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Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics. Outline: 1. Background: basic ideas about heating & acceleration 2. Corona and solar wind: 3. Chromosphere: acoustic waves & discrete sources?.

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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

slide2
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

slide3
Thanks
  • 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.

George Collins

Stan Owocki

John Kohl

slide4
The solar atmosphere

Heating is everywhere!

the solar wind
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
Heating mechanisms
  • A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)
heating mechanisms1
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?

vs.

waves

shocks

eddies

(“AC”)

twisting

braiding

shear

(“DC”)

vs.

interact with

inhomog./nonlin.

turbulence

reconnection

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

ac versus dc heating
AC versus DC heating?
  • Are they really so very different?
  • Waves cascade into MHD turbulence (eddies), which tends to:
  • 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.

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

Onofri et al. (2006)

slide9
Outline:

1. Background: basic ideas about heating & acceleration

2. Corona and solar wind:

3. Chromosphere: acoustic waves & discrete sources?

  • Alfvénic turbulence
  • Ion-cyclotron resonance
uvcs soho
UVCS / SOHO
  • 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.

slit field of view:

  • Mirror motions select height
  • Instrument rolls indep. of spacecraft
  • 2 UV channels: LYA & OVI
  • 1 white-light polarimetry channel
uvcs results solar minimum 1996 1997
On-disk profiles: T = 1–3 million K

Off-limb profiles: T > 200 million K !

UVCS results: solar minimum (1996-1997)
  • 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 uvcs
The impact of UVCS

UVCS 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)
ion cyclotron waves in the corona
Alfven wave’s oscillating

E and B fields

ion’s Larmor motion around radial B-field

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

lower Z/A

faster diffusion

where do cyclotron waves come from
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).

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

Both scenarios have problems . . .

opaque cyclotron damping 1
“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
“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
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
freq.

horiz. wavenumber

horiz. wavenumber

something else?

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.

How then are the ions heated & accelerated?

  • 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)?

cyclotron resonance-like phenomena

MHD turbulence

an alfv n wave heating model
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
Inter-granular bright points

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

turbulent heating models
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
  • 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:
turbulent heating models1
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
SUPERSONIC coronal heating:

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

M same, u

vs.

SUBSONIC coronal heating:

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

M u

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:

Banaszkiewicz et al. (1998)

why is the fast slow wind fast slow1
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):
slide27
Outline:

1. Background: basic ideas about heating & acceleration

2. Corona and solar wind:

3. Chromosphere: acoustic waves & discrete sources?

  • Alfvénic turbulence
  • Ion-cyclotron resonance
the classical chromosphere
The “classical” chromosphere

Vernazza, Avrett, & Loeser (1981)

solar convection surface waves
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 waves1
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!
slide31
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...
slide32
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 ~ 0.2

Imax/Imin ~ 4

CS model: Uitenbroek (2002)

Imax/Icont ~ 0.8

Imax/Imin ~ 100

slide33
Musielak et al. (1994)

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)
slide34
Exploratory study of discrete sources
  • Cranmer et al. (2006) evolved a simple set of wave/shock energy balance equations in various “non-magnetic” geometries:

vertical flux

vertical “slab”

expanding “cone”

energy-balance temperature

f = 10%

f = 100%

slide35
Exploratory study of discrete sources
  • Simulate thermodynamics of cylindrical slabs / discrete sources (all at z=1800 km)

“CS-like” 1D model

“weak-shock” models

Base:

veach = 0.06 km/s

filling = 1%

veff = 0.006 km/s

Base:

v=0.3 km/s

Base:

v = 0.006 km/s

conclusions
More plasma diagnostics

Better understanding!

Conclusions
  • 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:
  • next-generation UVCS . . . with imaging?
  • high-resolution chromospheric T(x,y,z,t)

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

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