Plasma Physics in the Solar System Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics.

Plasma Physics in the Solar System

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

Plasma Physics in the Solar System Steven Cranmer, February 9, 2009ITC Monday Pizza Lunch

Outline: a whirlwind tour...

Overview

The solar activity cycle & the solar dynamo

Convection: turbulence & MHD waves

Heating the chromosphere (non-magnetic?)

Heating the corona: dominated by closed/twisted fields

Accelerating the solar wind (collisionless heliosphere)

Coronal mass ejections (CMEs)

“Space weather” and the Earth’s magnetosphere


The Sun’s overall structureCore:

• Nuclear reactions fuse hydrogen atoms into helium.

Radiation Zone:• Photons bounce around in the

dense plasma, taking millions of years to escape the Sun.

Convection Zone:• Energy is transported by

boiling, convective motions. Photosphere:

• Photons stop bouncing, and start escaping freely.

Corona:• Outer atmosphere where gas

is heated from ~5800 K to several million degrees!


Where’s the plasma?


Where’s the plasma?

protons

electrons

O+5

O+6


The solar activity cycle

Yohkoh/SXT


The solar dynamo

• Differential rotation shears poloidal (Bθ) fields into the toroidal (Bφ) direction

• Strong fields are buoyant; small kinks are amplified & twisted by Coriolis forces• Diffusion and meridional

circulation bring weak fields to the poles (of opposite polarity)

• Fully self-consistent models still do not exist!


Convection in stellar interiors• If the internal temperature gradient is too steep, a rising

parcel (which remains in pressure balance with its surroundings) will be hotter and less dense. It will continue rising until the local conditions change . . .

• MHD drives the downflows together into faster “plumes.”

Cattaneoet al. 2003


Convection creates waves & turbulence• All solar-type stars with sub-photospheric convection appear to exhibit “p-mode”

acoustic oscillations at (and beneath) their surfaces . . .

• Lighthill (1952) showed how turbulent convection can generate acoustic power.

• These ideas have been more recently generalized to MHD, with flux-tube waves being excited as well: longitudinal (“sausage”) and transverse (“kink”) modes.


Properties of MHD waves• In the absence of a magnetic field, acoustic waves propagate at the sound speed

(restoring force is gas pressure)…

• B-field exerts “magnetic pressure” as well as “magnetic tension” transverse to the field. The characteristic speed of MHD fluctuations is the Alfvén speed…

• Plasma β = (gas pressure / magnetic pressure) ~ (cs/VA)2

“high beta:” fluid motions push the field lines around

“low beta:” fluid flows along “frozen in” field lines


Properties of MHD waves

• Phase speeds: Alfven, fast, slow mode; ● = sound speed, ● = Alfven speed

β = 12 β = 2.4 β = 0.6β = 1.2 β = 0.12

• F/S modes damp collisionally in low corona; Alfven modes are least damped.

• Standard MHD dispersion applies only for frequencies << particle Larmor freq’s.

• For high freq & low β, Alfven mode → “ion cyclotron;” fast mode → “whistler.”


Turbulence• It is highly likely that somewhere in the interior

and/or atmosphere the fluctuations become turbulent and cascade from large to small scales.

• The original Kolmogorov (1941) theory of incompressible fluid turbulence describes a constant energy flux from the largest “stirring” scales to the smallest “dissipation” scales.

• Largest eddies have kinetic energy ~ ρv2 and a turnover time-scale =l/v, so the rate of transfer of energy goes as ρv2/ ~ ρv3/l .

• Dimensional analysis can give the spectrum of energy vs. eddy-wavenumber k: Ek ~ k–5/3


MHD turbulence: two kinds of “anisotropy”

• 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.

• Phenomenological expressions are good at reproducing numerical results:

Z+

Z–Z–

(e.g., Hossain et al. 1995; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Oughton et al. 2006)


The solar photosphere• Photosphere displays convective motion on a broad range of time/space scales:

β << 1

β ~ 1

β > 1


The solar chromosphere


The need for chromospheric heating

Not huge in radial extent, but contains order of magnitude more mass than the layers above . . .


“Traditional” chromospheric heating • Vertically propagating acoustic waves

conserve flux (in a static atmosphere):

• Amplitude eventually reaches Vph and wave-train steepens into a shock-train.

• Shock entropy losses go into heat; only works for periods < 1–2 minutes…

• New idea: “Spherical” acoustic wave fronts from discrete “sources” in the photosphere (e.g., enhanced turbulence or bright points in inter-granular lanes) may do the job with longer periods.

Bird (1964)

~


Time-dependent chromospheres?• 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...


Runaway to the transition region (TR) • Whatever the mechanisms for heating, they must be balanced by radiative losses to

maintain chromospheric T.

• Why then isn’t the corona 109 K? Downward heat conduction smears out the “peaks,” and the solar wind also “carries” away some kinetic energy. Conduction also steepens the TR to be as thin as it is.

• When shock strengths “saturate,” heating depends on density only:


Overview of coronal observations

“Quiet” regions

Active regions

Coronal hole (open)

• Plasma at 106 K emits most of its spectrum in the UV and X-ray . . .


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 between ions and electrons (i.e., friction?) release energy as heat.

Heating Solar wind acceleration!


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.



• Where does the mechanical energy come from?

• How rapidly 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


Reconnection in closed loops• Models of how coronal heating (FX) scales with magnetic flux (Φ) are growing

more sophisticated . . .

• Closed loops: Magnetic reconnection

e.g., Longcope & Kankelborg 1999

Gudiksen & Nordlund (2005)


Turbulence & reconnection: inseparable?• Waves cascade into MHD turbulence (eddies), which

tends to:

Onofri et al. (2006)

e.g., Rappazzo et al. (2008)

» break up into thin reconnecting sheets on its smallest scales.

» accelerate electrons along the field and generate currents.

• Pre-existing 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.


A small fraction of the flux is OPEN

Peter (2001)

Tu et al. (2005)

Fisk (2005)


Open flux tubes “feed” the solar wind

• 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!)


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.”


In situ solar wind: properties• Mariner 2 (1962): first direct confirmation of continuous fast & slow solar wind.

• Uncertainties about which type is “ambient” persisted because measurements were limited to the ecliptic plane . . .

• 1990s: Ulysses left the ecliptic; provided first 3D view of the wind’s source regions.

By ~1990, it was clear the fast wind needs something besides gas pressure to accelerate so fast!

speed (km/s)

Tp (105 K)

Te (105 K)

Tion / Tp

O7+/O6+, Mg/O

600–800

2.4

1.0

> mion/mp

low

300–500

0.4

1.3

< mion/mp

high

fast slow


Ulysses’ view over the poles


Particles are not in “thermal equilibrium”

Helios at 0.3 AU(e.g., Marsch et al. 1982)WIND at 1 AU

(Collier et al. 1996)

WIND at 1 AU(Steinberg et al. 1996)

…especially in the high-speed wind.

mag. field


Particles are not in “thermal equilibrium”• Spectroscopy of the “extended corona”

also reveals collisionless effects.

• The UVCS (Ultraviolet Coronagraph Spectrometer) instrument on SOHO, designed and built at SAO, led to new views of the wind’s acceleration region.

• 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.

kHz frequency Alfven waves

have oscillatingE and B fields...

...that resonate with ion cyclotron

(Larmor) motions?


Fluctuations & turbulence• Fourier transform of B(t), v(t), etc., into frequency:

The inertial range is a “pipeline” for transporting magnetic energy from the large scales to the small scales, where dissipation can occur.

f -1 “energy containing range”

f -5/3

“inertial range”

f -3

“dissipation range”

0.5 Hzfew hours

Mag

net

ic P

ower

• How much of the “power” is due to spacecraft flying through flux tubes rooted on the Sun?


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 holesactive regions

Wang et al. (2000)


Coronal magnetic fields• Coronal B is notoriously difficult to

measure . . .

• Potential field source surface (PFSS) models have been successful in reproducing observed structures and mapping between Sun & in situ.

• Wang & Sheeley (1990) found that flux tubes that expand more (from Sun to SS) have lower wind speeds at 1 AU.

0.4 -1267.5 410 km sss ssu f

Wind SpeedWind Speed

Expansion FactorExpansion Factor

(e.g., Arge & Pizzo 2000)


Why is the fast (slow) wind fast (slow)?

vs.

• What determines how much energy and momentum goes into the solar wind?

Waves & turbulence input from below?

Reconnection & mass input from loops?

• Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models of individual open flux tubes.

• Boundary conditions imposed only at the photosphere (no arbitrary “heating functions”).

• Wind acceleration determined by a combination of magnetic flux-tube geometry, gradual Alfvén-wave reflection, and outward wave pressure.


The inherently filamentary wind . . .

• Solar coronagraphs occult the bright solar disk to view much fainter emission from the extended corona.

• SOHO/LASCO “wavelet” decomposition technique reveals even more detail (Stenborg & Cobelli 2003)

• Still, these features mainly represent only ~10% density variations...


Do “blobs” trace out the slow wind?• The blobs are very low-

contrast and thus may be passive “leaves in the wind.”

Sheeley et al. (1997)


Coronal mass ejections• Coronal mass ejections (CMEs) are magnetically driven eruptions from the Sun

that carry energetic, twisted strands of plasma into the solar system . . .

solar flare

prominence eruption


Coronal mass ejections• Forbes & Priest (1995) and Lin & Forbes (2000) developed a theory of CMEs as

a loss of magnetostatic equilibrium in a twisted “flux rope.”

• The current sheet energizes both the CME (above) and a “two-ribbon flare” (below)


Earth’s magnetosphere

• Blah...


Conclusions

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

• The Sun/heliosphere system is a nearby “laboratory without walls” for studying plasma physics in regimes of parameter space inaccessible in Earth-based laboratories.

• 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.

Plasma Physics in the Solar System Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics.

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