Coronal Heating due to Low-Frequency Wave-Driven Turbulence

1. Coronal Heating due to low frequency wave-driven turbulenceW H MatthaeusBartol Research Institute, University of DelawareCollaborators: P. Dmitruk, L. Milano, D. Mullan, G. Zank and S Oughton Smithsonian Astrophysical Observatory, April 22, 2002

2. Overview • Observations and issues in heating the open field line corona • problems/constraints • MHD modeling • Quasi-2D cascade model driven by low frequency waves • Factors influencing sustainment of turbulence: Reflection + nonpropagating structures • Origin of the coronal heat function Q(r) • Kinetic processes • What we learn from the solar wind • Test particles in turbulent reconnection • Lessons from the aurora • A proposed kinetic heating model

3. Observations

4. Open and closed Parker (1972), Priest et al (1998), Einaudi et al (1996)... Parker (1991), Axford and McKenzie (1995)

5. High and low f [McKenzie et al, 1995; Axford and McKenzie, 1997]

6. Two problems • High frequency waves dissipated too rapidly by heavy ions – not enough left for protons. Need coronal generation. (Cranmer, 2000) • Difficult to power high frequency channel: Low frequency MHD cascade is mainly towards high k-perp, not towards higher wave frequency. (Matthaeus et al, 1996; Leamon et al, 2000) Heating model based upon low frequency MHD cascade?

7. Model overview Physical structure of a low frequency wave-driven model Rate of transmission: Alfven Speed / parallel “box” length Rate of Reflection: Rate of turbulent dissipation

8. RMHD model - Must add reflection terms for inhomogeneous cases - Fluctuation energy injected/removed at boundaries or by volume force

9. Wave driving at bottom (1000 sec)with reflection and nonpropagating structures “turned on” • Cross helicity  statistically steady, mixed value • Dissipation efficiency ~40% • Spectral transfer  turbulent dissipation • broadband “-5/3” spectrum

10. RMHD simulation domain with radial expansion and coronal profile

11. What kind of heating is needed in the corona? A well-known but Ad hoc Heat Function Q(r): • Used in a variety of studies of solar and stellar winds(Holzer and Axford (1970), Kopp and Orrall (1976), Hammer (1982) • Can account for many observed properties of the fast wind and polar coronal holes(McKenzie et al (1995), Habbal et al (1995), Axford and McKenzie (1997) r0 = Solar radius L ~ 1/4 - 1/2

12. Simulation Example:128 x 128 x 16 (Fourier-Fourier-Chebyshev) • snapshot of the magnetic field and current density in the turbulent region 0.2 Rs above the coronal base • current and magnetic field associated with the oscillatory driving at coronal base

13. Comparison of three simulations Comparison of three simulations with different density profiles Heating/volume is ~exponentially confined

14. Comparison of simulation and phenomenology Simulation Phenomenology With modeled nonlinearities

15. Sequence of profiles from phenomenology, varying perpendicular correlation scale Perp correlation scale = 1.0, 0.5, 0.1, and 0.02 (units of 30,000 km) Dashed line is correlation Scale = 0 limit, “strong turbulence”

16. MHD cascade  Kinetic dissipation Interface between MHD turbulence scales and kinetic plasma microphysics

17. Simulation example, 512 x 512 x 16 wave driven turbulence Arrows: transverse magnetic field Color: vertical Electric current density

18. Electric current density Electric field Bottom Top

19. Suggestion: Key to understanding dissipation and heating is to be found in the kinetic plasma response to turbulent reconnection • Solar wind and coronal MHD energy cascade terminates in driven, random, turbulent reconnection phenomena • How does kinetic plasma respond? • Turbulent reconnection electric field • Electron and ion beams • Instabilities and nonlinear effects (Leamon et al, 2000)

20. What do we learn from the solar wind? • Fluctuation geometry • Cascade theory and heating • Dissipation processes

21. Solar Wind Heating • Perpendicular MHD cascade/transport theory accounts for radial evolution from 1 AU to >50 AU • Proton temperature • Fluctuation level • Correlation scale(?) ADIABATIC Matthaeus et al, PRL, 1999 Smith et al, JGR 2001

22. Solar wind fluctuation geometry • “Maltese cross” – two component model • Slab + 2D • Cosmic ray scattering parallel mean free paths  20% - 80% • NI MHD Theory –20% - 80% • Direct measurement  20 % - 80% A significant fraction (~80%) of the fluctuation energy is in highly oblique (70+ deg) modes Maltese: Matthaeus et al, 1990 Cos Ray: Bieber et al, 1994 NI MHD: Zank and Matthaeus, 1991 Direct: Bieber et al, 1996

23. steepening near 1 Hz (at 1 AU) -- breakpoint scales best with ion inertial scale Helicity signature  proton gyroresonant contributions ~50% Appears inconsistent with solely parallel resonances and are both involved Consistent with dissipation in oblique current sheets Solar Wind Dissipation Leamon et al, 1998, 1999, 2000

24. Kinetic plasma response to reconnection electric fields • Could be very nonsteady and and nonlinear • Full plasma kinetic problem is very “stiff” • Photosphere: 100-1000 sec motions • Proton gyrofrequency 100-1000 Hz • Hybrid and electron scales (9 orders of magnitude!)

25. Test particle response to reconnection First step towards linking MHD with kinetic physics

26. Test particle acceleration by turbulent reconnection Ambrosiano et al, Phys. Fluids, 1988 • 2D MHD reconnection • Not equilibrium • Broadband fluctuations • - fast reconnection Particle speed distribution High energy particles Particles are accelerated (direct and velocity diffusion) in region between X- and O-points. Powerlaw/exponential distributions.

27. Test Particles in turbulent reconnection: beams form near X-points Ambrosiano et al, Phys. Fluids, 1988 • “hot spots” of acceleration near neutral points • Beams form in vertical direction • Beams pitch angle scatter

28. Kinetic plasma response to reconnection electric fields • Relevant observations?  Await next generation UVCS, RAM….  response to parallel electric fields in the AURORA

29. Auroral regions: upward and downward currents From Carlson, GRL, 25, 2013 (1998)

30. FAST data: From Ergun et al, GRL Contrast of Upward and Downward current regions

31. FAST Data: Carlson et al, GRL • Electron beams • Broadband noise • Perpendicular Ion heating

32. FAST Data: from Ergun et al, GRL • Broadband magnetic power • Downward current: deficit at cyclotron harmonics • Upward Current enhancements at cyclotron harmonics

33. FAST data: Ergun et al, PRL, 1998 • ‘Solitary structures” • “electron phase space holes” • Interpretation: • deficit of negative charge • propagating at e-beam speed (> e-thermal speed) • Characteristic E-field • Response to strong parallel electric field • Parallel size: Debye scale • Perp size: related to ions • Here they are: D Newmann, U C Boulder

34. A possible scenario for the corona • Low frequency waves  reflection  strong RMHD cascade • MHD reconnection • Turbulent reconnection electric field: • Upward E: • Sparse electron beams downward (“aurora”?) • Dense proton beams upward  ion cyclotron wave generation • Downward E: • Powerful upwards electron beams • Electron phase space holes propagate upwards • Perpendicular heating of protons by (nonresonant) stochastic interaction with electron holes • Broadband wave excitation in “ULF” regime around ion cyclotron frequency • Gravitational confinement makes this a “pressure cooker” for protons, which are heated up to escape speed