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Waves and turbulence in the solar wind

Waves and turbulence in the solar wind. Tim Horbury Imperial College London. The solar wind as a turbulence laboratory Global structure of the heliosphere Key results: Alfvén waves Active turbulent cascade Intermittency Anisotropy Open questions Future opportunities Useful references.

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Waves and turbulence in the solar wind

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  1. Waves and turbulence in the solar wind Tim Horbury Imperial College London • The solar wind as a turbulence laboratory • Global structure of the heliosphere • Key results: • Alfvén waves • Active turbulent cascade • Intermittency • Anisotropy • Open questions • Future opportunities • Useful references 26 September 2003

  2. Notes on this file • This talk was presented at the Summer School at Chalkidiki, in September 2003, organised by Loukas Vlahos. • I generated this version of the presentation after the meeting and there are some changes to the original: • I have added a short list of good review articles at the end • I have attributed a few of the more important figures, with their full reference • Some of the material, particularly that on anisotropy, is unpublished • The file does not contain movies, to save space • If anyone has any comments or questions, they are welcome to contact me at t.horbury@imperial.ac.uk Tim Horbury, London, 7th October 2003 26 September 2003

  3. What is the solar wind? • Collisionless, magnetised plasma • Continual, but variable, outflow from Sun’s corona • Blows a cavity in interstellar medium: heliosphere • At edge of heliosphere, merges with interstellar medium • Interacts with planets and other bodies • Supersonic (super-Alfvénic, …) • Hot: >105 K • Rarefied: few per cm3 at Earth • Complex due to solar variability, solar rotation, and in situ processes • Variable on all measured scales, from sub-second  centuries 26 September 2003

  4. What does the solar wind look like? • Very rarefied • Can’t usually see it • Near-Sun solar wind is visible during eclipses 26 September 2003

  5. Origin of the solar wind • Sun’s upper corona expands into space • Accelerates and forms the solar wind • Variable speed, density, temperature • Carries magnetic field from corona • Also carries waves and turbulence… SoHO coronagraph (LASCO) Artificial eclipse See http://sohowww.nascom.nasa.gov for movies 26 September 2003

  6. Solar wind as a turbulence laboratory • Characteristics • Collisionless plasma • Variety of parameters in different locations • Contains turbulence, waves, energetic particles • Measurements • In situ spacecraft data • Magnetic and electric fields • Bulk plasma: density, velocity, temperature, … • Full distribution functions • Energetic particles • The only collisionless plasma we can sample directly 26 September 2003

  7. Importance of waves and turbulence Energetic particle transport • Controls cosmic rays throughout the solar system Effect on the Earth • Can trigger reconnection, substorms, aurorae, … Understanding solar processes • Signature of coronal heating, etc. Application to astrophysical plasmas • Turbulence is pervasive Turbulence as a universal phenomenon • Comparison with hydrodynamics 26 September 2003

  8. Global structure of the solar wind • Source in the corona • Relation to coronal structure • Effect of solar rotation • Solar cycle dependence • Transient events • Interaction with the interstellar medium 26 September 2003

  9. The solar corona • Hot rarefied atmosphere above visible surface • Plasma beta <<1 in corona •  magnetic field dominates • Closed magnetic field: plasma trapped • Open magnetic field: plasma can expand into interplanetary space 26 September 2003

  10. Skylab: the first movies of the corona • First US space station • Launched 1973 • Converted Saturn upper stage • Carried early X ray solar camera 26 September 2003

  11. Skylab movie of the corona • First movies of the Sun’s corona in X-rays • Coronal holes • dark regions, often near poles • Active regions • bright regions, associated with sunspots 26 September 2003

  12. The solar corona: modern instruments • Movie from the SoHO spacecraft • In orbit since 1996 • Several coronal holes • Very active corona • Lots of structure 26 September 2003

  13. Expansion of the upper corona • Corona is very hot • Pressure is higher than ambient interstellar medium • Expands into interplanetary space (Parker, 1958): solar wind • Carves a cavity in interstellar medium: heliosphere • Nearly radial flow • Accelerates to full speed by ~20 solar radii SoHO coronagraph (LASCO) Artificial eclipse 26 September 2003

  14. Cosmic rays Heliopause Solar wind Interstellar medium Termination shock The heliosphere • Solar wind blows bubble in interstellar medium • Probably around 100 AU from Sun at the nose • Cosmic rays enter heliosphere: motion controlled by turbulent magnetic field 26 September 2003

  15. Interstellar bowshocks • Shocks also form between stellar winds and interstellar medium • General shape is probably similar to the Sun’s bowshock NASA and The Hubble Heritage Team (STScI/AURA) 26 September 2003

  16. Three months of solar wind data Ulysses: 4.5 AU • Field and particle measurements • MHD on these scales • Variable speed, density, magnetic field, … • Not random: presence of large scale structures • 30-day repeats • We can explain this structure 26 September 2003

  17. High latitudes: fast, from coronal hole Low latitudes: slow, variable Solar wind: relation to coronal structure • Fast and slow 26 September 2003

  18. Latitude variation in solar wind speed • Solar minimum: dipolar solar magnetic field • Ulysses measurements • High latitudes dominated by high speed wind from polar coronal holes • Low latitudes: fast and slow streams, very variable • Different magnetic polarity in each hemisphere: solar dipole 26 September 2003

  19. The corona and the solar cycle Solar minimum Dipolar magnetic field Open fields over poles Solar maximum Complex magnetic field No latitude dependence 26 September 2003

  20. Large scale structure of the heliosphere • Fast and slow solar wind streams • Sun’s rotation winds structures into spirals: compressions and rarefactions • Just like a lawn sprinkler… • These data derived from ground-based interplanetary scintillation measurements (Bernie Jackson: see http://cassfos02.ucsd.edu/solar/tomography/ for more info) 26 September 2003

  21. Magnetic field: the Parker spiral • Solar rotation drags out solar wind magnetic field into Archimedian spiral • Predicted by Gene Parker • Parker spiral • Winding angle depends on wind speed, but: • ~45º at Earth • ~90º by 10 AU 26 September 2003

  22. Density and temperature anticorrelated Magnetic field ~0º from radial Typical conditions at 0.3 AU • Closest measurements to date • Before stream-stream interactions are important • Highest density in slow wind 26 September 2003

  23. Density and temperature correlated: compression at velocity increase Magnetic field ~45º from radial: Parker spiral Typical conditions at 1.0 AU • Stream-stream interactions more important • Shocks beginning to form 26 September 2003

  24. Coronal mass ejections • Sun can eject discrete structures into space • Coronal mass ejections (CMEs) • Around 1 per day (varies with the solar cycle) 26 September 2003

  25. Flares, CMEs and energetic particles • Fast-moving particles produced by flare and associated shocks • Particles can sometimes reach Earth • Propagation of particles controlled by magnetic field • Scattered by waves and turbulence • Aside: is the slow wind formed of many small ejecta? 26 September 2003

  26. The magnetosphere • Interaction of solar wind with Earth’s magnetic field • Bowshock: high Mach number shock • Magnetosheath: shocked solar wind plasma • Magnetosphere: very low beta plasma Good: Different conditions Many spacecraft High data rate Bad: Taylor’s hypothesis not satisfied (more later) Very complicated 26 September 2003

  27. You are here Significant spacecraft Wind, ACE (present) • Near-Earth (L1). Good, modern instrumentation Helios (1975-1984?) • Closest approach to the Sun (0.29 AU, 63 solar radii) Ulysses (1990-2006) • Only measurements at high latitudes Voyager 1 &2 , Pioneer 10 & 11 (mid-1970’s, some still operating) • Only outer heliosphere measurements (80+AU) 26 September 2003

  28. Ulysses See http://sci.esa.int/ulysses/ for more info • Launch 1990, still operating • First spacecraft to explore high latitudes: up to 80º • Eccentric orbit: 1.3 - 5.4 AU • Orbit has provided long intervals of near-stationary data 26 September 2003

  29. Helios • Closest approach to Sun: 0.29 AU • Two spacecraft, launch 1974 & 1976 • Provide measurements of very “young” solar wind 26 September 2003

  30. Cluster • Launch 2000 • Four spacecraft in formation in Earth orbit • Separations vary: ~100 km, ~600 km, ~5000km • Measures magnetosphere, magnetosheath, solar wind • Combine four spacecraft data to determine information about the 3D structure of the plasma • http://sci.esa.int/cluster 26 September 2003

  31. Spacecraft particle measurements Measure: • Bulk distribution function, for ions and electrons Calculate: • Moments of distribution function: velocity, temperature, density, etc. • Particle composition (protons, helium, oxygen, etc.) • Ion charge states • Time variations at sub-gyroperiod scales 26 September 2003

  32. Spacecraft magnetic and electric field measurements • Measure magnetic and electric field from DC up to ~Hz, as time series • Measure higher frequencies (can be up to MHz) using spectra Spacecraft measurements are difficult: • Very low fluxes and fields • Spacecraft contamination • Instrument effects • Low power and mass • Telemetry constraints 26 September 2003

  33. Why we need to understand the data • No instrument provides an exact measurement of any physical quantity • We must know how a measurement is made, and its limitations, before we can use it with confidence Example 1: SoHO EIT (ultraviolet) image of the Sun Flare (bottom right) is overexposed, and light “bleeds” into neighbouring pixels to left and right These pixels do not accurately represent the real intensity We are familiar with such effects - but other artefacts are much more subtle… 26 September 2003

  34. Why we need to understand the data Example 2: Cluster magnetic field data Wave-like variation visible, particularly in second field component (BY) Period of wave is ~4s This is spin period of spacecraft - a big hint! In fact, this signal is an artefact of the instrument calibration process, and can be removed with better calibration 26 September 2003

  35. Why we need to understand the data Example 3: The Earth’s radiation belts (“Van Allen” belts) The radiation belts around the Earth (composed of trapped cosmic rays) were discovered in 1958 by James Van Allen using Explorers 1 and 3. Both spacecraft carried a single Geiger counter to measure fluxes of energetic particles In parts of the orbit, the rate was zero Van Allen correctly interpreted a zero rate as saturation of the detector, and hence high fluxes of particles - radiation belts! 26 September 2003

  36. The turbulent solar wind f-1 • Fluctuations on all measured scales turbulence f-5/3 waves • Power spectrum • Broadband • Low frequencies: f -1 • High frequencies: f -5/3 26 September 2003

  37. Fundamental observations of waves and turbulence Alfvén waves • Waves of solar origin Active turbulent cascade • Not just remnant fluctuations from corona Intermittency • Similar high order statistics to hydrodynamics Field-aligned anisotropy • Fundamental difference to hydrodynamics 26 September 2003

  38. Interpreting spacecraft measurements • In the solar wind (usually), VA ~50 km/s, VSW >~300 km/s • Therefore, VSW>>VA • Taylor’s hypothesis: time series can be considered a spatial sample • We can convert spacecraft frequency f into a plasma frame wavenumber k: k = 2f / VSW • Almost always valid in the solar wind • Makes analysis much easier • Not valid in, e.g. magnetosheath, upper corona 26 September 2003

  39. Interpreting spacecraft measurements • Solar wind flows radially away from Sun, over spacecraft • Time series is a one dimensional spatial sample through the plasma • Measure variations along one flow line Flow 26 September 2003

  40. Alfvén waves Field-parallel Alfvén wave: • B and V variations anti-correlated Field-anti-parallel Alfvén wave: • B and V variations correlated • See this very clearly in the solar wind • Most common in high speed wind 26 September 2003

  41. Average magnetic field sunward Positive correlation Propagating anti-parallel to field Propagating away from Sun in plasma frame Average magnetic field anti-sunward Negative correlation Propagating parallel to field Propagating away from Sun in plasma frame Propagation direction of Alfvén waves • Waves are usually propagating away from the Sun 26 September 2003

  42. Spectral analysis of Alfvén waves • For an Alfvén wave: b = v, • Where b = B /(0)1/2 • Calculate Elsässer variables: e = b v • Convention: e+ corresponds to anti-sunward (so flip e+ and e- if B away from Sun) • Also power spectrum Z (f) = PSD (e) • If pure, outward Alfvén waves, e+ >> e- Z+ >> Z- 26 September 2003

  43. Inward and outward spectrum Note: • When e+>>e-, magnetic field spectrum ~ e+ spectrum Define: Normalised cross helicity C = (e+-e-)/(e++e-) • C = 1 for pure, outward waves • C = 0 for mixed waves Fast wind Slow wind 26 September 2003

  44. Slow: coronal hole boundary e+ ~ e- Fast: within coronal hole e+ >> e- Speed dependence of turbulence • Character of fluctuations varies with wind speed Tu et al, Geophys. Res. Lett., 17, 283, 1990 26 September 2003

  45. Fast wind Positive cross helicity: anti-sunward Alfvén waves Sharp transition To mixed sense waves Slow wind Mixed sense, but very variable Stream dependence: cross helicity • Wavelets: measure time and frequency dependence of waves 26 September 2003

  46. Dominance of outward-propagating waves Speed Solar wind speed • Solar wind accelerates as it leaves the corona • Alfvén speed decreases as field magnitude drops • Alfvén critical point: equal speed (~10-20 solar radii) • Above critical point, all waves carried outward Therefore, • Outward-propagating low frequency waves generated in corona! Critical point Alfvén speed Distance from Sun 26 September 2003

  47. Energy transfer Active turbulent cascade in fast wind • Bavassano et al (1982) • Fast wind: “knee” in spectrum • Spectrum steepens further from the Sun • Evidence of energy transfer between scales: turbulent cascade Power (log scale) after Bavassano et al, J. Geophys. Res., v87, 3617, 1982 26 September 2003

  48. Interpretation • Initial broadband 1/f spectrum close to Sun • High frequencies decay, transfer energy • Spectrum steepens • Progressively lower frequencies decay with time (distance) • Breakpoint in spectrum moves to lower frequencies • Breakpoint is the highest frequency unevolved Alfvén wave 26 September 2003

  49. Alfvén waves Inertial range Dissipation Structures Summary: spectral index in fast wind • Ulysses polar measurements • Magnetic field component • Inertial range • Development of cascade • 1/f Alfvén waves at low frequencies Not shown or considered here: • Dissipation at higher frequencies • Structures at lower frequencies 26 September 2003

  50. Large scale variations in power levels • Power in high speed wind, low and high latitudes • Ulysses agrees well with Helios • Data taken 25+ years apart • Increasing scatter in Helios reflects stream-stream interactions 26 September 2003

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