Solar dynamo and the effects of magnetic diffusivity by DgjB6vi


									            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
      <> and <>

2. High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000,
      Boulder, CO 80307 <> and <>

Presented at the American Physical Society NW Section Meeting
     University of Victoria, BC, Canada, 13-14 May 2005
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
• 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
         Solar cycle observations

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

                Courtesy: NASA/MSFC/Hathaway
   Solar magnetism affects Earth
                 • More magnetic sunspots
                 • Strong, twisted B fields
                 • Magnetic tearing releases
CME                energy and radiation 
movie            • Cell phone disruption
                 • Bright, widespread aurorae
                 • Solar flares, prominences,
                   and coronal mass ejections
                 • Global warming?
                 • next solar max around 2011
       Magnetic field components
                           • Poloidal field

                           • Toroidal field

We model changes in the poloidal magnetic field.
        Poloidal flux diffusion cycle

Diffuse poloidal field migrates poleward as the mean solar field
reverses ssl/pad/solar/dynamo.htm
What’s going on inside the Sun?
Solar dynamo processes

           Ω-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
            Solar dynamo questions…

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

           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

                      ( v  B)  h B

• where B=magnetic field and
• magnetic diffusivity h = resistivity/permeability.
• Model reproduces observations of recent solar cycles.
         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.
  Poloidal fields in meridional plane
evolve due to circulation and diffusion


        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
    How does magnetic diffusivity change
        across the convection zone?
• Strength of magnetic diffusivity hsurface at the
  photosphere (upper boundary, r/R=1) 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
We tested four profiles for h(r):



• Find how evolution of diffuse poloidal field depends on
• Constrain both strength and shape of h(r) for better
  understanding of structure and dynamics of convection
  zone  better dynamo models

• 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.
           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            X   dynamo/pcfast/etacor0001/ieta0/poster/ssplt3.eps

  Field diffuses quickly at the
  solar surface
Lower h 1011 cm2 /s
  Field follows the conveyor belt
  all the way to the pole
                                  Compare different profiles:
                                gradients in h concentrate flux,
                                  especially when htach is low
Single-step profile
yields excessive 10                            12     h

flux concentration 10                          8

                                                    0.6       r/R   1.0

Linear profile
yields reasonable10
flux diffusion    10                       8                              
                                                    0.6       r/R   1.0
 dynamo/ pcfast/etacor0001/ieta3/poster/ssplt3.eps
              Higher diffusivity htach at tachocline
            relaxes flux bunching due to h gradients
             htach = 108 cm2 /s
            1012     h
                   0.6      r/R           1.0

             htach = 1010 cm2 /s


             Linear h(r) with higher htach is
             consistent with observations of
                 surface flux evolution

1012    h

       0.6     r/R          1.0

 Double-step diffusivity profile is
also consistent with observations of
       surface flux evolution

        Results of numerical experiments
• 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
• If h is low near the base of the convection zone, then the
  flux concentrates near the equator and tachocline
• Diffusivity gradients concentrate magnetic flux
• Linear and double-step profiles are most consistent with
  observed surface flux diffusion
                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
• How will a more detailed understanding of diffusivity
  affect flux transport and solar dynamo modeling ?
                 Future work
• Generate butterfly diagrams from our data
• Try different meridional flow patterns
• Compare numerical experiments directly with
• 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
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 Sun’s 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
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.
                             Sources of figures
Ω-effect and a-effect: Carroll and Ostlie, Introduction to modern astrophysics,
   Addison – Wesley, 1995.

Meridional circulation:

Solar structure: Kenneth Lang, The Cambridge Encyclopedia of the Sun,
   Cambridge UP, 2001.

Butterfly diagram:

Olympic Mountains: Dr. Ron Blakely,

Our runs are available at

Our papers and presentations are available at
HAO/Evergreen solar dynamo team

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