turbulence as a unifying principle in coronal heating and solar/stellar wind acceleration steven r....
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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
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.”
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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?
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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
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)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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 . . .
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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 in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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
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)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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).
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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
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.
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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 in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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”).
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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).
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
Energy conservation in outer stellar atmospheres
PhotosphereChromosphere
Transition region & low coronaSupersonic wind (r >> R*)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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• 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)
≈
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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).
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
Results for 47 cool stars with measured M.
Cranmer & Saar 2011 (o)
χ2 = 0.504
Schröder & Cuntz 2005 (o)
χ2 = 1.131
Measurements (x)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
Extra slides . . .
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
• 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 . . .
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
Mass loss on an ideal main sequence
• Is there really a basal “floor” in the age-rotation-activity relationship?
Prot
SaturationSuper-saturation?
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
Cranmer et al. (2007): other results
UlyssesSWICS
Helios(0.3-0.5 AU)
UlyssesSWICS
ACE/SWEPAM ACE/SWEPAM
Wang & Sheeley (1990)
Turbulence in Coronal Heating & Solar Wind Acceleration SSP Seminar, April 29, 2013
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.