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.