Title: Modeling the Solar Wind: A survey of theoretical ideas for the origins of fast
1Modeling the Solar Wind A survey of
theoretical ideas for the origins of fast slow
streams
Steven R. CranmerHarvard-SmithsonianCenter for
Astrophysics
2Modeling the Solar Wind A survey of
theoretical ideas for the origins of fast slow
streams
Outline 1. Brief historical background 2.
The coronal heating problem 3. Solar wind
acceleration waves vs. reconnection? 4.
(Suggestive hints from collisionless ion
diagnostics)
Steven R. CranmerHarvard-SmithsonianCenter for
Astrophysics
3The solar wind discovery
- 18601950 Evidence slowly builds for outflowing
magnetized plasma in the solar system - 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.
- solar flares ? aurora, telegraph snafus,
geomagnetic storms - comet ion tails point anti-sunward (no matter
comets motion)
4In 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 winds source regions. - Helios saw strong departures from Maxwellians.
By 1990, it was clear the fast wind needs
something besides gas pressure to accelerate so
fast!
5Solar wind connectivity to the corona
- High-speed wind strong connections to the
largest coronal holes
hole/streamer boundary (streamer edge) streamer
plasma sheet (cusp/stalk) small coronal
holes active regions
- Low-speed wind still no agreement on the full
range of coronal sources
6Empirical trends
- Wind speed is roughly anticorrelated with flux
tube expansion factor between Sun and
potential field source surface (PFSS). - Wang Sheeley (1990) flux-tube expansion
correlation, modified by, e.g., Arge Pizzo
(2000) and others
- Other correlations based on coronal hole size
(Vršnak et al. 2007), surface field (Kojima et
al. 2004), and chromospheric wave phase
properties (Leamon McIntosh 2007) are also
useful.
7Empirical trends are helpful, but they are not
always accurate . . . To make qualitative
improvements in long-term space weather
forecasting (i.e., to know when the empirical
trends are going to work, and when they wont),
its key to know the physical processes that give
rise to the heating acceleration.
8The coronal heating problem
- We still dont 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!
9Coronal heating mechanisms
- So many ideas, taxonomy is needed! (Mandrini et
al. 2000 Aschwanden et al. 2001)
- Where does the mechanical energy come from?
vs.
10Coronal heating mechanisms
- So many ideas, taxonomy is needed! (Mandrini et
al. 2000 Aschwanden et al. 2001)
- 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?
vs.
waves shocks eddies (AC)
twisting braiding shear (DC)
vs.
interact with inhomog./nonlin.
reconnection
turbulence
collisions (visc, cond, resist, friction) or
collisionless
11The 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
arXiv 0804.3058
12Reconnection / Loop-Opening models
- There is a natural appeal to the RLO idea, since
only a small fraction of the Suns 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
13Reconnection / 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
14Wave / Turbulence-Driven models
- No matter the relative importance of RLO events,
we do know that waves and turbulent motions are
present everywhere... from photosphere to
heliosphere. - How much can be accomplished by only WTD
processes? (Occams razor?)
15Building an Alfvén wave model
- In dark intergranular lanes, strong-field
photospheric flux tubes are shaken by an
observed spectrum of horizontal motions. - In mainly open-field regions, Alfvén waves
propagate up along the field, and partly reflect
back down (non-WKB). - Nonlinear couplings allow a (mainly
perpendicular) turbulent cascade, terminated by
damping ? gradual heating over several solar
radii.
16MHD 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., Matthaeus et al. 1999 Dmitruk et al. 2002)
17Self-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 collisionless
streaming
18Results turbulent heating acceleration
T (K)
Ulysses SWOOPS
Goldstein et al. (1996)
reflection coefficient
19Results other fast/slow diagnostics
- FIP effect (using Lamings 2004 theory)
Ulysses SWICS
Cranmer et al. (2007)
20Multi-fluid collisionless effects?
Polar coronal hole model
21Multi-fluid collisionless effects?
O5
O6
protons
electrons (thermal core only)
22Departures from thermal equilibrium
- UVCS/SOHO observations rekindled theoretical
efforts to understand collisionless heating and
acceleration effects in the extended corona.
- Ion cyclotron waves (1010,000 Hz) suggested as a
natural energy source that can be tapped to
preferentially heat accelerate heavy ions.
cyclotron resonance-like phenomena
MHD turbulence
23What next?
- Both WTD and RLO paradigms have passed some basic
tests of comparison with observations. What
could this imply?
- A combination of both ideas could work best?
- Existing models dont contain the right physics
once that is included, one or the other idea may
fail to work? - Comparisons with observations havent been
comprehensive enough to allow their true
differences to be seen?
24What next?
- Both WTD and RLO paradigms have passed some basic
tests of comparison with observations. What
could this imply?
- A combination of both ideas could work best?
- Existing models dont contain the right physics
once that is included, one or the other idea may
fail to work? - Comparisons with observations havent been
comprehensive enough to allow their true
differences to be seen?
- Some basic issues of energy budget still to
resolve
- Do reconnections between open closed regions
cover enough of the solar surface to account for
the majority of the solar wind? - Does MHD turbulence produce the right mixture
of collisionless kinetic effects?
25Conclusions
- The debate between waves/turbulence and
reconnection/loop-opening mechanisms of solar
wind acceleration goes on . . . - Theoretical advances in MHD turbulence continue
to feed back into global models of the solar
wind. - The extreme plasma conditions in coronal holes
(Tion gtgt Tp gt Te ) have guided us to discard
some candidate processes, further investigate
others, and have cross-fertilized other areas of
plasma physics and astrophysics.
vs.
For more information http//www.cfa.harvard.edu
/scranmer/
26Extra slides . . .
27The extended solar atmosphere . . .
Heating is everywhere . . .
. . . and everything is in motion
28The Suns outer atmosphere
- The solar photosphere radiates like a blackbody
its spectrum gives T, and dark Fraunhofer lines
reveal its chemical composition. - Total eclipses let us see the vibrant outer solar
corona but what is it? - 1870s spectrographs pointed at corona
- Is there a new element (coronium?)
- 1930s Lines identified as highly ionized ions
Ca12 , Fe9 to Fe13 its hot!
- Fraunhofer lines (not moon-related)
- unknown bright lines
29Particles are not in thermal equilibrium
especially in the high-speed wind.
mag. field
WIND at 1 AU (Steinberg et al. 1996)
Helios at 0.3 AU (e.g., Marsch et al. 1982)
WIND at 1 AU (Collier et al. 1996)
30Waves? Start in the photosphere . . .
- Photosphere displays convective motion on a broad
range of time/space scales
ß ltlt 1
ß 1
ß gt 1
31Turbulence
- It is highly likely that somewhere in the outer
solar 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 ?v2 and a
turnover time-scale ? l/v, so the rate of
transfer of energy goes as ?v2/? ?v3/l . - Dimensional analysis can give the spectrum of
energy vs. eddy-wavenumber k Ek k5/3
32Progress towards a robust recipe
Not too bad, but . . .
- Because of the need to determine non-WKB
(nonlocal!) reflection coefficients, it may not
be easy to insert into global/3D MHD models. - Doesnt 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)
33The 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 winds
acceleration region) seen with UV spectroscopy.
34Exploring 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.
35The UVCS instrument on SOHO
- 19791995 Rocket flights and Shuttle-deployed
Spartan 201 laid groundwork.
- 1996present 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
36UVCS 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., O5) line emission in the extended corona
revealed surprisingly wide line profiles . . .
37Emission 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 theres 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.
38Doppler 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 gt 100 million K. - R lt 1 implies anisotropy!
39Preferential 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 (1010,000 Hz) suggested as a
natural energy source that can be tapped to
preferentially heat accelerate heavy ions.
cyclotron resonance-like phenomena
MHD turbulence
40Anisotropic 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.
41Anisotropic 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 . . .
42So 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). - 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 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 heat ions perpendicularly via
collisions (Ergun et al. 1999 Cranmer van
Ballegooijen 2003).
43Coronal holes over the solar cycle
- Even though large coronal holes have similar
outflow speeds at 1 AU (gt600 km/s), their
acceleration (in O5) in the corona is different!
(Miralles et al. 2001)
Solar minimum
Solar maximum
44Waves remote-sensing techniques
The following techniques are direct (UVCS ion
heating was more indirect)
Tomczyk et al. (2007)
45Overview of in situ fluctuations
- Fourier transform of B(t), v(t), etc., into
frequency
- How much of the power is due to spacecraft
flying through flux tubes rooted on the Sun?
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 -3dissipation range
0.5 Hz
few hours
46Future diagnostics more spectral lines!
- How/where do plasma fluctuations drive the
preferential ion heating and acceleration, and
how are the fluctuations produced and damped? - Observing emission lines of additional ions
(i.e., more charge mass combinations) would
constrain the specific kinds of waves and the
specific collisionless damping modes.
Comparison of predictions of UV line widths for
ion cyclotron heating in 2 extreme limits (which
UVCS observations black circles cannot
distinguish). Cranmer (2002), astro-ph/0209301
47Future Diagnostics electron VDF
- Simulated H I Lyman alpha broadening from both H0
motions (yellow) and electron Thomson scattering
(green). Both proton and electron temperatures
can be measured.
48Synergy 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 shock-trains. 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)