Solar dynamo and the effects of magnetic diffusivity E.J. Zita and Night Song, The Evergreen State College 1 Mausumi Dikpati and Eric McDonald, HAO/NCAR 2 1. The Evergreen State College, Lab II, Olympia WA and 2. High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder, CO and Presented at the American Physical Society NW Section Meeting University of Victoria, BC, Canada, May

Abstract 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 cycles.

Outline 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 energy and radiation  Cell phone disruption Bright, widespread aurorae Solar flares, prominences, and coronal mass ejections Global warming? next solar max around 2011 CME movie

Magnetic field components Poloidal field Toroidal field We model changes in the poloidal magnetic field. poloidal toroidal

Poloidal flux diffusion cycle science.nasa.gov/ ssl/pad/solar/dynamo.htm Diffuse poloidal field migrates poleward as the mean solar field reverses

What’s going on inside the Sun?

Solar dynamo processes Ω-effect: Differential rotation creates toroidal field from poloidal field  -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  (r) vary through the convection zone? How does the shape and strength of  (r) affect the evolution of poloidal field and the solar dynamo?  r

2D kinematic dynamo model “Evolve” code by Mausumi Dikpati et al. uses set flow rates v(r, ,t). Equatorward propagating dynamo wave is the source for poloidal magnetic field. Calculate evolution of magnetic field B(r, , t) with induction equation where B=magnetic field and magnetic diffusivity  = resistivity/permeability. Model reproduces observations of recent solar cycles.

Poloidal magnetic field evolution 2 sources for the poloidal field *  effect at the tachocline *  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 Tachocline Surface

Magnetic diffusivity depends on plasma properties and dynamics Diffusivity  = resistivity/permeability Classical resistivity depends on temperature (~ T -3/2 ) Convective turbulence enhances resistivity and therefore enhances diffusion Estimate ranges for magnetic diffusivity  surface ( cm 2 s -1 ) and  tachocline ( cm 2 s -1 ) Lower  : higher conductivity: slower field changes Higher  : higher resistivity: faster field changes

How does magnetic diffusivity change across the convection zone? Strength of magnetic diffusivity  surface at the photosphere (upper boundary, r/R=1) is estimated at cm 2 /s Strength of magnetic diffusivity  tach at the tachocline (lower boundary, r/R= in these simulations) is unknown Shape of solar diffusivity profile  (r) is unknown Convective turbulence may cause diffusivity gradients We tested four shapes, or profiles, of  (r) We tested each  (r) profile for various values of  tach

We tested four profiles for  (r) : Single-Step Double-Step Flat

GOALS: Find how evolution of diffuse poloidal field depends on  (r) Constrain both strength 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 Analyze evolution of fields with new  (r) profiles.

Compare different  strengths: field diffuses if diffusivity is too high Test: let  r  be uniform and try two different strengths Higher  = cm 2 /s Field diffuses quickly at the solar surface Lower  cm 2 /s Field follows the conveyor belt all the way to the pole dynamo/pcfast/etacor0001/etasurf01/ssplt3.eps dynamo/pcfast/etacor0001/ieta0/poster/ssplt3.eps X  r/R

Compare different profiles: gradients in  concentrate flux, especially when  tach is low Single-step profile yields excessive flux concentration Linear profile yields reasonable flux diffusion X r/R 1.0  r/R 1.0  dynamo/pcfast/etacor0001/ieta1/sacposter/ssplt3.eps dynamo/ pcfast/etacor0001/ieta3/poster/ssplt3.eps

Higher diffusivity  tach at tachocline relaxes flux bunching due to  gradients r/R 1.0  dynamo/pcfast/etacor0001/ieta1/sacposter/ssplt3.eps  tach = 10 8 cm 2 /s X dynamo/ss/var/etasurf1/etacor01/ieta1/pb3.8/movtd/ssplt3.eps  tach = cm 2 /s

dynamo/ss/var/etasurf1/etacor01/ieta3/pb3.8/movtd/ssplt3.eps Linear  r  with higher  tach is consistent with observations of surface flux evolution 0.6 r/R 1.0 

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

Results of numerical experiments Diffusivity surface : If  is too low at the surface, then magnetic flux becomes concentrated there – particularly at the poles If  is too high the flux diffuses too much Diffusivity tachocline : If  is low near the base of the convection zone, then the flux concentrates near the equator and tachocline Shape: 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  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 zone? 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 observations Compare results with theoretical estimates of turbulence-enhanced magnetic diffusivity near the base of the convection zone 3D dynamo simulations with  r  Predict future solar cycles

References Carroll, B.W. and Ostlie, D.A., Introduction to modern astrophysics, Addison – Wesley, Choudhuri, A.R., The physics of fluids and plasmas: an introduction for astrophysicists, Cambridge: Cambridge UP, 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

Acknowledgements 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

Sources of figures Ω-effect and  -effect: Carroll and Ostlie, Introduction to modern astrophysics, Addison – Wesley, Meridional circulation: Solar structure: Kenneth Lang, The Cambridge Encyclopedia of the Sun, Cambridge UP, Butterfly diagram: Olympic Mountains: Dr. Ron Blakely, Our runs are available at Our papers and presentations are available at

HAO/Evergreen solar dynamo team