Estimates of the forthcoming solar cycles 24 and 25 Kirill Kuzanyan IZMIRAN, Russian Academy of Sciences, Moscow region, Russia and National Astronomical Observatories of Chinese Academy of Sciences, Beijing, China

Questions: (no question) Why advance knowledge of solar activity is important! Can we reliably predict the solar activity? What methods of prediction are used? Are we approaching another “global” Maunder-like minimum?

How the activity was in the past? continuous 1749-2006 = looks normal 2006-2009 very low!

The Butterfly Diagram

Reconstruction of activity over the Maunder minimum (1645-1710)

Global Minima! … and there were several similar minima in the past!

The methods of prediction? 1. Use data themselves: The time series is too short for reliable prediction The noise level is too high -- neural networks (training on previous cycles) -- data assimilation -- time series in analysis of dynamical systems Very little knowledge of physics is involved but mainly mathematical assumptions

Example 1: Data Assimilation method prediction of the solar cycle 24 published by Kitiashvili & Kosovichev 2008

Example 2: Singular Spectral Analysis (SSA) after Loskutov et al. 2001 (up to 18 yr)

Physics of the solar cycle Solar dynamo theory Regeneration of magnetic fields due to rotation and turbulent convection periodic in time travelling wave Parker 1955 dynamo wave Babcock & Leighton 1961-69 Krause & Rädler 1980 mean-field model

2. Prediction based on models Numerical models are not capable to attain realistic parameter range Simplified “toy” models with very few parameters can not simulate complex turbulent processes irrelatively of the choice of values: any small number of parameters is insufficient.

Example: Dikpati et al. or other similar models well reproduced the past activity but prediction of the solar cycle 24 was inaccurate! The prediction based on pure theoretical models made in 2004 has been later several times “corrected” in order to accommodate the current course of the solar cycle (i.e., the prolonged minimum). Now, how reliable it is?

3. Precursor methods It is attractive to use additional sources of data as proxies of the of the current and precursors of the forthcoming activity: Polar magnetic fields on the Sun are being converted into low-latitudinal sunspots The growth rate of the solar cycle is correlated with future maximum: the shorter the higher (after Waldmeirer 1935)

Physical reasons for precursors Positive Feedback between Toroidal and Poloidal parts of magnetic energy requires time, => so delay between the polar and equatorial manifestations of the solar magnetic activity (polar is ahead of the equatorial!)

We can try other activity proxies (e.g. geomagnetic aa-index) Observations of polar faculae can be used in prediction of the sunspots We can try other activity proxies (e.g. geomagnetic aa-index) Makarov & Sivaraman 1989

Other precursors? Global Minimum Asymmetry between Northern and Southern hemispheres (see Zolotova’s presentation), also noted in Helicity Butterfly Diagram => possible signature of Global Minimum

Helicity overlaid with butterfly diagram

More precursors? Global Minimum Global (large-scale) magnetic field; solar dipolar moment; Interplanetary Magnetic Field (IMF) See Obridko papers etc. => possible signature of Global Minimum

Obridko and Shelting 2009

Different forecasts for cycle 24 (incl. precursor methods) Neither worse but nor better than the other methods!

Summary No absolutely effective methods of prediction are developed so far Despite vast inconsistency between the models we still may try to estimate the forthcoming activity The two forthcoming cycles 24 and 25 will likely be relatively low compared to those over the recent centuries (sign of a Minimum?!)

Thank you!

Supplementary material Appendix Supplementary material

Anti-Correlation between the solar activity and cosmic rays Comparison of the total open flux BE derived from photospheric field measurements with the radial IMF strength ¦ Bx¦ recorded at Earth. Here MWO datawere used for 1967–1976 and 1995–2000, while WSO data were used for the remaining intervals. Also plotted is the sunspot number RI (after Wang Y-M et al., 2006).

Anti-Correlation between the solar activity and cosmic rays Temporal changes of CR intensity (% to 1976), flare index Fx, sunspot numbers W, average values of solar magnetic field strength – index Bss and partial indexes ZO, ZE, SO, and SE (mkT).

Anti-Correlation between the solar activity and cosmic rays Temporal changes of CR intensity (% to 1976), flare index Fx, sunspot numbers W, average values of solar magnetic field strength – index Bss and partial indexes ZO, ZE, SO, and SE (mkT).