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 ?
Longitudinally-averaged field vs. time:
+90
Observations
0
Model
-90
0
11
Time (years)
 Good approximation of large-scale field
22
MHD sims.: Sun-heliosphere coupling
Flux emergence
in a dipolar field
MHD simulations by Riley
Courtesy
Pete Riley
Total flux on the Sun: cycle-to-cycle modulation
(1022 Mx)
The total flux on the Sun through time, based on a model
driven by historical sunspot numbers:
Polar-cap (>60) absolute flux
(1022 Mx)
The polar-cap field “capacitor” does not simply
alternate in strength or even polarity:
No polar
polarity
inversion?
What if flux “decayed” by 3D transport effects?
(1022 Mx)
Example of polar-cap fluxes with a decay time with flux
half-life of 5 years:
Comparing model and historical records
(1022 Mx)
With polar-cap behavior ‘regularized’, the model heliospheric
flux and inferred cosmic-ray flux are (roughly) anti-correlated:
Scaled
10Be
isotope concentration
Model heliospheric flux
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)],

[Schrijver et al. 2002 (ApJ 577, 1006)]
(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)]
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
Harvey 1993 (PhD thesis)
Coin flips (no ‘cycle bias’):
+ St. dev.
Sample cumulative
gains/losses
Expectation value
- St. dev.
No. of flips
 Long series of flips:


no net gain or loss expected, but
likelihood of near ‘lossless’ game diminishes.
Coin flips with cyclic bias:
1-sigma envelope
+ St. dev.
Cycle-pair expectation
- St. dev.
No. of flips
 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 3rd run shows no polar-cap reversals for this period
Conclusions:
 At least two processes appear to contribute to longterm 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