Dynamics of the solar convection zone Matthias Rempel HAONCAR

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Dynamics of the solar convection zoneMatthias
Rempel (HAO/NCAR)
High Altitude Observatory (HAO) National Center
for Atmospheric Research (NCAR) The National
Center for Atmospheric Research is operated by
the University Corporation for Atmospheric
Research under sponsorship of the National
Science Foundation. An Equal Opportunity/Affirmati
ve Action Employer.
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Outline

• Observations
• Large scale magnetic field
• Solar cycle
• Large scale flows differential rotation,
  meridional flow
• Differential rotation
• Structure of convection
• Origin of differential rotation
• Solar dynamo
• Basic ingredients of a dynamo
• Formation of sunspots

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Measurement of magnetic field

• Zeeman effect
• Splitting of spectral lines
• LinearCircular polarization
• Thermal and turbulent broadening of spectral
  lines
• Splitting not observable except for strongest
  field (sunspots)
• Most field diagnostics are based on polarization
  signal
• Gives strength and orientation of field

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Sunspots on solar disc
PSPT (CaK)
PSPT (blue)

• Regions of strong magnetic field (3000 Gauss)
• About 20000km diameter
• Lifetime of a few weeks

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Changing X-ray activity over 11 years
Yohkoh X-ray images
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Butterfly diagram sunspot area over time
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Hales law
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Joys law
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Solar cycle properties

• Butterfly diagram
• Equatorward propagation of activity starting from
  35 degrees latitude over 11 years (individual
  lifetimes of sunspots a few weeks)
• Hales polarity law
• Opposite polarity of bipolar groups in north and
  south hemisphere
• Polarity in individual hemisphere changes every
  11 years
• Joys law
• Bipolar groups are tilted to east-west direction
• Leading polarity closer to equator
• Tilt angle increases with latitude

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Evolution of radial surface field
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Everything together
D. Hathaway NASA (MSFC)
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Longterm variations
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Variability over the past 10000 years

• Cosmogenic isotopes
• 14C and 10Be produced by energetic cosmic rays
• Cosmic rays modulated by magnetic field in
  heliosphere
• Longterm record in ice cores (14C and 10Be ) and
  treerings (14C)
• Normal activity interrupted by grant minima 100
  years duration
• Persistent 11 year cycle

Usokin et al. (2007)
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Large scale flows
R. Howe (NSO)

• Differential rotation in convection zone, uniform
  rotation in radiation zone (shear layer in
  between Tachocline)
• Cycle variation of DR (torsional oscillations, 1
  amplitdude)

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Differential rotation and meridional flow changes
through solar cycle
Changes is DR
Meridional flow
Butterfly diagram
Radial field
Surface Doppler measurement R. Ulrich (2005)
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Internal dynamics of convection zone

• What drives large scale mean flows (differential
  rotation meridional flow)?
• Answer small scale flows
• Reynolds stresses
  (correlations of turbulent motions) can drive
  large scale flows
• Relevant for angular momentum transport

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How to model the solar convection zone

• 3D numerical simulations
• Solve the full set of equations (including small
  and large scale flows) on a big enough computer
• Problem Computers not big enough
• Only possible to simulate ingredients
• Meanfield models
• Solve equations for mean flows only
• Problem need good model for correlations of
  small scale flows (not always available)
• Can address the full problem, but not from first
  principles

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Correlations caused by Coriolis force
Latitudinal transport
North-South motions negative
(poleward) East-West motions positive
(equatorward)
Average zero unless East-West dominates
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Structure of convection close to surface
3D simulation (M. Miesch)
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Structure of convection in lower convection zone
3D simulation (M. Miesch)
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Coriolis-force causes large scale convection
rolls in deep convection zone

• Balance between pressure and Coriolis force
• Cyclonic rolls lower pressure
• Anti-cyclonic rolls higher pressure

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Angular momentum transport

• Positive
• Faster rotating equator
• ?-component of momentum equation
• What determines radial profile of DR?
• Force balance between Coriolis, pressure and
  buoyancy forces
• r-?-component of momentum equation

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Profile of differential rotation

• Latitudinal variation of entropy essential for
  solar like rotation profile
• Possible causes
• Anisotropic convective energy transport
  (influence of rotation on convection
• Tachocline
• About 10K temperature difference between pole and
  equator (T106 K at base of CZ)

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Results from 3D simulations
3D simulation (M. Miesch)
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Summary differential rotation

• Turbulent angular momentum transport
• Correlations between meridional (north south) and
  longitudinal (east west) motions caused by
  Coriolis force
• Anisotropic convection (banana cells)
• Radial profile of differential rotation
• Determined through force balance in meridional
  plane
• Thermal effects important (about 10K latitudinal
  temperature variation needed)
• Boundary layer (tachocline) important

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The MHD induction equation

• Basic laws (Ohms law, non-relativistic field
  transformation, Amperes law
• Combination of the three

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Differential rotation
Axisymmetry differential rotation
Induction equation in spherical coordinates
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Properties of solution

• Poloidal field always decaying
• Toroidal field can grow significantly in the
  beginning
• Stretching of field lines
• Toroidal field is also decaying in the long run
• The source of toroidal field decays with the
  poloidal field
• What is missing?
• Regeneration of poloidal field
• Who can do it?
• Again small scale field and flows

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Meanfield induction equation

• Decomposition of velocity and magnetic field
• Averaging of induction equation
• Turbulent induction effects

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Induction effect of helical convection
Negative kinetic helicity in northern hemisphere
Induces a poloidal field from toroidal field
parallel to the current of the toroidal field
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Turbulent induction effects

• ?-effect induces field parallel to electric
  current
• ?t increases the effective diffusivity for
  meanfield (turbulent diffusivity)

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Meanfield Dynamos

• The ?-effect closes the dynamo loop regeneration
  of poloidal field from toroidal field

? ?
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Some more general properties

• ?2-dynamo
• Stationary field
• Poloidal, toroidal field similar strength

• ??-dynamo
• Periodic solutions, travelling waves
• Toroidal field much stronger than poloidal field

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So what is the sun doing?

• Strong differential rotation (observed), periodic
  behaviour ? ??-dynamo
• Propagation of activity belt
• Dynamo wave (requires radial shear)
• Advection effect (meridional flow)
• Location of ?-effect
• Bulk of convection zone (helical convection ?
  positive ?)
• Base of convection zone (helical convection ?
  negative ?, tachocline instabilities ? ? of both
  signs )
• Rising flux tubes (positive ?)

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Dynamo wave

• Surface shear layer
• Positive ?
• Very short time scales
• Significant flux loss

• Tachocline shear layer
• Negative ? (in low latitudes)
• Longer time scales, stable stratification allows
  for flux storage

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Role of tachocline
Browning et al. (2006)

• Stable stratification, long time scales
• Formation of large scale field, likely origin of
  field forming sunspots
• Problems of a pure tachocline dynamo
• Much stronger shear of opposite sign in high
  latitudes (strong poleward propagating activity
  belt)
• Very short wavelength of dynamo wave (strongly
  overlapping cycles)

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Advection

• Meridional flow
• Poleward at surface (observed)
• Return flow not observable through
  helioseismology (so far)
• Equatorward at base of CZ
• Mass conservation
• Theory meanfield models 3D simulations
• Additional also turbulent advection effects
  (latitudinal pumping)

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Rising magnetic flux tubes

• Flux tubes bundle of fieldlines form in
  tachocline
• Rising field due to buoyancy
• Fluid draining from apex
• Coriolis force causes tilt of the top part of
  tube
• Tilt increases with latitude as observed
• Net effect positive ?

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3D simulation of rising flux-tube
(Y. Fan)

• Flux tube looses a lot of flux during rise (tube
  has to be twisted in the beginning)
• Twist reduces tilt angle

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Observations of Surface ?-Effect and Flux
Transport
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Schematic of flux-transport dynamo
.

• Latitudinal shear producing toroidal field
• ?-effect from decay of active regions
• Transport of field by meridional flow

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Flux-transport dynamo with Lorentz-force feedback
on DR and meridional flow

• Feedback of Lorentz-force on DR and MC included
• Moderate variations of DR and MC
• No significant change of dynamo
• High latitude variations of DR
• Poleward propagation, amplitude similar to
  observed

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Summary The essential ingredients of the solar
dynamo I

• The sun is a ??-dynamo
• Differential rotation profile (helioseismology)
• Dominance of toroidal field (sunspots)
• Cyclic behavior
• Tachocline important for large scale organization
  of toroidal field (boundary layer)
• Bulk of convection has too short time scales
• Flux loss in convection zone due to magnetic
  buoyancy and pumping
• Stable stratification allows for storage

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Summary The essential ingredients of the solar
dynamo II

• Advection by meridional flow
• Certainly important at surface (observed)
• Equatorward meridional flow in lower convection
  zone (theory, mass conservation)
• How important compared to turbulent effects?
• Magnetic diffusivity
• Turbulent pumping (in radius and latitude)
• Flux-transport dynamos are very successful models
  (consistent with observational constraints), but
  more research required

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Summary The essential ingredients of the solar
dynamo III

• Sunspot formation
• Origin of field stable stratification at base of
  convection zone
• Strong magnetic flux tubes rising through
  convection zone (magnetic buoyancy)
• Coriolis force leads to systematic tilt
• Open questions
• How to keep flux tube coherent in turbulent
  convection zone?
• Initial twist of tube required, but that also
  influences tilt angle
• Rising tubes prefer long wave numbers (m1,2)
• Sunspots are of much shorter wave number
• Decoupling between emerged sunspot and its
  magnetic root at base of convection zone?

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The Future

• Much more computing power
• Better understanding of essential ingredients in
  the short run
• 3D dynamo model in the long run
• Observational constraints
• Helioseismology
• Meridional flow
• Magnetic field in convection zone?
• Solar-stellar connection
• How do cycle properties depend on rotation rate
  and depth of convection zone?