Comparison of Cylindrical Interplanetary Flux-Rope Model Fitting with Different Boundary Pitch-Angle Treatments

Abstract

Interplanetary flux ropes (IFRs) observed in the solar wind have been investigated through application of the Lundquist model, which is a cylindrical flux-rope model with a constant-$\alpha$ force-free magnetic-field model. This study evaluated two Lundquist-model fitting methods by applying them to magnetic-obstacle (MO) events observed by the Wind and Solar TErrestrial RElations Observatory (STEREO) spacecraft and by comparing the results. In one method, the pitch angle of the magnetic field at the IFR boundary is assumed to be $90^{\circ}$, whereas in the other method this restriction is relaxed and the pitch angle is handled as a free parameter [$\alpha _{\mathrm{p}}$]. We found that the angle between the axial and radial directions in radial tangential normal (RTN) coordinates (cone angle) and the magnetic flux of the IFR were significantly different for approximately 30% of these events. However, both methods yielded similar values for the direction of the IFR axis projected onto the T–N plane in the RTN coordinates (tilt angle). We also found that the statistical distribution of $\alpha _{\mathrm{p}}$, which was estimated using the generalized method, shows a spread of $34^{\circ}$ centered at $82^{\circ}$, implying that a highly twisted magnetic-field line surrounds the surface of the IFR for approximately 60% of the events. On the other hand, it was noted that a significant number of events (approximately 25%) have a small $\alpha _{\mathrm{p}}$ (${<}\,60^{\circ}$). These results prove that it is better to use the generalized method than the conventional method for solving the cone angle, magnetic flux, or pitch angle of the flux rope, which would lead to a more accurate derivation of the properties of IFRs.