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Turbulent Origins of the Solar Wind
Steven R. Cranmer
Harvard-Smithsonian Center for Astrophysics
Turbulent Origins of the Solar Wind
Outline:
1. A tour of magnetic connectivity & plasma properties:
wind
corona
chromosphere
photosphere
2. Energy transport: turbulent coronal heating “recipe”
Steven R. Cranmer
Harvard-Smithsonian Center for Astrophysics
Overview: the solar atmosphere
Heating is everywhere!
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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 wind’s source regions.
fast
slow
600–800
300–500
Tp (105 K)
2.4
0.4
Te (105 K)
1.0
1.3
> mion/mp
< mion/mp
low
high
speed (km/s)
Tion / Tp
O7+/O6+, Mg/O
Turbulent Origins of the Solar Wind
By ~1990, it was clear the
fast wind needs something
besides gas pressure to
accelerate so fast!
Steven R. Cranmer
SHINE Workshop, July 31, 2006
In situ solar wind: connectivity
• High-speed wind: strong connections to the largest coronal holes
• Low-speed wind: still no agreement
on the full range of coronal sources:
hole/streamer boundary (streamer “edge”)
streamer plasma sheet (“cusp/stalk”)
small coronal holes
active regions
Wang et al. (2000)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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).
Wind Speed
uss  267.5  410 f ss0.4 km s-1
Expansion Factor
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Coronal magnetic fields: solar minimum
A(r) ~ B(r)–1 ~ r2 f(r)
Banaszkiewicz et al. (1998)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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):
SUPERSONIC coronal heating:
subsonic region is unaffected.
Energy flux has nowhere else to
go:
M same, u
vs.
SUBSONIC coronal heating:
“puffs up” scale height, draws
more particles into wind:
Banaszkiewicz et al. (1998)
Turbulent Origins of the Solar Wind
M
u
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Wind origins in open magnetic regions
• UV spectroscopy shows blueshifts in supergranular network (e.g., Hassler et al. 1999)
Leighton
(1963)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Supergranular “funnels”
Peter (2001)
Fisk
(2005)
Tu et al. (2005)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Granules & Supergranules
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Inter-granular bright points (close-up)
• It’s widely believed that
the G-band bright points
are strong-field (1500 G)
flux tubes surrounded
by much weaker-field
plasma.
100–200 km
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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:”
splitting/merging
bending
(kink-mode wave)
Turbulent Origins of the Solar Wind
torsion
longitudinal
flow/wave
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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:”
splitting/merging
bending
(kink-mode wave)
torsion
longitudinal
flow/wave
In reality, it’s not just the “pure”
kink mode. . . (Hasan et al. 2005)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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.
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
How is magnetic energy dissipated along
these open flux tubes?
How does this energy get into the corona to
heat & accelerate the solar wind?
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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
wind’s acceleration region) seen with UV
spectroscopy.
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
UVCS/SOHO: fast solar wind
• In coronal holes, heavy ions (e.g., O+5) 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)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Heating mechanisms
• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Heating mechanisms
• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
energy come from?
Turbulent Origins of the Solar Wind
vs.
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Heating mechanisms
• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
• How is this energy coupled
to the coronal plasma?
Turbulent Origins of the Solar Wind
waves
shocks
eddies
(“AC”)
vs.
twisting
braiding
shear
(“DC”)
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Heating mechanisms
• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
waves
shocks
eddies
• How is this energy coupled
to the coronal plasma?
(“AC”)
interact with
inhomog./nonlin.
• How is the energy dissipated
vs.
twisting
braiding
shear
(“DC”)
turbulence
reconnection
and converted to heat?
collisions (visc, cond, resist, friction) or collisionless
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Heating mechanisms
• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
waves
shocks
eddies
• How is this energy coupled
to the coronal plasma?
(“AC”)
interact with
inhomog./nonlin.
• How is the energy dissipated
vs.
twisting
braiding
shear
(“DC”)
turbulence
reconnection
and converted to heat?
collisions (visc, cond, resist, friction) or collisionless
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
MHD turbulence
• It is highly likely that somewhere in the outer solar
atmosphere the fluctuations become turbulent and
cascade from large to small scales:
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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
Z–
Z+
field is far from isotropic:
Z–
(e.g., Matthaeus et al. 1999; Dmitruk et al. 2002)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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; modified by “cascade efficiency?”
• Z+ and Z– : need to solve non-WKB Alfven wave reflection equations.
refl. coeff =
|Z+|2/|Z–|2
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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 onefluid plasma state along a flux tube:
photosphere to heliosphere
• Ingredients: • Alfven waves: non-WKB reflection, turbulent
damping, wave-pressure acceleration
• Acoustic waves: shock steepening, TdS &
conductive damping, full spectrum, wave-pressure
acceleration
• Rad. losses: transition from optically thick (LTE)
to optically thin (CHIANTI + PANDORA)
• Heat conduction: transition from collisional
(electron & neutral H) to collisionless “streaming”
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Turbulent heating models
• For a polar coronal hole flux-tube:
• Basal acoustic flux: 108 erg/cm2/s
(equiv. “piston” v = 0.3 km/s)
T (K)
• Basal Alfvenic perpendicular
amplitude: 0.4 km/s
• Basal turbulent scale: 120 km
(G-band bright point size!)
Transition region is too high
(8 Mm instead of 2 Mm),
but otherwise not bad . . .
Turbulent Origins of the Solar Wind
reflection
coefficient
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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):
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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):
Turbulent Origins of the Solar Wind
“Geometry is destiny?”
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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.
• Doesn’t specify proton vs. electron heating (they conduct differently!)
• Probably doesn’t 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)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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.
More plasma diagnostics
Better understanding!
• For more information:
http://cfa-www.harvard.edu/~scranmer/
Turbulent Origins of the Solar Wind
SOHO: 1995–20??
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Extra slides . . .
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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.
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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:
Turbulent Origins of the Solar Wind
• Mirror motions select height
• Instrument rolls indep. of spacecraft
• 2 UV channels: LYA & OVI
• 1 white-light polarimetry channel
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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., O+5) line emission in the
extended corona revealed surprisingly wide line profiles . . .
On-disk profiles: T = 1–3 million K
Turbulent Origins of the Solar Wind
Off-limb profiles: T > 200 million K !
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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., O+5)
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)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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.
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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 > 100 million K.
• R < 1 implies anisotropy!
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Coronal holes: over the solar cycle
• Even though large coronal holes have similar outflow speeds at 1 AU (>600 km/s),
their acceleration (in O+5) in the corona is different! (Miralles et al. 2001, 2004)
Solar minimum:
Solar maximum:
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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:
Alfven wave’s
oscillating
E and B fields
ion’s Larmor
motion around
radial B-field
lower Z/A
faster diffusion
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
But does turbulence generate cyclotron waves?
• Preliminary models say “probably not”
in the extended corona. (At least not in
a straightforward way!)
freq.
• In the corona, “kinetic Alfven waves”
with high k heat electrons (T >> T )
when they damp linearly.
horiz. wavenumber
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 Debyescale electron phase space holes, which heat ions perpendicularly via “collisions”
(Ergun et al. 1999; Cranmer & van Ballegooijen 2003)?
MHD turbulence
Turbulent Origins of the Solar Wind
something
else?
cyclotron resonancelike phenomena
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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!
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
Streamers with UVCS
• Streamers viewed “edge-on”
look different in H0 and O+5
• 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)
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006
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),
(Our understanding of ion cyclotron resonance is
based essentially on just one ion!)
• 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”).
UVCS has shown that answering these questions is possible, but
cannot make the required observations.
Turbulent Origins of the Solar Wind
Steven R. Cranmer
SHINE Workshop, July 31, 2006