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

2011 ILWS Science Workshop. Solar cycle prediction using dynamos and its implication for the solar cycle. Jie Jiang National Astronomical Observatories, China. Two groups of most prediction methods. Extrapolation models: prediction from a purely mathematical analysis of the past records

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

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  1. 2011 ILWS Science Workshop Solar cycle prediction using dynamos and its implication for the solar cycle Jie Jiang National Astronomical Observatories, China 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 ILWS Science Workshop

  3. Solar cycle prediction with diff. dynamo models Dikpati et al., GRL, 2006 Dikpati & Gilman, (DG), ApJ, 2006 cy. 24 will be 30%-50% stronger than cy. 23 Choudhuri, et al., Phys. Rev. Lett., 2007 Jiang, et al.(JCC), Mon. Not. R. Astron. Soc., 2007 cy. 24 will be ~ 30% weaker than cy. 23 2011 ILWS Science Workshop

  4. Poloidal Field Toroidal Field Differential Rotation ? Their common choice – flux transport dynamo Dynamo ? Weak diffuse field P  T Courtesy Choudhuri T  P (mean field dynamo): helical twisting of T by convective turbulence Strong active regions field quenching  alternative ideas 2011 ILWS Science Workshop

  5. Courtesy Nandy, D. Their common choice – flux transport dynamo BL-type flux transport dynamo ? 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 ILWS Science Workshop

  6. How to derive the poloidal field ? How long is the time delay ? Their common choice – flux transport dynamo Why is BL-type flux transport dynamo chosen ? • 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 2011 ILWS Science Workshop

  7. Toroidal Poloidal Toroidal Poloidal Toroidal partly random regular predictable partly random regular predictable Strategy of JCC prediction (1) 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 ILWS Science Workshop

  8. Strategy of JCC prediction (2) Average of Br 3-yr before the minima Observational corrected A(poloidal field) Input to dynamo Next cycle strength 2011 ILWS Science Workshop

  9. Results of JCC prediction • Cycles 21-23 are modeled well; • Cycle 24 is predicted to be a very weak cycle! 2011 ILWS Science Workshop

  10. P C T • 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 High diffusivity ! C --> T diffusion takes 5-10 years (time delay between C and T) Dynamo used in JCC prediction 2011 ILWS Science Workshop

  11. ImplicationsfromJCC prediction (1) 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 ? • 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 2011 ILWS Science Workshop

  12. ImplicationsfromJCC prediction (2) Polar field VS next cy.(Indirect obs.) Recon. from Surface Flux Transport Model Hathaway, 2010, Liv. Rev. Sol. Phys. Cameron, Jiang, Schmitt and Schuessler, 2010, ApJ 2011 ILWS Science Workshop

  13. Direct obs. data ImplicationsfromJCC prediction (3) Polar field VS preceding cy. Recon. from Surface Flux Transport model Indirect obs. data Cameron, Jiang, Schmitt and Schuessler, 2010, ApJ Cameron, Jiang, Schmitt and Schuessler, 2010, ApJ Cameron, Jiang, Schmitt and Schuessler, 2010, ApJ NO CORRELATION between polar field at the minimum and the preceding cycle strength !! 2011 ILWS Science Workshop

  14. Diff. rotation; diffusion Diffusion; Meri. flow diffusion Reasons behind the NO CORRELATION (1) • 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 ?) 2011 ILWS Science Workshop

  15. Reasons behind the NO CORRELATION (2) 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 2011 ILWS Science Workshop

  16. Reasons behind the NO CORRELATION (3) scattering dis. of tilt angle scattering dis. of latitude Both the latitude and the tilt angle present scattering distribution Randomness 2011 ILWS Science Workshop

  17. Anti-correlations between tilt angle & latitude dis. with cy. strength deterministic factors in the generation of polar (poloidal) field • Scattering of tilt angle and latitude of each AR random Reasons behind the NO CORRELATION (4) 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 Neither the nonlinear effects nor the random effects are included in their method to derive the poloidal field !! • AR tilt angles are cycle-independent 2011 ILWS Science Workshop

  19. Results of DG prediction • The model can correctly simulate the relative peaks of cycles 16 (12) -- 23 • Cy. 24 will be 30% -- 50% stronger than cy. 23 2011 ILWS Science Workshop

  20. P C T Courtesy Dikpati Dynamo used in DG prediction • 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 consistent with the observation ! 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 ILWS Science Workshop

  22. Possible origin of DG postdicting skill (2) Predictor is determined by the flux emergence in the later phase of the cycle & is sensitive to the definition of the source latitudes Cameron & Schüssler, 2007, ApJ 2011 ILWS Science Workshop

  23. Possible origin of DG postdicting skill (3) • Cycle overlap • Waldmeier effect Cameron & Schüssler, 2007, ApJ Level and timing of the minimum depend on the strength of the next cycle Without requiring any direct physical connection between precursor & following cycle 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 ILWS Science Workshop

  25. 2011 ILWS Science Workshop

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