The physics of coronal heating and solar wind acceleration
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Ongoing Research and Unanswered Questions. The Physics of Coronal Heating and Solar Wind Acceleration:. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics. Ongoing Research and Unanswered Questions. The Physics of Coronal Heating and Solar Wind Acceleration:. Outline:

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Ongoing Research and

Unanswered Questions

The Physics of Coronal Heating and Solar Wind Acceleration:

Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics


Ongoing Research and

Unanswered Questions

The Physics of Coronal Heating and Solar Wind Acceleration:

  • Outline:

  • Brief overview of the Sun-Heliosphere system

  • Exciting new measurements: remote & in situ

  • Major unsolved puzzles . . .

Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics


The extended solar atmosphere

The “coronal heating problem”


The photosphere and chromosphere

  • The lower boundary for space weather is the top of the convective zone:

  • Optically thick photosphere:

β << 1

β ~ 1

β > 1

  • Optically thin (heated) chromosphere:


The solar corona

  • Plasma at 106 K emits most of its spectrum in the UV and X-ray . . .

Although there is more than enough kinetic energy at the lower boundary, we still don’t understand the physical processes that heat the plasma.

Most suggested ideas involve 3 steps:

1.Churning convective motions tangle up magnetic fields on the surface.

2.Energy is stored in twisted/braided/ swaying magnetic flux tubes.

3.Something on small (unresolved?) scales releases this energy as heat.

  • Particle-particle collisions?

  • Wave-particle interactions?


A small fraction of magnetic flux is OPEN

Peter (2001)

Fisk (2005)

Tu et al. (2005)


2008 Eclipse:

M. Druckmüller (photo)

S. Cranmer (processing)

Rušin et al. 2010 (model)


In situ solar wind: properties

  • 1958: Eugene Parker proposed that the hot corona provides enough gas pressure to counteract gravity and produce steady supersonic outflow.

  • Mariner 2 (1962): first confirmation of fast & slow wind.

  • 1990s: Ulysses left the ecliptic; provided first 3D view of the wind’s source regions.

  • 1970s: Helios (0.3–1 AU). 2007: Voyagers @ term. shock.

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


  • Outline:

  • Overview: Our complex “variable star”

  • Exciting new measurements: remote & in situ

  • Major unsolved puzzles . . .


AIA on the Solar Dynamics Observatory (SDO)

  • SDO is the 1st “Living With a Star” mission.

  • Geosynchronous orbit allows continuous monitoring. AIA telescopes obtain EUV images (16 megapixel) every ~10 seconds:

  • 2 Terabytes per day sent down to the ground!

  • See Dean Pesnell’s talk (A112 S3, 08:30)


AIA 171 Å (sensitive to T ~ 106 K)


MHD waves in the corona

  • Remote sensing provides several direct (and indirect) wave detection techniques:

  • Alfvén waves have been detected via spectroscopy (Doppler shifts) and imaging (plane-of-sky swaying).

Tomczyk et al. (2007)

  • Fast & slow mode magnetosonic waves have been detected via intensity fluctuations (δρ2) and motion tracking to measure phase speeds.


Erupting jets in the corona

  • Open-field regions show frequent jet-like events.

  • Evidence of magnetic reconnection between open and closed fields?

  • How much of the solar wind emerges in jets?

Hinode/SOT: Nishizuka et al. (2008)

  • STEREO imagers allow 3D MHD structure of jets to be disentangled . . .


Coronal heating: multi-fluid & collisionless

O+5

protons

In the lowest density solar wind streams . . .

electron temperatures

proton temperatures

heavy ion temperatures


In situ fluctuations & turbulence

  • Fourier transform of B(t), v(t), etc., into frequency:

f -1 energy containing range

f -5/3

inertial range

The inertial range is a “pipeline” for transporting magnetic energy from the large scales to the small scales, where dissipation can occur.

Magnetic Power

f -3dissipation range

few hours

0.5 Hz


In situ MHD turbulence

  • A single spacecraft can’t tell the difference between spatial and time variations.

  • Theories say an MHD cascade is highly anisotropic in wavenumber space . . .

  • CLUSTER consists of 4 formation flying spacecraft, and has finally disentangled temporal from spatial variability: solar wind turbulence IS anisotropic!

Sahraoui et al. (2010)


  • Outline:

  • Overview: Our complex “variable star”

  • Exciting new measurements: remote & in situ

  • Major unsolved puzzles . . .


What is the source of solar wind mass?

  • Until relatively recently, the dominant idea was that a steady rate of “evaporation” is set by a balance between downward conduction, upward enthalpy flux, and local radiative cooling (Hammer 1982; Withbroe 1988).

heat conduction

radiation losses

  • On the other hand, new observations of spicules and jets (e.g., Aschwanden et al. 2007; De Pontieu et al. 2011; McIntosh et al. 2011) fuel the idea that a lot of the corona’s mass is injected impulsively from below.

5

2

— ρvkT

Schrijver (2001)


What is the dominant source of energy?

i.e., what heats the corona in open flux tubes? Two general ideas have emerged . . .

  • Wave/Turbulence-Driven (WTD) models, in which open flux tubes are jostled continuously from below. MHD fluctuations propagate up and damp.

  • Reconnection/Loop-Opening (RLO) models, in which energy is injected from closed-field regions in the “magnetic carpet.”

vs.

Counterpoint:

Roberts (2010) says WTD doesn’t work.

Cranmer & van Ballegooijen (2010) say RLO doesn’t work.


How much do impulsive events contribute?

  • There is 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 perturbing the field, much of which is connected tenuously to the wind via “quasi-separatrix layers” (Antiochos et al. 2011).

  • But is there enough mass & energy released (in the subset of reconnection events that turn closed fields into open fields) to account for the solar wind’s requirements?


Waves & turbulence

  • No matter the relative importance of RLO events, we do know that waves and turbulent motions are present everywhere... from photosphere to heliosphere.

  • How much can be accomplished by only WTD processes? (Occam’s razor?)

Hinode/SOT

SUMER/SOHO

G-band bright points

UVCS/SOHO

Helios & Ulysses

Undamped (WKB) waves

Damped (non-WKB) waves


Waves & turbulence

  • A number of recent models seem to be converging on a combination of turbulent dissipation (heating) and wave ponderomotive forces (acceleration) as being both sufficient to accelerate the wind and consistent with coronal & in situ observations.

  • For example, wave/turbulence processes can produce:

Realistic/variable coronal heating (Suzuki & Inutsuka 2006):

3D heliospheric variability

(Breech et al. 2009; Usmanov et al. 2011)

See also Cranmer et al. (2007)


Controversies about waves & turbulence

  • Where does the turbulent cascade begin? Chromosphere? Low corona? Some say it doesn’t become “fully developed” turbulence until < 1 AU.

~

In simulations that include flux-tube expansion, complex turbulent motions are induced, even down in the middle chromosphere!

(van Ballegooijen et al. 2011)

Simple motions input at photospheric lower boundary.


Controversies about waves & turbulence

  • The low-frequency (1/f) part of the spectrum at 1 AU contains most of the power. What is its origin?

  • The self-consistent product of a turbulent cascade?

  • Spacecraft passage through “spaghetti-like” flux tubes rooted on the solar surface? (Borovsky 2008)

  • New high-resolution magnetographs make possible better “mappings.”

(SOLIS Vector SpectroMagnetograph on Kitt Peak)


What’s next?

  • Data at 1 AU shows us plasma that has been highly “processed” on its journey . . . Models must keep track of 3D dynamical effects, Coulomb collisions, etc.

McGregor et al. (2011)

Kasper et al. (2010)

  • New missions!

  • In ~2018, Solar Probe Plus will go in to r ≈ 9.5 Rs to tell us more about the sub-Alfvénic solar wind.

  • The Coronal Physics Investigator (CPI) has been proposed as a follow-on to UVCS/SOHO to observe new details of minor ion heating & kinetic dissipation of turbulence in the extended corona (see arXiv:1104.3817).


Conclusions

  • Advances in plasma physics (turbulence, waves, reconnection) continue to help improve our understanding about coronal heating and solar wind acceleration.

  • It is becoming easier to include “real physics” in 1D → 2D → 3D models of the complex Sun-heliosphere system.

  • However, we still do not have complete enough observational constraintsto be able to choose between competing theories.

SDO/AIA

For more information: http://www.cfa.harvard.edu/~scranmer/


Extra slides . . .


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)


Turbulent dissipation = coronal heating?

  • In hydrodynamics, von Kármán, Howarth, & Kolmogorov worked out cascade energy flux via dimensional analysis:

  • In MHD, cascade is possible only if there are counter-propagating Alfvén waves…

(“cascade efficiency”)

Z–

Z+

  • n = 1: an approximate “golden rule” from theory

  • Caution: this is an order-of-magnitude scaling.

(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)

Z–


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.

  • Some details about the 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


Implementing the wave/turbulence idea

  • Cranmer et al. (2007) computed self-consistent solutions for waves & background plasma along flux tubes going from the photosphere to the heliosphere.

  • Only free parameters: radial magnetic field & photospheric wave properties. (No arbitrary “coronal heating functions” were used.)

  • Self-consistent coronal heating comes from gradual Alfvén wave reflection & turbulent dissipation.

  • Is Parker’s critical point above or below where most of the heating occurs?

  • Models match most observed trends of plasma parameters vs. wind speed at 1 AU.

Ulysses 1994-1995


Cranmer et al. (2007): other results

Wang & Sheeley (1990)

ACE/SWEPAM

ACE/SWEPAM

Ulysses

SWICS

Ulysses

SWICS

Helios

(0.3-0.5 AU)


Alfven wave’s oscillating

E and B fields

ion’s Larmor motion around radial B-field

Preferential ion heating & acceleration

  • Parallel-propagating ion cyclotron waves (10–10,000 Hz in the corona) have been suggested as a natural energy source . . .

instabilities

dissipation

lower qi/mi

faster diffusion

(e.g., Cranmer 2001)


However . . .

Does a turbulent cascade of Alfvén waves (in the low-beta corona) actually produce ion cyclotron waves?

Most models say NO!


Anisotropic MHD turbulence

  • When magnetic field is strong, the basic building block of turbulence isn’t an “eddy,” but an Alfvén wave packet.

k

?

Energy input

k


Anisotropic MHD turbulence

  • When magnetic field is strong, the basic building block of turbulence isn’t an “eddy,” but an Alfvén wave packet.

  • 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


Anisotropic MHD turbulence

  • When magnetic field is strong, the basic building block of turbulence isn’t an “eddy,” but an Alfvén wave packet.

  • 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


Parameters in the solar wind

  • What wavenumber angles are “filled” by anisotropic Alfvén-wave turbulence in the solar wind? (gray)

  • What is the angle that separates ion/proton heating from electron heating? (purple curve)

θ

k

k

Goldreich &Sridhar (1995)

electron heating

proton & ion heating


Preliminary coupling results

  • Chandran (2005) suggested that weak turbulence couplings (AAF, AFF) may be sufficient to transfer enough energy to Alfvén waves at high parallel wavenumber.

  • New simulations in the presence of strong Alfvénic turbulence (e.g., Goldreich & Sridhar 1995) show that these couplings may give rise to wave power that looks like a kind of “parallel cascade” (Cranmer, Chandran, & van Ballegooijen 2011)

r = 2 Rs

β ≈ 0.003


Other ideas . . .

  • When MHD turbulence cascades to small perpendicular scales, the small-scale shearing motions may be unstable to the generation of ion cyclotron waves (Markovskii et al. 2006).

  • Turbulence may lead to dissipation-scale current sheets that may preferentially spin up ions (Dmitruk et al. 2004).

  • If there are suprathermal tails in chromospheric velocity distributions, then collisionless velocity filtration (Scudder 1992) may give heavy ions much higher temperatures than protons (Pierrard & Lamy 2003).

  • If nanoflare-like reconnection events in the low corona are frequent enough, they may fill the extended corona with electron beams that would become unstable and produce ion cyclotron waves (Markovskii 2007).

  • If kinetic Alfvén waves reach large enough amplitudes, they can damp via stochastic wave-particle interactions and heat ions (Voitenko & Goossens 2006; Wu & Yang 2007; Chandran 2010).

  • Kinetic Alfvén wave damping in the extended corona could lead to electron beams, Langmuir turbulence, and Debye-scale electron phase space holes which could heat ions perpendicularly (Matthaeus et al. 2003; Cranmer & van Ballegooijen 2003).


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