Ultra-fast simulations of the solar dipole and open flux

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.

5 pages, 1 figure, Accepted for publication in A&A

References in corpus (12)

• The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: SHARPs -- Space-weather HMI Active Region Patches
• Effects of the scatter in sunspot group tilt angles on the large-scale magnetic field at the solar surface
• Surface Flux Transport on the Sun
• Improvement of solar cycle prediction: Plateau of solar axial dipole moment
• Towards an algebraic method of solar cycle prediction I. Calculating the ultimate dipole contributions of individual active regions
• How good is the bipolar approximation of active regions for surface flux transport?
• Role of observable nonlinearities in solar cycle modulation
• Optimization of surface flux transport models for the solar polar magnetic field
• Predicting the Timing of the the Solar Cycle 25 Polar Field Reversal
• Algebraic quantification of an active region's contribution to the solar cycle
• Straight outta photosphere: Open solar flux without coronal modeling
• Active regions and the large-scale magnetic field of solar cycle 24