1. Plasma Physics in the Solar System Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

2. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Outline: a whirlwind tour...  Overview  The solar activity cycle & the solar dynamo  Convection: turbulence & MHD waves  Heating the chromosphere (non-magnetic?)  Heating the corona: dominated by closed/twisted fields  Accelerating the solar wind (collisionless heliosphere)  Coronal mass ejections (CMEs)  “Space weather” and the Earth’s magnetosphere

3. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The Sun’s overall structure Core: Nuclear reactions fuse hydrogen atoms into helium. Radiation Zone: Photons bounce around in the dense plasma, taking millions of years to escape the Sun. Convection Zone: Energy is transported by boiling, convective motions. Photosphere: Photons stop bouncing, and start escaping freely. Corona: Outer atmosphere where gas is heated from ~5800 K to several million degrees!

4. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Where’s the plasma?

5. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Where’s the plasma? protons electrons O +5 O +6

6. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The solar activity cycle Yohkoh/SXT

7. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The solar dynamo Differential rotation shears poloidal (B θ ) fields into the toroidal (B φ ) direction Strong fields are buoyant; small kinks are amplified & twisted by Coriolis forces Diffusion and meridional circulation bring weak fields to the poles (of opposite polarity) Fully self-consistent models still do not exist!

8. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Convection in stellar interiors If the internal temperature gradient is too steep, a rising parcel (which remains in pressure balance with its surroundings) will be hotter and less dense. It will continue rising until the local conditions change... MHD drives the downflows together into faster “plumes.” Cattaneo et al. 2003

9. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Convection creates waves & turbulence All solar-type stars with sub-photospheric convection appear to exhibit “p-mode” acoustic oscillations at (and beneath) their surfaces... Lighthill (1952) showed how turbulent convection can generate acoustic power. These ideas have been more recently generalized to MHD, with flux-tube waves being excited as well: longitudinal (“sausage”) and transverse (“kink”) modes.

10. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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) ~ (c s /V A ) 2 “high beta:” fluid motions push the field lines around “low beta:” fluid flows along “frozen in” field lines

11. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Properties of MHD waves Phase speeds: Alfven, fast, slow mode; ● = sound speed, ● = Alfven speed β = 12β = 2.4β = 0.6β = 1.2β = 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.”

12. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Turbulence It is highly likely that somewhere in the interior and/or 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 ~ ρv 2 and a turnover time-scale  =l/v, so the rate of transfer of energy goes as ρv 2 /  ~ ρv 3 /l. Dimensional analysis can give the spectrum of energy vs. eddy-wavenumber k: E k ~ k –5/3

13. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch MHD turbulence: two 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. Phenomenological expressions are good at reproducing numerical results: Z+Z+ Z–Z– Z–Z– (e.g., Hossain et al. 1995; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Oughton et al. 2006)

14. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The solar photosphere Photosphere displays convective motion on a broad range of time/space scales: β << 1 β ~ 1 β > 1

15. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The solar chromosphere

16. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The need for chromospheric heating Not huge in radial extent, but contains order of magnitude more mass than the layers above...

17. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch “Traditional” chromospheric heating Vertically propagating acoustic waves conserve flux (in a static atmosphere): Amplitude eventually reaches V ph and wave-train steepens into a shock-train. Shock entropy losses go into heat; only works for periods < 1–2 minutes… 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. Bird (1964) ~

18. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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...

19. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Runaway to the transition region (TR) Whatever the mechanisms for heating, they must be balanced by radiative losses to maintain chromospheric T. Why then isn’t the corona 10 9 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. When shock strengths “saturate,” heating depends on density only:

20. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Overview of coronal observations “Quiet” regions Active regions Coronal hole (open) Plasma at 10 6 K emits most of its spectrum in the UV and X-ray...

21. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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!

22. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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.

23. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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? waves shocks eddies (“AC”) vs. twisting braiding shear (“DC”) vs.

24. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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

25. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Reconnection in closed loops Models of how coronal heating (F X ) scales with magnetic flux (Φ) are growing more sophisticated... Closed loops: Magnetic reconnection e.g., Longcope & Kankelborg 1999 Gudiksen & Nordlund (2005)

26. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Turbulence & reconnection: inseparable? Waves cascade into MHD turbulence (eddies), which tends to: Onofri et al. (2006) e.g., Rappazzo et al. (2008) » break up into thin reconnecting sheets on its smallest scales. » accelerate electrons along the field and generate currents. Pre-existing current sheets are unstable in a variety of ways to growth of turbulent motions which may dominate the energy loss & particle acceleration. Turbulence may drive “fast” reconnection rates (Lazarian & Vishniac 1999), too.

27. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch A small fraction of the flux is OPEN Peter (2001) Tu et al. (2005) Fisk (2005)

28. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Open flux tubes “feed” the solar wind 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!)

29. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The solar wind: discovery 1860–1950: Evidence slowly builds for outflowing magnetized plasma in the solar system: solar flares  aurora, telegraph snafus, geomagnetic “storms” comet ion tails point anti-sunward (no matter comet’s motion) 1958: Eugene Parker proposed that the hot corona provides enough gas pressure to counteract gravity and accelerate a “solar wind.”

30. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch In situ solar wind: properties Mariner 2 (1962): first direct confirmation of continuous fast & slow solar wind. Uncertainties about which type is “ambient” persisted because measurements were limited to the ecliptic plane... 1990s: Ulysses left the ecliptic; provided first 3D view of the wind’s source regions. 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

31. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Ulysses’ view over the poles

32. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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

33. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Particles are not in “thermal equilibrium” Spectroscopy of the “extended corona” also reveals collisionless effects. The UVCS (Ultraviolet Coronagraph Spectrometer) instrument on SOHO, designed and built at SAO, led to new views of the wind’s acceleration region. The fast solar wind becomes supersonic much closer to the Sun (~2 R s ) than previously believed. In coronal holes, heavy ions (e.g., O +5 ) both flow faster and are heated hundreds of times more strongly than protons and electrons, and have anisotropic temperatures. kHz frequency Alfven waves have oscillating E and B fields......that resonate with ion cyclotron (Larmor) motions?

34. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Fluctuations & turbulence 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?

35. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch 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)

36. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Coronal magnetic fields Coronal B is notoriously difficult to measure... Potential field source surface (PFSS) models have been successful in reproducing observed structures and mapping between Sun & in situ. Wang & Sheeley (1990) found that flux tubes that expand more (from Sun to SS) have lower wind speeds at 1 AU. Wind Speed Expansion Factor (e.g., Arge & Pizzo 2000)

37. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Why is the fast (slow) wind fast (slow)? vs. What determines how much energy and momentum goes into the solar wind?  Waves & turbulence input from below?  Reconnection & mass input from loops? Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models of individual open flux tubes. Boundary conditions imposed only at the photosphere (no arbitrary “heating functions”). Wind acceleration determined by a combination of magnetic flux-tube geometry, gradual Alfvén-wave reflection, and outward wave pressure.

38. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch The inherently filamentary wind... Solar coronagraphs occult the bright solar disk to view much fainter emission from the extended corona. SOHO/LASCO “wavelet” decomposition technique reveals even more detail (Stenborg & Cobelli 2003) Still, these features mainly represent only ~10% density variations...

39. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Do “blobs” trace out the slow wind? The blobs are very low- contrast and thus may be passive “leaves in the wind.” Sheeley et al. (1997)

40. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Coronal mass ejections Coronal mass ejections (CMEs) are magnetically driven eruptions from the Sun that carry energetic, twisted strands of plasma into the solar system... solar flare prominence eruption

41. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Coronal mass ejections Forbes & Priest (1995) and Lin & Forbes (2000) developed a theory of CMEs as a loss of magnetostatic equilibrium in a twisted “flux rope.” The current sheet energizes both the CME (above) and a “two-ribbon flare” (below)

42. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Earth’s magnetosphere Blah...

43. Plasma Physics in the Solar System Steven Cranmer, February 9, 2009 ITC Monday Pizza Lunch Conclusions For more information: http://www.cfa.harvard.edu/~scranmer/ The Sun/heliosphere system is a nearby “laboratory without walls” for studying plasma physics in regimes of parameter space inaccessible in Earth-based laboratories. 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.