Effects of magnetic diffusion profiles on the evolution of solar surface poloidal fields. Night Song The Evergreen State College Olympia, WA with Mausumi Dikpati, Eric McDonald, and E.J. Zita presented at HAO/NCAR, Boulder, CO Tuesday 27 July 2004

Outline Observations of solar magnetism Solar dynamo: understanding, questions, model Poloidal field diffuses as field reverses Magnetic diffusivity  affects field evolution Goals and methods Tests of model with variable diffusivity Preliminary results constrain profile and magnitude of magnetic diffusivity Future work Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Observations of solar magnetism Solar mean field reverses every 11 years Sunspots peak during reversal (“solar max”) Sunspots migrate equatorward Diffuse poloidal field migrates poleward as the mean solar field reverses Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Solar dynamo is partly understood Ω-effect: Differential rotation creates toroidal field from poloidal field  -effect: Coriolis force 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 Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Some solar dynamo questions How does poleward flow of surface poloidal field contribute to mean field reversal? How does equatorward flow of field at tachocline contribute to solar dynamo? How does the magnetic diffusivity  (r) vary across the convection zone? How does the  profile affect magnetic dynamics in the convection zone? Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

More about flux diffusion… dikp-ati et al 1998 say… Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

2D kinematic dynamo model “Evolve” code by Mausumi Dikpati et al. Inputs specified flows v(r, ,t) Calculates evolution of magnetic field B(r, , t) with induction equation Another point? ________ Reproduces many observations of recent solar cycles Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Dynamo model reproduces observations Specification of observed flows yields observed magnetic field evolution Meridional circulation yields ________ Reverse cell yields ________ What was the third thing?___________ Combining all three flows yields reasonable magnetic field evolution Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Magnetic dynamics depend on magnetic diffusivity Magnetic diffusivity  = Induction equation Lower  : higher conductivity: slower field changes Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Magnetic diffusivity depends on plasma properties and dynamics Resistivity depends on temperature (Spitzer  s  = ) Turbulence can enhance resistivity:  =  s  * Convective turbulence near surface enhances resistivity and diffusion Estimate ranges for  surf (__-__) and  tachocline (__-__) Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

How does magnetic diffusivity change across the convection zone? Shape of solar diffusivity profile  (r) is unknown We tested three shapes of  (r) Linear ( Single-Step …/ dynamo/ss/var/etasurf1/etacor01/ieta1/etaplt.eps Double-Step …/ dynamo/ss/var/etasurf1/etacor01/ieta2/etaplt.eps Night Song, presentation at HAO/NCAR, Tuesday 27 July ^12 10^ r/R 1.0

The magnitude of diffusivity shapes the evolution of the poloidal field Value at tachocline  tach is unknown Treat  as constant and change magnitude High  : cm 2 s -1 Effects: Low  turb : cm 2 s -1 Effects: Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004 dynamo/ss/var/ieta0/eta01/ssplt2.eps dynamo/ss/var/ieta0/eta1/ssplt2.eps

GOALS and methods Find how evolution of diffuse poloidal field depends on  (r) Constrain both magnitude and shape of  (r) for better understanding of structure and dynamics of convection zone  better dynamo models METHODS: Write “evolveta” to include variable  (r) profiles in evolution of magnetic fields in convection zone Test against established steady-states Analyze evolution of fields with new  (r) profiles. Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Bad runs constrain the magnitude of  Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004 Single-step  r  Diffusion is too low near the tachocline Field is bunched up dynamo/ss/var/etasurf1/etacor0001/ieta1/ssplt2.epsdynamo/ss/var/etasurf1/etacor01/ieta1/etaplt.eps

Bad runs constrain the shape of  r  Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004 dynamo/ss/var/etasurf1/etacor0001/ieta3/ssplt2.eps Linear  r  Diffusion looks reasonable Same magnitude as previous single-step  r  10^12 10^ r/R 1.0

Linear  r  shows … Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004 dynamo/ss/var/etasurf1/etacor01/ieta3/movie Good runs shed light on role of  r  in solar dynamo process

Single-step  r  shows … Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004 Dynamo/ss/var/etasurf1/etacor01/ieta1/movie

Double-step  r  shows … Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004 Dynamo/ss/var/etasurf1/etacor01/ieta2/movie

Preliminary results of numerical experiments Etasurf Etacore Shape Dynamics Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Outstanding questions Why How What Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Future work Generate butterfly diagrams from our data New runs… Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

References and acknowledgements Carroll, and Ostlie, Introduction to astrophysics, _____________ Choudhuri, A.R., The physics of fluids and plasmas: an introduction for astrophysicist, 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 We thank Mausumi Dikpati and Eric McDonald for teaching us how to undertake these analyses, and E.J. Zita for her assistance and support. This work was supported by NASA's Sun-Earth Connection Guest Investigator Program, NRA 00-OSS-01 SEC Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Sources of figures Ω-effect and  -effect: Meridional circulation: Solar structure: More… Our runs are available at This talk is available at Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004

Title Text Night Song, presentation at HAO/NCAR, Tuesday 27 July 2004