1. Testing and Refining Models of Slow Solar Wind Acceleration Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

2. Testing and Refining Models of Slow Solar Wind Acceleration Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics Outline: 1.Perspective: Source Regions of the Slow Wind 2.Successes of Wave/Turbulence-Driven Models 3.Open Questions & Controversies

3. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Connectivity to the large-scale 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”) smallest coronal holes active regions v > 550 km/s 350 < v < 550 km/s v < 350 km/s Luhmann et al. (2002) applied the Wang & Sheeley (1990) speed/flux-expansion relation to several solar cycles of PFSS reconstructions... MINMAX (see also Nolte et al. 1976; Hick et al. 1995; Liewer et al. 2004; Sakao et al. 2007)

4. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Multiple types of “slow solar wind” Quiescent equatorial streamers (solar min.) vs. “active region streamers” (not min.) Wang et al. (2000) UVCS/SOHO showed that AR streamers are denser, have higher T e, but lower T p and T ion than QE streamers (Ko et al. 2002; Strachan et al. 2004; Kohl et al. 2006). Wang et al. (2009) showed that slow wind mapped back to ARs has larger expansion factors, stronger B-fields, higher mass fluxes, higher O 7+ /O 6+, and higher FIP ratios than slow wind associated with QE streamers.

5. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia The Debate in ’08 ’09 Two broad classes of models have evolved that attempt to self-consistently answer the question: How are fast and slow wind streams accelerated? Wave/Turbulence-Driven (WTD) models Reconnection/Loop-Opening (RLO) models Opinionated position paper: arXiv: 0804.3058

6. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Waves & turbulence in open flux tubes 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)

7. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Magnetic flux tubes & expansion factors polar coronal holesf ≈ 4 quiescent equ. streamersf ≈ 9 “active regions”f ≈ 25 A(r) ~ B(r) –1 ~ r 2 f(r) (Banaszkiewicz et al. 1998) Wang & Sheeley (1990) defined the expansion factor between “coronal base” and the source-surface radius ~2.5 R s. TR

8. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Self-consistent 1D models Cranmer, van Ballegooijen, & Edgar (2007) computed solutions for the waves & background one-fluid plasma state along various flux tubes... going from the photosphere to the heliosphere. The only free parameters: radial magnetic field & photospheric wave properties. Ingredients: Alfvén waves: non-WKB reflection with full spectrum, turbulent damping, wave-pressure acceleration Acoustic waves: shock steepening, TdS & conductive damping, full spectrum, wave-pressure acceleration Radiative losses: transition from optically thick (LTE) to optically thin (CHIANTI + PANDORA) Heat conduction: transition from collisional (electron & neutral H) to a collisionless “streaming” approximation

9. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Dissipation of MHD turbulence Standard nonlinear terms have a cascade energy flux that gives phenomenologically simple heating: Z+Z+ Z–Z– Z–Z– We used a generalization based on unequal wave fluxes along the field... n = 1: usual “golden rule;” we also tried n = 2. Effectively, n < 0 for closed loops. (“cascade efficiency”) (e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002; Oughton et al. 2006) (e.g., Gomez et al. 2000; Rappazzo et al. 2007, 2008)

10. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Results: turbulent heating & acceleration T (K) reflection coefficient Goldstein et al. (1996) Ulysses SWOOPS

11. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Results: flux tubes & critical points Wind speed is ~anticorrelated with flux-tube expansion & height of critical point. Cascade efficiency: n=1 n=2 r crit r max (where T=T max )

12. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Results: heavy ion properties Frozen-in charge states FIP effect (using Laming’s 2004 theory) Cranmer et al. (2007) Ulysses SWICS

13. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia New result: solar wind “entropy” Pagel et al. (2004) found ln(T/n γ–1 ) (at 1 AU) to be strongly correlated with both wind speed and the O 7+ /O 6+ charge state ratio. (empirical γ = 1.5) The Cranmer et al. (2007) models (black points) do a reasonably good job of reproducing ACE/SWEPAM entropy data (blue). Because entropy should be conserved in the absence of significant heating, the quantity measured at 1 AU may be a long-distance “proxy” for the near-Sun locations of strong coronal heating.

14. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia New result: scaling with magnetic flux density Mean field strength in low corona: If the regions below the merging height can be treated with approximations from “thin flux tube theory,” then: B ~ ρ 1/2 Z ± ~ ρ –1/4 L ┴ ~ B –1/2 B ≈ 1500 G (universal?) f ≈ 0.002–0.1 B ≈ f B,....... and since Q/Q ≈ B/B, the turbulent heating in the low corona scales directly with the mean magnetic flux density there (e.g., Pevtsov et al. 2003; Schwadron et al. 2006; Kojima et al. 2007; Schwadron & McComas 2008)... Thus,

15. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Progress towards a “module” for 3D codes? The form of the turbulent dissipation rate is approximate... but Tuesday’s session on turbulence (Chandran & Boldyrev) may help refine it. The non-WKB Alfvén wave reflection requires CPU-intensive solutions of differential equations; one for each wave frequency & each time step. Doesn’t specify proton vs. electron heating (they conduct differently!) Doesn’t deal with preferential heating & acceleration of minor ions. Can RLO-type energy-injection events be incorporated into this type of model? Existing results are promising, but......working on it!

16. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia What about the RLO paradigm? Can a comparison of time scales help resolve the controversy? Fisk (2005) There’s a natural appeal to the RLO idea, since only a small fraction of the Sun’s magnetic flux is open. Open flux tubes are always near closed loops! The “magnetic carpet” is continuously churning. Open-field regions show frequent coronal jets (Hinode/XRT). Polar jet lifetime: Flux replacement lifetime: Supergranule lifetime: < 1 hr 2–20 hr 1–2 days RLO:WTD: Define a wind acceleration time scale: base crit / T max fast: slow (QS): slow (AR): 3 hr 18 hr / 2.5 hr 24 hr / 0.2 hr

17. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia A controversial stand? Fast wind Slow wind (quiescent streamers) Slow wind (active regions) WTD dominates (burden of proof is on RLO) I’ll still hedge! RLO dominates (burden of proof is on WTD) I don’t think I believe it, but...

18. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Is this the whole story?

19. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia protons electrons O +5 O +6 Multi-fluid collisionless effects! coronal holes / fast wind (effects also present in slow wind)

20. Testing and Refining Models of Slow Solar Wind Acceleration S. R. Cranmer, August 6, 2009 SHINE, Wolfville, Nova Scotia Conclusions For more information: http://www.cfa.harvard.edu/~scranmer/ The debate between waves/turbulence and reconnection/loop-opening mechanisms of solar wind acceleration goes on. We need to better define the observations needed to make conclusive constraints on (& decisions between!) the theories. Theoretical advances in MHD turbulence continue to feed back into global models of the solar wind, as well as into many other areas of plasma physics and astrophysics. vs.