Surface Flux Transport (SFT) describes the latter part of the dynamo
, in which the flows on the surface of the Sun transport the magnetic flux from the
belts to the poles. During solar maximum the
previous cycle's polar fields
are cancelled and a new poloidal
field with the opposite polarity begins to grow. At solar minimum, the strength of this new
poloidal field becomes the seed to the next solar cycle.
SFT begins with the emergence of bipolar magnetic active regions with the characteristic Hale’s
polarity and Joy’s Law tilt (Hale et al. 1919; Howard 1991). Initially, the active regions emerge
at about 30° latitude. As the cycle progresses, they emerge at progressively lower latitudes,
eventually stopping near the equator. The magnetic flux in the active regions is shredded off
by turbulent convective motions (over a period of a few days or weeks) and is dispersed into the
surrounding plasma. The dispersed flux is then transported by the surface
: differential rotation, meridional circulation, and the turbulent cellular motions of
convection. The weak magnetic elements are carried to the edges of the convective structures
(granules and supergranules) by flows within those convective cells, forming a magnetic network.
Once concentrated in the magnetic network, the flux is then carried (along with the convective
cells) by the axisymmetric differential rotation and meridional circulation.
While the majority of the active region flux will cancel with the opposite polarity from the
active region itself or with future active regions, some residual flux remnants will remain.
The lower latitude leading polarity flux remnants will eventually cancel across the equator,
while the higher latitude following polarity flux remnants migrate to the poles. The following
polarity flux cancels with the original global poloidal field and creates a new poloidal field
with opposite polarity, from which the new solar cycle is born.
Most previous SFT models have been highly parameterized, in particular with respect to active
region emergence, the meridional flow, and the convective motions. Previous models have been
restricted to simulating active region emergence by inserting artificial bipolar active region
sources (though some have been based on observed active regions). The adopted meridional flow
profiles (sharply peaked at low latitudes, stopping short of the poles, exaggerated variations
around active regions) deviate substantially from the observed profiles. Additionally, these
models have typically neglected the variability in the meridional flow altogether (the
meridional flow is faster at solar cycle minimum and slower at maximum). Furthermore, virtually
all previous models have parameterized the turbulent convection by a diffusivity with widely
varying values from model to model.
When we set out to create our SFT model, the Advective Flux Transport (AFT) model, our primary
goal was to create the most realistic SFT model possible by incorporating the observed active
regions and surface flows directly, with minimal parameterizations. The AFT model uses the
measured axisymmetric flows along with a convective simulation to explicitly model the surface
flows produced by the convective flows. The convective simulation uses vector spherical harmonics
to create a convective velocity field that reproduces the spectral characteristics of the
convective flows observed on the Sun. The spectral coefficients evolve, giving the simulated
convective cells finite lifetimes and moving them with the observed differential rotation and
meridional flow. Strong magnetic fields on the Sun inhibit convection; therefore when the flow
velocities are employed, they are dampened where the magnetic field is strong. This magnetic
field strength dependent effect is difficult to reproduce with the diffusivity used in other
models. Advecting the flows with the simulated convection allows the model to surpass the
realism that can be obtained by using a diffusivity coefficient.
Magnetic sources can be incorporated in two different ways: either by manually inserting
bipolar active regions (e.g., using active region databases like NOAA to insert flux daily as the
active region grows) or by assimilating magnetic data directly from magnetograms. This gives the AFT
model additional flexibility. While manual insertion allows the AFT model to be used to investigate
flows and to make predictions, the assimilation process provides the closest contact to the
observations, producing the most accurate synchronic maps of the entire Sun. These maps, referred
to as the Baseline data set, can be used as a metric for evaluating SFT or as source data for
models that extend into the solar atmosphere and the heliosphere.