Modeling the Sun’s global magnetic field

1. Modeling the Sun’s global magnetic field Karel Schrijver SHINE 2006 "[The] most important attitude is to find which forgotten physical processes are responsible for something we do not understand" Evry Schatzman

2. Observations Model Large-scale solar field • Large-scale solar field depends on source function, flux dispersal, meridional flow, differential rotation, and ? Longitudinally-averaged field vs. time: +90 0 -90 0 11 22 Time (years) • Good approximation of large-scale field

3. MHD sims.: Sun-heliosphere coupling Flux emergence in a dipolar field Courtesy Pete Riley MHD simulations by Riley

4. (1022 Mx) Total flux on the Sun: cycle-to-cycle modulation The total flux on the Sun through time, based on a model driven by historical sunspot numbers:

5. No polar polarity inversion? Polar-cap (>60) absolute flux The polar-cap field “capacitor” does not simply alternate in strength or even polarity: (1022 Mx)

6. What if flux “decayed” by 3D transport effects? Example of polar-cap fluxes with a decay time with flux half-life of 5 years: (1022 Mx)

7. Comparing model and historical records With polar-cap behavior ‘regularized’, the model heliospheric flux and inferred cosmic-ray flux are (roughly) anti-correlated: (1022 Mx) Scaled 10Be isotope concentration Model heliospheric flux

8. [Wang et al. 2002 (ApJL 577, 53)] [Schrijver et al. 2002 (ApJ 577, 1006)] Global and polar field • On time scales of years to decades, time-independent flux transport system models require a new process acting on the global scale: • 3d flux transport; precludes long-term hysteresis in global/polar field [Schrijver et al. 2002 (ApJ 577, 1006); Baumann et al. 2006 (A&A 446, 307)], (implications for Dikpati’s findings?) • evolving meridional advection [Wang et al. 2002 (ApJL 577, 53)], or AR tilt angles [?] or source correlations [?] cause cycle strength and advected polar flux to be nearly the same from cycle to cycle

9. Harvey 1993 (PhD thesis) Dipole tilt angles Dipoles emerge with a size-dependent spread about a preferred mean tilt angle. The net N-S dipole moment contributes to the polar-cap fields

10. Coin flips (no ‘cycle bias’): • Long series of flips: • no net gain or loss expected, but • likelihood of near ‘lossless’ game diminishes. + St. dev. Sample cumulative gains/losses Expectation value - St. dev. No. of flips

11. Coin flips with cyclic bias: • Long series of flips with cycle bias: • no net gain or loss expected, but • likelihood of near ‘lossless’ game diminishes. • With cyclic bias variation, loss-gain (or polar polarity) reversals increasingly unlikely, while zero-crossings drift off antiphase with bias cycle. 1-sigma envelope + St. dev. Cycle-pair expectation - St. dev. No. of flips

12. Standard solar model runs: • Three different realizations of randomized sources (gray area enclosed by the extremes of the 3 runs).

13. Standard solar model runs: • Timing of polar-cap polarity reversals is affected by the spread around mean Joy angle + latitude distribution + nesting/magnetoconvective coupling + ...: N S N.B. The 3rd run shows no polar-cap reversals for this period

14. Conclusions: • At least two processes appear to contribute to long-term polar-cap behavior not in the ‘standard model’: • conveyor-belt variations and • 3D flux transport (CZ “diffusion”) • If tilt-angle, latitude-spread, and AR nesting are truly random, and solar field memory were ‘infinite’, then polar-cap reversals should perturb the anti-phase timing of polar field and spot cycle. • Do ARs evolve to comply with average Joy’s law prior to dispersal? Are there hidden correlations in latitude, tilt, and flux of emerging regions? What sets the effective mean tilt angle when flux becomes ‘disconnected’ from the deep sources? Or does 3D flux transport wipe out solar memory?

15. ‘Incomplete knowledge’ : Having observations of only ¼- 1/3 of the solar surface introduces substantial uncertainties (2nd half of the movie) not seen in a model with perfect knowledge (1st half of the movie). Note the substantial field deflections from the sub-solar point to the photosphere!

16. Towards understanding the quiescent Sun-Heliosphere coupling • Need to observe: • Field evolution in at least the full activity belt to measure the dispersal of flux from many ARs over multiple weeks [tilt angles] to months [global transport] • Need to model: • Global magnetoconvection / dynamo • global photosphere-heliosphere coupling