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.

SIMULATING AND PREDICTING SOLAR CYCLES USING A FLUX-TRANSPORT DYNAMO

Mausumi DikpatiHigh Altitude Observatory, NCAR

Principal collaborator:

Other collaborators:

Peter Gilman (HAO/NCAR)

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)

Random vs. persistent, cyclic features

butterfly diagram, polar reversal

mixed-polarity turbulent fields

Courtesy: D.H. Hathaway

Courtesy:

T. Berger

Courtesy: G. de Toma

active longitudes

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

Observational signature forrandom evolution of magnetic fields

Courtesy: P. Sutterlin,

Dutch Open Telescope Team, SUI

Observational signature for systematic, cyclic evolution of solar magnetic fields

Courtesy:

D.H. Hathaway

Many evidences for coexistence of small-scale and large-scale dynamos

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

<

A possible α-effect arising from decay of tilted bipolar active regions

Babcock 1961, ApJ, 133, 572

Mathematical Formulation

Under 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

Displacing andtwisting effect

by kinetic helicity

Diffusion(turbulent + molecular)

(1)

(2)

. BBUB

ηt

, BBBUB

ηαt

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

Analogy with ocean conveyor belt

Broecker 1991

Calibrated Flux-transport Dynamo Model

Near-surface diffusivity same as used by Wang, Shelley & Lean, 2002; Schrijver 2002

in their surface flux-transport models.

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?

Precursor methods

Schatten 2005, GRL

We postulate that “magnetic persistence”,

or the duration of the Sun’s “memory” of its own magnetic field, is

controlled by meridional circulation.

Flux-transport Dynamo-based Prediction Scheme

<

Correlation between spot area and surface magnetic flux

Construction of surface poloidal source from observations

Construction of surface poloidal source from observations (contd.)

Period adjusted to average cycleOriginal 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 (model fed by surface poloidal source continuously)

Observed cycles

We reproduce the sequence of peaks of cycles 16 through 23

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

We obtain similar results for diffusivities between and

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

Skill test for different magnetic diffusivities

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? (Contd.)

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, in preparation)

Comparison of effects of zero and continuously updated surface sources on predicted cycles

Continuous poloidal source updating Zero poloidal source

Can we forecast beyond one cycle ahead?

C

Peak of cycle 20 is the same as when continually update surface poloidal source; but cycle 21 is nearly zero. This is true for diffusivities up to about Above that, dynamo is increasingly diffusion-dominated, and loses

memory of past cycles

Surface poloidal source

constructed from the predicted

bottom toroidal field; BL flux-

transport dynamo in self-excited mode

Skill tests

Zero poloidal source for predicted cycles

Babcock-Leighton poloidal source (from bottom toroidal field) for predicted cycles

Summary and future directions

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

We will do specific forecast for cycle 25 in the near future

Test forecast-model back to cycle 1

Simulate and forecast differences between N and S hemispheres

Go beyond longitude-averaged solar cycle features, e.g., simulate and predict ‘active longitudes’ (in progress – supported by opportunity fund)