Transcript No Slide Title

Applications of MHD Turbulence
to Modeling Solar (and Stellar)
Coronal Heating and Winds
Steven R. Cranmer
Harvard-Smithsonian
Center for Astrophysics
Applications of MHD Turbulence
1. Turbulence as a driver of coronal heating & wind acceleration
to Modeling Solar (and Stellar)
• Results of recent modeling (“successes”)
Coronal
Heating and(“failures”)
Winds
• Open issues
Outline:
2. Kinetic partitioning to protons, electrons, and ions
• Ion cyclotron resonance?
• A laundry list of other possibilities . . .
Steven R. Cranmer
Harvard-Smithsonian
Center for Astrophysics
My own history . . .
1992–1996:
hot star theory
2004–now:
Why is the whole plasma
heated & accelerated?
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
1996–1999:
UVCS data analysis
1999–2004:
Why are heavy ions
preferentially heated
& accelerated?
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The Debate in ’08
• Two broad classes of models have evolved that attempt to self-consistently answer
the question: How are fast and slow wind streams accelerated?
Wave/Turbulence-Driven
(WTD) models
Reconnection/Loop-Opening
(RLO) models
Opinionated “position paper:” arXiv: 0804.3058
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
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!)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Alfvén wave reflection
• 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:
refl. coeff =
|z+|2/|z–|2
TR
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Wave / Turbulence-Driven models
• Cranmer & van Ballegooijen (2005) solved the transport equations for a grid of
“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)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Anisotropic cascade and dissipation
• Traditional (RMHD-like) nonlinear terms have a cascade
energy flux that gives phenomenologically simple heating:
• We used a generalization based on unequal wave fluxes along the field . . .
Z–
Z+
• n = 1: usual “golden rule;” we also tried n=2.
Z–
(e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou &
Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
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.
• 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
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Results: turbulent heating & acceleration
T (K)
Ulysses
SWOOPS
Goldstein et al.
(1996)
reflection
coefficient
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Results: other fast/slow diagnostics
• The wind speed is anticorrelated with flux-tube expansion . . .
“active region”
fields
Cascade efficiency:
n=1
n=2
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Results: in situ turbulence
• 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.
Helios (0.3–0.5 AU)
Tu et al. (1992)
Cranmer et al. (2007)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Results: heavy ion properties
• Frozen-in charge states
• FIP effect
(using Laming’s 2004 theory)
Ulysses SWICS
Cranmer et al. (2007)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Aside: application to T Tauri winds
• Recent work has extended these models to accretion-driven winds of young,
solar-type stars (Cranmer 2008, arXiv:0808.2250)
• Accretion proceeds by free-falling inhomogeneous clumps impacting the star, and
generating MHD waves on the surface (like solar Moreton/EIT waves?).
• These “extra” waves give input orders of magnitude more energy into an MHD
cascade, and can give rise to stellar winds with dM/dt up to ~10–8 M/yr !
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Turbulent mass loss
solar parameter study
“proper” solar models
T Tauri models
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Turbulent mass loss
solar parameter study
“proper” solar models
T Tauri models
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
New result: solar wind “entropy”
• Pagel et al. (2004) found ln(T/nγ–1) (at 1 AU) to be strongly correlated with both
wind speed and the O7+/O6+ charge state ratio.
(empirical γ = 1.5)
• The Cranmer et al. (2007) models do a good job of reproducing ACE/SWEPAM
entropy data (blue region) & Ulysses charge state trends (brown regions).
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The correlation length: apples to oranges?
Smith et al. (2001): Voyager & Omnitape
Helios & other 1 AU…
Cranmer et al. (2007) L
(pole, equator)
Joe Borovsky’s
“walls” (ACE)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Problem: too hot at 1 AU ?
standard
(n=1) model
rapid-quenching
(n=2) model
Ulysses Tp
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Electron heat conduction
• At ~1 AU, the modeled T(r) is a
balance between adiabatic cooling &
collisionless conduction.
• We’ve used Hollweg (1974):
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Progress towards a robust “recipe”
Not too bad, but . . .
• The turbulent dissipation rate scaling is approximate; needs refining?
• 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)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Multi-fluid collisionless effects?
O+5
O+6
protons
electrons
Polar coronal hole
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Preferential ion heating & acceleration
• 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 (10–10,000 Hz)
suggested as a “natural” energy source that
can be tapped to preferentially heat &
accelerate heavy ions.
Alfven wave’s
oscillating
E and B fields
ion’s Larmor
motion around
radial B-field
lower Z/A
faster diffusion
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Evidence for ion cyclotron resonance
Indirect:
• UVCS (and SUMER) remote-sensing data
• Helios (0.3–1 AU) proton velocity distributions (Tu & Marsch 2002)
• Wind (1 AU): more-than-mass-proportional heating (Collier et al. 1996)
(more) Direct:
• Leamon et al. (1998): at ω ≈ Ωp, magnetic helicity shows deficit of protonresonant waves in “diffusion range,” indicative of cyclotron absorption.
• Jian, Russell, et al. (2008) (COSPAR poster): STEREO shows isolated bursts
of ~monochromatic waves with ω ≈ 0.1–1 Ωp
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
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).
Problems:
• Incompatible with radio IPS power spectra
(Hollweg 1999)
• Minor ions would damp waves before they
could resonate with O5+ or protons (Cranmer
2000, 2001)
(2) Secondary generation: low-frequency
Alfven waves may be converted into
cyclotron waves gradually in the corona.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Charge/mass dependence
• Assuming there is enough “replenishment” (via, e.g., turbulent cascade?) to
counteract local damping, the degree of ion heating depends on the assumed
distribution of wave power vs. frequency (or parallel wavenumber).
• A simple assumption of a power-law vs. parallel wavenumber shows that the
charge-to-mass dependence of the heating may be increasing or decreasing...
UVCS O VI (O+5)
measurement was used to
normalize the heating rate.
Mg X (Mg+9) showed a
much narrower line
profile (despite being so
close to O+5 in its chargeto-mass ratio)!
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Anisotropic MHD cascade
• Can MHD turbulence generate ion cyclotron waves? Many models say no!
• Simulations & analytic models
predict cascade from small to
large k ,leaving k ~unchanged.
“Kinetic Alfven waves” with
large k do not necessarily
have high frequencies.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Anisotropic MHD cascade
• Can MHD turbulence generate ion cyclotron waves? Many models say no!
• Simulations & analytic models
predict cascade from small to
large k ,leaving k ~unchanged.
“Kinetic Alfven waves” with
large k do not necessarily
have high frequencies.
• In a low-beta plasma, KAWs
are Landau-damped, heating
electrons preferentially!
• Cranmer & van Ballegooijen
(2003) modeled the anisotropic
cascade with advection &
diffusion in k-space and found
some k “leakage” . . .
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
An advection-diffusion cascade model
• The Cranmer & van Ballegooijen (2003) advection-diffusion equation:
• “Critical balance” (Higdon/Goldreich/Sridhar/others) was built into the eqns . . .
• Rapid decay to higher k║ is contained in f(x). Cho et al. (2002) examined various
functional forms as fits to numerical simulations (not enough dynamic range?).
• CvB2003 solved an approximate version of the advection-diffusion eqn to get:
• Key parameter: (β/γ). van Ballegooijen (1986) argued for β/γ ≈ 1 (random walk)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Missed KAW opportunities...?
• Hidden in the CvB 2003 paper were a few results that could have been highlighted
better... e.g., a prediction for the KAW k┴–7/3 inertial range slope, and:
Bale et al. (2005)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Advection-diffusion cascade results
• Taking the anisotropic spectrum and using linear Maxwell-Vlasov dissipation rates,
the ratio of proton vs. electron heating can be derived as a function of position in
the fast solar wind (using the Cranmer & van Ballegooijen 2005 model):
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
New SUMER constraints
• Landi & Cranmer (2009, arXiv:0810.0018)
analyzed a set of SUMER line widths that
suggest preferential ion heating at r ≈ 1.05 to
1.2 Rs in coronal holes.
• We produced and compared two independent
Te
models:
(1) Solve a semi-empirical ion heating equation with an arbitrary
normalization for the ion cyclotron wave power. (Each ion is modeled
independently of the others.) Normalization varied till agrees w/ data.
(2) Use the Cranmer & van Ballegooijen (2003, 2005) models to predict the
ion cyclotron wave power spectrum at a given height.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Example heating model for O VI
• How well do we really know the proton temperature? Vary as free parameter...
UVCS
constraints
SUMER
constraints
• The yellow/green
curves seem to do
the best... they
imply strong
Coulomb collisional
coupling at the
SUMER heights!
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Compare all ions at r = 1.069 Rs
• Colors: different choices for proton temperature. Black curves: theoretical resonant
spectra from Cranmer & van Ballegooijen (2003) advection-diffusion model.
y-axis:
wave power
needed to
produce ion
heating
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Power increase at large Z/A ?
• This is not predicted by simple turbulent cascade models.
• If it is real, it might be:
• Increased wave power from plasma instabilities that are centered
around either the alpha (Z/A = 0.5) or proton (Z/A = 1) resonances
(Markovskii 2001; Zhang 2003; Laming 2004; Markovskii et al.
2006) ?
• Predicted “spectral flattening” due to oblique propagation and/or
compressibility effects in dispersion relation? Harmon & Coles
(2005) invoked these effects to model the observed IPS density
fluctuation spectra.
• A kind of “bottleneck effect” wherein the power piles up near the
dissipation scale, due to nonlocal interactions between disparate
scales in k-space (Falkovich 1994; Biskamp et al. 1998) ???
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
So does turbulence generate cyclotron waves?
Directly from the linear waves? Probably not! How then are the ions heated
and accelerated?
• When MHD turbulence cascades to small perpendicular scales, the small-scale shearing
motions may be able to generate ion cyclotron waves (Markovskii et al. 2006).
• Dissipation-scale current sheets may preferentially spin up ions (Dmitruk et al. 2004)?
• If MHD turbulence exists for both Alfvén and fast-mode waves, the two types of waves
can nonlinearly couple with one another to produce high-frequency ion cyclotron
waves (Chandran 2006).
• 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 waveparticle interactions and heat ions (Voitenko & Goossens 2006; Wu & Yang 2007).
• 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).
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
What to do next?
• Many of the proposed mechanisms
haven’t been tested with realistic
coronal plasma conditions! (i.e.,
plasma beta, driving wave amplitudes
& frequencies, etc.)
• The mechanisms of “parallel cascade”
in low-beta plasmas need to be more
fully worked out! (the tail that wags
the dog?) The CvB (2003) “advectiondiffusion” model is a crass local
approx. to a truly nonlocal effect.
• Explore relationships between
turbulence and reconnection theory...
• Better measurements are needed: both
remote and in situ!
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Future missions
• Solar Probe Plus (in to ~20 Rs) is finally
moving forward.
• CPEX (Coronal Physics Explorer) currently
in Phase A concept study: next-generation
UVCS & LASCO, capable of probing dozens
of ions in coronal holes at UVCS heights!
• More traditional “solar
physics” missions (SDO)
will put new constraints on
physics of reconnection &
turbulent heating!
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Conclusions
• UV coronagraph spectroscopy has led to
fundamentally new views of the collisionless
acceleration regions of the solar wind.
• Theoretical advances in MHD turbulence
continue to feed back into global models of
coronal heating and the solar wind.
• The extreme plasma conditions in coronal
holes (Tion >> Tp > Te ) have guided us to
discard some candidate processes, further
investigate others, and have cross-fertilized
other areas of plasma physics & astrophysics.
• Next-generation observational programs are
needed for conclusive “constraints.”
For more information: http://www.cfa.harvard.edu/~scranmer/
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Extra slides . . .
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The solar wind: discovery
• 1860–1950: Evidence slowly builds for outflowing magnetized plasma in the
solar system:
• solar flares  aurora, telegraph snafus, geomagnetic storms
• comet ion tails point anti-sunward (no matter comet’s motion)
• 1958: Eugene Parker proposed that the hot corona provides enough gas pressure
to counteract gravity and accelerate a “solar wind.”
• 1962: Mariner 2 provided direct confirmation.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
In situ solar wind: properties
• Mariner 2 detected two phases of solar wind: slow (mostly) + fast streams
• Uncertainties about which type is “ambient”
persisted because measurements were limited to
the ecliptic plane . . .
• Ulysses left the ecliptic; provided 3D view of the
wind’s source regions.
• Helios saw strong departures from Maxwellians.
fast
slow
600–800
300–500
Tp (105 K)
2.4
0.4
Te (105 K)
1.0
1.3
> mion/mp
< mion/mp
low
high
speed (km/s)
Tion / Tp
O7+/O6+, Mg/O
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
By ~1990, it was clear the fast
wind needs something besides
gas pressure to accelerate so fast!
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Solar wind: connectivity to the corona
• 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 holes
active regions
Wang et al. (2000)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The coronal heating problem
• We still don’t understand the physical processes responsible for heating up the
coronal plasma.
A lot of the heating occurs in a narrow “shell.”
• Most suggested ideas involve 3 general steps:
1. Churning convective motions that tangle up
magnetic fields on the surface.
2. Energy is stored in tiny twisted & braided
magnetic flux tubes.
3. Collisions (particle-particle? wave-particle?)
release energy as heat.
Heating
Solar wind acceleration!
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Coronal heating mechanisms
• So many ideas, taxonomy is needed!
(Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
waves
shocks
eddies
• How rapidly is this energy
coupled to the coronal
plasma?
(“AC”)
interact with
inhomog./nonlin.
vs.
twisting
braiding
shear
(“DC”)
turbulence
reconnection
• How is the energy dissipated
and converted to heat?
collisions (visc, cond, resist, friction) or collisionless
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Reconnection / Loop-Opening models
• 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 churning . . .
• Open-field regions show coronal jets (powered by
reconnection?) that contribute to the wind mass flux.
Fisk
(2005)
Hinode/XRT (X-ray)
http://xrt.cfa.harvard.edu
STEREO/EUVI (195 Å)
courtesy S. Patsourakos
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Reconnection / Loop-Opening models
• Emerging loops inject both mass and Poynting flux into open-field regions.
• Feldman et al. (1999) found correlation between loop-size & coronal temperature.
• Fisk et al. (1999), Fisk (2003), Gloeckler et al. (2003), Schwadron & McComas
(2003), Schwadron et al. (2005) worked out the solar wind implications . . .
Ulysses SWICS
Fisk (2003) theory
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Departures from thermal equilibrium
• UVCS/SOHO observations rekindled theoretical efforts to understand collisionless
heating and acceleration effects in the extended corona.
• Ion cyclotron waves (10–10,000 Hz)
suggested as a “natural” energy source that
can be tapped to preferentially heat &
accelerate heavy ions.
MHD turbulence
something
else?
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
Alfven wave’s
oscillating
E and B fields
ion’s Larmor
motion around
radial B-field
cyclotron resonancelike phenomena
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The extended solar atmosphere . . .
Heating is everywhere . . .
. . . and everything is in motion
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Waves? Start in the photosphere . . .
• Photosphere displays convective motion on a broad range of time/space scales:
β << 1
β~1
β>1
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The need for extended heating
• The basal coronal heating problem is not yet
solved, but the field seems to be “homing in on”
the interplay between emerging flux, reconnection,
turbulence, and helicity (shear/twist).
X
• Above ~2 Rs , some other kind of energy deposition is needed in order to . . .
» accelerate the fast solar wind
(without
artificially boosting mass loss and peak Te ),
» produce the proton/electron temperatures
seen in situ (also magnetic moment!),
» produce the strong preferential heating and
temperature anisotropy of ions (in the
wind’s acceleration region) seen with UV
spectroscopy.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Exploring the extended corona
• “Off-limb” measurements (in the 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.
• The Ultraviolet Coronagraph Spectrometer
(UVCS) on SOHO combines these features to
measure plasma properties of coronal protons,
ions, and electrons between 1.5 and 10 solar radii.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
The UVCS instrument on SOHO
• 1979–1995: Rocket flights and Shuttle-deployed Spartan 201 laid groundwork.
• 1996–present: 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!
slit field of view:
• Mirror motions select height
• UVCS “rolls” independently of spacecraft
• 2 UV channels: LYA (120–135 nm)
OVI (95–120 nm + 2nd ord.)
• 1 white-light polarimetry channel
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
UVCS results: over the poles (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 . . .
On-disk profiles: T = 1–3 million K
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
Off-limb profiles: T > 100 million K !
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Waves: remote-sensing techniques
The following techniques are direct… (UVCS ion heating was more indirect)
• Intensity modulations . . .
• Motion tracking in images . . .
Tomczyk et al.
(2007)
• Doppler shifts . . .
• Doppler broadening . . .
• Radio sounding . . .
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Particles are not in “thermal equilibrium”
…especially in the
high-speed wind.
mag.
field
WIND at 1 AU
(Steinberg et al. 1996)
WIND at 1 AU
(Collier et al. 1996)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
Helios at 0.3 AU
(e.g., Marsch et al. 1982)
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
“Opaque” cyclotron damping (1)
• If high-frequency waves originate only at the base of the corona, extended heating
must “sweep” across the frequency spectrum.
• For proton cyclotron resonance only (Tu & Marsch 1997):
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
“Opaque” cyclotron damping (2)
• However, minor ions can damp the waves as well:
• Something very similar happens to
resonance-line photons in winds of
super-luminous massive 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.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Aside: two other (non-cyclotron) ideas . . .
• Kinetic Alfven waves with nonlinear
amplitudes generate E fields that can
scatter ions non-adiabatically and heat
them perpendicularly (Voitenko &
Goossens 2004).
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
• If the corona is filled with “thin” MHD
shocks, an ion’s upstream v becomes
oblique to the downstream field. Some
gyro-motion arises before the ion
“knows” it! (Lee & Wu 2000).
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Overview of “in situ” fluctuations
• Fourier transform of B(t), v(t), etc., into frequency:
Magnetic Power
f -1 “energy containing range”
• How much of the “power”
is due to spacecraft flying
through flux tubes rooted
on the Sun?
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.
f -3
“dissipation
range”
few hours
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
0.5 Hz
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Synergy with other systems
• T Tauri stars: observations suggest a “polar wind” that scales with the mass
accretion rate. Cranmer et al. (2007) code is being adapted to these systems...
• Pulsating variables: Pulsations “leak” outwards as non-WKB waves and shocktrains. New insights from solar wave-reflection theory are being extended.
• AGN accretion flows: A similarly collisionless (but pressure-dominated) plasma
undergoing anisotropic MHD cascade, kinetic wave-particle interactions, etc.
Freytag et al. (2002)
Matt & Pudritz (2005)
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
Emission lines as plasma diagnostics
• Many of the lines seen by UVCS are formed by resonantly scattered disk photons.
• If profiles are Doppler shifted up or down in wavelength (from the known rest
wavelength), this indicates the bulk flow speed along the line-of-sight.
• The widths of the profiles tell us about random motions along the line-of-sight
(i.e., temperature)
• The total intensity (i.e., number of
photons) tells us mainly about the
density of atoms, but for resonant
scattering there’s also another
“hidden” Doppler effect that tells
us about the flow speeds
perpendicular to the line-of-sight.
• If atoms are flow in the same direction as incoming
disk photons, “Doppler dimming/pumping” occurs.
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence
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!
Applications of MHD Turbulence to Modeling
Solar (and Stellar) Coronal Heating and Winds
S. R. Cranmer, October 2008, Santa Fe, NM
Plasma Dissipation & MHD Turbulence