1. 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)

2. 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

3. 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

4. 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

5. Poloidal Magnetic Field Evolution Two sources for the poloidal field 1)  -effect at the tachocline 2)  -e ffect 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

6. 2D Kinematic Dynamo Model Uses fixed velocity field v(r,  ) Calculates evolution of magnetic field B(r, , t) with induction equation  = 10 8 cm 2 /s  = 10 12 cm 2 /s  = ?

7. Poloidal Fields in Meridional Plane Tachocline Surface

8. Four Diffusivity Profiles

9. Comparison of Different Diffusivities Using the same diffusivity profile, tailor the diffusivity range differently. Higher  =10 12 cm 2 /s Field diffuses away quickly Lower  = 10 11 cm 2 /s Field follows the conveyor belt all the way to the pole

10. Comparison of Different Profiles Single-step profile yields greater flux concentration compared to what linear profiles yield.

11. Comparison of Different Profiles

12. Results Diffusivity surface : If  is too low at the surface, then magnetic flux becomes concentrated there If  is too high the flux diffuses excessively Diffusivity tachocline : 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

13. Outstanding Questions What is a reasonable range for magnetic diffusivity in the convection zone? 10 10 -10 12 cm 2 /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?

14. 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.