Solar dynamo and the effects of magnetic diffusivity

E.J. Zita and Night Song, The Evergreen State College1

Mausumi Dikpati and Eric McDonald, HAO/NCAR2

1. The Evergreen State College, Lab II, Olympia WA 98505<zita@evergreen.edu> and <lunarsong@yahoo.com>

2. High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307 <dikpati@hao.ucar.edu> and <mcdonald@hao.ucar.edu>

Presented at the American Physical Society NW Section MeetingUniversity of Victoria, BC, Canada, 13-14 May 2005

http://www.phys.uvic.ca/APSNW2005/

AbstractWe 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.

( )t

B

v B B

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 planeevolve 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 (1012-14 cm2 s-1) and tachocline (108-10 cm2 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 1012 cm2/s

• Strength of magnetic diffusivity tach at the tachocline (lower boundary, r/R= 0.6-0.65 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 rbe uniform and try two different strengths

Higher = 1012 cm2 /s

Field diffuses quickly at the solar surface

Lower 1011 cm2 /s

Field follows the conveyor belt all the way to the pole

dynamo/pcfast/etacor0001/etasurf01/ssplt3.eps

dynamo/pcfast/etacor0001/ieta0/poster/ssplt3.epsX

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

1012

108

0.6 r/R 1.0

1012

108

0.6 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

1012

108

0.6 r/R 1.0

dynamo/pcfast/etacor0001/ieta1/sacposter/ssplt3.eps

tach = 108 cm2 /s

X

dynamo/ss/var/etasurf1/etacor01/ieta1/pb3.8/movtd/ssplt3.eps

tach = 1010 cm2 /s

dynamo/ss/var/etasurf1/etacor01/ieta3/pb3.8/movtd/ssplt3.eps

Linear rwith higher tach is consistent with observations of

surface flux evolution

0.6 r/R 1.0

1012

1010

Double-step diffusivity profile is also consistent with observations of

surface flux evolution

Results of numerical experiments

Diffusivitysurface:• 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

Diffusivitytachocline:• If is low near the base of the convection zone, then the

flux concentrates near the equator and tachoclineShape:• 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, 1995.

Choudhuri, A.R., The physics of fluids and plasmas: an introduction for astrophysicists, Cambridge: Cambridge UP, 1998.

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-10175.

Sources of figures

Ω-effect and -effect: Carroll and Ostlie, Introduction to modern astrophysics, Addison – Wesley, 1995.

Meridional circulation: http://science.nasa.gov/ssl/pad/solar/dynamo.htm

Solar structure: Kenneth Lang, The Cambridge Encyclopedia of the Sun, Cambridge UP, 2001.

Butterfly diagram: http://www.mhhe.com/physsci/astronomy/fix/student/chapter17/17f35.html

Olympic Mountains: Dr. Ron Blakely, http://jan.ucc.nau.edu/~rcb7/Oceanography.html

Our runs are available at http://download.hao.ucar.edu/pub/green/dynamo/

Our papers and presentations are available at http://academic.evergreen.edu/z/zita/research/summer2004/dynamo/

HAO/Evergreen solar dynamo team