Historical TSI Reconstructions: Calibrating the Polar Fields in the Advective Flux Transport Model Using Joy’s Law Tilt

Historical reconstructions of total solar irradiance (TSI) rely on estimates of the solar open and closed magnetic flux obtained by simulating the flux emergence and transport. The Advective Flux Transport (AFT) model is a realistic surface flux transport model that has demonstrated its ability to reproduce flux emergence and evolution on the Sun. We have created synthetic active region databases based on the Sunspot Indices and Long-term Solar Observations (SILSO) 2.0 revised sunspot-number record. These synthetic databases include the timing, position, Joy’s tilt, and strength of solar active regions and have been used as input into AFT to create historical reconstructions. While these reconstructions produce realistic magnetic maps and solar cycles with alternating Hale’s polarity, the change in the polar axial dipole (which is the basis for the estimates of the open flux) from the beginning of the cycle to the end of the cycle was weaker than expected. We show that modifying the distribution of Joy’s Law tilt (i.e., the scatter about the standard Joy’s Law tilt) allows us to modulate the rate at which the polar fields change. In particular, we find that increasing the variability in Joy’s Law tilt significantly increases the change in the polar axial dipole from one cycle to the next. We have used the observed relationship between the strength of the polar fields at minimum and the amplitude of the next solar cycle to estimate how much the axial dipolar fields should change over the course of each historical cycle. We then modify the Joy’s Law tilt distribution in each cycle to ensure that desired change in the polar fields for that cycle is achieved. In this way, we are able to calibrate the polar field evolution in the simulations to produce more realistic solar cycles. Finally, we show the impact that these changes have on the historical reconstructions of TSI.