Advancing solar magnetic field extrapolations through multiheight magnetic field measurements

The force-free assumption is a valid approximation at coronal heights, but for the dense plasma conditions in the lower atmosphere, this assumption is not satisfied. In this study, we utilize multiheight magnetic field measurements in combination with physics-informed neural networks to advance solar magnetic field extrapolations.

We include a flexible height-mapping, which allows us to account for the different formation heights of the observed magnetic field measurements. The comparison to analytical and simulated magnetic fields demonstrates that including chromospheric magnetic field measurements leads to a significant improvement of our magnetic field extrapolations. We also apply our method to chromospheric line-of-sight magnetograms from the Vector Spectromagnetograph (VSM) on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) observatory, in combination with photospheric vector magnetograms from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO).