1. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics
Plasma Unbound: New Insights into Heating the Solar Atmosphere and Accelerating the Solar Wind
Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

2. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics
Plasma Unbound: New Insights into Heating the Solar Atmosphere and Accelerating the Solar Wind
Outline:
Overview and brief historical background
Heating the chromosphere (sound waves & shocks)
Heating the coronal base (reconnection & turbulence)
Heating and accelerating the extended corona (waves & turbulence)
Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

3. Motivations Solar corona & solar wind:
Space weather can affect satellites, power grids, astronaut safety, etc.
The Sun’s mass-loss & X-ray history impacted planetary formation and atmospheric erosion.
The Sun is a “laboratory without walls” for many basic processes in physics, at regimes (T, P) inaccessible on Earth!
plasma physics
nuclear physics
non-equilibrium thermodynamics
electromagnetic theory

4. The extended solar atmosphere
Heating is everywhere . . .
. . . and everything is in motion

5. The extended solar atmosphere
Heating is everywhere . . .
. . . and everything is in motion

6. Too-brief history
Total eclipses let us see the vibrant outer solar corona: but what is it?
1870s: spectrographs pointed at corona:
1930s: Lines identified as highly ionized ions: Ca+12 , Fe+9 to Fe+13  it’s hot!
Fraunhofer lines (not moon-related)
unknown bright lines
1860–1950: Evidence slowly builds for outflowing magnetized plasma in the solar system:
solar flares  aurora, telegraph snafus, geomagnetic “storms”
comet ion tails point anti-sunward (no matter comet’s motion)
1958: Eugene Parker proposed that the hot corona provides enough gas pressure to counteract gravity and accelerate a “solar wind.”

7. In situ solar wind: properties
1962: 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 wind’s source regions.
speed (km/s)
Tp (105 K)
Te (105 K)
Tion / Tp
O7+/O6+, Mg/O
600–800
2.4
1.0
> mion/mp
low
300–500
0.4
1.3
< mion/mp
high
fast
slow
By ~1990, it was clear the fast wind needs something besides gas pressure to accelerate so fast!

8. Ulysses’ view over the poles
McComas et al. (2008)
(Sept , 2009)
“Understanding a Peculiar Solar Minimum”

9. Exploring the solar wind (1970s to present)
Space probes have pushed out the boundaries of the “known” solar wind . . .
Helios 1 & 2: inner solar wind (Earth to Mercury)
Ulysses: outer solar wind (Earth to Jupiter, also flew over N/S poles)
Voyager 1 & 2: far out past Pluto: recently passed the boundary between the solar wind and the interstellar medium
CLUSTER: multiple spacecraft probe time and space variations simultaneously

10. The solar photosphere
The photosphere reveals interior convective motions & complex magnetic fields:
β << 1
β ~ 1
β > 1

11. The solar chromosphere

12. The need for chromospheric heating
Not huge in radial extent, but contains orders of magnitude more mass than the layers above . . .

13. “Traditional” chromospheric heating
Vertically propagating acoustic waves conserve flux (in a static atmosphere):
Amplitude eventually reaches Vph and wave-train steepens into a shock-train.
Shock entropy losses go into heat; only works for periods < 1–2 minutes…
Bird (1964) ~
New idea: “Spherical” acoustic wave fronts from discrete “sources” in the photosphere (e.g., enhanced turbulence or bright points in inter-granular lanes) may do the job with longer periods.

14. Time-dependent chromospheres?
Carlsson & Stein (1992, 1994, 1997, 2002, etc.) produced 1D time-dependent radiation-hydrodynamics simulations of vertical shock propagation and transient chromospheric heating. Wedemeyer et al. (2004) continued to 3D...

15. Runaway to the transition region (TR)
Whatever the mechanisms for heating, they must be balanced by radiative losses to maintain chromospheric T.
When shock strengths “saturate,” heating depends on density only:
Why then isn’t the corona 109 K? Downward heat conduction smears out the “peaks,” and the solar wind also “carries” away some kinetic energy. Conduction also steepens the TR to be as thin as it is.

16. Overview of coronal observations
Plasma at 106 K emits most of its spectrum in the UV and X-ray . . .
Coronal hole (open)
“Quiet” regions
Active regions

17. 1990s: SOHO’s new view of the corona

18. 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:
Wang et al. (2000)

19. The coronal heating problem
We still don’t 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 between ions and electrons (i.e., friction?) release energy as heat.
Heating Solar wind acceleration!

20. 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.

21. 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?
vs.
waves
shocks
eddies
(“AC”)
twisting
braiding
shear
(“DC”)
vs.

22. 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.
turbulence
reconnection
collisions (visc, cond, resist, friction) or collisionless

23. Turbulence
It is highly likely that somewhere in the 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 ~ ρv2 and a turnover time-scale  =l/v, so the rate of transfer of energy goes as ρv2/ ~ ρv3/l .
Dimensional analysis can give the spectrum of energy vs. eddy-wavenumber k: Ek ~ k–5/3

24. Turbulence in coronal loops?
Many stochastic processes can be described roughly using a turbulent “language.”
Coronal loops are always in motion, with waves & bulk flows propagating back and forth along the field lines.
Counter-propagating Alfvén waves interact over shorter time intervals  thus the cascade takes longer to develop.
However, the weaker character of the cascade makes it able to gradually “send” more energy down to the ever-smaller eddies, and thus lead to more dissipation!
n = 0 (Kolmogorov), 3/2 (Gomez et al. 2000), 5/3 (Kraichnan), 2 (van Ballegooijen; Rappazzo et al.)

25. Reconnection & Turbulence
Ultimately, the actual dissipation and heating in loops appears to occur in regions of magnetic reconnection.
This is still understandable from a turbulence paradigm, since on its smallest scales, MHD turbulence tends to:
break up into thin reconnecting sheets.
accelerate electrons along the field to generate currents.
Dmitruk et al. (2004)
Rappazzo et al. (2008)
Even pre-existing current sheets are unstable in a variety of ways to growth of turbulent motions, which may dominate the energy loss & particle acceleration.
Onofri et al. (2006)

26. 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 wind’s acceleration region) seen with UV spectroscopy.

27. Extended heating requires “unified” models
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.

28. MHD turbulence: two kinds of anisotropy
Outside closed loops, we can revert to standard Kolmogorov (1941) scaling, but with two modifications:
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., Hossain et al. 1995; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Oughton et al. 2006)

29. “The kitchen sink”
Cranmer, van Ballegooijen, & Edgar (2007) computed self-consistent solutions of waves & background one-fluid plasma state along various flux tubes... going from the photosphere to the heliosphere.
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”

30. Results: turbulent heating & acceleration
T (K)
reflection coefficient
Ulysses SWOOPS
Goldstein et al.
(1996)

31. Synergy with other systems
Pulsating hot (O, B, Wolf-Rayet) stars: Pulsations “leak” outwards as non-WKB waves and shocks. New insights from solar wave theory are being applied.
T Tauri stars: Cranmer (2008) extended solar wave/turbulence models to include accretion-generated waves on stellar surface, from inhomogeneous impacts.
AGN accretion flows: A similarly collisionless (but pressure-dominated) plasma undergoing anisotropic MHD cascade and kinetic wave-particle interactions...

32. Conclusions
The Sun/heliosphere system is a nearby “laboratory without walls” for studying plasma physics in regimes of parameter space inaccessible in Earth-based laboratories.
Theoretical advances in plasma physics and MHD turbulence continue to feed back into global models of atmospheric heating and solar wind acceleration.
Observational advances (both space-based and ground-based) have guided us to discard some candidate theories, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics.
For more information:

33. Extra slides about collisionless plasma effects . . .

34. Multi-fluid collisionless effects?

35. Multi-fluid collisionless effects?
protons
electrons

36. 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)

37. 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.

38. 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., O+5) line emission in the extended corona revealed surprisingly wide line profiles . . .
Off-limb profiles: T > 100 million K !
On-disk profiles: T = 1–3 million K

39. Preferential ion heating & acceleration
UVCS & SUMER observations have rekindled theoretical efforts to understand heating and acceleration of the plasma in the acceleration region of the wind.

40. Preferential ion heating & acceleration
UVCS & SUMER observations have rekindled theoretical efforts to understand heating and acceleration of the plasma in the acceleration region of the wind.
Alfven wave’s oscillating
E and B fields
ion’s Larmor motion around radial B-field
Ion cyclotron waves (10–10,000 Hz) suggested as a “natural” energy source that can be tapped to preferentially heat & accelerate heavy ions.
something else?
cyclotron resonance-like phenomena
MHD turbulence

41. What produces “emission lines” in a spectrum?
There are 2 general ways of producing extra photons at a specific wavelength.
Both mechanisms depend on the quantum nature of atoms: “bound” electrons have discrete energies . . .
The incoming particle can be either:
Incoming particle
Electron absorbs energy
Energy
re-emitted as light
A free electron from some other ionized atom (“collisional excitation”)
A photon at the right wavelength from the bright solar disk (“resonant scattering”)
There is some spread in wavelength

42. 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 there’s 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.

43. 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!

44. Extra slides . . .

45. The solar activity cycle
Yohkoh/SXT

46. Waves: remote-sensing techniques
The following techniques are direct… (UVCS ion heating was more indirect)
Intensity modulations . . .
Motion tracking in images . . .
Doppler shifts . . .
Doppler broadening . . .
Radio sounding . . .
Tomczyk et al. (2007)

47. Strongest fields in supergranular “funnels?”
Peter (2001)
Fisk (2005)
Tu et al. (2005)

48. Alfvén waves: from Sun to Earth
Velocity amplitudes of fluctuations measured (mainly) perpendicular to the background magnetic field.

49. Why is the fast (slow) wind fast (slow)?
What determines how much energy and momentum goes into the solar wind?
Waves & turbulence input from below?
Reconnection & mass input from loops?
vs.
Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models of individual open flux tubes.
Boundary conditions imposed only at the photosphere (no arbitrary “heating functions”).
Wind acceleration determined by a combination of magnetic flux-tube geometry, gradual Alfvén-wave reflection, and outward wave pressure.

50. Results: other fast/slow diagnostics
The wind speed is anticorrelated with flux-tube expansion . . .
“active region” fields
Cascade efficiency:
n=1
n=2

51. Results: in situ turbulence
To compare modeled wave amplitudes with in-situ fluctuations, knowledge about the spectrum is needed . . .
“e+”: (in km2 s–2 Hz–1 ) defined as the Z– energy density at 0.4 AU, between 10–4 and 2 x 10–4 Hz, using measured spectra to compute fraction in this band.
Helios (0.3–0.5 AU)
Tu et al. (1992)
Cranmer et al. (2007)

52. Results: heavy ion properties
Frozen-in charge states
FIP effect (using Laming’s 2004 theory)
Ulysses SWICS
Cranmer et al. (2007)

53. New result: solar wind “entropy”
Pagel et al. (2004) found ln(T/nγ–1) (at 1 AU) to be strongly correlated with both wind speed and the O7+/O6+ charge state ratio (empirical γ = 1.5)
The Cranmer et al. (2007) models do a good job of reproducing ACE/SWEPAM entropy data (blue region) & Ulysses charge state trends (brown regions).

54. Do blobs trace out the slow wind?
The blobs are very low-contrast and thus may be passive “leaves in the wind.”
Sheeley et al. (1997)

55. Polar plumes and jets
Dense, thin flux tubes permeate polar coronal holes. They live for about a day, but can recur from the same footpoint over several solar rotations.
Short-lived “polar jets” are energetic events that appear to eject plasma into the solar wind. Hinode/XRT
(DeForest et al. 1997)

56. 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)

57. Coronal mass ejections
Forbes & Priest (1995) and Lin & Forbes (2000) developed a theory of CMEs as a loss of magnetostatic equilibrium in a twisted “flux rope.”
The current sheet energizes both the CME (above) and a “two-ribbon flare” (below)

58. First observations of “stellar outflows”
Coronae & Aurorae seen since antiquity . . .
“New stars”
1572: Tycho’s supernova
1600: P Cygni outburst (“Revenante of the Swan”)
1604: Kepler’s supernova in “Serepentarius”