1. The Physics of Coronal Heating and Solar Wind Acceleration:
Ongoing Research and
Unanswered Questions
Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

2. The Physics of Coronal Heating and Solar Wind Acceleration:
Ongoing Research and
Unanswered Questions
Outline:
Brief overview of the Sun-Heliosphere system
Exciting new measurements: remote & in situ
Major unsolved puzzles . . .
Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

3. The extended solar atmosphere
The “coronal heating problem”

4. The photosphere and chromosphere
The lower boundary for space weather is the top of the convective zone:
Optically thick photosphere:
β << 1
β ~ 1
β > 1
Optically thin (heated) chromosphere:

5. The solar corona
Plasma at 106 K emits most of its spectrum in the UV and X-ray . . .
Although there is more than enough kinetic energy at the lower boundary, we still don’t understand the physical processes that heat the plasma.
Most suggested ideas involve 3 steps:
1. Churning convective motions tangle up magnetic fields on the surface.
2. Energy is stored in twisted/braided/ swaying magnetic flux tubes.
3. Something on small (unresolved?) scales releases this energy as heat.
Particle-particle collisions?
Wave-particle interactions?

6. A small fraction of magnetic flux is OPEN
Peter (2001)
Fisk (2005)
Tu et al. (2005)

7. 2008 Eclipse:
M. Druckmüller (photo)
S. Cranmer (processing)
Rušin et al (model)

8. In situ solar wind: properties
1958: Eugene Parker proposed that the hot corona provides enough gas pressure to counteract gravity and produce steady supersonic outflow.
Mariner 2 (1962): first confirmation of fast & slow wind.
1990s: Ulysses left the ecliptic; provided first 3D view of the wind’s source regions.
1970s: Helios (0.3–1 AU) : term. shock.
speed (km/s)
density
variability
temperatures
abundances
600–800
low
smooth + waves
Tion >> Tp > Te
photospheric
300–500
high
chaotic
all ~equal
more low-FIP
fast
slow

9. Outline:
Overview: Our complex “variable star”
Exciting new measurements: remote & in situ
Major unsolved puzzles . . .

10. AIA on the Solar Dynamics Observatory (SDO)
SDO is the 1st “Living With a Star” mission.
Geosynchronous orbit allows continuous monitoring. AIA telescopes obtain EUV images (16 megapixel) every ~10 seconds:
2 Terabytes per day sent down to the ground!
See Dean Pesnell’s talk (A112 S3, 08:30)

11. AIA 171 Å (sensitive to T ~ 106 K)

12. MHD waves in the corona
Remote sensing provides several direct (and indirect) wave detection techniques:
Alfvén waves have been detected via spectroscopy (Doppler shifts) and imaging (plane-of-sky swaying).
Tomczyk et al. (2007)
Fast & slow mode magnetosonic waves have been detected via intensity fluctuations (δρ2) and motion tracking to measure phase speeds.

13. Erupting jets in the corona
Open-field regions show frequent jet-like events.
Evidence of magnetic reconnection between open and closed fields?
How much of the solar wind emerges in jets?
Hinode/SOT: Nishizuka et al. (2008)
STEREO imagers allow 3D MHD structure of jets to be disentangled . . .

14. Coronal heating: multi-fluid & collisionless
protons
electron temperatures
proton temperatures
heavy ion temperatures
In the lowest density solar wind streams . . .

15. In situ fluctuations & turbulence
Fourier transform of B(t), v(t), etc., into frequency:
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 -3 dissipation range
few hours
0.5 Hz

16. In situ MHD turbulence
A single spacecraft can’t tell the difference between spatial and time variations.
Theories say an MHD cascade is highly anisotropic in wavenumber space . . .
CLUSTER consists of 4 formation flying spacecraft, and has finally disentangled temporal from spatial variability: solar wind turbulence IS anisotropic!
Sahraoui et al. (2010)

17. Outline:
Overview: Our complex “variable star”
Exciting new measurements: remote & in situ
Major unsolved puzzles . . .

18. What is the source of solar wind mass?
Until relatively recently, the dominant idea was that a steady rate of “evaporation” is set by a balance between downward conduction, upward enthalpy flux, and local radiative cooling (Hammer 1982; Withbroe 1988).
heat conduction
radiation losses
— ρvkT 5 2
On the other hand, new observations of spicules and jets (e.g., Aschwanden et al. 2007; De Pontieu et al. 2011; McIntosh et al. 2011) fuel the idea that a lot of the corona’s mass is injected impulsively from below.
Schrijver (2001)

19. What is the dominant source of energy?
i.e., what heats the corona in open flux tubes? Two general ideas have emerged . . .
Wave/Turbulence-Driven (WTD) models, in which open flux tubes are jostled continuously from below. MHD fluctuations propagate up and damp.
Reconnection/Loop-Opening (RLO) models, in which energy is injected from closed-field regions in the “magnetic carpet.”
vs.
Counterpoint:
Roberts (2010) says WTD doesn’t work.
Cranmer & van Ballegooijen (2010) say RLO doesn’t work.

20. How much do impulsive events contribute?
There is a natural appeal to the RLO idea, since only a small fraction of the Sun’s magnetic flux is open. Open flux tubes are always near closed loops!
The “magnetic carpet” is continuously perturbing the field, much of which is connected tenuously to the wind via “quasi-separatrix layers” (Antiochos et al. 2011).
But is there enough mass & energy released (in the subset of reconnection events that turn closed fields into open fields) to account for the solar wind’s requirements?

21. Waves & turbulence
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? (Occam’s razor?)
Hinode/SOT
G-band bright points
SUMER/SOHO
Helios & Ulysses
UVCS/SOHO
Undamped (WKB) waves
Damped (non-WKB) waves

22. Waves & turbulence
A number of recent models seem to be converging on a combination of turbulent dissipation (heating) and wave ponderomotive forces (acceleration) as being both sufficient to accelerate the wind and consistent with coronal & in situ observations.
For example, wave/turbulence processes can produce:
Realistic/variable coronal heating (Suzuki & Inutsuka 2006):
3D heliospheric variability
(Breech et al. 2009; Usmanov et al. 2011)
See also Cranmer et al. (2007)

23. Controversies about waves & turbulence
Where does the turbulent cascade begin? Chromosphere? Low corona? Some say it doesn’t become “fully developed” turbulence until < 1 AU. ~
In simulations that include flux-tube expansion, complex turbulent motions are induced, even down in the middle chromosphere!
(van Ballegooijen et al. 2011)
Simple motions input at photospheric lower boundary.

24. Controversies about waves & turbulence
The low-frequency (1/f) part of the spectrum at 1 AU contains most of the power. What is its origin?
The self-consistent product of a turbulent cascade?
Spacecraft passage through “spaghetti-like” flux tubes rooted on the solar surface? (Borovsky 2008)
New high-resolution magnetographs make possible better “mappings.”
(SOLIS Vector SpectroMagnetograph on Kitt Peak)

25. What’s next?
Data at 1 AU shows us plasma that has been highly “processed” on its journey Models must keep track of 3D dynamical effects, Coulomb collisions, etc.
McGregor et al. (2011)
Kasper et al. (2010)
New missions!
In ~2018, Solar Probe Plus will go in to r ≈ 9.5 Rs to tell us more about the sub-Alfvénic solar wind.
The Coronal Physics Investigator (CPI) has been proposed as a follow-on to UVCS/SOHO to observe new details of minor ion heating & kinetic dissipation of turbulence in the extended corona (see arXiv: ).

26. Conclusions
Advances in plasma physics (turbulence, waves, reconnection) continue to help improve our understanding about coronal heating and solar wind acceleration.
It is becoming easier to include “real physics” in 1D → 2D → 3D models of the complex Sun-heliosphere system.
However, we still do not have complete enough observational constraints to be able to choose between competing theories.
SDO/AIA
For more information:

27. Extra slides . . .

28. Waves & turbulence in open flux tubes
Photospheric flux tubes are shaken by an observed spectrum of horizontal motions.
Alfvén waves propagate along the field, and partly reflect back down (non-WKB).
Nonlinear couplings allow a (mainly perpendicular) cascade, terminated by damping.
(Heinemann & Olbert 1980; Hollweg 1981, 1986; Velli 1993; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Cranmer & van Ballegooijen 2003, 2005; Verdini et al. 2005; Oughton et al. 2006; many others)

29. Turbulent dissipation = coronal heating?
In hydrodynamics, von Kármán, Howarth, & Kolmogorov worked out cascade energy flux via dimensional analysis: Z+ Z–
In MHD, cascade is possible only if there are counter-propagating Alfvén waves…
n = 1: an approximate “golden rule” from theory
Caution: this is an order-of-magnitude scaling.
(“cascade efficiency”)
(e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002; Oughton et al. 2006)

30. 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.
Some details about the 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 a collisionless “streaming” approximation

31. Implementing the wave/turbulence idea
Cranmer et al. (2007) computed self-consistent solutions for waves & background plasma along flux tubes going from the photosphere to the heliosphere.
Only free parameters: radial magnetic field & photospheric wave properties. (No arbitrary “coronal heating functions” were used.)
Ulysses
Self-consistent coronal heating comes from gradual Alfvén wave reflection & turbulent dissipation.
Is Parker’s critical point above or below where most of the heating occurs?
Models match most observed trends of plasma parameters vs. wind speed at 1 AU.

32. Cranmer et al. (2007): other results
Wang & Sheeley (1990)
ACE/SWEPAM
ACE/SWEPAM
Ulysses
SWICS
Ulysses
SWICS
Helios
( AU)

33. Preferential ion heating & acceleration
Parallel-propagating ion cyclotron waves (10–10,000 Hz in the corona) have been suggested as a natural energy source . . .
Alfven wave’s oscillating
E and B fields
ion’s Larmor motion around radial B-field
instabilities
dissipation
lower qi/mi
faster diffusion
(e.g., Cranmer 2001)

34. However . . .
Does a turbulent cascade of Alfvén waves (in the low-beta corona) actually produce ion cyclotron waves?
Most models say NO!

35. Anisotropic MHD turbulence
When magnetic field is strong, the basic building block of turbulence isn’t an “eddy,” but an Alfvén wave packet. k ?
Energy input k

36. Anisotropic MHD turbulence
When magnetic field is strong, the basic building block of turbulence isn’t an “eddy,” but an Alfvén wave packet. k
Alfvén waves propagate ~freely in the parallel direction (and don’t interact easily with one another), but field lines can “shuffle” in the perpendicular direction.
Thus, when the background field is strong, cascade proceeds mainly in the plane perpendicular to field (Strauss 1976; Montgomery 1982).
Energy input k

37. Anisotropic MHD turbulence
When magnetic field is strong, the basic building block of turbulence isn’t an “eddy,” but an Alfvén wave packet. k
Alfvén waves propagate ~freely in the parallel direction (and don’t interact easily with one another), but field lines can “shuffle” in the perpendicular direction.
Thus, when the background field is strong, cascade proceeds mainly in the plane perpendicular to field (Strauss 1976; Montgomery 1982).
ion cyclotron waves
Ωp/VA
kinetic Alfvén waves
In a low-β plasma, cyclotron waves heat ions & protons when they damp, but kinetic Alfvén waves are Landau- damped, heating electrons.
Energy input k
Ωp/cs

38. Parameters in the solar windk
What wavenumber angles are “filled” by anisotropic Alfvén-wave turbulence in the solar wind? (gray)
What is the angle that separates ion/proton heating from electron heating? (purple curve) θ k
Goldreich &Sridhar (1995)
electron heating
proton & ion heating

39. Preliminary coupling results
Chandran (2005) suggested that weak turbulence couplings (AAF, AFF) may be sufficient to transfer enough energy to Alfvén waves at high parallel wavenumber.
New simulations in the presence of strong Alfvénic turbulence (e.g., Goldreich & Sridhar 1995) show that these couplings may give rise to wave power that looks like a kind of “parallel cascade” (Cranmer, Chandran, & van Ballegooijen 2011)
r = 2 Rs
β ≈ 0.003

40. Other ideas . . .
When MHD turbulence cascades to small perpendicular scales, the small-scale shearing motions may be unstable to the generation of ion cyclotron waves (Markovskii et al ).
Turbulence may lead to dissipation-scale current sheets that may preferentially spin up ions (Dmitruk et al. 2004).
If there are suprathermal tails in chromospheric velocity distributions, then collisionless velocity filtration (Scudder 1992) may give heavy ions much higher temperatures than protons (Pierrard & Lamy 2003).
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 stochastic wave-particle interactions and heat ions (Voitenko & Goossens 2006; Wu & Yang 2007; Chandran 2010).
Kinetic Alfvén wave damping in the extended corona could lead to electron beams, Langmuir turbulence, and Debye-scale electron phase space holes which could heat ions perpendicularly (Matthaeus et al. 2003; Cranmer & van Ballegooijen 2003).