Three-dimensional Model Fitting to Magnetic Clouds for Multiple In Situ Spacecraft Measurements

Abstract We have performed an optimal model fitting analysis to a magnetic cloud (MC) event on December 1-3, 2023, when Wind and STA spacecraft crossed the same structure along closely separated paths. The Solar Orbiter (Sol) spacecraft, with a relatively larger separation distance from Earth (Wind), also appeared to have crossed the same structure at an earlier time. The analytic model employed for the optimal fitting to the magnetic field data is based on a linear force-free field formulation, possessing three-dimensional (3D) spatial variations, and is dubbed Friedberg solution (FS). By employing both Wind and STA in-situ measurements along their separate paths across the same MC structure, we obtain the set of parameters characterizing the FS model fit with an optimal reduced $\chi^2$ value of 3.60. We then compare the FS model output along the STA spacecraft path with the actual magnetic field measurements and obtain a correlation coefficient, $cc_1=$0.94 - 0.96. By examining the magnetic field line configuration more closely, we also find that the Sol spacecraft may have crossed the same MC body along its path at a relatively larger distance away from the Wind spacecraft path and over a shorter time interval. A similar comparison between the FS model output and the Sol data yields a correlation coefficient $cc_2=$0.81 - 0.90. For completeness, we also perform the two-dimensional (2D) Grad-Shafranov (GS) reconstruction of the MC structure by using the Wind spacecraft data only. A similar analysis yields $cc_1=$0.93 - 0.96, and $cc_2= -0.37$ - 0.11 for the GS reconstruction result. Hence our interpretation is that the analysis results based on three spacecraft datasets are consistent with the 3D spatial magnetic field configuration of the FS model output for this MC event to the degree indicated by the aforementioned quantitative metrics.