Connecting the Solar Wind to the Corona

1. Connecting the Solar Wind to the Corona Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics A. van Ballegooijen, J. Kohl, B. Chandran, L. Woolsey

2. Connecting the Solar Wind to the Corona • Outline: • Bridging the Sun/heliosphere gap: observations & models • Survival of coronal “flux tubes” to 1 AU ? • Preferential ion heating & acceleration Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics A. van Ballegooijen, J. Kohl, B. Chandran, L. Woolsey

3. The Sun-heliosphere plasma system

4. The Sun-heliosphere plasma system

5. The Sun-heliosphere plasma system In situ: UV spectroscopy: O+6 O+5 electrons protons B

6. Magnetic connectivity of the open field Cranmer & van Ballegooijen (2005) Fisk (2005) Tu et al. (2005)

7. Is a time-steady approach doomed? • Open-field regions show frequent jet-like events. • Evidence of magnetic reconnectionbetween open and closed fields. • How much of the solar wind is ejected like this? Hinode/SOT: Nishizuka et al. (2008) Antiochos et al. (2011) • Is there enough mass & energy released to heat/accelerate the entire solar wind? (Cranmer & van Ballegooijen [2010] said no...)

8. What processes drive solar wind acceleration? • No matter the relative importance of reconnection events, we do know that waves and turbulent motions are present everywhere... from photosphere to heliosphere. • How much can be accomplished by only these processes? (Occam’s razor?) Hinode/SOT SUMER/SOHO G-band bright points UVCS/SOHO Helios & Ulysses Undamped (WKB) waves Damped (non-WKB) waves

9. Turbulence-driven solar wind models • 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 (including composition!) Ulysses 1994-1995 (see also, e.g., Suzuki & Inutsuka 2006; Verdini et al. 2010; Usmanov et al. 2011; Matsumoto & Suzuki 2011; Chandran et al. 2012)

10. Outline: • Bridging the Sun/heliosphere gap: observations & models • Survival of coronal “flux tubes” to 1 AU ? • Preferential ion heating & acceleration

11. Increase the complexity of the field . . . • Existing models used low-resolution magnetic fields. What will happen when we solve for the time-steady plasma conditions along higher-resolution field structures (with higher rates of shear, more QSLs, etc.)? 8727 field lines: Δt = 1 min. Δφ = 0.01o Δx on surface = 100 km 1 SOLIS pixel ≈ 800 km Overkill? \Maybe not... SOLIS Vector SpectroMagnetograph on Kitt Peak + PFSS

12. Expectations from flux-tube expansion Wang & Sheeley (1990) found an anticorrelation between flux tube expansion and wind speed at 1 AU . . . low f FAST high f SLOW

13. Extremely preliminary results Cranmer et al. (2007) ZEPHYR output ~WS90 scaling SOLIS B-field “stretch” into non-potential pressure-balanced flux tubes ACE

14. Do the “flux tubes” survive to 1 AU? • Fast/slow wind stream structure leads to corotating interaction regions (CIRs) and shocks in the heliosphere. • We applied the upwind differencing method of Riley & Lionello (2011) to the empirical u–f relationship. • Finest-scale variations may be wiped out at 1 AU, but a lot survives. (Borovsky 2008) r = 20 Rs r = 40 Rs r = 1 AU

15. Outline: • Bridging the Sun/heliosphere gap: observations & models • Survival of coronal “flux tubes” to 1 AU ? • Preferential ion heating & acceleration B

16. Anisotropic MHD turbulence • Can MHD turbulence explain the presence of perpendicular ion heating?Maybe not! k ? Energy input k

17. Anisotropic MHD turbulence • Can MHD turbulence explain the presence of perpendicular ion heating?Maybe not! • 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

18. Anisotropic MHD turbulence • Can MHD turbulence explain the presence of perpendicular ion heating?Maybe not! • 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

19. Multi-mode coupling? • Fast-mode waves propagate – and cascade – more isotropically than Alfvén waves. • Chandran (2005) suggested that Alfvén and fast-mode waves may share energy via nonlinear couplings (AAF, AFF). If coupling is strong enough, some high-frequency fast-mode wave energy may feed back to the Alfvén modes → ion cyclotron! We model the wave transport → cascade → coupling → heating, in fast solar wind. • First, we solve radial transport equations for the energy densities (Um) of the individual Alfvén, fast, and slow mode fluctuations. (Jacques 1977) Damping rate: • turb. cascade • visc/cond/Ohm • For the Alfvén waves, Qm depends on: • Wave reflection:Z+ ≠ Z– (Chandran & Hollweg 2009) • Turb. correlation length L (obeys its own transport eqn.)

20. Alfvén, fast, & slow mode waves in fast wind • We compute how the A, F, S modes perturb velocity, magnetic field, & density: • Free parameters: lower boundary conditions on Um & normalization for corr. length.

21. Alfvén, fast, & slow mode waves in fast wind • Caveat: changing correlation length (L ~ 1/kouter) changes collisional damping a lot: • Our standard model for fast-mode waves is a representative example, not a definitive prediction! Latr = Rs: Earlier estimates: 75 km (CvB07) 300 km (CvB05) 300 km 200 km 130 km 100 km • It’s unlikely for Sun-generated slow-mode waves to survive to large heights, so we ignore them for remainder of this work (see, however, Howes et al. 2011). 50 km 30 km

22. Model cascade + Alfvén/fast-mode coupling • Turbulent cascade modeled as time-steady advection/diffusion in wavenumber space. • Dissipation from KAW Landau damping (A) and transit-time damping (F) included. • Coupling between A & F modes treated with Chandran (2005) weak turb. timescale. Pure Alfvén mode: Alfvén mode with AAF/AFF coupling:

23. Preliminary coupling results • We computed heating rates for protons & electrons from Vlasov-Maxwell dispersion. Fast-mode wave power varied up & down from the standard model . . . Helios & Ulysses

24. Preferential heavy ion heating • UV spectroscopy provides constraints on Qion for O+5 ions in the corona . . . SUMER (Landi & Cranmer 2009); UVCS (Cranmer et al. 1999)

25. Conclusions • Advances in MHD turbulence theory continue to help improve our understanding about kinetic effects & MHD connectivity from the corona to the solar wind. • There is still a lot that can be done with “time-steady” wave/turbulence models. • Our Alfvén/fast-mode coupling mechanism is only one possibility. 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/

26. extra slides . . .

28. CPI is a large-aperture ultraviolet coronagraph spectrometer that has been proposed to be deployed on the International Space Station (ISS). • The primary goal of CPI is to identify and characterize the physical processes that heat and accelerate the plasma in the fast and slow solar wind. • CPI follows on from the discoveries of UVCS/SOHO, and has unprecedented sensitivity, a wavelength range extending from 25.7 to 126 nm, higher temporal resolution, and the capability to measure line profiles of He II, N V, Ne VII, Ne VIII, Si VIII, S IX, Ar VIII, Ca IX, and Fe X, never before seen in coronal holes above 1.3 solar radii. See white paper at:http://arXiv.org/abs/1104.3817 • 2011 September 29: NASA selected CPI as an Explorer Mission of Opportunity project to undergo an 11-month Phase A concept study.