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

Turbulence as a Unifying Principlein Coronal Heating and

Solar/Stellar Wind Acceleration

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

A. van Ballegooijen, L. Woolsey, J. Kohl, M. Miralles, M. Asgari-Targhi

Turbulence as a Unifying Principlein Coronal Heating and

Solar/Stellar Wind Acceleration

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

A. van Ballegooijen, L. Woolsey, J. Kohl, M. Miralles, M. Asgari-Targhi

Outline:

1. Brief history of solar wind & stellar winds

2. Links between wind acceleration & coronal heating

3. Turbulence micro-tutorial

4. Successful predictions of observed wind properties

Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013

Brief history: stellar winds

• 1830–1860: Eta Carinae’s remarkable mass loss episodes: V = 8 → –1• Milne (1924): radiation pressure can eject atoms/ions from stellar atmospheres.

• Early 1600s: two closely timed “stellar mass loss” events made a big cultural splash . . .

Kepler’s supernova (in “Serpentarius”) P Cygni LBV outburst


Brief history: stellar winds

O supergiant (Morton 1967)

M supergiant (Bernat 1976)

• 1920s-30s: P Cygni profiles 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)

• Also: IR excesses, maser emission, “plain” blueshifts.


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/coronagraph pB → ne(r) hydrostatic scale heights also show T ~ 106 K.


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.”


In situ solar wind: discovery!• 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.

• 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.

speed (km/s)

density

variability

temperatures

abundances

600–800

low

smooth + waves

Tion >> Tp > Te

photospheric

300–500

high

chaotic

all ~equal

more low-FIP

fast slow


Stellar winds across the H-R Diagram

Massive stars: radiation-driven

winds

Solar-type stars: coronal winds (driven by MHD

turbulence?)

Cool luminous stars:

pulsation/dust-driven winds?


Outline:






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?

• 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

Habbal et al. (2010)


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:

1. transported up to the corona,

2. converted to magnetic energy,

3. dissipated as heat, (and/or)

4. 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


Waves versus reconnectionSlow 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”)

• 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!)

However . . .


Waves go along with reconnectionTo complicate things even more . . .

• Waves cascade into MHD turbulence (eddies), which tends to:

Onofri et al. (2006)

e.g., Dmitruk et al. (2004)

break up into thin reconnecting sheets on its smallest scales.

accelerate electrons along the field and generate currents.

• Coronal current sheets can emit waves, and can be unstable to growth of turbulent motions which may dominate the energy loss & particle acceleration.

• Turbulence may drive “fast” reconnection rates (Lazarian & Vishniac 1999), too.


The churning magnetic carpet

Tu et al. (2005)

Fisk (2005)

• 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

β ~ 1

β > 1


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)


Outline:






Turbulence: pure hydrodynamics

The inertial range is a “pipeline” for transporting

energy from the large scales to the small scales,

where dissipation can occur.

energy injection range

dissipation range

frequency or wavenumber

Fluc

tuat

ion

pow

er

• The original von Karman & Howarth (1938) theory of fluid turbulence assumed a constant energy flux from large to small eddies.

Kolmogorov (1941)


Anisotropic MHD turbulence

• MHD simulations inspire phenomenological scalings for the cascade/heating rate:

• 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.

(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)


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:

• 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

B ≈ 1500 G (universal?)

f ≈ 0.002 – 0.1B ≈ f B ,

• Thus, Q/Q ≈ B/B as was found by Pevtsov et al. (2003); Schwadron et al. (2006).


Outline:






Open flux tubes feeding the solar wind

vs.

• 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?

SDO/AIA

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.

Roberts (2010) says neither idea works !?

Cranmer & van Ballegooijen (2010) say reconn./loop-opening doesn’t work.


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

G-band bright points

SUMER/SOHO

Helios & Ulysses

UVCS/SOHO

Undamped (WKB) wavesDamped (non-WKB) waves


Photospheric origin of waves

< 0.1″

• Much of the magnetic field is concentrated into small inter-granular flux tubes, which ultimately connects up to the corona & wind.

• Observations of G-band bright points show a spectrum of both random walks and intermittent “jumps” (Cranmer & van Ballegooijen 2005; Chitta et al. 2012).


Turbulence-driven solar wind models

Goldstein et al.(1996)

Ulysses SWOOPS

• 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.


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”).


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.

• Photospheric Alfvén waves are driven by turbulent convection (Musielak & Ulmschneider 2002).


Energy conservation in outer stellar atmospheres

PhotosphereChromosphere

Transition region & low coronaSupersonic 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)

≈


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 density ρ) 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.

• Alfvén wave pressure may take the place of gas pressure (Holzer et al. 1983).


Results for 47 cool stars with measured M.

Cranmer & Saar 2011 (o)

χ2 = 0.504

Schröder & Cuntz 2005 (o)

χ2 = 1.131

Measurements (x)


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.


Extra slides . . .


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

heat conduction

radiation losses

— ρvkT52

. . . along open flux tubes!

Wang (1998)


• Mass flux depends on the area covered by open field lines at the TR:

A = 4πr2 f

f TR ≈ f*

θ

f ∞ → 1

f* θ ≈ 0.3 to 0.5

Open magnetic flux tubes

• Measurements of Zeeman-broadened lines constrain the filling factor of (open + closed) photospheric B-field.

low-qual. data

high-qual. data Sun

G, K, M dwarfs

• The evolution of Qheat with height depends on the magnetic field . . .


Mass loss on an ideal main sequence

• Is there really a basal “floor” in the age-rotation-activity relationship?

Prot

SaturationSuper-saturation?


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 –4 Ms/yr.

(Struck et al. 2004)


Cranmer et al. (2007): other results

UlyssesSWICS

Helios(0.3-0.5 AU)

UlyssesSWICS

ACE/SWEPAM ACE/SWEPAM

Wang & Sheeley (1990)


The power of off-limb UV spectroscopy

(Kohl et al. 1995, 1997, 1998, 1999, 2006; Cranmer et al. 1999, 2008; Cranmer 2000,

2001, 2002)

• 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.

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