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 0 11 22

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

(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:

Polar-cap (>60) absolute flux

(1022

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:

(1022

Mx)

Comparing model and historical records

(1022

Mx)

Scaled 10Be isotope concentrationModel 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. 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

[Wang et al. 2002 (ApJL 577, 53)]

[Schrijver et al. 2002 (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 + ...:

NS

N.B. The 3rd 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 (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!

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