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Solar Wind Origin & Heating 2

Solar Wind Origin & Heating 2. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics. Logistics. Part 1: Observations. Part 2: Theory. 1. Photosphere: tip of the iceberg of the convection zone 2. Chromosphere: waves start to propagate and bump into the magnetic field

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Solar Wind Origin & Heating 2

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  1. Solar Wind Origin & Heating 2 Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

  2. Logistics Part 1: Observations Part 2: Theory 1. Photosphere: tip of the iceberg of the convection zone 2. Chromosphere: waves start to propagate and bump into the magnetic field 3. Corona: magnetic field is king; heating still a “problem” 4. “Other” wind acceleration ideas; evolution of waves & turbulence 5. Future directions for theory...? 1. Background & history 2. In situ solar wind 3. Radio scintillations 4. Coronal remote-sensing (empirical connections between corona & solar wind) 5. Chromosphere & photosphere 6. Future instrumentation (discussions afterward?) Everything is online at: http://www.cfa.harvard.edu/~scranmer/NSO/

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

  4. Energy budget overview What sets the temperature? • Photosphere: optical depth ~unity, with radiation dominating heating/cooling: • Chromosphere: optically thin, radiation cools the plasma (all photons escape!) Heating is provided “mechanically,” by irreversible damping of kinetic motions • Transition region & low corona: complicated balance of radiation, mechanical heating, downward conduction, and upward advection (enthalpy flux) • Extended corona: direct heating balances upward advection (adiabatic cooling) • Heliosphere: advection (adiabatic cooling) balances outward conduction

  5. Convection excites waves • All cool stars with sub-photospheric convection undergo “p-mode” oscillations: • Lighthill (1952) showed how turbulent motions generate acoustic power. • These ideas have been more recently generalized to MHD. . . Cattaneo et al. (2003)

  6. Convection excites waves • All cool stars with sub-photospheric convection undergo “p-mode” oscillations: • Lighthill (1952) showed how turbulent motions generate acoustic power. • These ideas have been more recently generalized to MHD. . .

  7. Granules and Supergranules

  8. Inter-granular bright points (close-up) • It’s widely believed that the G-band bright points are strong-field (1500 G) flux tubes surrounded by much weaker-field plasma. 100–200 km

  9. splitting/merging torsion longitudinal flow/wave bending (kink-mode wave) Waves in thin flux tubes • Statistics of horizontal BP motions gives power spectrum of “kink-mode” waves. • BPs undergo both random walks & intermittent (reconnection?) “jumps:”

  10. splitting/merging torsion longitudinal flow/wave bending (kink-mode wave) Waves in thin flux tubes • Statistics of horizontal BP motions gives power spectrum of “kink-mode” waves. • BPs undergo both random walks & intermittent (reconnection?) “jumps:” In reality, it’s not just the “pure” kink mode. . . (Hasan et al. 2005)

  11. “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.

  12. 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...

  13. 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.

  14. 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!

  15. 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.

  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? • How rapidly is this energy coupled to the coronal plasma? vs. waves shocks eddies (“AC”) twisting braiding shear (“DC”) 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? • 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

  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 • 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. Properties of MHD waves • In the absence of a magnetic field, acoustic waves propagate at the sound speed (restoring force is gas pressure)… • B-field exerts “magnetic pressure” as well as “magnetic tension” transverse to the field. The characteristic speed of MHD fluctuations is the Alfvén speed… • Plasma β = (gas pressure / magnetic pressure) ~ (cs/VA)2 “high beta:” fluid motions push the field lines around “low beta:” fluid flows along “frozen in” field lines

  21. Properties of MHD waves • Phase speeds:Alfven,fast,slowmode; ● = sound speed, ● = Alfven speed β = 12 β = 2.4 β = 1.2 β = 0.6 β = 0.12 • F/S modes damp collisionally in low corona; Alfven modes are least damped. • Standard MHD dispersion applies only for frequencies << particle Larmor freq’s. • For high freq & low β, Alfven mode → “ion cyclotron;” fast mode → “whistler.”

  22. A(r) Alfvén wave evolution • Energy density & flux: • Static medium:

  23. A(r) Alfvén wave evolution • Energy density & flux: • Static medium: • Non-zero wind speed (“wave action conservation”): • Alfvén waves also reflect & refract as the background properties change…

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

  25. lower Z/A faster diffusion Ion cyclotron waves in the corona • Dissipation of ion cyclotron waves produces diffusion in velocity space along contours of ~constant energy in the frame moving with wave phase speed:

  26. Where do cyclotron waves come from? Alfvén waves with frequencies > 10 Hz have not yet been observed in the corona or solar wind, but ideas for their origin abound . . . . (1) Base generation by, e.g., “microflare” reconnection in the lanes that border convection cells (e.g., Axford & McKenzie 1997). Problem: “minor” ions consume base-generated wave energy before it can be absorbed by ions seen by UVCS. (2) Secondary generation: low-frequency Alfvén waves may be converted into cyclotron waves gradually in the corona. Problem: Turbulence produces mainly small-scale eddies in the direction transverse to the field; these don’t have high frequencies!

  27. something else? Where do cyclotron waves come from? • How then are the ions heated & accelerated? • Impulsive plasma micro-instabilities that locally generate high-freq. waves (Markovskii 2004)? • Non-linear/non-adiabatic KAW-particle effects (Voitenko & Goossens 2004)? • Coupling with fast-mode waves that do cascade to high-freq. (Chandran 2006)? • If the corona is filled with thin collisionless shocks, ions can pass through them and aquire gyromotion when the background field changes direction (Lee & Wu 2000)? • Collisionless velocity filtration from intrinsically suprathermal velocity distributions (Pierrard et al. 2004)? • Larmor “spinup” in dissipation-scale current sheets (Dmitruk et al. 2004)? • KAW damping leads to electron beams, further (Langmuir) turbulence, and Debye-scale electron phase space holes, which heat ions perpendicularly via “collisions” (Ergun et al. 1999; Cranmer & van Ballegooijen 2003)? cyclotron resonance-like phenomena MHD turbulence • We can compute a net heating rate from the cascade, even if we don’t know how the energy gets “partitioned” to the different particle species.

  28. 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 ~ v2 and a “turnover” time-scale  =l/v, so the rate of transfer of energy goes as v2/ ~ v3/l . • Dimensional analysis can give the spectrum of energy vs. eddy-wavenumber k: Ek ~ k–5/3

  29. MHD turbulence: 2 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: Z– Z– Z+ (e.g., Hossain et al. 1995; Matthaeus et al. 1999; Dmitruk et al. 2002)

  30. 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!)

  31. Alfvén wave amplitudes: Sun to 1 AU • Pure wave-action conservation produces either too much power at 1 AU, or too little in the corona. Turbulence seems to damp and heat at just the right level… Cranmer & van Ballegooijen (2005)

  32. Solving the Parker solar wind equation • Parker (1958) noticed that the equation of motion exhibits a “singular point…” time-steady; isothermal • Solution depends on knowing T(r); all equations should be solved simultaneously. • Key issue: Is the heating “deposited” above or below the critical point?

  33. Alfvén wave pressure (“pummeling”) Contours: wind speed at 1 AU (km/s) • Just as E/M waves carry momentum and exert pressure on matter, acoustic and MHD waves do work on the gas via similar net stress terms: P C H • This works only for an inhomogeneous (radially varying) background plasma. • Wave pressure & gas pressure work together to produce high-speed solar wind; each point in this grid represents a solution to the Parker critical pt. eqn.

  34. “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. (astro-ph/0703333) • 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”

  35. Polar coronal hole model: it works! • Grids of exploratory models led to the optimal choice for lower boundary parameters: • Basal acoustic flux: 108 erg/cm2/s (equivalent “piston” v = 0.3 km/s) • Basal Alfvenic perpendicular amplitude: 0.255 km/s • Basal turbulent scale: 75 km (G-band bright point size?) T (K) reflection coefficient Transition region is too high (7 Mm instead of 2 Mm), but otherwise not bad . . .

  36. Magnetic flux tubes • Vary the magnetic field, but keep lower-boundary parameters fixed. “active region” fields T (K) reflection coefficient

  37. Fast vs. slow wind emerges naturally • The wind speed & density at 1 AU behave mainly as observed. Cascade efficiency: n=1 n=2 Ulysses SWOOPS Goldstein et al. (1996)

  38. Progress toward better understanding Existing models are not too bad, but . . . • 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)

  39. Plumes and jets: more reconnection? • How much do plumes and jets contribute to the “mean” solar wind? Still debated… • Wang (1994, 1998) suggested that small-scale magnetic reconnection events at the coronal base gives rise to plumes. Is this what Hinode/XRT sees? • These events may be hotter than mean plasma at the base, but cooler higher up! (Fisk et al. 1999)

  40. Future directions for theory Generation and nonlinear evolution of the solar wind fluctuation spectra must be understood. Self-consistent kinetic models (from corona to wind) of protons, electrons, & ions are needed. • Because these processes interact with one another on a wide range of scales, their impact can only be evaluated when all are included together. • There’s a need for “phenomenological” terms that encapsulate what we learn from micro-scale simulations, so that macro-scale modeling can proceed!

  41. More plasma diagnostics Better understanding Conclusions • The past decade, SOHO (especially UVCS) has led to fundamentally new views of the collisionless acceleration regions of the solar wind. • Theoretical advances in MHD turbulence are “feeding back” into global solar wind models. • The extreme plasma conditions in coronal holes (T ion>> Tp > Te ) have guided us to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics. • There’s a lot to do (theory & observation)! For more information: http://www.cfa.harvard.edu/~scranmer/

  42. Extra slides . . .

  43. “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):

  44. “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.

  45. Charge/mass dependence • Assuming enough “replenishment” (via, e.g., turbulent cascade?) to counteract local damping, the degree of preferential ion heating depends on the assumed distribution of wave power vs. frequency (or parallel wavenumber): O VI (O+5) measurement used to normalize 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)!

  46. Future diagnostics: additional ions? • For one specific choice of the power-law index, we can also include either: enough “local” damping (depending on “tau”) or enough Coulomb collisions to produce the narrower Mg+9 profile widths . . . (Cranmer 2002, astro-ph/0209301)

  47. Aside: two other (non-cyclotron) ideas . . . • 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). • Kinetic Alfven waves with nonlinear amplitudes generate E fields that can scatter ions non-adiabatically and heat them perpendicularly (Voitenko & Goossens 2004).

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