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Plasma Unbound: New Insights into Heating the Solar Corona and Accelerating the Solar Wind Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics Outline: 1. Brief historical background 2. Solar wind acceleration: waves vs. reconnection?

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plasma unbound new insights into heating the solar corona and accelerating the solar wind

Plasma Unbound:New Insights into Heating the Solar Corona and Accelerating the Solar Wind

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

plasma unbound new insights into heating the solar corona and accelerating the solar wind2

Outline:

1. Brief historical background

2. Solar wind acceleration: waves vs. reconnection?

3. Successes of wave/turbulence models (1D → 3D)

4. The Young Sun: an accretion-powered stellar wind!

Plasma Unbound:New Insights into Heating the Solar Corona and Accelerating the Solar Wind

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

motivations
Motivations

Solar corona & solar wind:

  • Space weather can affect satellites, power grids, and astronaut safety.
  • The Sun’s mass-loss & X-ray history impacted planetary formation and atmospheric erosion.
  • The Sun is a “laboratory without walls” for many basic processes in physics, at regimes (T, P) inaccessible on Earth!
  • plasma physics
  • nuclear physics
  • non-equilibrium thermodynamics
  • electromagnetic theory
the extended solar atmosphere
The extended solar atmosphere

Everywhere one looks,

the plasma is

“out of equilibrium!”

too brief history

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.”
Too-brief history
  • Total eclipses let us see the vibrant outer solar corona: but what is it?
  • 1870s: spectrographs pointed at corona:
  • 1930s: Lines identified as highly ionized ions: Ca+12 , Fe+9 to Fe+13 it’s hot!
  • Fraunhofer lines (not moon-related)
  • unknown bright lines
the solar corona
The solar corona
  • Plasma at 106 K emits most of its spectrum in the UV and X-ray . . .

Coronal hole (open)

“Quiet” regions

Active regions

slide7

The coronal heating problem

  • We still do not 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.Something releases this energy as heat.

Particle-particle collisions?

Wave-particle interactions?

“I think you should be more explicit here in step two.”

a small fraction of magnetic flux is open
A small fraction of magnetic flux is OPEN

Peter (2001)

Fisk (2005)

Tu et al. (2005)

in situ solar wind properties
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.
  • 1970s: Helios (0.3–1 AU). 2007: Voyagers @ term. shock.

fast

slow

300–500

high

chaotic

all ~equal

more low-FIP

speed (km/s)

density

variability

temperatures

abundances

600–800

low

smooth + waves

Tion >> Tp > Te

photospheric

what processes drive solar wind acceleration
What processes drive solar wind acceleration?

Two broad paradigms have emerged . . .

  • Wave/Turbulence-Driven (WTD) models, in which flux tubes “stay open”
  • Reconnection/Loop-Opening (RLO) models, in which mass & energy are injected from closed-field regions.

vs.

  • There’s 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 evolving and making new connections.
  • Open-field regions show frequent coronal jets (SOHO, Hinode/XRT).
waves turbulence in the photosphere
Waves & turbulence in the photosphere
  • Helioseismology: direct probe of wave oscillations below the photosphere (via modulations in intensity & Doppler velocity)
  • How much of that wave energy “leaks” up into the corona & solar wind?

Still a topic of vigorous debate!

  • Measuring horizontal motions of magnetic flux tubes is more difficult . . . but may be more important?

splitting/merging

torsion

0.1″

longitudinal flow/wave

bending

(kink-mode wave)

waves in the corona
Waves in the corona
  • Remote sensing provides several direct (and indirect) detection techniques:
  • Intensity modulations . . .
  • Motion tracking in images . . .
  • Doppler shifts . . .
  • Doppler broadening . . .
  • Radio sounding . . .

SOHO/LASCO (Stenborg & Cobelli 2003)

waves in the corona13
Waves in the corona
  • Remote sensing provides several direct (and indirect) detection techniques:
  • Intensity modulations . . .
  • Motion tracking in images . . .
  • Doppler shifts . . .
  • Doppler broadening . . .
  • Radio sounding . . .

Tomczyk et al. (2007)

waves in the corona14
Waves in the corona
  • Remote sensing provides several direct (and indirect) detection techniques:
  • The Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO has measured plasma properties of protons, ions, and electrons in low-density collisionless regions of the corona (1.5 to 10 solar radii).
  • Ion cyclotron waves (10–10,000 Hz) have been suggested as a “natural” energy source that can be tapped to preferentially heat & accelerate the heavy ions, as observed.
in situ fluctuations turbulence
In situ fluctuations & turbulence
  • Fourier transform of B(t), v(t), etc., into frequency:

f -1 “energy containing range”

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.

Magnetic Power

f -3“dissipation range”

few hours

0.5 Hz

waves turbulence the big picture
Waves & turbulence: the big picture
  • Various observations can be “stitched together” to form a reasonably consistent picture of Alfvénic fluctuations from photosphere to heliosphere . . .
  • Some kind of damping is needed (e.g., Cranmer & van Ballegooijen 2005)
turbulent dissipation coronal heating
Turbulent dissipation = coronal heating?
  • In hydrodynamics, von Kármán, Howarth, & Kolmogorov worked out cascade energy flux via dimensional analysis:
  • In MHD, cascade is possible only if there are counter-propagating Alfvén waves…

(“cascade efficiency”)

Z–

Z+

  • n = 1: an approximate “golden rule” from theory
  • Caution: this is an order-of-magnitude scaling!

(e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002; Oughton et al. 2006)

Z–

self consistent models along a flux tube
Self-consistent models along a flux tube
  • 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)

magnetic flux tubes expansion factors
Magnetic flux tubes & expansion factors

A(r) ~ B(r)–1 ~ r2 f(r)

(Banaszkiewicz et al. 1998)

Wang & Sheeley (1990) defined the expansion factor between “coronal base” and the source-surface radius ~2.5 Rs.

TR

polar coronal holes f ≈ 4

quiescent equ. streamers f ≈ 9

“active regions” f ≈ 25

results of wave turbulence models
Results of wave/turbulence models
  • Cranmer et al. (2007) computed self-consistent solutions for waves & background plasma along flux tubes going from the photosphere to the heliosphere.
  • Only free parameters:superradial flux tube expansion & photospheric wave properties. (No arbitrary “coronal heating functions” were used.)
  • Self-consistent coronal heating comes from gradual Alfvén wave reflection & turbulent dissipation.
  • Mass flux determined by allowing transition region to “float” until energy balance is stable.
  • Flux-tube geometry determines where Parker’s “critical point” occurs.
  • Low rcrit: supersonic heating → fast wind
  • High rcrit: subsonic heating → slow wind

(Leer & Holzer 1980; Pneuman 1980)

cranmer et al 2007 other results
Cranmer et al. (2007): other results

Wang & Sheeley (1990)

ACE/SWEPAM

ACE/SWEPAM

Ulysses

SWICS

Ulysses

SWICS

Helios

(0.3-0.5 AU)

where do we go from here
Where do we go from here?

3D global MHD models

Real-time

“space weather” predictions?

Self-consistent WTD models

Z–

Z+

Z–

how is wave reflection treated
How is wave reflection treated?
  • 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:

3e–5

1e –4

3e –4

0.001

0.003

0.01

0.03

0.1

0.3

0.9

“refl. coef” = |z+|/|z–|

TR

reflection in simple limiting cases
Reflection in simple limiting cases . . .
  • Many earlier studies solved these equations numerically (e.g., Heinemann & Olbert 1980; Velli et al. 1989, 1991; Barkhudarov 1991; Cranmer & van Ballegooijen 2005).
  • As wave frequency ω→ 0, the superposition of inward & outward waves looks like a standing wave pattern:

phase shift → 0

  • As wave frequency ω→∞, reflection becomes weak . . .

phase shift → – π/2

  • Cranmer (2010) presented approximate “bridging” relations between these limits to estimate the non-WKB reflection without the need to integrate along flux tubes.
  • See also Chandran & Hollweg (2009); Verdini et al. (2010) for other approaches!
results numerical integration vs approx
Results: numerical integration vs. approx.

3e–5

1e –4

3e –4

0.001

0.003

0.01

0.03

0.1

0.3

0.9

“refl. coef” = |z+|/|z–|

TR

3e–5

1e –4

3e –4

0.001

0.003

0.01

0.03

0.1

0.3

0.9

ω0

results coronal heating rates
Results: coronal heating rates
  • Each “row” of the contour plot contributes differently to the total, depending on the power spectrum of Alfven waves . . .

Tomczyk & McIntosh (2009)

f –5/3

Cranmer & van Ballegooijen (2005)

observational constraints on heating rates

slide27

How did we get here?

  • The Young Sun:
  • Kelvin-Helmholz contraction: An ISMcloud fragment becomes a “protostar;” gravitational energy is converted to heat.
  • Hayashi track: protostar reaches approx. hydrostatic equilibrium, but slower gravitational contraction continues. Observed as the T Tauri phase.
  • Henyey track: Tcore reaches ~107 K and hydrogen burning begins to dominate → ZAMS.
t tauri stars active accretion outflows
T Tauri stars: active accretion & outflows
  • T Tauri stars exhibit signatures of disk accretion (outer parts), “magnetospheric accretion streams” & X-ray corona (inner parts), and dense(polar?)outflows.
  • Nearly every observational diagnostic varies in time, sometimes with stellar rotation, but often more irregularly.

(Romanova et al. 2007)

(Matt & Pudritz 2005, 2008)

accretion driven t tauri winds
Accretion-driven T Tauri winds
  • Cranmer (2008, 2009) extended the solar wave/turbulence models to the outer atmospheres of young, solar-type stars.
  • The impact of inhomogeneous “clumps” on the stellar surface generates MHD waves that propagate horizontally (like solar Moreton & EIT waves!).
  • These “extra” waves input orders of magnitude more energy into a turbulent MHD cascade, and can give rise to stellar winds with dM/dt up to 106 times solar!
accretion driven t tauri winds30
Accretion-driven T Tauri winds
  • Results: wind mass loss rate increases ~similarly with the accretion rate.
  • For high enough densities, radiative cooling “kills” the coronal heating!
conclusions
Conclusions
  • Theoretical advances in MHD turbulence are helping improve our understanding about coronal heating, solar wind acceleration, and other astrophysical environments.
  • It is becoming easier to include “real physics” in 1D → 2D → 3D models of the complex Sun-heliosphere system.
  • We still do not have complete enough observational constraintsto be able to choose between competing theories…
  • but progress on all fronts is being made.

vs.

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

slide33

Results: turbulent heating & acceleration

T (K)

Ulysses SWOOPS

Goldstein et al.

(1996)

reflection coefficient

results flux tubes critical points
Results: flux tubes & critical points
  • Wind speed is ~anticorrelated with flux-tube expansion & height of critical point.

Cascade efficiency:

n=1

n=2

rcrit

rmax

(where T=Tmax)

results heavy ion properties
Results: heavy ion properties
  • Frozen-in charge states
  • FIP effect (using Laming’s 2004 theory)

Ulysses SWICS

Cranmer et al. (2007)

results in situ 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)

results scaling with magnetic flux density

B ≈ 1500 G (universal?)

f ≈ 0.002–0.1

B ≈ f B ,

.

.

.

.

.

.

  • Thus,

. . . and since Q/Q ≈ B/B , the turbulent heating in the low corona scales directly with the mean magnetic flux density there (e.g., Pevtsov et al. 2003; Schwadron et al. 2006; Kojima et al. 2007; Schwadron & McComas 2008).

Results: scaling with magnetic flux density
  • Mean field strength in low corona:
  • If the regions below the merging height can be treated with approximations from “thin flux tube theory,” then:

B ~ ρ1/2

Z± ~ ρ–1/4

L┴ ~ B–1/2

results solar wind entropy
Results: 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 (black points) do a reasonably good job of reproducing ACE/SWEPAM entropy data (blue).
  • Because entropy should be conserved in the absence of significant heating, the quantity measured at 1 AU may be a long-distance “proxy” for the near-Sun locations of strong coronal heating.
slide39

X

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).
  • 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.
slide40

Multi-fluid collisionless effects!

O+5

O+6

protons

electrons

coronal holes / fast wind

(effects also present in slow wind)

the uvcs instrument on soho

Mirror motions select height

  • UVCS “rolls” independently of spacecraft
  • 2 UV channels:
  • 1 white-light polarimetry channel

LYA (120–135 nm)

OVI (95–120 nm + 2nd ord.)

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:

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 Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii.
  • In June 1996, the first measurements of heavy ion (e.g., O+5) line emission in the extended corona revealed surprisingly wide line profiles . . .
coronal holes the impact of uvcs
Coronal holes: the impact of UVCS

UVCS/SOHO has led to new views of the acceleration regions of the solar wind.

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. 1998, 2006)
slide44

Alfven wave’s oscillating

E and B fields

ion’s Larmor motion around radial B-field

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.

lower Z/A

faster diffusion

slide45

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 proton-resonant waves in “diffusion range,” indicative of cyclotron absorption.
  • Jian, Russell, et al. (2009) : STEREO shows isolated bursts of ~monochromatic waves with ω≈ 0.1–1 Ωp
can turbulence preferentially heat ions
Can turbulence preferentially heat ions?

If turbulent cascade doesn’t generate the “right” kinds of waves directly, the question remains:How 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 2005).
  • 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 wave-particle 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).