The Solar Cycle: Observations

and Dynamo Modeling

Mausumi Dikpati

HAO/NCAR

1

Some

milestones

in defining

solar cycle

1611: discovery

of sunspot with

telescope

Some milestones in defining the solar cycle (contd.)

Heinrich Schwabe 1843: Sunspot cycle with periodicity of ~10 year (Astronomische Nachrichten, vol. 20., no. 495, 1843)

Rudolf Wolf

1848:

Historical

reconstruction

of sunspot

cycle

Richard Christopher

Carrington 1860:

Differential rotation from

sunspots

Some milestones in defining the solar cycle (contd.)

Edward Maunder 1890: Butterfly diagram; signature of cycle

(original diagram resides at HAO)

George Ellery Hale 1908: Strong magnetic fields in sunspots

Lat

itu

de

Time

What causes solar cycle?

If solar magnetic fields were primordial, they wouldn’t vary cyclically

Furthermore if there wouldn’t have been regeneration of magnetic fields,

all would have vanished from the convection zone in just 10 years

Hypothesis: There must be an oscillatory dynamo inside the Sun which

is responsible for generation and cyclic evolution of magnetic fields

What is the nature of that dynamo?

Milestones in understanding the solar cycle

Eugene Parker (1955) proposed the first solar dynamo

model by including the Sun’s differential rotation and

helical turbulence

Parker’s model can be understood if the Sun’s

vector magnetic fields be decomposed into its

toroidal and poloidal components

Generation of toroidal field by

shearing a pre-existing poloidal field

by differential rotation (Ω-effect )

Milestones in understanding the solar cycle

• Parker obtained an equatorward-propagating

oscillatory dynamo-wave solution from his

model

• He introduced the concept of “magnetic

buoyancy” to explain how magnetic flux rises to

the surface of the Sun

• Identifying the sunspots as the toroidal fluxtubes

risen to the surface, their equatorward

propagation was explained by the dynamo wave

To close the dynamo loop, it is necessary to regenerate the poloidal

fields from toroidal fields

Parker proposed the re-

generation of poloidal

field by lifting and

twisting a toroidal flux

tube by helical

turbulence (α-effect)

lifting

twisting

Field line

Evidence of twisted loops from 3D MHD simulations

Nelson, Brown, Brun, Miesch & Toomre, 2014, Solar Phys.

Conditions for equatorward propagation of dynamo wave

•Rising convective plume expands into lower

density layers

•Coriolis force (NH) turns flow vectors to their

right

•Thus, curl V < 0, clockwise vorticity is

generated

•For rising plume, w > 0

•So kinetic helicity < 0 in NH

•For isotropic turbulence, α ~ -(kinetic helicity)

So α > 0 (NH)

German school (Steenbeck, Krause & Radler 1969)

developed mean-field formalism to mathematically

solve for equatorward dynamo wave solution

dΩ/dr < 0

α > 0

The first theoretical solution of solar cycle from

an oscillatory αω dynamo

In 1960’s and 70’s, equatorward

propagating dynamo wave was

obtained by assuming a radial

differential rotation increasing

inward throughout the convection

zone.

3D mean-field αω dynamo

Stix (1971) formulated a classical 3D αω dynamo with the aim

of understanding sector boundary structure, which shows a

certain large-scale longitude dependence that varies with solar

cycle

An alternative

concept for

identifying the

poloidal field

generation

developed by

Babcock (1961)

and Leighton

(1969)

dΩ/dr < 0

α > 0

α-effect works near the surface, Ω-effect in the convection zone

Identifying the poloidal source as arising from

the decay of tilted, bipolar active regions

Babcock and Leighton showed the poleward

dispersal of the large-scale poloidal fields, and

hence the polar reversal every 11 -year can be

explained by preferential poleward drift of

trailing flux by a random walk from

supergranules.

Long-term modulation of

amplitude of 11-year solar cycle

Jack Eddy (1976) reexamined historical sunspot

records as well as geomagnetic and

concentration to definitively show the existence of

multicycle time durations of extremely low solar

activity

The grand minimum occurred between 1645-1715

he named the “Maunder minimum”

C14

Little Ice age and Maunder minimum

A new search for differential

rotation and dynamo model

Differential rotation

(cylindrical contours):

Taylor-Proudman state

Helicity

negative at

sunspot

latitudes

Gilman & Miller (1981): development of first

full 3D convective dynamo

Poleward migration of toroidal fields was found (Gilman 1983)

So either the differential rotation or the dynamo was wrong !

This new challenge led to further development of full 3D convective

models; therefore solar dynamo model developments proceeded on two

parallel tracks since 1980s: (i) mean-field approach and (ii) full 3D

convective simulation

∂Ω∕∂r > 0 α > 0

Biggest challenge posed by helioseismology in 1990s

Tim Brown (1989) and colleagues showed there is almost no ∂Ω∕∂r in convection zone,

and strong ∂Ω∕∂r > 0 exists at convection zone base at low latitudes

Thompson (1991) and

colleagues showed:

convection zone base is

located at 0.713R; below

is radiative zone, and

above is subadiabatic overshoot zone

Biggest challenge posed by helioseismology in 1990s

Tim Brown (1989) and colleagues showed there is almost no ∂Ω∕∂r in convection zone,

and strong ∂Ω∕∂r > 0 exists at convection zone base at low latitudes

Thompson (1991) and

colleagues showed:

convection zone base is

located at 0.713R; below

is radiative zone, and

above is subadiabatic overshoot zone

Storage issue of strong toroidal field in the turbulent convection zone became

highlighted. Can toroidal fields be stored long enough at cz base to be amplified to the

strength needed to produce sunspot fields at the surface?

Mean-field αω convection zone dynamos do

not work for the Sun !

Plausible remedy I: Thin-layer dynamos

Ed DeLuca

(PhD thesis)

See De Luca & Gilman 1986

Gilman, Morrow & De Luca 1989

Brandenburg & Charbonneau 1992

Ferriz-Mas, Schmitt & Schuessler 1994

Axel Brandenburg

(HAO Postdoc

in 1990s)

Explored thin-layer dynamos, locating the shear layer as well as α-effect

in a thin layer at the base of the convection zone

Cherri Morrow

(Grad Student in 1990s)

Plausible remedy II: Interface dynamos

Paul Charbonneau Keith Macgregor Colin Roald

(Grad student in late 1990s)

Explored interface dynamos, locating the shear layer below

the core-envelope interface and α-effect above that See Parker 1993

MacGregor & Charbonneau 1996

Tobias 1996

Charbonneau & Macgregor 1997

Roald 1997

Another big challenge

from magnetogram

Sunspot-belt migrates

equatorward

Large-scale diffuse fields drift

poleward

There is a phase relationship

between these two

components; polar reversal

happens during sunspot

maximum

A paradigm shift: Babcock-Leighton flux-transport

dynamos

Po

le

+ Equator

Meridional

circulation

1R

0.7R

0.6R

Observed NSO map of

longitude-averaged

photospheric fields

Contours: toroidal fields at CZ base

Gray-shades: surface radial fields

Dikpati, de Toma, Gilman, Arge & White 2004

Wang & Sheeley, 1991 Choudhuri, Schüssler, & Dikpati, 1995 Durney, 1995 Dikpati & Charbonneau, 1999

Küker, Rüdiger & Schültz, 2001 And many others

Dick White

Giuliana de Toma

2D dynamical Babcock-Leighton flux-transport dynamos

Matthias Rempel

Lorentz force (jXB) back-

reaction creates

curvature stress which

creates, in turn, prograde

and retrograde jets on top

of average rotation – can

explain torsional

oscillation at high

latitudes.

Combining

thermal effect

along with jXB

back-reaction,

mean-field flux-

transport

dynamos can

simulate low-

latitude torsional

oscillation

2D Babcock-Leighton flux-transport

dynamo-based prediction scheme

3 predictions were

issued for solar

cycle 24:

Delayed onset of cycle 24

Strong cycle 24

South stronger than North

✓ ✗ ✓

Dikpati, De Toma & Gilman 2006

Dikpati et al. 2007

Dikpati et al. 2010

2D Babcock-Leighton flux-transport dynamo-based

prediction scheme

3 predictions were

issued for solar

cycle 24:

Delayed onset of cycle 24

Strong cycle 24

South stronger than North

✓ ✗ ✓

Wrong tilts of a few large spots at the

end of cycle 23 may have reduced the

poloidal seed field

Data was nudged for entire 12 cycles

without frequent updates

Reasons for failure in amplitude prediction:

Dikpati et al.

(2006) did not

consider phase-

shift between

North and South

Bernadett Belucz is investigating N/S

asymmetry in solar cycle (her PhD thesis)

3D Babcock-Leighton flux-transport dynamos

At low latitudes, small-

scale features appear

due to eruption of tilted

bipolar spots, but their

dispersal by diffusion,

meridional circulation

and differential rotation

produces mean poloidal

fields

• Trailing flux drifts towards the

poles in a series of streams

and cause polar reversal

• Toroidal field butterfly

diagram shows equatorward

migration, cycle period is

governed by meridional

circulation

Miesch & Dikpati (2014); See also Yeates & Munoz-Zaramillo (2013)

Mark Miesch

Full 3D convective

dynamo simulations I.

Miesch & colleagues

Augustson et al. (2015)

Grand

Minimum!

Origins of Flux Emergence!

Nelson et al. (2013)

Kyle Augustson (ASP Postdoc)

Solar convective dynamo: self-consistent maintenance of the solar differential

rotation and emerging flux (Fan and Fang 2014, ApJ, 789, 35)

Full 3D convective dynamo

simulations II. Fan & Fang

Summary

First solar dynamo model was built 70 years ago

Babcock-Leighton flux-transport solar dynamos were created as a paradigm shift

to overcome challenges posed by helioseismology and magnetic butterfly

diagram, and remain as a leading class of solar dynamo models

Full 3D convective dynamos are continuing in a parallel track since the first model

of Gilman & Miller (1981), and have reached the level that they self-consistently

produce cycles and flux emergence

HAO has always been one of the leaders in both dynamo approaches

3D Babcock-Leighton dynamo models are progressing for operating in data-

assimilative mode and hence are showing prospects for improvements in

predictions

Ultimate goal is to merge the two parallel approaches and build a grand solar

dynamo model