1. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics
Plasma Unbound: New Insights into Heating the Solar Corona 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 Corona and Accelerating the Solar Wind
Outline:
1. Brief historical background
2. Heating the “coronal base” with reconnection
3. Heating & accelerating “extended corona” with turbulence
4. Preferential ion heating collisionless kinetics!
Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

3. Motivations Solar corona & solar wind:
Space weather can affect satellites, power grids, and astronaut safety.
The Sun’s mass-loss history may have 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 Sun’s 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: Ca+12 , Fe+9 to Fe it’s hot!
Fraunhofer lines (not moon-related)
unknown bright lines

6. The solar wind: discovery
1860–1950: 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 comet’s motion)

7. 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 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

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. 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)

11. 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

12. 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)

13. The SOHO mission
SOHO (the Solar and Heliospheric Observatory) was launched in Dec with the goal of solving long-standing mysteries about the Sun.
12 instruments on SOHO probe:
solar interior (via “seismology”)
solar atmosphere (images, movies, spectra)
solar wind (collect particles, measure fields)
interstellar gas (some photons backscatter)
L1 orbit provides
24-hour viewing

14. High-resolution UV images of the low corona

15. 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!

16. 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.

17. 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.

18. 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

19. Reconnection in closed loops e.g., Longcope & Kankelborg 1999
Models of how coronal heating (FX) scales with magnetic flux (Φ) are growing more sophisticated . . .
Closed loops: Magnetic reconnection
e.g., Longcope & Kankelborg 1999
Gudiksen & Nordlund (2005)

20. 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.

21. Waves? Start in the photosphere . . .
Photosphere displays convective motion on a broad range of time/space scales:
β << 1
β ~ 1
β > 1

22. Alfvén waves from cradle to grave
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.

23. 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 ~ 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. MHD turbulence: two kinds of “anisotropy”
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.
Phenomenological expressions are good at reproducing numerical results: Z– Z– Z+
(e.g., Hossain et al. 1995; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Oughton et al. 2006)

25. “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”

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

27. Multi-fluid collisionless effects?
Polar coronal hole model

28. Multi-fluid collisionless effects?
Polar coronal hole model
protons
electrons

29. Multi-fluid collisionless effects?
protons
electrons

30. 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.

31. 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

32. 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.

33. 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.

34. 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.
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

35. 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.

36. 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!

37. 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” . . .

38. 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).

39. Streamers and CMEs
UVCS sees slow-wind outflow regions (“legs”) & closed fields (“core”).
White-light images show morphology; UV spectra constrain “energy budget.”

40. 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)

41. More plasma diagnostics
Conclusions
UV coronagraph spectroscopy has led to fundamentally new views of the collisionless acceleration regions of the solar wind.
Theoretical advances in MHD turbulence continue to “feed back” into global models of the solar wind.
The extreme plasma conditions in coronal holes (Tion >> Tp > Te ) have guided us to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics.
Get involved! 12+ years of UVCS data is only beginning to be analyzed fully!
More plasma diagnostics
Better understanding
For more information:

42. Extra slides . . .

43. 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”

44. 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

45. The UVCS instrument on SOHO
1979–1995: Rocket flights and Shuttle-deployed Spartan 201 laid groundwork.
1996–present: 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
UVCS “rolls” independently of spacecraft
2 UV channels:
1 white-light polarimetry channel
LYA (120–135 nm)
OVI (95–120 nm + 2nd ord.)

46. 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!

47. 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)
Solar minimum:
Solar maximum:

48. 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)

49. 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)

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

51. 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)

52. 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)

53. The chromospheric network
Large numbers of lines (Mg, Ca; also IR, mm continuum) constrain the temperature “plateau.”
There is more heating in the network “lanes” than in the cell-center regions.
Vernazza, Avrett, & Loeser (1981)
A: darkest cell-center
C: avg. quiet Sun
F: brightest network lane
Leighton (1963)

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

55. 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 -3 “dissipation range”
few hours
0.5 Hz

56. 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/

57. 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.

58. Future Diagnostics: suprathermal tails
Measuring non-Maxwellian velocity distributions of electrons and positive ions would allow us to test specific models of, e.g., velocity filtration, cyclotron resonance, and MHD turbulence.
(Also these “seed particles” allow us to test models of SEP acceleration…)
Cranmer (1998, 2001)