The Physics of Coronal Heating and Solar Wind Acceleration:

1. Ongoing Research and Unanswered Questions The Physics of Coronal Heating and Solar Wind Acceleration: Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics

2. Ongoing Research and Unanswered Questions The Physics of Coronal Heating and Solar Wind Acceleration: • Outline: • Brief overview of the Sun-Heliosphere system • Exciting new measurements: remote & in situ • Major unsolved puzzles . . . Steven R. CranmerHarvard-SmithsonianCenter 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. 2010 (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). 2007: Voyagers @ term. shock. fast slow 300–500 high chaotic all ~equal more low-FIP speed (km/s) density variability temperatures abundances 600–800 low smooth + waves Tion >> Tp > Te photospheric

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 O+5 protons In the lowest density solar wind streams . . . electron temperatures proton temperatures heavy ion temperatures

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 -3dissipation 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 • 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. 5 2 — ρvkT 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 SUMER/SOHO G-band bright points UVCS/SOHO Helios & Ulysses 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:1104.3817).

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 constraintsto be able to choose between competing theories. SDO/AIA For more information: http://www.cfa.harvard.edu/~scranmer/

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: • In MHD, cascade is possible only if there are counter-propagating Alfvén waves… (“cascade efficiency”) Z– Z+ • n = 1: an approximate “golden rule” from theory • Caution: this is an order-of-magnitude scaling. (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) Z–

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.) • 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. Ulysses 1994-1995

32. Cranmer et al. (2007): other results Wang & Sheeley (1990) ACE/SWEPAM ACE/SWEPAM Ulysses SWICS Ulysses SWICS Helios (0.3-0.5 AU)

33. Alfven wave’s oscillating E and B fields ion’s Larmor motion around radial B-field Preferential ion heating & acceleration • Parallel-propagating ion cyclotron waves (10–10,000 Hz in the corona) have been suggested as a natural energy source . . . 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. • 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). k 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. • 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). k 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 wind • 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 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. 2006). • 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).