1. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

2. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics Outline: 1.Turbulence as a driver of coronal heating & wind acceleration 2.Kinetic partitioning to protons, electrons, and ions Results of recent modeling Open issues (“successes”) (“failures”) Ion cyclotron resonance? A laundry list of other possibilities...

3. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence My own history... 1992–1996: hot star theory 1996–1999: UVCS data analysis 1999–2004: Why are heavy ions preferentially heated & accelerated? 2004–now: Why is the whole plasma heated & accelerated?

4. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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 Opinionated “position paper:” arXiv: 0804.3058

5. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Open flux tubes: global model 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!)

6. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Alfvén wave reflection refl. coeff = |z + | 2 /|z – | 2 At photosphere: empirically-determined frequency spectrum of incompressible transverse motions (from statistics of tracking G-band bright points) At all larger heights: self-consistent distribution of outward (z – ) and inward (z + ) Alfvenic wave power, determined by linear non-WKB transport equation: TR

7. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Wave / Turbulence-Driven models Cranmer & van Ballegooijen (2005) solved the transport equations for a grid of “monochromatic” periods (3 sec to 3 days), then renormalized using photospheric power spectrum. One free parameter: base “jump amplitude” (0 to 5 km/s allowed; ~3 km/s is best)

8. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Anisotropic cascade and dissipation Traditional (RMHD-like) nonlinear terms have a cascade energy flux that gives phenomenologically simple heating: Z+Z+ Z–Z– Z–Z– (e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002) We used a generalization based on unequal wave fluxes along the field... n = 1: usual “golden rule;” we also tried n=2.

9. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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 a collisionless “streaming” approximation

10. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Results: turbulent heating & acceleration T (K) reflection coefficient Goldstein et al. (1996) Ulysses SWOOPS

11. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Results: other fast/slow diagnostics The wind speed is anticorrelated with flux-tube expansion... Cascade efficiency: n=1 n=2 “active region” fields

12. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Results: in situ turbulence To compare modeled wave amplitudes with in-situ fluctuations, knowledge about the spectrum is needed... “e + ”: (in km 2 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. Cranmer et al. (2007) Helios (0.3–0.5 AU) Tu et al. (1992)

13. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Results: heavy ion properties Frozen-in charge states FIP effect (using Laming’s 2004 theory) Cranmer et al. (2007) Ulysses SWICS

14. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Aside: application to T Tauri winds Recent work has extended these models to accretion-driven winds of young, solar-type stars (Cranmer 2008, arXiv:0808.2250) Accretion proceeds by free-falling inhomogeneous clumps impacting the star, and generating MHD waves on the surface (like solar Moreton/EIT waves?). These “extra” waves give input orders of magnitude more energy into an MHD cascade, and can give rise to stellar winds with dM/dt up to ~10 –8 M  /yr !

15. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Turbulent mass loss solar parameter study “proper” solar models T Tauri models

16. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Turbulent mass loss solar parameter study “proper” solar models T Tauri models

17. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence New result: solar wind “entropy” Pagel et al. (2004) found ln(T/n γ–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).

18. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence The correlation length: apples to oranges? Cranmer et al. (2007) L  (pole, equator) Helios & other 1 AU… Smith et al. (2001): Voyager & Omnitape Joe Borovsky’s “walls” (ACE)

19. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Problem: too hot at 1 AU ? Ulysses T p standard (n=1) model rapid-quenching (n=2) model

20. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Electron heat conduction At ~1 AU, the modeled T(r) is a balance between adiabatic cooling & collisionless conduction. We’ve used Hollweg (1974):

21. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Progress towards a robust “recipe” The turbulent dissipation rate scaling is approximate; needs refining? Because of the need to determine non-WKB (nonlocal!) reflection coefficients, it may not be easy to insert into global/3D MHD models. Doesn’t 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) Not too bad, but...

22. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Multi-fluid collisionless effects? Polar coronal hole protons electrons O +5 O +6

23. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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. lower Z/A faster diffusion

24. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Evidence for ion cyclotron resonance UVCS (and SUMER) remote-sensing data Helios (0.3–1 AU) proton velocity distributions (Tu & Marsch 2002) Wind (1 AU): more-than-mass-proportional heating (Collier et al. 1996) Indirect: (more) Direct: Leamon et al. (1998): at ω ≈ Ω p, magnetic helicity shows deficit of proton- resonant waves in “diffusion range,” indicative of cyclotron absorption. Jian, Russell, et al. (2008) (COSPAR poster): STEREO shows isolated bursts of ~monochromatic waves with ω ≈ 0.1–1 Ω p

25. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Where do cyclotron waves come from? (1) Base generation by, e.g., “microflare” reconnection in the lanes that border convection cells (e.g., Axford & McKenzie 1997). Problems: Incompatible with radio IPS power spectra (Hollweg 1999) Minor ions would damp waves before they could resonate with O 5+ or protons (Cranmer 2000, 2001) (2) Secondary generation: low-frequency Alfven waves may be converted into cyclotron waves gradually in the corona.

26. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Charge/mass dependence Assuming there is enough “replenishment” (via, e.g., turbulent cascade?) to counteract local damping, the degree of ion heating depends on the assumed distribution of wave power vs. frequency (or parallel wavenumber). A simple assumption of a power-law vs. parallel wavenumber shows that the charge-to-mass dependence of the heating may be increasing or decreasing... UVCS O VI (O +5 ) measurement was used to normalize the heating rate. Mg X (Mg +9 ) showed a much narrower line profile (despite being so close to O +5 in its charge- to-mass ratio)!

27. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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.

28. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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”...

29. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence An advection-diffusion cascade model The Cranmer & van Ballegooijen (2003) advection-diffusion equation: “Critical balance” (Higdon/Goldreich/Sridhar/others) was built into the eqns... Rapid decay to higher k ║ is contained in f(x). Cho et al. (2002) examined various functional forms as fits to numerical simulations (not enough dynamic range?). CvB2003 solved an approximate version of the advection-diffusion eqn to get: Key parameter: (β/γ). van Ballegooijen (1986) argued for β/γ ≈ 1 (random walk)

30. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Missed KAW opportunities...? Hidden in the CvB 2003 paper were a few results that could have been highlighted better... e.g., a prediction for the KAW k ┴ –7/3 inertial range slope, and: Bale et al. (2005)

31. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Advection-diffusion cascade results Taking the anisotropic spectrum and using linear Maxwell-Vlasov dissipation rates, the ratio of proton vs. electron heating can be derived as a function of position in the fast solar wind (using the Cranmer & van Ballegooijen 2005 model):

32. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence (1)Solve a semi-empirical ion heating equation with an arbitrary normalization for the ion cyclotron wave power. (Each ion is modeled independently of the others.) Normalization varied till agrees w/ data. (2)Use the Cranmer & van Ballegooijen (2003, 2005) models to predict the ion cyclotron wave power spectrum at a given height. New SUMER constraints Landi & Cranmer (2009, arXiv:0810.0018) analyzed a set of SUMER line widths that suggest preferential ion heating at r ≈ 1.05 to 1.2 R s in coronal holes. We produced and compared two independent models: TeTe

33. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Example heating model for O VI How well do we really know the proton temperature? Vary as free parameter... SUMER constraints UVCS constraints The yellow/green curves seem to do the best... they imply strong Coulomb collisional coupling at the SUMER heights!

34. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Compare all ions at r = 1.069 R s Colors: different choices for proton temperature. Black curves: theoretical resonant spectra from Cranmer & van Ballegooijen (2003) advection-diffusion model. y-axis: wave power needed to produce ion heating

35. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Power increase at large Z/A ? This is not predicted by simple turbulent cascade models. If it is real, it might be: Increased wave power from plasma instabilities that are centered around either the alpha (Z/A = 0.5) or proton (Z/A = 1) resonances (Markovskii 2001; Zhang 2003; Laming 2004; Markovskii et al. 2006) ? Predicted “spectral flattening” due to oblique propagation and/or compressibility effects in dispersion relation? Harmon & Coles (2005) invoked these effects to model the observed IPS density fluctuation spectra. A kind of “bottleneck effect” wherein the power piles up near the dissipation scale, due to nonlocal interactions between disparate scales in k-space (Falkovich 1994; Biskamp et al. 1998) ???

36. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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). Dissipation-scale current sheets may preferentially spin up ions (Dmitruk et al. 2004)? 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 could heat ions perpendicularly (Matthaeus et al. 2003; Cranmer & van Ballegooijen 2003).

37. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence What to do next? Many of the proposed mechanisms haven’t been tested with realistic coronal plasma conditions! (i.e., plasma beta, driving wave amplitudes & frequencies, etc.) The mechanisms of “parallel cascade” in low-beta plasmas need to be more fully worked out! (the tail that wags the dog?) The CvB (2003) “advection- diffusion” model is a crass local approx. to a truly nonlocal effect. Explore relationships between turbulence and reconnection theory... Better measurements are needed: both remote and in situ!

38. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Future missions Solar Probe Plus (in to ~20 R s ) is finally moving forward. CPEX (Coronal Physics Explorer) currently in Phase A concept study: next-generation UVCS & LASCO, capable of probing dozens of ions in coronal holes at UVCS heights! More traditional “solar physics” missions (SDO) will put new constraints on physics of reconnection & turbulent heating!

39. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Conclusions For more information: http://www.cfa.harvard.edu/~scranmer/ 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 coronal heating and the solar wind. The extreme plasma conditions in coronal holes (T ion >> T p > T e ) have guided us to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics. Next-generation observational programs are needed for conclusive “constraints.”

40. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Extra slides...

41. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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)

42. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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. Helios saw strong departures from Maxwellians. By ~1990, it was clear the fast wind needs something besides gas pressure to accelerate so fast! speed (km/s) T p (10 5 K) T e (10 5 K) T ion / T p O 7+ /O 6+, Mg/O 600–800 2.4 1.0 > m ion /m p low 300–500 0.4 1.3 < m ion /m p high fastslow

43. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Solar wind: connectivity to the corona High-speed wind: strong connections to the largest coronal holes Low-speed wind: still no agreement on the full range of coronal sources: hole/streamer boundary (streamer edge) streamer plasma sheet (“cusp/stalk”) small coronal holes active regions Wang et al. (2000)

44. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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 (particle-particle? wave-particle?) release energy as heat. Heating Solar wind acceleration!

45. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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? waves shocks eddies (“AC”) vs. twisting braiding shear (“DC”) vs. reconnectionturbulence interact with inhomog./nonlin. collisions (visc, cond, resist, friction) or collisionless

46. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Reconnection / Loop-Opening models Fisk (2005) 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 churning... Hinode/XRT (X-ray) http://xrt.cfa.harvard.edu STEREO/EUVI (195 Å) courtesy S. Patsourakos Open-field regions show coronal jets (powered by reconnection?) that contribute to the wind mass flux.

47. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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

48. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Departures from thermal equilibrium UVCS/SOHO observations rekindled theoretical efforts to understand collisionless heating and acceleration effects in the extended corona. 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. MHD turbulence cyclotron resonance- like phenomena something else?

49. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence The extended solar atmosphere... Heating is everywhere...... and everything is in motion

50. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Waves? Start in the photosphere... Photosphere displays convective motion on a broad range of time/space scales: β << 1 β ~ 1 β > 1

51. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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 R s, some other kind of energy deposition is needed in order to... » accelerate the fast solar wind (without artificially boosting mass loss and peak T e ), » 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. X

52. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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.

53. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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 + 2 nd ord.) 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:

54. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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... On-disk profiles: T = 1–3 million K Off-limb profiles: T > 100 million K !

55. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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)

56. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Particles are not in “thermal equilibrium” Helios at 0.3 AU (e.g., Marsch et al. 1982) WIND at 1 AU (Collier et al. 1996) WIND at 1 AU (Steinberg et al. 1996) …especially in the high-speed wind. mag. field

57. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence “Opaque” cyclotron damping (1) If high-frequency waves originate only at the base of the corona, extended heating must “sweep” across the frequency spectrum. For proton cyclotron resonance only (Tu & Marsch 1997):

58. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence “Opaque” cyclotron damping (2) However, minor ions can damp the waves as well: Something very similar happens to resonance-line photons in winds of super-luminous massive stars! Cranmer (2000, 2001) computed “tau” for >2500 ion species. If cyclotron resonance is indeed the process that energizes high-Z/A ions, the wave power must be replenished continually throughout the extended corona.

59. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Aside: two other (non-cyclotron) ideas... Kinetic Alfven waves with nonlinear amplitudes generate E fields that can scatter ions non-adiabatically and heat them perpendicularly (Voitenko & Goossens 2004). If the corona is filled with “thin” MHD shocks, an ion’s upstream v becomes oblique to the downstream field. Some gyro-motion arises before the ion “knows” it! (Lee & Wu 2000).

60. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence Overview of “in situ” fluctuations Fourier transform of B(t), v(t), etc., into frequency: The inertial range is a “pipeline” for transporting magnetic energy from the large scales to the small scales, where dissipation can occur. f -1 “energy containing range” f -5/3 “inertial range” f -3 “dissipation range” 0.5 Hzfew hours Magnetic Power How much of the “power” is due to spacecraft flying through flux tubes rooted on the Sun?

61. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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. Matt & Pudritz (2005) Freytag et al. (2002)

62. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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.

63. Applications of MHD Turbulence to Modeling Solar (and Stellar) Coronal Heating and Winds S. R. Cranmer, October 2008, Santa Fe, NM Plasma Dissipation & MHD Turbulence 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 O 5+ outflow speed passes 175 and 370 km/s. The ratio R of 1032 to 1037 intensity depends on both the bulk outflow speed (of O 5+ ions) and their parallel temperature... The line widths constrain perpendicular temperature to be > 100 million K. R < 1 implies anisotropy!