Space Weather Magnetic Field Origins Helioseismology Dynamo Theory

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Space WeatherMagnetic Field OriginsHelioseismol
ogyDynamo Theory
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Motivation

• Solar magnetic fields are the driver of space
  weather without the magnetic field there is no
  space weather. Can someone tell me why that is?
• Magnetic fields originate under the solar
  surface.
• There are short and long term changes in the
  fields.
• How can we predict these changes?

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Outline

• Helioseismology
• What is it
• What are the measurements
• What is the mathematics
• What do the results look like
• Solar Dynamo
• Basic concept What is a dynamo?
• Current understanding (pun not intended)

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Solar Structure
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Pressure and Gravity Mode Rays
Courtesy Juri Toomre and Douglas Gough
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Helioseismology

• Phenomenon
• 5 minute oscillations of the visible surface
• Sound waves
• resonantly trapped below the surface
• excited by convection just below the surface
• Methodology
• 107 normal modes of varying radial/latitudinal
  extent
• Comparison of frequencies with model calculations
• Inverse methods
• Local helioseismology and running waves
• Results
• Physics GR, neutrinos, EoS, opacities,
  diffusion,
• Stellar Structure temperature, density,
  abundances, rotation, flows,
  "turbulence", ... Implies stellar evolution.
• Variability modes, 3-D structures
• Frontier
• Asteroseismology
• Gravity Modes

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The Solar Surface
Courtesy of Luc Rouppe van der Voort, Oslo, from
the Swedish Solar Telescope, La Palma
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Wiggle Line Spectrum
100
50
0
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Telescope

• Ordinary white light telescope, need not be very
  large, good enough for 1 resolution
• Blocking filter to isolate one desirable spectral
  line
• Tunable interference filter to make measurements
  in several locations through line to make Doppler
  line profiles.
• CCD detector.
• Output is a line profile at each 1 element on
  the Sun

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Data-Velocity Image
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Disentangling the Modes
Courtesy Frank Hill
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Mathematical Form
From Annual Reviews of Astronomy and Astrophysics
1984, 22, 593, Deubner and Gough
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Equation of Motion
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Surface velocity changes
Steve Musman and Dave Rust, Solar Physics
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Temporal Power Spectrum
Courtesy Dick White and Milton Cha
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A Testable Prediction
p-modes
g-modes
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The Outcome
Courtesy Franz-Ludwig Deubner
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And Rapid Improvement
Courtesy Franz-Ludwig Deubner, Roger Ulrich, and
Ed Rhodes
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Caricature of the Scientific Method

• Serendipitous Discovery
• Many Different Descriptions
• Testable Prediction of Unobserved Phenomenon
• Confirmation
• Use Remaining Small Deviations as Tool

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A Typical l -? Diagram
5000
4000
? (Frequency)
3000
2000
1000
0
500
l (Spherical Harmonic Degree)
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The Global Rotation Picture
Courtesy of Rachel Howe
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Sub-surface Flows
Jesus Patron et al.
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Structure of Sunspot
Courtesy Tom Ducall
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High Resolution Near Surface Flows
Courtesy of Junwei Zhao
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The Farside
Courtesy Doug Braun
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What we have learned, are learning, and hope to
learn

• Successes
• The phenomenon itself, Neutrinos, J2, Internal
  Rotation, Helium abundance, Opacities, Depth of
  Convection Zone, Structures, etc, etc, etc
• Challenges
• Origins of solar magnetism
• Differential rotation, torsional oscillations,
  and meridional circulation
• Sub-surface inhomogeneities
• How all of this should manifest itself in other
  stars
• How these tools can contribute to a predictive
  understanding of space weather.
• Frontiers
• Asteroseismology G-modes

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• Dynamo

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Coexistence of magnetic fields consisting of
widely different length scales, magnitudes and
temporal scales

Hierarchy in length scale

• Network fields 100 km size
  

• Sunspots, ephemeral regions, plage 10000-30000
  km diameter

• Unipolar regions 100,000 km extent

Hierarchy in flux and/or field strength

• Spots, active regions, network fields a few
  thousand Gauss

• Plage a few hundred Gauss

• Large-scale diffuse fields a few tens of Gauss

Hierarchy in temporal variations

• Persistent, cyclic features butterfly diagrams,
  polar reversal, active longitudes
  

• Random features small-scale mixed-polarity
  turbulent fields

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What is a dynamo?
A dynamo is a process by which the magnetic field
in an electrically conducting fluid is maintained
against Ohmic dissipation
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Lets Build A Homopolar-disc Dynamo
A copper disc that can rotate about its axis
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Lets Build A Homopolar-disc Dynamo
Supply kinetic energy to rotate the disc
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Lets Build A Homopolar-disc Dynamo
Introduce magnetic fields an electromotive force
between the axis and the rim will be generated
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A Homopolar-disc Dynamo (Complete)
Connect a wire twisted in the same sense as the
sense of rotation magnetic fields will grow
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Observational signature for systematic, cyclic
evolution of solar magnetic fields
Courtesy D.H. Hathaway
Many evidences for coexistence of small-scale and
large-scale dynamos
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Large-scale dynamo historical background

• Generation of toroidal field by shearing a
  pre-existing poloidal field by differential
  rotation
• (O-effect )

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Large-scale dynamo historical background (contd.)
(ii) Re-generation of poloidal field by lifting
and twisting a toroidal flux tube by helical
turbulence (a-effect)
Proposed by Parker (1955) Mathematically
formulated by Steenbeck, Krause Radler (1969)
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(No Transcript)
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Large-scale dynamo historical background (contd.)

• In 1960s and 70s, equatorward propagating
  dynamo wave was obtained by assuming a radial
  differential rotation increasing inward
  throughout the convection zone.

• Sunspots were identified as that formed from
  strong toroidal flux tubes which rise to the
  surface due to their magnetic buoyancy

• Equatorward migration of sunspot-belt was
  explained by an equatorward propagating dynamo
  wave for the subsurface toroidal fields

Equatorward propagation of dynamo wave was
obtained by satisfying Parker-Yoshimura Sign
Rule a dO/dr lt 0, In North-hemisphere
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Historical Background (contd.)

• But, In 1980s, helioseismic analysis inferred
  that there is no radial shear in the convection
  zone, and the strong radial shear at or below the
  base of the convection zone is decreasing inward
  at sunspot latitudes.

(Courtesy Thierry Corbard)
Therefore, Convection Zone Dynamos Do Not Work
With Solar-like O
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FLUX-TRANSPORT DYNAMO
lt
Meridional circulation
Wang Sheeley, 1991
Choudhuri, Schüssler, Dikpati, 1995
Durney, 1995
Dikpati Charbonneau, 1999
Küker, Rüdiger Schültz, 2001
And certainly many others
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Mathematical Formulation
Under MHD approximation (i.e. electromagnetic
variations are nonrelativistic), Maxwells
equations generalized Ohms law lead to
induction equation
(1)
Applying mean-field theory to (1), we obtain the
dynamo equation as,
(2)
Diffusion (turbulent molecular)
Differential rotation and meridional circulation
Displacing and twisting effect by kinetic helicity
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Evolution of Magnetic FieldsIn a
Babcock-Leighton Flux-Transport Dynamo
Dynamo cycle period ( T ) primarily governed by
meridional flow speed
Dikpati Charbonneau 1999, ApJ, 518, 508
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Calibrated Flux-transport Dynamo Model
N-Pole
Red a -effect location
Green rotation contours
Blue meridional flow
Dikpati , Corbard, Thompson Gilman, 2001, ApJ,
575, L41
Above value of supergranular diffusivity is
consistent with that of Wang, Shelley Lean,
2002 Schrijver 2002
S-Pole
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Validity test of calibration
Contours toroidal fields at CZ base Gray-shades
surface radial fields
Observed NSO map of longitude-averaged
photospheric fields
(Dikpati, de Toma, Gilman, Arge White, 2004,
ApJ, 601, 1136)
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Predicting the onset of cycle 24
Simulated solar cycles
Next cycle will start late in 2007 or early in
2008
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22
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(Dikpati et al., 2004, AAS/SPD)
(Delayed onset of cycle 24 has also been
predicted by Sello 2003 using a different method)
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Can we go beyond decadal time-scale?
Can we predict Maunder minima or Medieval maxima?
Maunder minimum is the absence of sunspots, but
not the absence of cycle
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The origin of magnetic fields in the solar
interior

• Could solar cycle dynamo be a source
• for deep interior magnetic fields?

• Noticed flux-transport dynamo model diffusing
  toroidal field into low-diffusivity domain below
  tachocline.
• Artifact, or reality?

• Long-term transient or permanent?

• Nonreversing fields, but structure dependent on
  initial phase of cycle when diffusion starts?

Dikpati, Gilman MacGregor (2005, in preparation)