DYNAMO PREDICTIONS

1
DYNAMO PREDICTIONS

• Mausumi Dikpati
• High Altitude Observatory, NCAR

Principal collaborator
Peter Gilman (HAO/NCAR)
Other collaborators
C.N. Arge (AFGL), P. Charbonneau (Montreal), G.
de Toma (HAO/NCAR), D.H. Hathaway (NASA/MSFC),
K.B. MacGregor (HAO/NCAR), M. Rempel (HAO/NCAR),
O.R.White (HAO/NCAR)
2
Review simulations of relative peaks of cycle 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)
3
Review Timing prediction for cycle 24 onset
Dikpati, 2004, ESA-SP, 559, 233
4
Review End of cycle 23 in butterfly diagram
Pred. cycle 24 onset
Cycle 23 onset
5
Review End of cycle 23 in white light corona

Current coronal structure not yet close to
minimum more like 12-18 months before minimum
Corona at last solar minimum looked like this
6
Schematic summary of predictive flux-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.
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Mathematical Formulation
Under MHD approximation (i.e. electromagnetic
variations are nonrelativistic), Maxwells
equations generalized Ohms law lead to
induction equation
(1)
Applying mean-field theory to (1), we obtain the
dynamo equation as,
(2)
Turbulent magnetic diffusivity
Differential rotation and meridional circulation
from helioseismic data
Poloidal field source from active region decay
Assume axisymmetry, decompose into toroidal and
poloidal components
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Poloidal and toroidal field equations
(3a)
(3b)
(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
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An a-effect arising from decay of tilted bipolar
active regions
Babcock 1961, ApJ, 133, 572
A Babcock-Leighton type poloidal source-term can
be represented as,
Latitude dependence
Quenching
Confines in a thin layer near the surface
Amplitude
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Calibrated Model Solution
Contours toroidal fields at CZ base Gray-shades
surface radial fields
Observed NSO map of longitude-averaged
photospheric fields
(Dikpati, de Toma, Gilman, Arge White, 2004,
ApJ, 601, 1136)
11
Construction of surface poloidal source
In the Babcock-Leighton flux-transport dynamo
In the dynamo-based predictive tool
The equation (1b) remains unchanged. (1a) becomes
(3a)
(3b)
12
Construction of surface poloidal source (contd.)
Original data (from Hathaway)
Period adjusted to average cycle
Assumed pattern extending beyond present
13
Evolution of a predictive solution
Toroidal field
Latitudinal field
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)
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Sensitivity tests of predictive model

• Separating data into North and South hemispheres

• Varying the averaging length in the observed
  surface poloidal source

• Making more realistic latitudinal migration of
  the surface source, rather than steadily
  migrating Gaussian (see Cameron Schuessler,
  2006)

• Varying the meridional flow with time and depth,
  and diffusivity with depth

Constraints that should be applied

• Retain constraints from observations and theory,
  on differential rotation, meridional circulation,
  surface diffusivity, depth of convection zone and
  tachocline

• Recalibrate model to large-scale solar cycle
  features and correct period

15
Separating N S hemispheres and varying
averaging length

Model reproduces relative sequence of peaks in N
S separately, but smoothes short-time scale
solar cycle features
16
Skill tests for North and South
17
Correlation between area and flux
(Dikpati, Gilman de Toma, 2006, in preparation)
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Observed N/S Asymmetry in cycle peaks
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Skill testsfor N-S differences
20
Correlation coefficients as function of averaging
length in input data
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Summary

• High skill extends to input data separated into
  N S hemispheres

• Even short-period of averaging of input data
  leads to high skill in forecast when compared to
  the long-term averaged observations

• Forecasting of difference between N S
  hemisphere peaks has less but still significant
  skill

• 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

22
How helioseismology can help us to achieve our
future goals

• We will simulate and predict N S hemispheric
  features by simultaneously incorporating N S
  data, to examine effects of cross-equatorial
  transport and diffusion of flux
• We have partial information about N/S asymmetry
  in meridional flow (from Irene and Rudi) since
  2001. Could we get longer-term information as
  well as information about deeper layers ?

23
How helioseismology can help us to achieve our
future goals (contd.)

• Our active-longitude theory (Dikpati Gilman,
  2005, ApJ) predicts that tachocline bumps
  migrating in longitude govern the appearance and
  evolution of active longitudes.

• Could helioseismology tell us about such
  asphericities from sound speed anomalies?
  Expected longitudinal wavenumbers m1 and 2.

• These bumps are predicted to have a specific
  phase relationship with global velocity patterns
  at the same depth

• Could helioseismology find global m1 and 2
  velocity patterns in tachocline, using
  deep-focus time-distance measurements?

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Answering mean-field dynamo skeptics

• Our results speak for themselves skeptics have
  used no model that contains either meridional
  circulation or Babcock-Leighton type surface
  poloidal source. Cant use the output from
  (their) model B to disprove the skill of (our)
  model A

• Predicting solar cycle peaks using mean-field
  dynamo is impossible

• Too many assumed inputs

• Most inputs constrained by observations model
  calibrated to observations to set diffusivity

• Meridional circulation is unimportant, so can be
  ignored

• Meridional circulation is crucial for getting
  the correct phase between the poloidal and
  toroidal fields, and for transporting poloidal
  fields of previous cycles to high-latitudes at
  depth where seed for new cycle is created

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Answering mean-field dynamo skeptics (contd.)

• Babcock-Leighton poloidal source old-fashioned

• It is observed, so cant be ignored

• Solar dynamo is in deterministic chaos, and
  heavily nonlinear, therefore unpredictable

• We have demonstrated predictive skill by
  reducing the dynamo to a linear system forced at
  the upper boundary by the observed poloidal
  fields of previous cycles. Atmospheric models
  achieve predictive skill beyond chaotic limits
  if they involve known boundary forcing (El Nino
  forecasts and annual cycles). Nonlinear
  feedbacks of induced magnetic fields on inducing
  solar motions (e.g. differential rotation) are
  small (torsional oscillations)