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Discover the AFT Model!

Surface Flux Transport (SFT) describes the latter part of the dynamo process, in which the flows on the surface of the Sun transport the magnetic flux from the active region 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 flows: 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.

Discover AFT: Polar Field Predictions!

We have demonstrated the power of the AFT model by simulating Cycle 23 during the polar field reversal ( details in this paper). Starting with data 3 years ahead of the reversal, we were able to predict the timing of the field reversal to within four months, with four out of five predictions accurate to within a month. Furthermore, we found that our predictions for the polar field evolution stayed in remarkably good agreement with the baseline through to the end of the prediction, an additional 3 years after the reversal, demonstrating the ability to accurately predict the evolution of the Sun’s dipolar magnetic field several years in advance. The increase in the spread of the measurements over time highlights the stochastic nature and important role that supergranules play in the transport of flux.
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Solar Cycle 23 Simulations. Solar Cycle 23 simulations (each color represents a different realization of the convective pattern) of the axial dipole moment evolution are compared to MDI observations (black). (Note: the annual signal in the MDI data is due to instrumental effects.) These predictions were made using Cycle 17 active region data as magnetic sources. The Solar Cycle 23 polar field reversal is shown on the left. The approach to the Solar Cycle 23/24 minimum is shown on the right.

We went on to use the AFT model to predict the Solar Cycle 24 axial dipole moment reversal and subsequent magnetic field buildup, using Solar cycle 14 active regions as proxies for the continued active region emergence. Comparison of this prediction with the evolution of the axial dipole that has since occured, show remarkable agreement. Both feature a relapse in the reversal, leading up to the end of 2014, followed by a steady rise until the beginning of 2015. The axial dipole then plateaus defore taking off again at the beginning of 2016.
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Solar Cycle 24 Prediction. The axial dipole moment for the solar cycle 24 polar field reversal as predicted (left) and as observed with HMI magnetograms (right). The different colored tracks in the prediction represent different realizations of the convective motions.

Our prediction for Solar Cycle 25 can be found here.

Discover AFT: Active Region Simulations!

In addition to polar field evolutions, we have also investigated the finer details of individual active region evolution in the AFT model( details in this paper). We compared the total unsigned magnetic flux estimated from EUV 304 Å flux-luminosity relation directly to the total unsigned magnetic flux from the AFT baseline model. We found that the AFT model can accurately reproduce the active region evolution when the active region is not being observed by HMI and the model is operating without assimilation. Additional flux may emerge, however, while the active region is on the far-side. The AFT assimilation process corrects for this new emergence when this flux is observed by HMI and rotates over the East limb.
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AFT Active Region Evolution. The left plot shows the flux obtained from the 304 proxy and the flux for two area integrations of the AFT model (red and orange) for Active Region 11158 . Grey areas mark the times when the active region is on the Earth side, when data from HMI magnetograms is being assimilated. The EUV and AFT maps at the time near peak 304 °A intensity is shown on the right.