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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The physics of coronal heating and solar wind acceleration

Ongoing Research and

Unanswered Questions

The Physics of Coronal Heating and Solar Wind Acceleration:

Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics


The physics of coronal heating and solar wind acceleration1

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 extended solar atmosphere

The “coronal heating problem”


The photosphere and chromosphere

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

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

A small fraction of magnetic flux is OPEN

Peter (2001)

Fisk (2005)

Tu et al. (2005)


The physics of coronal heating and solar wind acceleration

2008 Eclipse:

M. Druckmüller (photo)

S. Cranmer (processing)

Rušin et al. 2010 (model)


In situ solar wind properties

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


The physics of coronal heating and solar wind acceleration

  • Outline:

  • Overview: Our complex “variable star”

  • Exciting new measurements: remote & in situ

  • Major unsolved puzzles . . .


Aia on the solar dynamics observatory sdo

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 sensitive to t 10 6 k

AIA 171 Å (sensitive to T ~ 106 K)


Mhd waves in the corona

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

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

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

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

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)


The physics of coronal heating and solar wind acceleration

  • Outline:

  • Overview: Our complex “variable star”

  • Exciting new measurements: remote & in situ

  • Major unsolved puzzles . . .


What is the source of solar wind mass

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

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

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

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 turbulence1

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

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 turbulence1

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

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

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/


The physics of coronal heating and solar wind acceleration

Extra slides . . .


Waves turbulence in open flux tubes

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

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–


The physics of coronal heating and solar wind acceleration

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

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

Cranmer et al. (2007): other results

Wang & Sheeley (1990)

ACE/SWEPAM

ACE/SWEPAM

Ulysses

SWICS

Ulysses

SWICS

Helios

(0.3-0.5 AU)


The physics of coronal heating and solar wind acceleration

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)


The physics of coronal heating and solar wind acceleration

However . . .

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

Most models say NO!


The physics of coronal heating and solar wind acceleration

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


The physics of coronal heating and solar wind acceleration

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


The physics of coronal heating and solar wind acceleration

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


The physics of coronal heating and solar wind acceleration

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


The physics of coronal heating and solar wind acceleration

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

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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