Turbulence as a Unifying Principle in Coronal Heating and Solar/Stellar Wind Acceleration

1. Turbulence as a Unifying Principlein Coronal Heating andSolar/Stellar Wind Acceleration Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics A. van Ballegooijen, L. Woolsey, J. Kohl, M. Miralles, M. Asgari-Targhi

2. Outline: • Brief history of solar wind & stellar winds • Links between wind acceleration & coronal heating • Turbulence micro-tutorial • Successful predictions of observed wind properties Turbulence as a Unifying Principlein Coronal Heating andSolar/Stellar Wind Acceleration Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics A. van Ballegooijen, L. Woolsey, J. Kohl, M. Miralles, M. Asgari-Targhi

3. Brief history: stellar winds • Early 1600s: two closely timed “stellar mass loss” events made a big cultural splash . . . Kepler’s supernova (in “Serpentarius”) P Cygni LBV outburst • 1830–1860: Eta Carinae’s remarkable mass loss episodes: V = 8 → –1 • Milne (1924): radiation pressure can eject atoms/ions from stellar atmospheres.

4. Brief history: stellar winds • 1920s-30s: P Cygniprofiles measured as clear diagnostics of stellar wind outflow. • O, B, WR, LBVs: Beals (1929); Swings & Struve (1940) • G, K, M giants, supergiants: Adams & MacCormack (1935); Deutsch (1956) O supergiant (Morton 1967) M supergiant (Bernat 1976) • Also: IR excesses, maser emission, “plain” blueshifts.

5. Corona & solar wind: pre-history • 1850–1950: 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) • 1870s: First off-limb solar spectroscopy: red, green emission lines. (“coronium?”) • 1930s: Spectroscopy helped determine that the corona is hot (> 1 million K). • Eclipse/coronagraphpB → ne(r) hydrostatic scale heights also show T ~ 106 K.

6. The solar wind: prediction • 1958: Treating the plasma like a single fluid, E. N. Parker proposed that the hot corona provides enough gas pressure to counteract gravity & accelerate a solar wind. • Momentum conservation: (a ≈ Vth) The time-steady version of the momentum equation has a “critical point.”

7. In situ solar wind: discovery! • Mariner 2 (1962): first direct confirmation of continuous fast &slowsolar wind. fast slow 300–500 high chaotic all ~equal more low-FIP speed (km/s) density variability temperatures abundances 600–800 low smooth + waves Tion >> Tp > Te photospheric • 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. • Helios probes went in to 0.3 AU . . . Voyagers have gone past termination shock. • Remote sensing: UVCS/SOHO discovered Tion >> Tp > Te in coronal holes.

9. Stellar winds across the H-R Diagram Cool luminous stars: pulsation/dust-driven winds? Massive stars: radiation-driven winds Solar-type stars: coronal winds (driven by MHD turbulence?)

10. Outline: • Brief history of solar wind & stellar winds • Links between wind acceleration & coronal heating • Turbulence micro-tutorial • Successful predictions of observed wind properties

11. Link to coronal heating: not so simple • The Parker (1958) theory says that a higher-temperature corona accelerates a faster wind. • Do observations of the coronal source regions back this up? Habbal et al. (2010) • No! (see also measurements of ion charge states in the solar wind) • It is clear the fast wind needs something besides gas pressure to accelerate so fast! Red: low Te Blue: high Te

12. Coronal heating problems • (Nearly!) everyone agrees that there is more than enough “mechanical energy” in the convection to heat the corona. How does a fraction (~1%) of that energy get: transported up to the corona, converted to magnetic energy, dissipated as heat, (and/or) provide direct wind acceleration • Waves (AC) vs. reconnection (DC) ? • Heating: top-down vs. bottom-up ? • Open-field: jostling vs. loop-feeding ? • Kinetics: MHD vs. “filtration” ? Source: Mats Carlsson

13. Waves versus reconnection Slow footpoint motions (τ > L/VA) cause the field to twist & braid into a quasi-static state; parallel currents build up and are released via reconnection. (“DC”) Rapid footpoint motions (τ < L/VA) propagate through the field as waves, which are eventually dissipated. (“AC”) However . . . • The Sun’s atmosphere exhibits a continuum of time scales bridging AC/DC limits. • “Waves” in the real corona aren’t just linear perturbations. • (amplitudes are large) (polarization relations are not “classical”) • “Braiding” in the real corona is highly dynamic. (see Hi-C!)

14. Waves go along with reconnection To complicate things even more . . . • Waves cascade into MHD turbulence (eddies), which tends to: • break up into thin reconnectingsheets on its smallest scales. • accelerate electrons along the field and generate currents. • Coronal current sheets can emit waves, and can be unstable to growth ofturbulent motions which may dominate the energy loss & particle acceleration. e.g., Dmitruk et al. (2004) • Turbulence may drive “fast” reconnection rates (Lazarian & Vishniac 1999), too. Onofri et al. (2006)

15. The churning magnetic carpet • The solar interior is convectively unstable, and the foot-points of all magnetic fields above the surface are moved around continually in a “random walk:” β << 1 Fisk (2005) β ~ 1 β > 1 Tu et al. (2005)

16. Turbulence: a unifying picture? Convection shakes & braids field lines... Alfvén waves propagate upward... partially reflect back down... ...and cascade from large to small eddies, eventually dissipating to heat the plasma. Turbulent eddies are formed and “shredded” by collisions of counter-propagating Alfvén wave packets. van Ballegooijen et al. (2011)

17. Outline: • Brief history of solar wind & stellar winds • Links between wind acceleration & coronal heating • Turbulence micro-tutorial • Successful predictions of observed wind properties

18. Turbulence: pure hydrodynamics • The original von Karman & Howarth (1938) theory of fluid turbulence assumed a constant energy fluxfrom large to small eddies. The inertial range is a “pipeline” for transporting energy from the large scales to the small scales, where dissipation can occur. energy injection range Fluctuation power Kolmogorov (1941) dissipation range frequency or wavenumber

19. Anisotropic MHD turbulence • 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. • Turbulent eddies are formed and “shredded” by collisions of counter-propagating Alfvén wave packets. • MHD simulations inspire phenomenological scalings for the cascade/heating rate: (e.g., Iroshnikov 1963; Kraichnan 1965; Strauss 1976; Shebalin et al. 1983; Hossain et al. 1995; Goldreich & Sridhar 1995; Matthaeus et al. 1999; Dmitruk et al. 2002)

20. Turbulent heating proportional to B • Sometimes wave/turbulence heating is contrasted with purely “magnetic” heating, but it’s often the case that the turbulent heating rate scales with field strength: • Mean field strength in low corona: B≈ 1500 G (universal?) f≈ 0.002 – 0.1 B ≈ f B, • If the low atmosphere can be treated with approximations from thin flux tube theory, and the turbulence is “balanced” (i.e., loops with similar footpoints) then: B ~ ρ1/2 v±~ ρ–1/4 L┴ ~ B–1/2 • Thus, Q/Q ≈ B/B as was found by Pevtsov et al. (2003); Schwadron et al. (2006).

21. Outline: • Brief history of solar wind & stellar winds • Links between wind acceleration & coronal heating • Turbulence micro-tutorial • Successful predictions of observed wind properties

22. Open flux tubes feeding the solar wind Once we have a ~106 K corona, we still don’t know if Parker’s (1958) theory for gas-pressure acceleration is sufficient for driving the solar wind. SDO/AIA • What is the source of mass, momentum, and energy that goes into the solar wind? • Wave/turbulence input in open tubes? • Reconnection & mass input from loops? vs. Cranmer & van Ballegooijen (2010) say reconn./loop-opening doesn’t work. Roberts (2010) says neither idea works !?

23. 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? Hinode/SOT SUMER/SOHO G-band bright points UVCS/SOHO Helios & Ulysses Undamped (WKB) waves Damped (non-WKB) waves

24. Photospheric origin of waves • Much of the magnetic field is concentrated into small inter-granular flux tubes, which ultimately connects up to the corona & wind. < 0.1″ • Observations of G-band bright points show a spectrum of both random walksand intermittent “jumps” (Cranmer & van Ballegooijen 2005; Chitta et al. 2012).

25. Turbulence-driven solar wind models • Cranmer et al. (2007) computed self-consistent solutions of waves & background one-fluid plasma state along various flux tubes. • Only free parameters:waves at photosphere & radial magnetic field. • Coronal heating occurs “naturally” with Tmax~ 1–2 MK. • Varying radial dependence of field strength (Br ~ A–1) changes location of the Parker (1958) critical point. • Crit. pt.low:most heating occurs above it → kinetic energy → fast wind. • Crit. pt.high:most heating occurs below it → thermal energy → denser and slower wind. Ulysses SWOOPS Goldstein et al. (1996)

26. Time-dependent turbulence models • van Ballegooijen et al. (2011) & Asgari-Targhi et al. (2012) simulated MHD turbulence in expanding flux tubes →3D fluctuations in loops & open fields. • Assumptions: • No background flows along field. • No density fluctuations. • Fluctuations confined to flux tube interior. • Reduced MHD equations govern nonlinear “wave packet collision” cascade interactions. • Chromospheric and coronal heating is of the right magnitude, and is highly intermittent (“nanoflare-like”).

27. Other stars: a simpler approach? • Cranmer et al. (2007) and others solved the full set of mass, momentum, and energy conservation equations. • Cranmer & Saar (2011) solved a simplified version of energy conservation to get just the mass loss rate as a function of the energy input from turbulence. • Same MHD heating rate used in stellar models as was used in the solar model. • PhotosphericAlfvén waves are driven by turbulent convection (Musielak& Ulmschneider 2002).

28. Energy conservation in outer stellar atmospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photosphere Chromosphere Transition region & low corona Supersonic wind (r>>R*) • Leer et al. (1982) and Hansteen et al. (1995) found that one can often simplify the energy balance to be able to solve for the mass flux: • However, the challenge is to determine values for all the parameters – both explicit and hidden! (e.g., filling factor of open flux tubes on stellar surface) ≈

29. Do Alfvén waves always heat a corona? • With the above inputs (and assuming v∞ ≈ Vesc), we can solve for the mass loss rate in the case of a “hot coronal wind.” • Sometimes, the heating rate Q drops off more steeply (with decreasing densityρ) than in the solar case, and radiative cooling always remains able to keep T < 104 K. • In those “cold” cases (usually for luminous giants), gas pressure cannot accelerate a wind. • Alfvénwave pressure may take the place of gas pressure (Holzer et al. 1983).

30. . Results for 47 cool stars with measured M Measurements (x) Cranmer & Saar 2011 (o) Schröder & Cuntz 2005 (o) χ2 = 1.131 χ2 = 0.504

31. Conclusions • Although the solar “problems” are not yet conclusively solved, we’re including more and more real physics (e.g., MHD turbulence) in models that are doing better at explaining obsesrved plasma heating & acceleration. • However, we still do not have complete enough observational constraints to be able to choose between competing theories. • For other stars, theories are doing okay, but only when lots of information about the star is known (e.g., luminosity, mass, age, rotation rate, magnetic field, pulsation properties). • Understanding is greatly aided by ongoing collaboration between the solar physics, plasma physics, & astrophysics communities.

32. Extra slides . . .

33. 5 2 — ρvkT What sets the Sun’s mass loss? • The sphere-averaged mass flux is remarkably constant. • Coronal heating seems to be ultimately responsible, but that varies by orders of magnitude over the solar cycle. • Hammer (1982) & Withbroe (1988) suggested an energy balance with a “thermostat.” • Only a fraction of total coronal heat flux conducts down, but in general, we expect something close to Wang (1998) heat conduction radiation losses . . . along open flux tubes!

34. Open magnetic flux tubes • The evolution of Qheat with height depends on the magnetic field . . . • Mass flux depends on the area covered by open field lines at the TR: • A = 4πr2f • Measurements of Zeeman-broadened lines constrain the filling factor of (open + closed) photospheric B-field. G, K, M dwarfs f ∞ → 1 f TR ≈ f*θ low-qual. data high-qual. data Sun f* θ≈ 0.3 to 0.5

35. Mass loss on an ideal main sequence • Is there really a basal “floor” in the age-rotation-activity relationship? Prot Saturation Super-saturation?

36. Evolved cool stars: RG, HB, AGB, Mira • The extended atmospheres of red giants and supergiants are likely to be cool (i.e., not highly ionized or “coronal” like the Sun). • High-luminosity: radiative driving... of dust? • Shock-heated “calorispheres”(Willson 2000) ? • Numerical models show that pulsations couple with radiation/dust formation to be able to drive mass loss rates up to 10 –5 to 10 –4Ms/yr. (Struck et al. 2004)

37. Cranmer et al. (2007): other results Wang & Sheeley (1990) ACE/SWEPAM ACE/SWEPAM Ulysses SWICS Ulysses SWICS Helios (0.3-0.5 AU)

38. The power of off-limb UV spectroscopy • UVCS/SOHO led to new views of the collisionless nature of solar wind acceleration. • 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 velocity distributions. (Kohl et al. 1995, 1997, 1998, 1999, 2006; Cranmer et al. 1999, 2008; Cranmer 2000, 2001, 2002)