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
2011/08/30 2011 ILWS Science Workshop 2
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
2011/08/30 2011 ILWS Science Workshop 3
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
2011/08/30 2011 ILWS Science Workshop 4
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
2011/08/30 2011 ILWS Science Workshop 5
Their common choice – flux transport dynamo
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
2011/08/30 2011 ILWS Science Workshop 6
Their common choice – flux transport dynamo
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 ?
2011/08/30 2011 ILWS Science Workshop 7
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
2011/08/30 2011 ILWS Science Workshop 8
Average of Br 3-yr before the minima
Observational corrected A (poloidal field)
Next cycle strength
Input to dynamo
Strategy of JCC prediction (2)
2011/08/30 2011 ILWS Science Workshop 9
Cycles 21-23 are modeled well;
Cycle 24 is predicted to be a very weak cycle!
Results of JCC prediction
2011/08/30 2011 ILWS Science Workshop 10
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)
2011/08/30 2011 ILWS Science Workshop 11
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)
2011/08/30 2011 ILWS Science Workshop 12
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
Implications from JCC prediction (2)
2011/08/30 2011 ILWS Science Workshop 13
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
Implications from JCC prediction (3)
Cameron, Jiang, Schmitt and Schuessler, 2010, ApJCameron, Jiang, Schmitt and Schuessler, 2010, ApJDirect obs. data
Indirect obs. data
2011/08/30 2011 ILWS Science Workshop 14
+
-
- +
-
+
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)
2011/08/30 2011 ILWS Science Workshop 15
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
Reasons behind the NO CORRELATION (2)
2011/08/30 2011 ILWS Science Workshop 16
scattering dis. of tilt angle
scattering dis. of latitude
Both the latitude and the tilt angle present scattering distribution
Randomness
Reasons behind the NO CORRELATION (3)
2011/08/30 2011 ILWS Science Workshop 17
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
Reasons behind the NO CORRELATION (4)
2011/08/30 2011 ILWS Science Workshop 18
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 !!
2011/08/30 2011 ILWS Science Workshop 19
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
2011/08/30 2011 ILWS Science Workshop 20
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 !
2011/08/30 2011 ILWS Science Workshop 21
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
2011/08/30 2011 ILWS Science Workshop 22
Possible origin of DG postdicting skill (2)
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
2011/08/30 2011 ILWS Science Workshop 23
Possible origin of DG postdicting skill (3)
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
2011/08/30 2011 ILWS Science Workshop 24
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
2011/08/30 2011 ILWS Science Workshop 25