Predictions for solar cycle 25 Robert Cameron

Basis for prediction

Observational analysis Duvall Jr. 1977, PhD thesis, stanford Duvall Jr. et al., 1979, Sol.Phys, 61,23 Camero, Duvall, Schüssler, Schunker, sub. Asymmetric component Yearly averaged MDI Fulldisk magnetogram Asymmetric component Latitude Time Latitude Symmetric component Also see Howard, 1974, Sol.Phys, 39, 275 Schauner & Scherrer, 1994, Sol.Phys., 153, 131 Symmetric component

Br and Bq give a symmetric signal in line of sight magnetic field. West Limb + East Limb Rotation axis Viewed from above

Bf gives an asymmetric signal in line of sight magnetic field. Viewed from above + West Limb - East Limb Rotation axis

Observational analysis Asymmetric component Yearly averaged MDI Fulldisk magnetogram Asymmetric component Latitude Time Latitude Symmetric component Symmetric component

Observational analysis Duvall Jr. 1977, PhD thesis, stanford Duvall Jr. et al., 1979, Sol.Phys, 61,233 <Bf> Yearly averaged MDI Fulldisk magnetogram Asymmetric component Latitude Time Latitude Symmetric component <Br, Bq >

Year-by-year comparison Cameron, Duvall, Schüssler, Schunker, submitted WSO MDI

Magnetic butterfly diagrams Br Bf

Interpretation: Flux emergence Camero, Duvall, Schüssler, Schunker, submitted L=Distance over which emergence occurs a=radius of tube Dz= height range over which magnetic signature is imprinted on the line. Fi= magnetic flux of emergence v=rise velocity

The horizontal field during flux emergence gives an asymmetric signal in line of sight magnetic component because of Hale’s law. + Rotation axis - Viewed from above

Magnetic butterfly diagrams

Toroidal flux Is mainly of one sign in each hemisphere at solar maxima The sign changes from one cycle to the next

How does the Sun generate net toroidal flux in each hemisphere? Consider Along `a´ Uq=0. Moving into a coordinate system corotating with `a´ Cameron & Schüssler (2015)

Helioseismology Schou et al 1998

How does the Sun generate net toroidal flux in each hemisphere? Consider Along `a´ <Uq>=0. Moving into a coordinate system corotating with `a´results in <Uf>=0 along `a´. So the integrand along `a´ vanishes in the corotating coordinate system. Along `b´ B=0. So the contribution along `b´vanishes. Along `c´ <Uq>=<Uf>=<Bq>=<Bf>=0 , so the contribution along `c´ vanishes. Only contribution is from `d´:

NSO/KPNO data

The geomagnetic aa index at end of a cycle are strongly correlated with the strength of the next cycle. Proxy for polar fields at minima Wang and Sheeley (2009).

So prediction of cycle strength  Prediction of polar fields

Question: What determines the amount of polar flux?

Simpler question: What is critical for determining the change in polar flux from the minimum of one cycle to the next?

Distribution of surface flux at minimum Cameron et al 2013 KPNO data

Simpler problem: What is critical for determining the change in polar flux from the minimum of one cycle to the next? <=> Even simpler: What is critical for determining change in net flux in northern hemisphere from minimum of one cycle to the next?

What is critical for determining change in net flux in northern hemisphere from minimum of one cycle to the next? The evolution of the magnetic field is governed by the induction equation U Axisymmetric flow B Axisymmetric magnetic field u Non-axisymmetric flow b Non-axisymmetric field <....> Axisymmetric component h Molecular diffusivity, very small

What is critical for determining change in net flux in northern hemisphere from minimum of one cycle to the next? Apply Stokes Theorem: R S Photosphere in northern hemisphere dS Equator at photosphere

Simpler problem: What is critical for determining the change in polar flux from the minimum of one cycle to the next? 2p <uqbr-urbq> Rdf, R equator

} < uqbr-urbq> Rdf, 2p < uqbr-urbq> Rdf, R } equator Sin(l) CR1685 Sin(l) CR1686 Ranom uq will carry more leading polarity flux across the equator. NSO/KPNO

} <uqbr-urbq > Rdf, 2p R equator Sin(l) CR1685 Sin(l) CR1686 } equator Sin(l) CR1685 Sin(l) CR1686 NSO/KPNO

} <uqbr-urbq > Rdf, 2p R equator Sin(l) CR1685 } equator Sin(l) CR1685 Events like this introduce a strong random component into polar fields and hence amount of toroidal field generated in next cycle. Sin(l) CR1686 NSO/KPNO

Does this explain why was 24 so weak? Jiang, Cameron & Schüssler, 2015 Joy’s law J

Jiang, Cameron & Schüssler, 2015 Joy’s law J

Prediction for cycle 25

Ephemeral regions of new cycle appearing during 2016 at high latitudes in one hemisphere. Considerable north-south asymmetry

- - - - 2 sigma Prediction: Strength of axial dipole moment & polar fields marginally higher than for end of cycle 23. But more emergences will occur => uncertainty in final values. Camero, Jinag, Schüssler (2016)

Predictions: Strength of next cycle marginally higher than that of cycle 24. -- But more emergences still to occur => lots of uncertainty in final values. Deep minimum (2019-2020) Slow rise out of minimum, similar to cycle 24.

Questions?