Exploring the biases of a new method based on minimum variance for interplanetary magnetic clouds

TL;DR

This paper investigates biases in the minimum variance method for modeling interplanetary magnetic clouds, identifies their origins, and proposes an improved approach to reduce these biases for more accurate flux rope axis determination.

Contribution

The authors analyze the biases of the MV method, identify their sources, and develop an improved version that reduces bias by balancing magnetic flux and optimizing boundary selection.

Findings

MV eigenvalue ratio is unreliable for axis precision

Boundary selection significantly affects axis orientation

Improved MV reduces bias to less than 6 degrees

Abstract

Magnetic clouds (MCs) are twisted magnetic structures ejected from the Sun and probed by in situ instruments. They are typically modeled as flux ropes (FRs). The determination of the FR global characteristics requires the estimation of the FR axis orientation. Among the developed methods, the minimum variance (MV) is the most flexible, and features only a few assumptions. However, as other methods, MV has biases. We aim to investigate the limits of the method and extend it to a less biased method. We first identified the origin of the biases by testing the MV method on cylindrical and elliptical models with a temporal expansion comparable to the one observed in MCs. Then, we developed an improved MV method to reduce these biases. In contrast with many previous publications we find that the ratio of the MV eigenvalues is not a reliable indicator of the precision of the derived FR axis direction. Next, we emphasize the importance of the FR boundaries selected since they strongly affect the deduced axis orientation. We have improved the MV method by imposing that the same amount of azimuthal flux should be present before and after the time of closest approach to the FR axis. We emphasize the importance of finding simultaneously the FR axis direction and the location of the boundaries corresponding to a balanced magnetic flux, so as to minimize the bias on the deduced FR axis orientation. This method can also define an inner flux-balanced sub-FR. We show that the MV results are much less biased when a compromise in size of this sub-FR is achieved. For weakly asymmetric field temporal profiles, the improved MV provides a very good determination of the FR axis orientation. The main remaining bias is moderate (lower than 6 degrees) and is present mostly on the angle between the flux rope axis and the plane perpendicular to the Sun-Earth direction.