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2011/08/302011 ILWS Science Workshop1 Solar cycle prediction using dynamos and its implication for the solar cycle Jie Jiang National Astronomical Observatories, China 2011 ILWS Science Workshop

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2011/08/302011 ILWS Science Workshop2 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

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2011/08/302011 ILWS Science Workshop3 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. Astron. Soc., 2007

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2011/08/302011 ILWS Science Workshop4 Their common choice – flux transport dynamo Dynamo ? Poloidal Field Toroidal Field Differential Rotation ? Strong active regions field Weak diffuse field P T T P (mean field dynamo): helical twisting of T by convective turbulence quenching alternative ideas Courtesy Choudhuri

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2011/08/302011 ILWS Science Workshop5 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

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2011/08/302011 ILWS Science Workshop6 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 ?

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2011/08/302011 ILWS Science Workshop7 Strategy of JCC prediction (1) Toroidal Poloidal partly random 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

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2011/08/302011 ILWS Science Workshop8 Average of B r 3-yr before the minima Observational corrected A (poloidal field) Next cycle strength Input to dynamo Strategy of JCC prediction (2)

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2011/08/302011 ILWS Science Workshop9 Cycles 21-23 are modeled well; Cycle 24 is predicted to be a very weak cycle! Results of JCC prediction

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2011/08/302011 ILWS Science Workshop10 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)

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2011/08/302011 ILWS Science Workshop11 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)

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2011/08/302011 ILWS Science Workshop12 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)

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2011/08/302011 ILWS Science Workshop13 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, ApJ Direct obs. data Indirect obs. data

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2011/08/302011 ILWS Science Workshop14 diffusion Diffusion; 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)

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2011/08/302011 ILWS Science Workshop15 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)

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2011/08/302011 ILWS Science Workshop16 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)

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2011/08/302011 ILWS Science Workshop17 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)

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2011/08/302011 ILWS Science Workshop18 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 !!

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2011/08/302011 ILWS Science Workshop19 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

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2011/08/302011 ILWS Science Workshop20 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 consistent with the observation !

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2011/08/302011 ILWS Science Workshop21 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

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2011/08/302011 ILWS Science Workshop22 Possible origin of DG postdicting skill (2) Cameron & Schüssler, 2007, ApJ Predictor is determined by the flux emergence in the later phase of the cycle & is sensitive to the definition of the source latitudes

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2011/08/302011 ILWS Science Workshop23 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

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2011/08/302011 ILWS Science Workshop24 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

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