)

• Where does the mechanical energy come from?
• How is this energy coupled to the coronal plasma?

vs.
waves shocks eddies (AC)
twisting braiding shear (DC)
vs.
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Heating mechanisms

• A surplus of proposed ideas? (Mandrini et al.
  2000 Aschwanden et al. 2001)

• Where does the mechanical energy come from?
• How is this energy coupled to the coronal plasma?
• How is the energy dissipated and converted to
  heat?

vs.
waves shocks eddies (AC)
twisting braiding shear (DC)
vs.
interact with inhomog./nonlin.
reconnection
turbulence
collisions (visc, cond, resist, friction) or
collisionless
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Heating mechanisms

• A surplus of proposed ideas? (Mandrini et al.
  2000 Aschwanden et al. 2001)

• Where does the mechanical energy come from?
• How is this energy coupled to the coronal plasma?
• How is the energy dissipated and converted to
  heat?

vs.
waves shocks eddies (AC)
twisting braiding shear (DC)
vs.
interact with inhomog./nonlin.
reconnection
turbulence
collisions (visc, cond, resist, friction) or
collisionless
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MHD turbulence

• It is highly likely that somewhere in the outer
  solar atmosphere the fluctuations become
  turbulent and cascade from large to small scales

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MHD turbulence

• It is highly likely that somewhere in the outer
  solar atmosphere the fluctuations become
  turbulent and cascade from large to small scales

• With a strong background field, it is easier to
  mix field lines (perp. to B) than it is to bend
  them (parallel to B).
• Also, the energy transport along the field is far
  from isotropic

Z
Z
Z
(e.g., Matthaeus et al. 1999 Dmitruk et al. 2002)
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A recipe for coronal heating?
Ingredients

• Outer scale correlation length (L) flux tube
  width (Hollweg 1986), normalized to something
  like 100 km at the photosphere.
• Z and Z need to solve non-WKB Alfven wave
  reflection equations.

refl. coeff Z2/Z2
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Turbulent heating models

• Cranmer van Ballegooijen (2005) solved the wave
  equations derived heating rates for a fixed
  background state.
• New models (preliminary!) self-consistent
  solution of waves background one-fluid plasma
  state along a flux tube photosphere to
  heliosphere
• Ingredients

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Turbulent heating models

• For a polar coronal hole flux-tube
• Basal acoustic flux 108 erg/cm2/s (equiv.
  piston v 0.3 km/s)
• Basal Alfvenic perpendicular amplitude 0.4 km/s
• Basal turbulent scale 120 km (G-band bright
  point size!)

T (K)
reflection coefficient
Transition region is too high (8 Mm instead of 2
Mm), but otherwise not bad . . .
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Why is the fast/slow wind fast/slow?

• Compare multiple 1D models in solar-minimum flux
  tubes with Ulysses 1st polar pass (Goldstein et
  al. 1996)

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Why is the fast/slow wind fast/slow?

• Compare multiple 1D models in solar-minimum flux
  tubes with Ulysses 1st polar pass (Goldstein et
  al. 1996) Geometry is
  destiny?

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Progress toward a robust recipe
Not too bad, but . . .

• Because of the need to determine non-WKB
  (nonlocal!) reflection coefficients, it may not
  be easy to insert into global/3D MHD models.
• Doesnt specify proton vs. electron heating
  (they conduct differently!)
• Probably doesnt work for loops (keep an eye on
  Marco Velli)
• Are there additional (non-photospheric) sources
  of waves / turbulence / heating for open-field
  regions? (e.g., flux cancellation events)

(B. Welsch et al. 2004)
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Conclusions

• Theoretical advances in MHD turbulence are
  continuing to feed back into global models of
  the solar wind.
• High-resolution adaptive-optics studies of
  photospheric flux tubes pay off as the bottom
  boundary condition to coronal heating!

• SOHO (especially UVCS) has led to fundamentally
  new views of the extended acceleration regions of
  the solar wind.

• For more information
• http//cfa-www.harvard.edu/scranmer/

SOHO 199520??
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Extra slides . . .
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The solar wind

• 1958 Gene Parker proposed that the hot corona
  provides enough gas pressure to counteract
  gravity and accelerate a solar wind. 1962
  Mariner 2 confirmed it!

• Momentum conservation

To sustain a wind, ?/?t 0, and RHS must be
naturally tuned
Cranmer (2004), Am. J. Phys.
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UVCS / SOHO

• SOHO (the Solar and Heliospheric Observatory) was
  launched in Dec. 1995 with 12 instruments probing
  solar interior to outer heliosphere.

• The Ultraviolet Coronagraph Spectrometer (UVCS)
  measures plasma properties of coronal protons,
  ions, and electrons between 1.5 and 10 solar
  radii.
• Combines occultation with spectroscopy to reveal
  the solar wind acceleration region.

slit field of view

• Mirror motions select height
• Instrument rolls indep. of spacecraft
• 2 UV channels LYA OVI
• 1 white-light polarimetry channel

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UVCS results solar minimum (1996-1997 )

• The fastest solar wind flow is expected to come
  from dim coronal holes.
• In June 1996, the first measurements of heavy ion
  (e.g., O5) line emission in the extended corona
  revealed surprisingly wide line profiles . . .

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The impact of UVCS
UVCS has led to new views of the collisionless
nature of solar wind acceleration. Key results
include

• The fast solar wind becomes supersonic much
  closer to the Sun (2 Rs) than previously
  believed.
• In coronal holes, heavy ions (e.g., O5) both
  flow faster and are heated hundreds of times more
  strongly than protons and electrons, and have
  anisotropic temperatures. (e.g., Kohl et al.
  1997,1998)

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Spectroscopic diagnostics

• Off-limb photons formed by both collisional
  excitation/de-excitation and resonant scattering
  of solar-disk photons.

• Profile width depends on line-of-sight component
  of velocity distribution (i.e., perp.
  temperature and projected component of wind flow
  speed).

• Total intensity depends on the radial component
  of velocity distribution (parallel temperature
  and main component of wind flow speed), as well
  as density.

• If atoms are flow in the same direction as
  incoming disk photons, Doppler dimming/pumping
  occurs.

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Doppler dimming pumping

• After H I Lyman alpha, the O VI 1032, 1037
  doublet are the next brightest lines in the
  extended corona.

• The isolated 1032 line Doppler dims like Lyman
  alpha.
• The 1037 line is Doppler pumped by neighboring
  C II line photons when O5 outflow speed passes
  175 and 370 km/s.
• The ratio R of 1032 to 1037 intensity depends on
  both the bulk outflow speed (of O5 ions) and
  their parallel temperature. . .
• The line widths constrain perpendicular
  temperature to be gt 100 million K.
• R lt 1 implies anisotropy!

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Coronal holes over the solar cycle

• Even though large coronal holes have similar
  outflow speeds at 1 AU (gt600 km/s), their
  acceleration (in O5) in the corona is different!
  (Miralles et al. 2001, 2004)

Solar minimum
Solar maximum
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Ion cyclotron waves in the corona

• UVCS observations have rekindled theoretical
  efforts to understand heating and acceleration of
  the plasma in the (collisionless?) acceleration
  region of the wind.

• Ion cyclotron waves (10 to 10,000 Hz) suggested
  as a natural energy source that can be tapped to
  preferentially heat accelerate heavy ions.
• Dissipation of these waves produces diffusion in
  velocity space along contours of constant energy
  in the frame moving with wave phase speed

lower Z/A faster diffusion
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But does turbulence generate cyclotron waves?

• Preliminary models say probably not in the
  extended corona. (At least not in a
  straightforward way!)
• In the corona, kinetic Alfven waves with high k
  heat electrons (T gtgt T ) when they damp
  linearly.

How then are the ions heated accelerated?

• Nonlinear instabilities that locally generate
  high-freq. waves (Markovskii 2004)?
• Coupling with fast-mode waves that do cascade to
  high-freq. (Chandran 2006)?
• KAW damping leads to electron beams, further
  (Langmuir) turbulence, and Debye-scale electron
  phase space holes, which heat ions
  perpendicularly via collisions (Ergun et al.
  1999 Cranmer van Ballegooijen 2003)?

cyclotron resonance-like phenomena
MHD turbulence
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Alfven wave amplitude (with damping)

• Cranmer van Ballegooijen (2005) solved
  transport equations for 300 discrete periods (3
  sec to 3 days), then renormalized using
  photospheric power spectrum.
• One free parameter base jump amplitude (0 to
  5 km/s allowed 3 km/s is best)

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Turbulent heating rate

• Solid curve predicted Qheat for a polar
  coronal hole.
• Dashed RGB regions empirical estimates of
  heating rate of primary plasma (models tuned to
  match conditions at 1 AU).
• What is really needed are direct measurements of
  the plasma (atoms, ions, electrons) in the
  acceleration region of the solar wind!

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Streamers with UVCS

• Streamers viewed edge-on look different in H0
  and O5
• Ion abundance depletion in core due to grav.
  settling?
• Brightest legs show negligible outflow, but
  abundances consistent with in situ slow wind.
• Higher latitudes and upper stalk show definite
  flows (Strachan et al. 2002).
• Stalk also has preferential ion heating
  anisotropy, like coronal holes! (Frazin et al.
  2003)

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The Need for Better Observations

• Even though UVCS/SOHO has made significant
  advances,
• We still do not understand the physical processes
  that heat and accelerate the entire plasma
  (protons, electrons, heavy ions),
• There is still controversy about whether the fast
  solar wind occurs primarily in dense polar plumes
  or in low-density inter-plume plasma,
• We still do not know how and where the various
  components of the variable slow solar wind are
  produced (e.g., blobs).

(Our understanding of ion cyclotron resonance is
based essentially on just one ion!)
UVCS has shown that answering these questions is
possible, but cannot make the required
observations.