1. Predictions for solar cycle 25
Robert Cameron

2. Basis for prediction

3. 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

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

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

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

7. 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 >

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

9. Magnetic butterfly diagramsBr Bf

10. 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

11. 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

12. Magnetic butterfly diagrams

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

14. 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)

15. Helioseismology
Schou et al 1998

16. 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´:

17. NSO/KPNO data

19. 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).

20. So prediction of cycle strength  Prediction of polar fields

21. Question: What determines the amount of polar flux?

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

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

24. 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?

25. 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

26. 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

27. 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

28. } < 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

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

30. } <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

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

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

33. Prediction for cycle 25

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

35. 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)

36. 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 ( )
Slow rise out of minimum, similar to cycle 24.

37. Questions?