the solar cycle: observations and dynamo modeling · dick white giuliana de toma. 2d dynamical...
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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