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

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

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

(10 22 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:

Polar-cap (>60  ) absolute flux (10 22 Mx) No polar polarity inversion? The polar-cap field “capacitor” does not simply alternate in strength or even polarity:

What if flux “decayed” by 3D transport effects? Example of polar-cap fluxes with a decay time with flux half-life of 5 years: (10 22 Mx)

Comparing model and historical records (10 22 Mx) Scaled 10 Be isotope concentration Model heliospheric flux With polar-cap behavior ‘regularized’, the model heliospheric flux and inferred cosmic-ray flux are (roughly) anti-correlated:

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 (ApJ 577, 1006); Baumann et al (A&A 446, 307)], (implications for Dikpati’s findings?) evolving meridional advection [Wang et al (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 [Wang et al (ApJL 577, 53)] [Schrijver et al (ApJ 577, 1006)]

Dipole tilt angles Harvey 1993 (PhD thesis) 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

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

Coin flips with cyclic bias: Cycle-pair expectation + St. dev. - St. dev. No. of flips 1-sigma envelope  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.

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

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 3 rd run shows no polar-cap reversals for this period

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?

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

Geometry/Mapping uncertainties  Outside ICMEs, solar wind models and observations have C~0.7  Residual 1-C caused by: model inadequacy, and [possibly dominant] uncertainty in source identification Empirical quiescent correlation Heliosphere-to-Sun mapping uncertainty (degrees)

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