2006 Hale Prize Lecture:

A 42 Year Quest To Understand The Solar Dynamo And Predict Solar Cycles

Peter A. Gilman

High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR)

The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Researchunder sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

Biographical Whimsy

I was born on May 28, 1941 in Hartford, Connecticut at 7 a.m.

Five hours later the de facto “curator” of the Hale Prize Medal, John Leibacher, was born in Chicago

Sixty-four years later John asks me how I want my name spelled on the medal.

Some people say we even look alike…..

Sarah and Patrick

Amy

Larry and Priscilla Sarah

Peggy and Peter

How I Started in Solar Physics (1964)

Professor of Meteorology at MIT.

Foremost authority at the time on observations of the general circulation of the Earth’s atmosphere.

My thesis advisor, who suggested I look at the sun.Goal: explain differential rotation using meteorological concepts.

Victor P. Starr

Leo Goldberg (Hale Prize 1984)

Professor of Astronomy at Harvard.

First solar astronomer I encountered

How I Started in Solar Physics (cont.)

Robert Howard

First solar astronomer I received data from.

(Hale Prize 2003)

Early Mount Wilson magnetogram

Three Who Commented on My ThesisJule Charney

Hannes Alfven

Ed Lorenz – (of Lorenz attractor theory )

Professor of Meteorology at MIT. Best known atmospheric dynamicist of his day.

At my thesis seminar (spring 1966) told me very politely that while my thesis was nice, I had really worked on the WRONG PROBLEM. I should have done a convective theory for the solar differential rotation.

Probably reviewer that rejected my thesis for publication, using words originally aimed at his work by Thomas Cowling when he critiqued Alfven’s 1946 theory of sunspots.

Professor Meteorology at MIT.

Rescued my thesis papers and published them in the Journal of the Atmospheric Sciences.

3 NCAR/HAO Mentors (all Directors of HAO)

Walter Orr Roberts

Founding Director of HAO, NCAR, President of UCAR

John Firor

Founding Chair of the Solar Physics Division , AAS.

Walt and John gave me my first science-management position: Chair of the Advanced Study Program, NCAR, 1971

Gordon Newkirk

Chair of the committee to establish the Hale Prize.

Arranged my first invited presentation (SPD, Albuquerque, 1973) and my first review article (Ann. Rev. Astron & Astrophysics 1974)

Scientific Tracks of Developments in Solar Dynamo Understanding

(in the order I became involved)

• ~2D Global MHD (started with my PhD thesis)[subadiabatic radial temperature gradient]

• 3D Global Convection/Differential Rotation/ Meridional Circulation/Dynamo Theory (what Charney recommended)[superadiabatic radial temperature gradient]

• Mean Field Solar Dynamo Theory (what Dikpati urged me to join)[no explicit radial temperature gradient]

• The Future

~2D Global MHD

• my thesis (1966) Baroclinic flow in a uniform magnetic field; goal: explain differential rotation and observed magnetic patterns.

• set aside until after solar tachocline discovered

• revisited 1996 – present as ~2D Global MHD instabilities of differential rotation and toroidal fields, applied to the tachocline

• leading to a theory for active longitudes

3D Global Convection/Differential Rotation/ Meridional Cirulation/Dynamo Theory

(What Charney told me I should have done!)

• 3D theory of solar differential rotation driven by global convection, through Reynolds stresses

• latitude differential rotation ok for sun, but radial rotation gradient and meridional circulation different from observations (learned later from helioseismology)

• 3D global MHD dynamos (Gilman and Miller 1981, ApJ Suppl, 46, 211;Gilman 1983, ApJ Suppl, 53, 243)

• work as dynamos, but not yet as solar dynamos (but work about the way mean field dynamo theory says they should)

• conflicts with helioseismic results

Gilman, Peter A. and Jack Miller, 1981: Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell, ApJ Supplement Series, 46, 211-238

Gilman, Peter A. and Jack Miller, 1981: Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell, ApJ Supplement Series, 46, 211-238

Gilman, Peter A. 1983: Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell. II. Dynamos with cycles and strong feedbacks, ApJ Supplement Series, 53, 243-268

Time

Gilman, Peter A. 1983: Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell. II. Dynamos with cycles and strong feedbacks, ApJ Supplement Series, 53, 243-268

Mean Field Solar Dynamo Theory

• starts with Parker 1954/1955 papers

• formalized by Potsdam school

• by 1970’s many thought solar dynamo problem “solved”, but needed solar rotation increasing inwards in bulk of convection zone

• 1980’s helioseismic results ruled that out

• that plus discovery of solar tachocline led to putting dynamo at base of convection zone; rise of so-called “interface” dynamos(Parker, 1993)

• but surface diffusion and transport could explain some solar cycle features (NRL school)

• led to “flux transport” dynamos, that include these processes, utilizing meridional flow. Correctly simulates many features(Dikpati and others)

• now works for prediction of relative peaks (Dikpati and others)

Classical Signature of Solar Cycle

Observational Constraints Solar Dynamo Theory

Differential rotation with latitude, depth, time Meridional circulation with latitude, depth, time Convection zone depth Existence of solar tachocline Other motions from helioseismic interferences (synoptic maps)

Stru

ctur

e &

Vel

ociti

es

Butterfly diagram for spots Hales polarity laws Field reversals Phase relation in cycle between toroidal & poloidal fields Field symmetry about equator Field “handedness” (current helicity, magnetic helicity) Solar cycle envelope Cycle period – cycle amplitude relation Active longitudes Sunspot group tilts (Joy’s Law), asymmetries between leaders & followers Others???

Mag

netic

Pro

pert

ies

Physical Processes That May beImportant in the Solar Dynamo

• Shearing of poloidal fields by differential rotation

• Lifting & twisting of fields by helical motions

• Rising of magnetically buoyant flux tubes (effect of Coriolis forces)

• Turbulent diffusion of fields (all directions)

• Random walk of surface fields (across photosphere)

• Turbulent pumping of fields (downward)

• Flux transport by meridional circulation

• Flux transport by other near surface flows

• Ejection of flux by CMEs

• Field reconnection in chromosphere, corona

• Field reconnection in convection zone

• Flux injection into convection zone by instability of toroidal field to rising loops

• Joint instability of differential rotation & toroidal field in the tachocline

• Others???

Angular Velocity Domains in Solar Convection Zone & Interior, from Helioseismology

First Solar Dynamo Paradox

• Mean field dynamo theory applied to sun required rotation increase inward

• Global convection models predicted rotation approximately constant on cylinders, but with equatorial acceleration ~30%

In 1970s prevailing view was that global convection theory must be wrong (I never shared that view).

In 1980s helioseismic inferences proved both were wrong, but dynamo theory more wrong than convection theory.

ConclusionMove dynamo to base of convection zone

(Ed DeLuca PhD thesis)

Second Solar Dynamo Paradox

• To produce sunspots in low latitudes requires toroidal fields ~105 gauss at the base of the convection zone (influence of Coriolis forces on rising tubes). Recent simulations by Fan indicate, for tubes of finite cross-section, may need Toroidal Field only 20-30kG.

• 105 gauss fields very hard to store – must be below convectively unstable layer (overshoot layer subadiabatic?)

• 105 gauss fields are 102 x equipartition – won’t that suppress dynamo action? (but apparently does not in geo case!)

ResolutionInterface Dynamos

Flux Transport Dynamos

My involvement in applying flux transportdynamos to the sun is to due to …

Mausumi Dikpati

In 1996 I introduced her to the problem of instability of differential rotation and toroidalfield in the solar tachocline.

In ~2000 she persuaded me to become involved in application of flux transportdynamos to simulate and predict solar cycles.

Properties of Solar Cycle

• Equatorward migration of sunspot-belt

• Poleward drift of large-scale radial fields, from follower spots

• Polar field reversal at sunspot maximum

Courtesy: D.H. Hathaway

Large-scale Dynamo Processes

(i) Generation of toroidal (azimuthal) field by

shearing a pre-existing poloidal field (component in

meridional plane) by differential rotation (Ω-

effect )

(ii) Re-generation of poloidal field by lifting and twisting a toroidal flux tube by helical

turbulence (α-effect)

(iii) Flux transport by meridional circulation

= FLUX-TRANSPORT DYNAMO

<

Sun’s “memory” of past cycles controlled by

meridional circulation.

Schematic Summary of PredictiveFlux-Transport Dynamo Model

Shearing of poloidal fields by differential rotation to produce new toroidal fields, followed by

eruption of sunspots.

Spot-decay and spreading to produce new surface global

poloidal fields.

Transport of poloidal fields by meridional circulation (conveyor belt)

toward the pole and down to the bottom, followed by regeneration of new toroidal fields of opposite sign.

Mathematical FormulationUnder MHD approximation (i.e. electromagnetic variations are nonrelativistic),

Maxwell’s equations + generalized Ohm’s law lead to induction equation :

Applying mean-field theory to (1), we obtain the dynamo equation as,

Differential rotationand meridional circulation

from helioseismic data

Poloidal field source from active region

decay

Turbulent magnetic diffusivity

(1)

(2)

. BBUB

ηt

, BBBUB

ηαt

Toroidal field Poloidal field Meridionalcirculation

Differentialrotation

, ˆ ,, ˆ ,, φφφ tθrAtθrB eeB ,ˆ ,Ωsin, φθrθrθr euU

Assume axisymmetry, decompose into toroidal and poloidal components:

Contours: toroidal fields at CZ base Gray-shades: surface radial fields

Observed NSO map of longitude-averaged photospheric fields

Validity Test of Calibration

(Dikpati, de Toma, Gilman, Arge & White, 2004, ApJ, 601, 1136)

Highlights Of RecentFlux Transport Dynamo Results

(prior to prediction results)

• Dikpati & Charbonneau 1999– Dynamo period inversely proportional to meridional circulation

speed (latitudinal flow at bottom controls)

• Dikpati and Gilman 2001– Addition of “α-effect” at bottom of convection zone, due to

multiple instabilities there, leads to strong preference for toroidal

and poloidal fields antisymmetric about the equator

Highlights Of RecentFlux Transport Dynamo Results (cont.)

• Dikpati et al 2004 - – “Calibrated” Flux Transport dynamo solutions simulate features of

polar field reversal in cycle 23 (current cycle)• late arriving polar field reversal, due to smaller flux being transported to

poles

• South pole reversal ~ 1 year later than North

Causes: - Smaller poloidal flux available for poleward transport in

cycle 23- slowdown in meridional circulation in 1996-2002

- small reversed mc in NH speeded up reversal there compared to SH

– Also established solar memory at near one full magnetic cycle (17-22 years) due to speed of meridional flow

(ApJ, 601, 1136)

Highlights Of RecentFlux Transport Dynamo Results (cont.)

• Dikpati, Gilman, and MacGregor 2005– If oscillatory poloidal fields unable to penetrate through

tachocline, due to magnetic “skin effect” (Garaud 1999), then can not get solar-type dynamo unless meridional circulation toward equator at the bottom of the convection zone of ~ 2 m/sec is present. So-called “interface dynamos” without meridional circulation, can not work.

• Dikpati, Gilman and MacGregor 2006– For a broad range of magnetic diffusivities for the overshoot

layer of the convection zone and below, flux transport dynamos that satisfy solar observational constraints also over time pump both oscillatory and non-reversing toroidal fields into the outer layers of the solar interior.

Period adjusted to average cycleOriginal data (from Hathaway)

Assumed pattern extending beyond present

Construction of Surface Poloidal Source From Observations

Three Techniques for Treating Surface Poloidal Source In Simulating and Forecasting Cycles

1) Continuously update observed surface source including cycle predicted (a form of 2D data assimilation)

2) Switch off observed surface source for cycle to be predicted

3) Substitute theoretical surface source, derived from dynamo-generated toroidal field at the bottom, for observed surface source

Forecasted quantity: integrated toroidal magnetic flux at the bottom in latitude range of 0 to 45 degree (which is the sunspot-producing field)

We use these three techniques in succession to simulate and forecast

Simulating relative peaks of cycles 12 through 24 We reproduce the sequence of peaks of cycles 16 through 23

We predict cycle 24 will be 30-50% bigger than cycle 23

(Dikpati, de Toma & Gilman, 2006, GRL)

Cycle 24 prediction using ‘precursor method’ (Schatten 2005)

Skill Test: Correlation Between Observed and Predicted Cycle Peaks

How Does The Model Work?

Red and blue contours are poloidal field lines in the plane of the board;

red (blue) denotes clockwise (counterclockwise) field directions

Color shades denote toroidal field strengths; orange/red denotes

positive (into board) fields, green/blue negative

Latitudinal component of poloidal fields near the bottom is primary

source of new toroidal fields

How Does The Model Work?

(cont.)

Latitudinal B Toroidal B

Latitudinal fields in the conveyor belt from past 3 cycles combine near the bottom to form the source of new cycle

toroidal field.

Mechanism is shearing by latitudinal differential

rotation.

(Dikpati & Gilman, 2006, ApJ, 20 Sep. issue, in press)

Next Steps in Solar Cycle Predictions

• Extend back to cycle 1• Extend to two cycles ahead• Separate N and S hemispheres• Shorten averaging length of input data

Generalizations of Flux Transport dynamo model• Include jxB feedbacks• Include low longitudinal wave number departures from

axisymmetry.

Properties of 2D MHD Instability of Differential Rotation and Toroidal Magnetic Field

ToroidalMagnetic Field

DifferentialRotation

Angular momentum transport toward the poles primarily by the Maxwell Stress (perturbations field lines tilt

upstream away from equator)

Magnetic flux transport away from the peak toroidal field by the Mixed Stress (phase difference in longitude between

perturbation velocities & magnetic fields)

Some Elements of a Theory of Active Longitudes (Dikpati and Gilman)

• h increases poleward• Toroidal ring shrinks• Fluid in ring spins up

m = 0

• h redistributes but no net poleward rise• Toroidal ring deforms, creating Maxwell Stress• Fluid flow inside ring deforms but does not spin up

m = 2

m = 1

• h redistributed but no net rise• Toroidal ring tips but remains

same circumference• Fluid in ring keeps same

speed but flow tips

Schematic Of Modes Of Instability

Nonlinear Tipping of Toroidal Fieldsin Tachocline

(Cally, Dikpati and Gilman, 2003)

Peak Toroidal Field 25 kG Peak Toroidal Field 100 kG

What is MHD Shallow Water System?

• Spherical Shell of fluid with outer boundary that can deform

• Upper boundary a material surface

• Horizontal flow, fields in shell are independent of radius

• Vertical flow, field linear functions of radius, zero at inner boundary

• Magnetohydrostatic radial force balance

• Horizontal gradient of total pressure is proportional to the horizontal gradient of shell thickness

• Horizontal divergence of magnetic flux in a radial column is zero

(Gilman, 2000)

Global Instabilities of Solar TachoclineAssume Differential Rotation from Helioseismology

Hydrostatic Models Result

2D HD Stable

2D MHD Unstable for wide range of toroidal fields

“Shallow Water” HD Overshoot part Unstable

Radiative part Stable

Shallow Water” MHD Both Parts Unstable

SW HD Instabilities suppressed for broad peak fields 10 kG

Multi-layer SW HD, MHD Expect Instability

3D HD, MHD Expect Instability; unstable for MHD when DR, TF independent of radius

3D Nonhydrostatic HD, MHD More modes of Instability

Magnetic buoyancy enters

Dyn

am

o P

ote

nti

al

Active Longitudesfrom Kitt Peak

Magnetograms at Start of Solar Cycle 23

(de Toma, White and Harvey,

ApJ 529, 1101 (2000) )

A Shallow-Water Theory of Active Longitudes(Dikpati & Gilman, 2005, ApJ, L193)

CR

1921

1927

1936

The Future

Stars

What works for the sun

likely to work for many stars

Implement non-linear MHD shallow water model for active longitudes.

Bring shallow water MHD and flux transport dynamo theory together, in low order non-axisymmetric

flux transport dynamo.