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SOLAR DYNAMO MODELING AND PREDICTION. Mausumi Dikpati High Altitude Observatory, NCAR. Observational signature for global evolution of solar magnetic fields. From url of D. Hathaway. What is a dynamo?. All these magnetic fields are maintained by dynamo action. - PowerPoint PPT Presentation
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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.
SOLAR DYNAMO MODELING AND PREDICTION
Mausumi DikpatiHigh Altitude Observatory, NCAR
Observational signature for global evolution of solar magnetic fields
From url of D. Hathaway
What is a dynamo?
A dynamo is a process by which the magnetic field in an electrically conducting fluid is maintained
against Ohmic dissipation
In astrophysical object, there can always be a dynamo whenever the plasma consists of seed magnetic fields
and flow fields
All these magnetic fields are maintained by dynamo action
Flux-transport Dynamo
(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
<
Fixing dynamo ingredients While Ω -effect and meridional circulation can be fixed from observations, the
α–effect could be of different types as suggested theoretically. One directly observed α–effect can arise from decay of tilted, bipolar active regions
Babcock 1961, ApJ, 133, 572
How a Babcock-Leighton Flux-transport dynamo works
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:
Poloidal and Toroidal Equations and Boundary Conditions(3a)
(3b)
, 222 ,,
sin1sin
sin1
φφ BBθrSAθr
ηAθrθrt
A
u
φθφr Buθ
Brurrt
φB 1 , 222
sin1ˆΩ sin φφφp Bθr
ηBηθr
eB
(i) Both poloidal and toroidal fields are zero at bottom boundary
(ii) Toroidal field is zero at poles, whereas poloidal field is parallel to polar axis
(iii) Toroidal field zero at surface; poloidal fields from interior match potential field above surface
(iv) Both poloidal and toroidal fields are antisymmetric about the equator
Evolution of Magnetic FieldsIn a Babcock-Leighton Flux-Transport Dynamo
Dikpati & Charbonneau 1999, ApJ, 518, 508 Dynamo cycle period ( T ) primarily governed by meridional flow speed
Refining a Babcock_Leighton flux-transport dynamo
A full-spherical-shell Babcock-Leighton dynamo relaxes to a quadrupole parity, violating the observed Hale’s polarity rule which
implies dipole parity about the equator Remedy: a tachocline α-effect
Dikpati & Gilman, 2001, ApJ, 559, 428; Bonanno et al, 2002, A&A, 390, 673
Calibrated Flux-transport Dynamo Model
Near-surface diffusivity same as used by Wang, Shelley & Lean, 2002; Schrijver 2002
in their surface flux-transport models.Zita is exploring in details the sensitivity of diffusivity profiles to flux-transport dynamo
N-Po
leS-
Pole
Red: α -effect locationGreen: rotation contoursBlue: meridional flow
Magnetic diffusivity used Flows derived from observations
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
Why is solar cycle prediction important?
Qian, Solomon & Roble; GRL, 2006
High atmosphere density varies as
function of solar cycle
Density variation at 400 km depth is 2-3 times that of cycle amplitude variation
Satellites are placed at that altitude, and so drag due to density
variation affects their lifetime
Issues with polar field precursor techniquesQ1. How can the 5.5 year-old polar fields from previous cycle determine
the next cycle’s amplitude?
Q2. Do they remain radial down to shear layer?
Q3. Are stronger radial fields associated with stronger or weaker latitudinal fields?
It depends on field geometry
inside convection zone: see 3
possible cases
< << 1. Weak radial;
strong latitudinal 3. Strong radial; weak latitudinal
2. Weak radial; weak latitudinal
Flux-transport dynamo-based prediction scheme
Meridional circulation plays an important role in this
class of model, by governing
a) the dynamo cycle period
b) the memory of the Sun’s past magnetic fields
<
Timing Prediction For Cycle 24 Onset
Dikpati, 2004, ESA-SP, 559, 233
Recent Support For Delayed Onset Of Cycle 24Cycle 23
onsetPred.
cycle 24 onset
Recent Support For Delayed Minimum At End of Cycle 23
Mar. 29, 2006
Early 1996Nov. 1994
This coronal structure not yet close to minimum; more like 18 months before minimum
Corona at last solar minimum looked like this
Amplitude prediction: Data-assimilation In Solar Cycle Models
• Given the strong correlation between area and flux, we apply data-assimilation techniques to our
calibrated dynamo
• Such techniques used in meteorology for 50 years, but just starting in solar physics
• Appropriate time for data-assimilation in solar physics: large new data-sets becoming available
• First example; predicting relative solar cycle peaks.
• Future goal: simultaneous predictions of cycle amplitude and timing, using “sequential” and
“variational” data-assimilation techniques
Construction Of Surface Poloidal Source: 2D Data Assimilation
Period adjusted to average cycle
Original data (from Hathaway)
Assumed pattern extending
beyond present
Three techniques for treating surface poloidal source in simulating and forecasting cycles
1) Continuously update of 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, 33, L05102
Evolution of predictive solution
Color shades denote latitudinal (left) and toroidal (right) field strengths; orange/red denotes positive fields, green/blue negative
Latitudinal fields from past 3 cycles are lined-up in high-latitude part of conveyor belt
These combine to form the poloidal seed for the new cycle toroidal field at the bottom
(Dikpati & Gilman, 2006, ApJ, 649, 498)
Latitudinal field Toroidal field
How Does The Model Work
Color shades denote latitudinal (top) and toroidal (bottom) field strengths;
orange/red denotes positive fields, green/blue negative
Latitudinal fields from past 3 cycles are lined-up in high-latitude part of
conveyor belt
These combine to form the poloidal seed for the new cycle toroidal field
at the bottom
Dikpati & Gilman, 2006, ApJ, 649, 498
Latitudinalfield
Toroidal field
Results from separating North and South hemispheres
Model reproduces:
N/S asymmetry when large
relative sequence of peaks in N & S separately
short time-scale (monthly) features within a cycle; high surface diffusivity and long
traversal time of surface poloidal fields to shear layer
smooths short-term features in the model
Model cannot reproduce:
Observations indicate N/S asymmetry, often persisting for several cycles, but
no systematic switching in strength between N & S
Dikpati, Gilman, de Toma & Ghosh 2007, Solar Physics (submitted)
How many cycles can we predict ?
Surface poloidal source constructed from the
predicted bottom toroidal field; BL flux-transport dynamo in
self-excited mode
Summary Meridional circulation is an essential ingredient for large-scale
solar dynamo
Flux-transport dynamo with input of observed surface magnetic flux displays high skill in forecasting peak of the next solar cycle, as
well as significant skill for 2 cycles ahead
High skill extends to input data separated into N & S hemispheres
High surface diffusivity and long transport time to the bottom together smooth out the short-term observational features; therefore we will not be able to forecast short-term solar cycle features by this
model
Future Directions
Going beyond axisymmetry: simulating and predicting the Sun’s active-longitudes
Simulating Grand-minima
Predict amplitude and timing simultaneously by applying “sequential” assimilation technique