Ultra-fast simulations of the solar dipole and open flux

TL;DR

The paper introduces a matrix-based dipole flux transport method that significantly accelerates solar magnetic field simulations, enabling rapid analysis of the solar dipole and open flux with high accuracy.

Contribution

A novel matrix method combining SFT with dipole vector representation that achieves 100-50,000 times faster simulations of the solar dipole.

Findings

DFT performs 100-1000 times faster than traditional SFT for single active regions.

Daily propagator matrices produce results within 1% of SFT for solar cycle 24.

DFT can run thousands of simulations in minutes on a basic laptop.

Abstract

Context. Solar dipole captures important information about the large-scale solar magnetic field. The evolution of the solar magnetic field including the solar dipole can be simulated with a surface flux transport (SFT) model, but these simulations are more extensive than is necessary to produce the evolution of the dipole alone. Aims. We present a dipole flux transport (DFT), matrix method that combines the classic SFT model with dipole vector representation of the solar magnetic field, allowing significantly faster simulations of the solar dipole. Methods. By simulating the evolution of basis vectors of a synoptic map, we constructed propagator matrices that produce the time evolution of the solar magnetic field by means of matrix multiplication. The computational speedup is achieved by compressing the propagator matrices to very small fraction $(< 10^{-4}$) of their original size with a recent vector sum method. Results. Depending on time resolution, the DFT performs 100-1000 times faster than a 4-year SFT simulation of a single active region while producing equivalent results. For multiple source regions, daily propagation matrices are sufficient to produce results that agree within 1\% with the SFT simulation of solar cycle 24, while performing 80 times faster. If the evolution of individual active regions is needed, the DFT performs 50000 times faster than the SFT model. Conclusions. DFT makes solar dipole simulations extremely fast, making it possible to run thousands of simulations in a few minutes with a basic laptop setup. As the magnitude of the dipole vector closely matches with open solar flux (OSF) from the potential field source surface model, the DFT can be used to study the development of OSF in various scenarios extremely efficiently.