Solar cycle prediction using dynamos and its implication for the solar cycle

2011/08/30 2011 ILWS Science Workshop 1

Solar cycle prediction using dynamos and its implication for the solar cycle

Jie Jiang

National Astronomical Observatories, China

2011 ILWS Science Workshop


Two groups of most prediction methods

Extrapolation models: prediction from a purely mathematical analysis of the past records limited success in the past

Precursor models: correlations between certain measured quantities in the declining phase of a cycle and the strength of the next cycle polar field & geomagnetic variations demonstrated high success


Solar cycle prediction with diff. dynamo models

cy. 24 will be 30%-50% stronger than cy. 23

cy. 24 will be ~ 30%weaker than cy. 23

Dikpati et al., GRL, 2006

Dikpati & Gilman, (DG), ApJ, 2006

Choudhuri, et al., Phys. Rev. Lett., 2007

Jiang, et al.(JCC), Mon. Not. R. Astro

n. Soc., 2007


Their common choice – flux transport dynamo

Dynamo ?

Poloidal Field

Toroidal Field

Differential Rotation ?

Strong active regions field

Weak diffuse fieldP T

T P (mean field dynamo):

helical twisting of T by convective turbulence

quenching alternative ideas

Courtesy Choudhuri



BL-type flux transport dynamo ?

Courtesy Nandy, D.

T P : Babcock (1961) & Leighton (1969) : Decay of tilted bipolar sunspots

Meridional Flow: connect the two separated fields

Magnetic Buoyancy: give rise to sunspots



Why is BL-type flux transport dynamo chosen ?(1) Poloidal field regeneration: accessible to direct

observation

(2) Time delay associated with the time for the surface P to the tachocline Surface fields observed today will be the source of T in the future

How to derive the poloidal field ?

How long is the time delay ?


Strategy of JCC prediction (1)

Toroidal Toroidal ToroidalPoloidal Poloidal

partly random

partly random

regular predictable

regular predictable

It is the poloidal field build-up during the declining phase of the cycle which introduces randomness in the solar cycle

Observed poloidal field component around the minima: the surface radial field Br or polar field (3 cycles) ---> observational input to the dynamo model


Average of Br 3-yr before the minima

Observational corrected A (poloidal field)

Next cycle strength

Input to dynamo

Strategy of JCC prediction (2)


Cycles 21-23 are modeled well;

Cycle 24 is predicted to be a very weak cycle!

Results of JCC prediction


Dynamo used in JCC prediction

Poloidal field at C swepts away to P and T simultaneously Gives rise to the polar field at P and the toroidal field at T Polar field at the minimum & next cy. strength appear correlated

C

P

T

High diffusivity ! C --> T diffusion takes 5-10 years (time delay between C and T)


Polar field VS next cy. (direct obs.)

Is there a positive corr. between the polar field at the mini. and the next cycle strength on the basis of the obs. data ?

Direct obs. data

Polar field at end of cy. n

Is there a positive corr. between the polar field at the mini. and the next cycle strength on the basis of the obs. data ?

Implications from JCC prediction (1)


Cameron, Jiang, Schmitt and Schuessler, 2010, ApJ

Hathaway, 2010, Liv. Rev. Sol. Phys.

Polar field VS next cy. (Indirect obs.)

Recon. from Surface Flux Transport Model



Polar field VS preceding cy.

NO CORRELATION between polar field at the minimum and the preceding cycle strength !!

Cameron, Jiang, Schmitt and Schuessler, 2010, ApJ

Recon. from Surface Flux Transport model


Cameron, Jiang, Schmitt and Schuessler, 2010, ApJCameron, Jiang, Schmitt and Schuessler, 2010, ApJDirect obs. data

Indirect obs. data


＋

－

－＋

－

＋

diffusionDiffusion;

Meri. flow

Diff. rotation; diffusion

The strength of polar (poloidal) field determined by:

total flux of ARs; (Positive correlate with cycle strength)

Tilt angle, latitude of each AR (Relation with cy. strength ?)

Reasons behind the NO CORRELATION (1)


Jiang, Cameron, Schmitt & Schuessler, 2011, A&A

Strong cycle small tilt angle & high latitude two nonlinear effects to quench the generation of polar field in strong cycle



scattering dis. of tilt angle

scattering dis. of latitude

Both the latitude and the tilt angle present scattering distribution

Randomness



Anti-correlations between tilt angle & latitude dis. with cy. strength

Scattering of tilt angle and latitude of each AR

deterministic

random

factors in the generation of polar (poloidal) field



Strategy of DG prediction (1)

Spot area from SOON for cycles 12 -- 23

Stretching or compression of each cycle to the duration of 10.75 yr

Latitude distribution: 35° -- equator for all the cycles

AR tilt angles are cycle-independent

Neither the nonlinear effects nor the random effects are included in their method to derive the poloidal field !!


The model can correctly simulate the relative peaks of cycles 16 (12) -- 23

Cy. 24 will be 30% -- 50% stronger than cy. 23

Results of DG prediction


Dynamo used in DG prediction

Courtesy Dikpati

C

P

T

Time delay between C and T is 17-23 yr (Polar field & next cy. strength: no corr.)

Low diffusivity (50 times smaller than JCC)

Not consiste

nt with

the observ

ation !


Possible origin of DG postdicting skill (1)

Cameron and Schüssler, 2007, ApJ

1-D surface flux transport model

Precursor of cycle strength: flux crossing the equator

Show considerable predictive skill with the DG treatment of the surface source term

Predictive skill is completely lost when the actually observed emergence latitudes are used



Cameron & Schüssler, 2007, ApJ

Predictor is determined by the flux emergencein the later phase of the cycle & is sensitive to the definition of the source latitudes



Cycle overlap

Waldmeier effect

Level and timing of the minimum depend on the strength of the next cycle

Cameron & Schüssler, 2007, ApJ

Without requiring any direct physical connection between precursor & following cycle


Conclusions on implications of solar cycle

The evolution of surface flux plays a crucial role in the dynamo process and affects the subsequent cycle strength, which supports the BL type of dynamo The generation of surface flux has random components, which cannot be derived from the preceding cycle strength The corr. between polar field and sub. cy. strength requires the magnetic memory is 5 - 10 yr, which is important to constrain the MF and diffusivity in solar interior

Solar cycle prediction using dynamos and its implication for the solar cycle

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