Solar dynamo and the effects of magnetic diffusivity

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Solar dynamo and the effects of magnetic
diffusivity

• E.J. Zita and Night Song, The Evergreen State
  College1
• Mausumi Dikpati and Eric McDonald, HAO/NCAR2
• 1. The Evergreen State College, Lab II, Olympia
  WA 98505
• ltzita_at_evergreen.edugt and ltlunarsong_at_yahoo.comgt
• 2. High Altitude Observatory, National Center for
  Atmospheric Research, PO Box 3000, Boulder, CO
  80307 ltdikpati_at_hao.ucar.edugt and
  ltmcdonald_at_hao.ucar.edugt
• Presented at the American Physical Society NW
  Section Meeting
• University of Victoria, BC, Canada, 13-14 May
  2005
• http//www.phys.uvic.ca/APSNW2005/

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Abstract

• We are closer to understanding how the Sun's
  magnetic field flips polarity every 11 years.
  Dikpati's kinematic dynamo model shows that in
  addition to the two familiar Babcock-Leighton
  effects (convection and differential rotation), a
  third mechanism is required. Meridional
  circulation was discovered by helioseismology,
  and its inclusion enables our model to accurately
  reproduce major features of the solar cycle.
• However, fundamental questions about the solar
  dynamo remain unanswered. How does magnetic
  reconnection release magnetic energy and change
  topology? How do magnetic fields diffuse in the
  convection zone, where the solar dynamo operates?
  How do resistivity and turbulence in the solar
  plasma determine the magnetic diffusivity? We
  explore some of these questions with our
  kinematic dynamo model.
• Our simulations show how meridional circulation
  carries evolving magnetic flux up from the base
  of the convection zone at the equator, poleward
  along the surface, and back down inside the Sun.
  Our tests give new clues about how magnetic
  diffusivity varies across the convection zone,
  and can lead to improved predictions of future
  solar cycles.

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Outline

• Observations of solar cycle
• Solar dynamo processes questions, model
• How magnetic diffusivity affects field evolution
• Goals and methods
• Test runs of model with variable diffusivity
• Preliminary results constrain profile and
  strength of magnetic diffusivity
• Future work

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Solar cycle observations

• Sunspots migrate equatorward
• Solar magnetic field gets tangled (multipolar)
  and weak during sunspot maximum
• Suns dipole magnetic field flips
• Process repeats roughly every 11 years

Courtesy NASA/MSFC/Hathaway
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Solar magnetism affects Earth

• More magnetic sunspots
• Strong, twisted B fields
• Magnetic tearing releases energy and radiation ?
• Cell phone disruption
• Bright, widespread aurorae
• Solar flares, prominences, and coronal mass
  ejections
• Global warming?
• next solar max around 2011

CME movie
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Magnetic field components

• Poloidal field
• Toroidal field

We model changes in the poloidal magnetic field.
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Poloidal flux diffusion cycle
Diffuse poloidal field migrates poleward as the
mean solar field reverses
science.nasa.gov/ ssl/pad/solar/dynamo.htm
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Whats going on inside the Sun?
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Solar dynamo processes

• O-effect Differential rotation creates toroidal
  field from poloidal field
• a-effect Helical turbulence twists rising flux
  tubes, which can tear, reconnect, and create
  reversed poloidal field
• Meridional circulation surface flow carries
  reverse poloidal field poleward equatorward
  flow near tachocline is inferred

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Solar dynamo questions

• How does the magnetic diffusivity h(r) vary
  through the convection zone?
• How does the shape and strength of h(r) affect
  the evolution of poloidal field and the solar
  dynamo?

h
r
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2D kinematic dynamo model

• Evolve code by Mausumi Dikpati et al. uses set
  flow rates v(r,q,t).
• Equatorward propagating dynamo wave is the source
  for poloidal magnetic field.
• Calculate evolution of magnetic field B(r, q, t)
  with induction equation
• where Bmagnetic field and
• magnetic diffusivity h resistivity/permeability.
  
• Model reproduces observations of recent solar
  cycles.

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Poloidal magnetic field evolution

• 2 sources for the poloidal field
• a effect at the tachocline
• a effect at the surface
• Pole reversal takes place when enough new flux
  reaches the poles to cancel the remnant field.
• Evolution of poloidal field depends on magnetic
  diffusivity and meridional circulation.

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Poloidal fields in meridional planeevolve due
to circulation and diffusion
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Magnetic diffusivity depends on plasma properties
and dynamics

• Diffusivity h resistivity/permeability
• Classical resistivity depends on temperature (
  T-3/2 )
• Convective turbulence enhances resistivity and
  therefore enhances diffusion
• Estimate ranges for magnetic diffusivity
• hsurface (1012-14 cm2 s-1) and htachocline
  (108-10 cm2 s-1)
• Lower h higher conductivity slower field
  changes
• Higher h higher resistivity faster field
  changes

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How does magnetic diffusivity change across the
convection zone?

• Strength of magnetic diffusivity hsurface at the
  photosphere (upper boundary, r/R1) is estimated
  at 1012 cm2/s
• Strength of magnetic diffusivity htach at the
  tachocline (lower boundary, r/R 0.6-0.65 in
  these simulations) is unknown
• Shape of solar diffusivity profile h(r) is
  unknown
• Convective turbulence may cause diffusivity
  gradients
• We tested four shapes, or profiles, of h(r)
• We tested each h(r) profile for various values of
  htach

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We tested four profiles for h(r)
Double-Step
Flat
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GOALS

• Find how evolution of diffuse poloidal field
  depends on h(r)
• Constrain both strength and shape of h(r) for
  better understanding of structure and dynamics of
  convection zone ? better dynamo models
• METHODS
• Write evolveta to include variable h(r)
  profiles in evolution of magnetic fields in
  convection zone
• Analyze evolution of fields with new h(r)
  profiles.

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Compare different h strengths field diffuses
if diffusivity is too high

• Test let h(r) be uniform and try two different
  strengths
• Higher h 1012 cm2 /s
• Field diffuses quickly at the solar surface
• Lower h 1011 cm2 /s
• Field follows the conveyor belt all the way to
  the pole

X
dynamo/pcfast/etacor0001/ieta0/poster/ssplt3.eps
?
dynamo/pcfast/etacor0001/etasurf01/ssplt3.eps
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Compare different profiles gradients in h
concentrate flux, especially when htach is low

• Single-step profile
• yields excessive
• flux concentration
• Linear profile
• yields reasonable
• flux diffusion

X
dynamo/pcfast/etacor0001/ieta1/sacposter/ssplt3.ep
s
h
?
dynamo/ pcfast/etacor0001/ieta3/poster/ssplt3.eps
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Higher diffusivity htach at tachocline relaxes
flux bunching due to h gradients
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Linear h(r) with higher htach is consistent with
observations of surface flux evolution
?
dynamo/ss/var/etasurf1/etacor01/ieta3/pb3.8/movtd/
ssplt3.eps
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Double-step diffusivity profile is also
consistent with observations of surface flux
evolution
?
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Results of numerical experiments

• Diffusivitysurface
• If h is too low at the surface, then magnetic
  flux becomes concentrated there particularly at
  the poles
• If h is too high the flux diffuses too much
• Diffusivitytachocline
• If h is low near the base of the convection zone,
  then the flux concentrates near the equator and
  tachocline
• Shape
• Diffusivity gradients concentrate magnetic flux
• Linear and double-step profiles are most
  consistent with observed surface flux diffusion

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Outstanding questions

• What are actual values of magnetic diffusivity in
  the convection zone? What are actual h(r)
  profiles?
• How can we gain more detailed understanding about
  the diffusivity profile inside the convection
  zone?
• Are there other diffusivity-enhancing mechanisms
  near the tachocline, e.g. velocity shear?
• What are the relevant observables that can
  further constrain our choice of diffusivity in
  the convection zone?
• How will a more detailed understanding of
  diffusivity affect flux transport and solar
  dynamo modeling ?

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Future work

• Generate butterfly diagrams from our data
• Try different meridional flow patterns
• Compare numerical experiments directly with
  observations
• Compare results with theoretical estimates of
  turbulence-enhanced magnetic diffusivity near the
  base of the convection zone
• 3D dynamo simulations with h(r,q,f)
• Predict future solar cycles

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References

• Carroll, B.W. and Ostlie, D.A., Introduction to
  modern astrophysics, Addison Wesley, 1995.
• Choudhuri, A.R., The physics of fluids and
  plasmas an introduction for astrophysicists,
  Cambridge Cambridge UP, 1998.
• Choudhuri, A.R., The solar dynamo as a model of
  the solar cycle, Chapter 6 in Dynamic Sun, ed.
  Bhola N. Dwivedi, 2003
• Dikpati, Mausumi and Paul Charbonneau, A
  Babcock-Leighton flux transport dynamo with
  solar-like differential rotation, 1999, ApJ,
  518.
•  Dikpati, M., et al. Diagnostics of polar field
  reversal in solar cycle 23 using a flux transport
  dynamo model, 2004, ApJ 601
• Dikpati, Mausumi and A. R. Choudhuri, The
  Evolution of the Suns poloidal field, 1994,
  Astronomy and Astrophysics, 291.
• Dikpati, Mausumi and A. R. Choudhuri, On the
  large-scale diffuse magnetic field of the sun,
  1995, Solar Physics, 161.
• Foukal, P, Solar Astrophysics, Wiley, 1990

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Acknowledgements
We thank the High Altitude Observatory (HAO) at
the National Center for Atmospheric Research
(NCAR) for hosting our summer visits Tom Bogdan
and Chris Dove for helpful conversations and
computing staff at Evergreen for setting up Linux
boxes with IDL in the Computer Applications Lab
and Physics homeroom. HAO/NCAR is supported by
the National Science Foundation. This work was
also supported by NASA's  Sun-Earth Connection
Guest Investigator Program, NRA 00-OSS-01 SEC,
NASA's Living With a Star Program, W-10107, and
NASA's Theory Program, W-10175.
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Sources of figures

• O-effect and a-effect Carroll and Ostlie,
  Introduction to modern astrophysics, Addison
  Wesley, 1995.
• Meridional circulation http//science.nasa.gov/s
  sl/pad/solar/dynamo.htm
• Solar structure Kenneth Lang, The Cambridge
  Encyclopedia of the Sun, Cambridge UP, 2001.
• Butterfly diagram http//www.mhhe.com/physsci/ast
  ronomy/fix/student/chapter17/17f35.html
• Olympic Mountains Dr. Ron Blakely,
  http//jan.ucc.nau.edu/rcb7/Oceanography.html
• Our runs are available at http//download.hao.ucar
  .edu/pub/green/dynamo/
• Our papers and presentations are available at
  http//academic.evergreen.edu/z/zita/research/summ
  er2004/dynamo/

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HAO/Evergreen solar dynamo team