Modeling the Solar Wind: A survey of theoretical ideas for the origins of fast

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Modeling the Solar Wind A survey of
theoretical ideas for the origins of fast slow
streams
Steven R. CranmerHarvard-SmithsonianCenter for
Astrophysics
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Modeling the Solar Wind A survey of
theoretical ideas for the origins of fast slow
streams
Outline 1. Brief historical background 2.
The coronal heating problem 3. Solar wind
acceleration waves vs. reconnection? 4.
(Suggestive hints from collisionless ion
diagnostics)
Steven R. CranmerHarvard-SmithsonianCenter for
Astrophysics
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The solar wind discovery

• 18601950 Evidence slowly builds for outflowing
  magnetized plasma in the solar system
• 1958 Eugene Parker proposed that the hot corona
  provides enough gas pressure to counteract
  gravity and accelerate a solar wind.
• 1962 Mariner 2 provided direct confirmation.

• solar flares ? aurora, telegraph snafus,
  geomagnetic storms
• comet ion tails point anti-sunward (no matter
  comets motion)

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In situ solar wind properties

• Mariner 2 detected two phases of solar wind
  slow (mostly) fast streams

• 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.
• Helios saw strong departures from Maxwellians.

By 1990, it was clear the fast wind needs
something besides gas pressure to accelerate so
fast!
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Solar wind connectivity to the corona

• 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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Empirical trends

• Wind speed is roughly anticorrelated with flux
  tube expansion factor between Sun and
  potential field source surface (PFSS).
• Wang Sheeley (1990) flux-tube expansion
  correlation, modified by, e.g., Arge Pizzo
  (2000) and others

• Other correlations based on coronal hole size
  (Vršnak et al. 2007), surface field (Kojima et
  al. 2004), and chromospheric wave phase
  properties (Leamon McIntosh 2007) are also
  useful.

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Empirical trends are helpful, but they are not
always accurate . . . To make qualitative
improvements in long-term space weather
forecasting (i.e., to know when the empirical
trends are going to work, and when they wont),
its key to know the physical processes that give
rise to the heating acceleration.
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The coronal heating problem

• We still dont understand the physical processes
  responsible for heating up the coronal plasma.
  A lot of the heating occurs in a narrow shell.

• Most suggested ideas involve 3 general steps

1. Churning convective motions that tangle up
magnetic fields on the surface. 2. Energy is
stored in tiny twisted braided magnetic flux
tubes. 3. Collisions (particle-particle?
wave-particle?) release energy as heat.
Heating Solar wind acceleration!
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Coronal heating mechanisms

• So many ideas, taxonomy is needed! (Mandrini et
  al. 2000 Aschwanden et al. 2001)

• Where does the mechanical energy come from?

vs.
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Coronal heating mechanisms

• So many ideas, taxonomy is needed! (Mandrini et
  al. 2000 Aschwanden et al. 2001)

• Where does the mechanical energy come from?
• How rapidly 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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The Debate in 08

• Two broad classes of models have evolved that
  attempt to self-consistently answer the question
  How are fast and slow wind streams accelerated?

Wave/Turbulence-Driven (WTD) models
Reconnection/Loop-Opening (RLO) models
arXiv 0804.3058
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Reconnection / Loop-Opening models

• There is a natural appeal to the RLO idea, since
  only a small fraction of the Suns magnetic flux
  is open. Open flux tubes are always near closed
  loops!
• The magnetic carpet is continuously churning .
  . .

• Open-field regions show coronal jets (powered by
  reconnection?) that contribute to the wind mass
  flux.

Fisk (2005)
Hinode/XRT (X-ray) http//xrt.cfa.harvard.edu
STEREO/EUVI (195 Å) courtesy S. Patsourakos
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Reconnection / Loop-Opening models

• Emerging loops inject both mass and Poynting flux
  into open-field regions.
• Feldman et al. (1999) found correlation between
  loop-size coronal temperature.
• Fisk et al. (1999), Fisk (2003), Gloeckler et al.
  (2003), Schwadron McComas (2003), Schwadron et
  al. (2005) worked out the solar wind implications
  . . .

Ulysses SWICS
Fisk (2003) theory
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Wave / Turbulence-Driven models

• No matter the relative importance of RLO events,
  we do know that waves and turbulent motions are
  present everywhere... from photosphere to
  heliosphere.
• How much can be accomplished by only WTD
  processes? (Occams razor?)

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Building an Alfvén wave model

• In dark intergranular lanes, strong-field
  photospheric flux tubes are shaken by an
  observed spectrum of horizontal motions.
• In mainly open-field regions, Alfvén waves
  propagate up along the field, and partly reflect
  back down (non-WKB).
• Nonlinear couplings allow a (mainly
  perpendicular) turbulent cascade, terminated by
  damping ? gradual heating over several solar
  radii.

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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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Self-consistent 1D models

• Cranmer, van Ballegooijen, Edgar (2007)
  computed solutions for the waves background
  one-fluid plasma state along various flux
  tubes... going from the photosphere to the
  heliosphere.
• The only free parameters radial magnetic field
  photospheric wave properties.
• Ingredients

• Alfvén waves non-WKB reflection with full
  spectrum, turbulent damping, wave-pressure
  acceleration
• Acoustic waves shock steepening, TdS
  conductive damping, full spectrum, wave-pressure
  acceleration
• Radiative losses transition from optically thick
  (LTE) to optically thin (CHIANTI PANDORA)
• Heat conduction transition from collisional
  (electron neutral H) to collisionless
  streaming

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Results turbulent heating acceleration
T (K)
Ulysses SWOOPS
Goldstein et al. (1996)
reflection coefficient
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Results other fast/slow diagnostics

• Frozen-in charge states

• FIP effect (using Lamings 2004 theory)

Ulysses SWICS
Cranmer et al. (2007)
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Multi-fluid collisionless effects?
Polar coronal hole model
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Multi-fluid collisionless effects?
O5
O6
protons
electrons (thermal core only)
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Departures from thermal equilibrium

• UVCS/SOHO observations rekindled theoretical
  efforts to understand collisionless heating and
  acceleration effects in the extended corona.

• Ion cyclotron waves (1010,000 Hz) suggested as a
  natural energy source that can be tapped to
  preferentially heat accelerate heavy ions.

cyclotron resonance-like phenomena
MHD turbulence
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What next?

• Both WTD and RLO paradigms have passed some basic
  tests of comparison with observations. What
  could this imply?

• A combination of both ideas could work best?
• Existing models dont contain the right physics
  once that is included, one or the other idea may
  fail to work?
• Comparisons with observations havent been
  comprehensive enough to allow their true
  differences to be seen?

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What next?

• Both WTD and RLO paradigms have passed some basic
  tests of comparison with observations. What
  could this imply?

• A combination of both ideas could work best?
• Existing models dont contain the right physics
  once that is included, one or the other idea may
  fail to work?
• Comparisons with observations havent been
  comprehensive enough to allow their true
  differences to be seen?

• Some basic issues of energy budget still to
  resolve

• Do reconnections between open closed regions
  cover enough of the solar surface to account for
  the majority of the solar wind?
• Does MHD turbulence produce the right mixture
  of collisionless kinetic effects?

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Conclusions

• The debate between waves/turbulence and
  reconnection/loop-opening mechanisms of solar
  wind acceleration goes on . . .
• Theoretical advances in MHD turbulence continue
  to feed back into global models of the solar
  wind.
• The extreme plasma conditions in coronal holes
  (Tion gtgt Tp gt Te ) have guided us to discard
  some candidate processes, further investigate
  others, and have cross-fertilized other areas of
  plasma physics and astrophysics.

vs.
For more information http//www.cfa.harvard.edu
/scranmer/
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Extra slides . . .
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The extended solar atmosphere . . .
Heating is everywhere . . .
. . . and everything is in motion
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The Suns outer atmosphere

• The solar photosphere radiates like a blackbody
  its spectrum gives T, and dark Fraunhofer lines
  reveal its chemical composition.
• Total eclipses let us see the vibrant outer solar
  corona but what is it?
• 1870s spectrographs pointed at corona
• Is there a new element (coronium?)
• 1930s Lines identified as highly ionized ions
  Ca12 , Fe9 to Fe13 its hot!

• Fraunhofer lines (not moon-related)
• unknown bright lines

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Particles are not in thermal equilibrium
especially in the high-speed wind.
mag. field
WIND at 1 AU (Steinberg et al. 1996)
Helios at 0.3 AU (e.g., Marsch et al. 1982)
WIND at 1 AU (Collier et al. 1996)
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Waves? Start in the photosphere . . .

• Photosphere displays convective motion on a broad
  range of time/space scales

ß ltlt 1
ß 1
ß gt 1
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Turbulence

• It is highly likely that somewhere in the outer
  solar atmosphere the fluctuations become
  turbulent and cascade from large to small scales.
• The original Kolmogorov (1941) theory of
  incompressible fluid turbulence describes a
  constant energy flux from the largest stirring
  scales to the smallest dissipation scales.
• Largest eddies have kinetic energy ?v2 and a
  turnover time-scale ? l/v, so the rate of
  transfer of energy goes as ?v2/? ?v3/l .
• Dimensional analysis can give the spectrum of
  energy vs. eddy-wavenumber k Ek k5/3

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Progress towards 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!)
• Does turbulence generate enough ion-cyclotron
  waves to heat the minor ions?
• 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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The need for extended heating

• The basal coronal heating problem is not yet
  solved, but the field seems to be homing in on
  the interplay between emerging flux,
  reconnection, turbulence, and helicity
  (shear/twist).

• Above 2 Rs , some other kind of energy
  deposition is needed 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 magnetic moment!),
• produce the strong preferential heating and
  temperature anisotropy of ions (in the winds
  acceleration region) seen with UV spectroscopy.

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Exploring the extended corona

• Off-limb measurements (in the solar wind
  acceleration region ) allow dynamic
  non-equilibrium plasma states to be followed as
  the asymptotic conditions at 1 AU are gradually
  established.

Occultation is required because extended corona
is 5 to 10 orders of magnitude less bright than
the disk!
Spectroscopy provides detailed plasma diagnostics
that imaging alone cannot.

• The Ultraviolet Coronagraph Spectrometer (UVCS)
  on SOHO combines these features to measure plasma
  properties of coronal protons, ions, and
  electrons between 1.5 and 10 solar radii.

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The UVCS instrument on SOHO

• 19791995 Rocket flights and Shuttle-deployed
  Spartan 201 laid groundwork.

• 1996present 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
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UVCS results over the poles (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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Emission lines as plasma diagnostics

• Many of the lines seen by UVCS are formed by
  resonantly scattered disk photons.

• If profiles are Doppler shifted up or down in
  wavelength (from the known rest wavelength), this
  indicates the bulk flow speed along the
  line-of-sight.
• The widths of the profiles tell us about random
  motions along the line-of-sight (i.e.,
  temperature)

• The total intensity (i.e., number of photons)
  tells us mainly about the density of atoms, but
  for resonant scattering theres also another
  hidden Doppler effect that tells us about the
  flow speeds perpendicular to the line-of-sight.

• 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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Preferential ion heating acceleration

• 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 (1010,000 Hz) suggested as a
  natural energy source that can be tapped to
  preferentially heat accelerate heavy ions.

cyclotron resonance-like phenomena
MHD turbulence
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Anisotropic MHD cascade

• Can MHD turbulence generate ion cyclotron waves?
  Many models say no!

• Simulations analytic models predict cascade
  from small to large k ,leaving k unchanged.
  Kinetic Alfven waves with large k do not
  necessarily have high frequencies.

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Anisotropic MHD cascade

• Can MHD turbulence generate ion cyclotron waves?
  Many models say no!

• Simulations analytic models predict cascade
  from small to large k ,leaving k unchanged.
  Kinetic Alfven waves with large k do not
  necessarily have high frequencies.
• In a low-beta plasma, KAWs are Landau-damped,
  heating electrons preferentially!
• Cranmer van Ballegooijen (2003) modeled the
  anisotropic cascade with advection diffusion in
  k-space and found some k leakage . . .

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So does turbulence generate cyclotron waves?
Directly from the linear waves? Probably not!
How then are the ions heated and accelerated?

• When MHD turbulence cascades to small
  perpendicular scales, the small-scale shearing
  motions may be able to generate ion cyclotron
  waves (Markovskii et al. 2006).
• If MHD turbulence exists for both Alfvén and
  fast-mode waves, the two types of waves can
  nonlinearly couple with one another to produce
  high-frequency ion cyclotron waves (Chandran
  2006).
• If nanoflare-like reconnection events in the low
  corona are frequent enough, they may fill the
  extended corona with electron beams that would
  become unstable and produce ion cyclotron waves
  (Markovskii 2007).
• If kinetic Alfvén waves reach large enough
  amplitudes, they can damp via wave-particle
  interactions and heat ions (Voitenko Goossens
  2006 Wu Yang 2007).
• Kinetic Alfvén wave damping in the extended
  corona could lead to electron beams, Langmuir
  turbulence, and Debye-scale electron phase space
  holes which heat ions perpendicularly via
  collisions (Ergun et al. 1999 Cranmer van
  Ballegooijen 2003).

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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)

Solar minimum
Solar maximum
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Waves remote-sensing techniques
The following techniques are direct (UVCS ion
heating was more indirect)
Tomczyk et al. (2007)
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Overview of in situ fluctuations

• Fourier transform of B(t), v(t), etc., into
  frequency

• How much of the power is due to spacecraft
  flying through flux tubes rooted on the Sun?

f -1 energy containing range
f -5/3 inertial range
The inertial range is a pipeline for
transporting magnetic energy from the large
scales to the small scales, where dissipation can
occur.
Magnetic Power
f -3dissipation range
0.5 Hz
few hours
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Future diagnostics more spectral lines!

• How/where do plasma fluctuations drive the
  preferential ion heating and acceleration, and
  how are the fluctuations produced and damped?
• Observing emission lines of additional ions
  (i.e., more charge mass combinations) would
  constrain the specific kinds of waves and the
  specific collisionless damping modes.

Comparison of predictions of UV line widths for
ion cyclotron heating in 2 extreme limits (which
UVCS observations black circles cannot
distinguish). Cranmer (2002), astro-ph/0209301
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Future Diagnostics electron VDF

• Simulated H I Lyman alpha broadening from both H0
  motions (yellow) and electron Thomson scattering
  (green). Both proton and electron temperatures
  can be measured.

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Synergy with other systems

• T Tauri stars observations suggest a polar
  wind that scales with the mass accretion rate.
  Cranmer et al. (2007) code is being adapted to
  these systems...
• Pulsating variables Pulsations leak outwards
  as non-WKB waves and shock-trains. New insights
  from solar wave-reflection theory are being
  extended.
• AGN accretion flows A similarly collisionless
  (but pressure-dominated) plasma undergoing
  anisotropic MHD cascade, kinetic wave-particle
  interactions, etc.

Freytag et al. (2002)
Matt Pudritz (2005)