Turbulence in the Solar Corona Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

Turbulence in the Solar Corona

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

Turbulence in the Solar Corona

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

Outline:

1. Observational evidence for waves & turbulent motions

2. The turbulent coronal heating “zoo”

3. “Macroscopic” coronal heating via MHD turbulence

Turbulence in the Solar CoronaSteven R. Cranmer, March 19, 2007

Turbulence & Nonlinear Processes in Astrophysical Plasmas

Turbulent “lower boundary”• Photosphere displays convective motion on a broad range of time/space scales:

β << 1

β ~ 1

β > 1



Wavelike motions in the corona• Remote sensing provides a wide range of direct detection techniques:

• Intensity modulations . . .

• Motion tracking in images . . .

• Doppler shifts . . .

• Doppler broadening . . .

• Radio sounding . . .

SOHO/LASCO (Stenborg & Cobelli 2003)



Indirect evidence (kinetic scales)

• The Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO measures plasma properties of protons, ions, and electrons (1.5 to 10 solar radii).

• UVCS led to new views of the collisionless nature of solar wind acceleration.

Kohl et al. (1995, 1997, 1998, 1999, 2006);Cranmer et al. (1999); Cranmer (2000, 2001, 2002)



Coronal heating mechanisms• So many ideas, taxonomy is needed! (Mandrini et al. 2000; Aschwanden et al. 2001)

• Where does the mechanical energy come from? vs.




• Where does the mechanical energy come from?

• How rapidly is this energy coupled to the coronal plasma?

wavesshockseddies

(“AC”)

vs.

twistingbraiding

shear

(“DC”)vs.






• 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






• 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?

• 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.

• Turbulence may drive “fast” reconnection rates (Lazarian & Vishniac 1999), too.



Highly sheared active regions

• The energy released in AR heating (and flares?) may have been “input” from photospheric footpoint motions, but it can be stored for long times in the shear.

• “Local” shear-driven turbulence may dominate the heating, with amplitudes and rates uncoupled from footpoint properties (van Ballegooijen & Cranmer, in prep).

Hinode/XRT



Open flux tubes: global model

• 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!)



Alfvén wave reflection

refl. coeff =|z+|2/|z–|2

• At photosphere: empirically-determined frequency spectrum of incompressible transverse motions (from statistics of tracking G-band bright points)

• At all larger heights: self-consistent distribution of outward (z–) and inward (z+) Alfvenic wave power, determined by linear non-WKB transport equation:

TR



“Anisotropic” cascade

• Traditional (RMHD-like) nonlinear terms have a cascade energy flux that gives phenomenologically simple heating:

Z+Z–

Z–(e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002)

• We use a generalization based on unequal wave fluxes along the field . . .

• n = 1: usual “golden rule;” we also tried n=2.



“The kitchen sink”• Cranmer, van Ballegooijen, & Edgar (2007) computed self-consistent solutions

of waves & background one-fluid plasma state along a flux tube . . . going from the photosphere to the heliosphere. (astro-ph/0703333)

• 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

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

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



Polar coronal hole model

• Grids of exploratory models led to the optimal choice for lower boundary parameters:

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

• Basal Alfvenic perpendicular amplitude: 0.255 km/s

• Basal turbulent scale: 75 km (G-band bright point size?)

T (K)

reflection coefficient

Transition region is too high (7 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)



Magnetic flux tubes• Vary the magnetic field, but keep lower-boundary parameters fixed.

“active region” fields



Magnetic flux tubes• Vary the magnetic field, but keep lower-boundary parameters fixed.

“active region” fields



Fast/slow wind diagnostics• The wind speed & density at 1 AU behave mainly as observed.

Goldstein et al.(1996)

Ulysses SWOOPS

Cascade efficiency:

n=1

n=2



Fast/slow wind diagnostics

• To compare modeled wave amplitudes with in-situ fluctuations, knowledge about the spectrum is needed . . .

• “e+”: (in km2 s–2 Hz–1 ) defined

as the Z– energy density at 0.4

AU, between 10–4 and 2 x 10–4 Hz, using measured spectra to compute fraction in this band.

Cranmer et al. (2007)

Helios (0.3–0.5 AU)

Tu et al. (1992)



Fast/slow wind diagnostics

• Frozen-in charge states • FIP effect (using Laming’s 2004 theory)

Cranmer et al. (2007)

Ulysses SWICS



Progress towards a robust “recipe”

• Because of the need to determine non-WKB (nonlocal!) reflection coefficients, it may not be easy to insert into global/3D MHD models.

• Doesn’t specify proton vs. electron heating (they conduct differently!)

• Does turbulence generate enough ion-cyclotron waves to heat the minor ions?

• Are there additional (non-photospheric) sources of waves / turbulence / heating for open-field regions? (e.g., flux cancellation events)

(B. Welsch et al. 2004)

Not too bad, but . . .



Conclusions

• Theoretical advances in MHD turbulence are continuing to “feed back” into global models of the solar wind.

• Coronal heating shouldn’t be split into “AC” (waves/turbulence) versus “DC” (reconnection/shear); both exist!

More plasma diagnostics

Better understanding

• SOHO (especially UVCS) has led to fundamentally new views of the extended acceleration regions of the solar wind.

SOHO: 1995–20??• For more information:

http://cfa-www.harvard.edu/~scranmer/



Extra slides . . .



The solar atmosphere

Heating is everywhere . . .

. . . and everything is in motion



Motivations . . .

• “Space weather” can affect satellites, power grids, and astronaut safety.

• Sun’s mass-loss history may have impacted planetary formation / atmospheres.

• The Sun is a “benchmark” for many basic processes in plasma physics.

Solar corona & wind:

• Mass loss affects evolutionary tracks (isochrones, cluster HB/RGB), SN yields.

• Hot-star winds influence ISM abundances & ionization state of Galaxy.

• Spectroscopy of wind lines extragalactic standard candles?

Stellar winds:



• Coronae & Aurorae seen since antiquity . . .

First observations of stellar outflows ?

• “New stars”

1572: Tycho’s supernova

1600: P Cygni outburst (“Revenante of the Swan”)

1604: Kepler’s supernova in “Serepentarius”



• Chromosphere: heating rad. losses

• Photosphere (& most of hot-star wind)

One-page stellar wind physics

• Momentum conservation:

• Energy conservation:

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

• Transition region & low corona

• Extended corona & cool-star wind



The need for both on-disk and off-limb data

• On-disk measurements help reveal basal coronal heating & lower boundary conditions for solar wind.

• Off-limb measurements (in solar wind “acceleration region” ) allow dynamic non-equilibrium plasma states to be followed as the asymptotic conditions at 1 AU are gradually established.

Occultation is required because extended corona is 5 to 10 orders of magnitude less bright than the disk!

Spectroscopy provides detailed plasma diagnostics that imaging

alone cannot.



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.

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



Spectroscopic diagnostics• Off-limb photons formed by both collisional excitation/de-excitation and resonant

scattering of solar-disk photons.

• Profile width depends on line-of-sight component of velocity distribution (i.e., perp. temperature and projected component of wind flow speed).

• If atoms are flow in the same direction as incoming disk photons, “Doppler dimming/pumping” occurs.

• Total intensity depends on the radial component of velocity distribution (parallel temperature and main component of wind flow speed), as well as density.



Doppler dimming & pumping• After H I Lyman alpha, the O VI 1032, 1037 doublet are the next brightest lines in

the extended corona.

• The isolated 1032 line Doppler dims like Lyman alpha.

• The 1037 line is “Doppler pumped” by neighboring C II line photons when O5+ outflow speed passes 175 and 370 km/s.

• The ratio R of 1032 to 1037 intensity depends on both the bulk outflow speed (of O5+ ions) and their parallel temperature. . .

• The line widths constrain perpendicular temperature to be > 100 million K.

• R < 1 implies anisotropy!



Coronal holes: over the solar cycle• Even though large coronal holes have similar outflow speeds at 1 AU (>600

km/s), their acceleration (in O+5) in the corona is different! (Miralles et al. 2001)

Solar minimum:

Solar maximum:



• 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?



Thin tubes merge into supergranular funnels

Peter (2001)

Tu et al. (2005)



Resulting wave amplitude (with damping)• Transport equations solved for 300 “monochromatic” periods (3 sec to 3 days),

then renormalized using photospheric power spectrum.

• One free parameter: base “jump amplitude” (0 to 5 km/s allowed; 3 km/s is best)



Turbulent heating rate

• Solid curve: predicted Qheat for a polar coronal hole.

• Dashed RGB regions: empirical estimates of heating rate of primary plasma (models tuned to match conditions at 1 AU).

• What is really needed are direct measurements of the plasma (atoms, ions, electrons) in the acceleration region of the solar wind!



Streamers: open and/or closed?

• High-speed wind: strong connections to the largest coronal holes

• Low-speed wind: still no agreement on the full range of coronal sources:

hole/streamer boundary (streamer “edge”)streamer plasma sheet (“cusp/stalk”)small coronal holesactive regions (some with streamer cusps)

Wang et al. (2000)



The Need for Better Observations

Even though UVCS/SOHO has made significant advances,

• We still do not understand the physical processes that heat and accelerate the entire plasma (protons, electrons, heavy ions),

• There is still controversy about whether the fast solar wind occurs primarily in dense polar plumes or in low-density inter-plume plasma,

• We still do not know how and where the various components of the variable slow solar wind are produced (e.g., “blobs”).

(Our understanding of ion cyclotron resonance is based essentially on just one ion!)

UVCS has shown that answering these questions is possible, but cannot make the required observations.

Documents

Turbulence in the Solar Corona Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics