Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind

Turbulence andWave Dissipation in the Chromosphere, Corona,

and Solar Wind

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

Outline:

1. Background: basic ideas about heating & acceleration

2. Corona and solar wind:

3. Chromosphere: acoustic waves & discrete sources?

• Alfvénic turbulence

• Ion-cyclotron resonance

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind

Steven R. CranmerSPD Annual Meeting, June 27, 2006

Thanks

George Collins Stan Owocki John Kohl

• Colleagues and collaborators: 1990 to present (including Prize Committee!)

• Experimental physicists who design, build, operate, and calibrate the telescopes and instruments on which we depend.



The solar atmosphere

Heating is everywhere!



The solar wind• 1958: Gene Parker proposed that the hot corona provides enough gas pressure to

counteract gravity and accelerate a “solar wind.” 1962: Mariner 2 confirmed it!

• Momentum conservation:To sustain a wind, /t = 0, and RHS must be naturally “tuned:”

Lambert W function (see Cranmer 2004)



Heating mechanisms• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)



Heating mechanisms• A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)

• Where does the mechanical energy come from?

• How is this energy coupled to the coronal plasma?

• How is the energy dissipated and converted to heat?

wavesshockseddies

(“AC”)

vs.

twistingbraiding

shear

(“DC”)vs.

reconnectionturbulenceinteract with

inhomog./nonlin.

collisions (visc, cond, resist, friction) or collisionless



AC versus DC heating?• Are they really so very different?

• 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 are unstable in a variety of ways to growth of turbulent motions which may dominate the energy loss & particle acceleration.



Outline:








UVCS / SOHO

slit field of view:• Mirror motions select height

• Instrument rolls indep. of spacecraft

• 2 UV channels: LYA & OVI

• 1 white-light polarimetry channel

• SOHO (the Solar and Heliospheric Observatory) was launched in Dec. 1995 with 12 instruments probing solar interior to outer heliosphere.

• The Ultraviolet Coronagraph Spectrometer (UVCS) measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii. (Kohl et al. 1995)

• Combines occultation with spectroscopy to reveal the solar wind acceleration region.



UVCS results: solar minimum (1996-1997 )

On-disk profiles: T = 1–3 million K Off-limb profiles: T > 200 million K !

• The fastest solar wind flow is expected to come from dim “coronal holes.”

• In June 1996, the first measurements of heavy ion (e.g., O+5) line emission in the extended corona revealed surprisingly wide line profiles . . .



The impact of UVCSUVCS has led to new views of the collisionless nature of solar wind acceleration.Key results include:

• The fast solar wind becomes supersonic much closer to the Sun (~2 Rs) than previously believed.

• 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 temperatures. (e.g., Kohl et al. 1997,1998)



• UVCS observations have rekindled theoretical efforts to understand heating and acceleration of the plasma in the (collisionless?) acceleration region of the wind.

Alfven wave’s oscillating

E and B fields

ion’s Larmor motion around radial B-field

• Ion cyclotron waves (10 to 10,000 Hz) suggested as a natural energy source that can be tapped to preferentially heat & accelerate heavy ions.

• Dissipation of these waves produces diffusion in velocity space along contours of ~constant energy in the frame moving with wave phase speed:

Ion cyclotron waves in the corona

lower Z/A

faster diffusion



Where do cyclotron waves come from?

(1) Base generation by, e.g., “microflare” reconnection in the lanes that border convection cells (e.g., Axford & McKenzie 1997).

Both scenarios have problems . . .

(2) Secondary generation: low-frequency Alfven waves may be converted into cyclotron waves gradually in the corona.



“Opaque” cyclotron damping (1)• If high-frequency waves originate only at the base of the corona, extended heating

“sweeps” across the spectrum.

• For proton cyclotron resonance (Tu & Marsch 1997):



“Opaque” cyclotron damping (2)

• However, minor ions can damp the waves as well:

• Something very similar happens to resonance-line photons in winds of O, B, Wolf-Rayet stars!

• Cranmer (2000, 2001) computed “tau” for >2500 ion species.

• If cyclotron resonance is indeed the process that energizes high-Z/A ions, the wave power must be replenished continually throughout the extended corona.



MHD turbulence• It is highly likely that somewhere in the outer solar

atmosphere the fluctuations become turbulent and cascade from large to small scales:

• 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:

Z+Z–

Z–

(e.g., Dmitruk et al. 2002)



But does turbulence generate cyclotron waves?

• Preliminary models say “probably not” in the extended corona. (At least not in a straightforward way!)

• In the corona, “kinetic Alfven waves” with high k heat electrons (T >> T ) when they damp linearly.

• Nonlinear instabilities that locally generate high-freq. waves (Markovskii 2004)?

• Coupling with fast-mode waves that do cascade to high-freq. (Chandran 2006)?

• KAW damping leads to electron beams, further (Langmuir) turbulence, and Debye-scale electron phase space holes, which heat ions perpendicularly via “collisions” (Ergun et al. 1999; Cranmer & van Ballegooijen 2003)?

How then are the ions heated & accelerated?

freq.

horiz. wavenumberhoriz. wavenumber

MHD turbulencecyclotron

resonance-like phenomena

something else?



An Alfvén wave heating model

• Cranmer & van Ballegooijen (2005) built a model of the global properties of incompressible non-WKB Alfvenic turbulence along an open flux tube.

• Background plasma properties (density, flow speed, B-field strength) were fixed empirically; wave properties were modeled with virtually no “free” parameters.

• Lower boundary condition: observed horizontal motions of G-band bright points.



Inter-granular bright points

For the movie, see: http://dot.astro.uu.nl/DOT_movies.html



Inter-granular bright points (close-up)

100–200 km



Thin tubes merge into supergranular funnels

Peter (2001)

Tu et al. (2005)



Turbulent heating models• Cranmer & van Ballegooijen (2005) solved the wave equations & derived heating

rates for a fixed background state.

• New models: (preliminary!) self-consistent solution of waves & background one-fluid plasma state along a flux tube: photosphere to heliosphere

• Ingredients: • Alfven waves: non-WKB reflection, turbulent damping, wave-pressure acceleration

• Acoustic waves: shock steepening, TdS & conductive damping, full spectrum, wave-pressure acceleration

• Rad. losses: transition from optically thick (LTE) to optically thin (CHIANTI + PANDORA)

• Heat conduction: transition from collisional (electron & neutral H) to collisionless “streaming”



Turbulent heating models

• For a polar coronal hole flux-tube:

• Basal acoustic flux: 108 erg/cm2/s (equiv. “piston” v = 0.3 km/s)

• Basal Alfvenic perpendicular amplitude: 0.4 km/s

• Basal turbulent scale: 120 km (G-band bright point size!)

T (K)

reflection coefficient

Transition region is too high (8 Mm instead of 2 Mm), but otherwise not bad . . .



Why is the fast/slow wind fast/slow?

• Several ideas exist; one powerful one relates flux tube expansion to wind speed (Wang & Sheeley 1990). Physically, the geometry determines location of Parker critical point, which determines how the “available” heating affects the plasma:

vs.

SUBSONIC coronal heating:“puffs up” scale height, draws more particles into wind:

M u

SUPERSONIC coronal heating:subsonic region is unaffected. Energy flux has nowhere else to go:

M same, u

Banaszkiewicz et al. (1998)



Why is the fast/slow wind fast/slow?• Compare multiple 1D models in solar-minimum flux tubes with Ulysses 1st polar

pass (Goldstein et al. 1996):



Outline:








The “classical” chromosphereVernazza, Avrett, & Loeser (1981)



Solar convection & surface waves• Cool stars with sub-photospheric convection undergo p-mode oscillations:

• Lighthill (1952) showed how turbulent motions generate acoustic power; more recently generalized to MHD. . . .

• The atmosphere is dynamic!

Cattaneo et al. (2003)

For the movie, see: http://flash.uchicago.edu/~cattaneo/



Solar convection & surface waves• Cool stars with sub-photospheric convection undergo p-mode oscillations:

• Lighthill (1952) showed how turbulent motions generate acoustic power; more recently generalized to MHD. . . .

• The atmosphere is dynamic!



Time-dependent models• Carlsson & Stein (1992, 1994, 1997, 2002, etc.) produced 1D time-dependent

radiation-hydrodynamics simulations of vertical shock propagation and transient chromospheric heating. Wedemeyer et al. (2004) continued to ~3D...



Problems with existing models . . .• The time-steady models (both semi-empirical and with “weak-shock theory”)

don’t reproduce the observed dynamics.

• 1D “CS” time-dependent models are too intermittent (too-strong shocks alternate with regions of no heating at all).

Obs: Liu (1974)Imax/Icont ~ 0.2Imax/Imin ~ 4

CS model: Uitenbroek (2002)Imax/Icont ~ 0.8Imax/Imin ~ 100



Ingredients of a “better” solution?

• Acoustic waves from small discrete “sources” in the photosphere (from, e.g., enhanced turbulence in intergranular lanes)

• High frequencies that are difficult to detect observationally (especially if they belong to ~horizontally propagating waves)

Musielak et al. (1994)



Exploratory study of discrete sources

vertical “slab” expanding “cone”

f = 10% f = 100%

vertical flux

energy-balance temperature

• Cranmer et al. (2006) evolved a simple set of wave/shock energy balance equations in various “non-magnetic” geometries:



Exploratory study of discrete sources• Simulate thermodynamics of cylindrical slabs / discrete sources (all at z=1800 km)

Base:v=0.3 km/s

Base:v = 0.006 km/s

“CS-like” 1D model

“weak-shock” models

Base:

veach = 0.06 km/s

filling = 1%

veff = 0.006 km/s



Conclusions

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

• Ultraviolet coronagraph spectroscopy has led to fundamentally new views of the acceleration regions of the solar wind.

• The surprisingly extreme plasma conditions in

solar coronal holes (T ion >> Tp > Te ) have guided theorists to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics.

• Future observational programs are needed:

More plasma diagnostics

Better understanding!

• next-generation UVCS . . . with imaging?

• high-resolution chromospheric T(x,y,z,t)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind

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