Incorporating Kinetic Effects into Global Models of the Solar Wind

1. Incorporating Kinetic Effects into Global Models ofthe Solar Wind Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics

2. Incorporating Kinetic Effects into Global Models ofthe Solar Wind • Outline: • Coronal heating & solar wind acceleration • Preferential ion heating • Possible explanations from MHD turbulence Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics

3. The extended solar atmosphere

4. The extended solar atmosphere The “coronal heating problem”

5. Solar wind acceleration • We still do not understand the processes responsible for heating the corona, but we know that T~ 106 K creates enough gas pressure to accelerate the solar wind. • A likely scenario is that the Sun produces MHD waves that propagate up open flux tubes, partially reflect back down, and undergo a turbulent cascade until they are damped at small scales, causing heating. Z– Z+ Z– (e.g., Matthaeus et al. 1999) • Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models, and found a wide range of agreement with observations. Ulysses 1994-1995

6. Coronal heating: multi-fluid, collisionless

7. Coronal heating: multi-fluid, collisionless O+5 O+6 In the lowest density solar wind streams . . . electron temperatures proton temperatures heavy ion temperatures

8. 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)

9. However . . . Does a turbulent cascade of Alfvén waves (in the low-beta corona) actually produce ion cyclotron waves? Most models say NO!

10. 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

11. 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

12. 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

13. 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

14. Nonlinear mode coupling? • There is observational evidence for compressive (non-Alfvén) waves, too . . . k k ion cyclotron waves Fast-mode waves (right-hand polarized) & Alfvén waves (left-hand polarized) k k

15. 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 indeed give rise to wave power that looks like a kind of “parallel cascade” (Cranmer, Chandran, & van Ballegooijen 2011) r = 2 Rs β ≈ 0.003

16. Conclusions • Advances in MHD turbulence theory continue to help improve our understanding about coronal heating and solar wind acceleration. • The postulated coupling mechanism is only one possible solution: see SH43D-03 (stochastic KAWs), SH54B-01 (gyrokinetic turb.), SH53A-01 (current sheets), ... • However, we still do not have complete enough observational constraintsto be able to choose between competing theories. For more information: http://www.cfa.harvard.edu/~scranmer/