influence of depth-dependent diffusivity profiles in governing the evolution of weak, large-scale...
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Influence of depth-dependent diffusivity profiles in governing the
evolution of weak, large-scale magnetic fields of the sun
Night Song and E.J. Zita, The Evergreen State College
Mausumi Dikpati and Eric McDonald, HAO
Presentation for NSO Workshop #22
Large Scale Structures and their Role in Solar Activity
Sunspot, NM (18-22 October 2004)
Outline
• Observations of solar cycle• Solar dynamo processes: questions, model• How magnetic diffusivity affects field evolution• Runs of model with different diffusivity profiles• Results• Future work
Observations of Solar Cycle
• Sunspots migrate equatorward• Diffuse poloidal field migrates poleward as the
mean solar field reverses• Solar mean field reverses about every 11 years• Sunspots peak during polar reversal
Courtesy: NASA/MSFC/Hathaway
Solar Dynamo Processes
-effect: Differential rotation creates toroidal field from poloidal field
-effect: Helical motions in the tachocline and/or core-envelope interface, and decay of tilted bipolar active regions at the surface, can regenerate poloidal field with reversed sign.
Meridional circulation: surface flow carries poloidal field poleward; equatorward flow near tachocline is inferred
Carroll and Ostlie, Introduction to modern astrophysics, Addison – Wesley, 1995.
http://science.nasa.gov/ssl/pad/solar/images/theflows.gif
Poloidal Magnetic Field Evolution
• Two sources for the poloidal field
1) -effect at the tachocline
2) -effect near the surface
• Evolution of poloidal field is governed by diffusivity and meridional circulation
• Pole reversal takes place when enough new flux reaches the poles to cancel the remnant field
2D Kinematic Dynamo Model• Uses fixed velocity field v(r, )• Calculates evolution of magnetic field B(r, , t) with
induction equation
= 108 cm2 /s
= 1012 cm2 /s
= ?
Poloidal Fields in Meridional Plane
Tachocline
Surface
Four Diffusivity Profiles
Comparison of Different Diffusivities
Using the same diffusivity profile, tailor the diffusivity range differently.
Higher =1012 cm2 /s
Field diffuses away quickly
Lower =1011 cm2 /s
Field follows the conveyor belt all the way to the pole
Comparison of Different Profiles
Single-step profile
yields greater
flux concentration
compared to what
linear profiles
yield.
Comparison of Different Profiles
Results
Diffusivitysurface:
• If is too low at the surface, then magnetic flux becomes concentrated there
• If is too high the flux diffuses excessively
Diffusivitytachocline:
• If is low near the base of the convection zone, then the flux concentrates in that region
Shape:• Diffusivity gradients concentrate magnetic flux • Linear (r) can handle greater ranges of diffusivity
Outstanding Questions
• What is a reasonable range for magnetic diffusivity in the convection zone? 1010-1012 cm2/s?
• How can we gain more detailed understanding about the diffusivity profile inside the convection zone?
• What are the relevant observables that can further constrain our choice of diffusivity in the convection zone?
Future Work
• Explore with different meridional flow patterns
• Compare model output produced by these diffusion profiles with surface observables
Acknowledgements:
We acknowledge that the motivation for this study came from some helpful comments from Jack Harvey.
Night Song and E.J. Zita gratefully acknowledge helpful conversations with Tom Bogdan and Chris Dove.
This work was 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.