Feature Detection in Magnetic Field Perturbations Using Möbius Transformations

The Heliospheric Current Sheet (HCS) is an excellent laboratory for exploring feature detection and dynamic range in magnetometer data analysis because of the broad range of positive, negative, and zero-amplitudes of magnetic field intensity present in that region. The Parker Solar Probe (PSP) crossed the HCS during the perihelion of several orbits and is continuing to provide data of previously unexplored regions of the inner heliosphere. In this work, we show PSP magnetometer data timeseries and hodogram analysis using Radial, Tangential, Normal (RTN) coordinates and compare these timeseries to analyses using a set of Möbius transformations. These transformations are interesting because they are conformal, meaning they preserve angles between magnetic field components while distorting amplitudes. The amplitude distortions from Möbius transformations allow for feature detection with very small and very large background magnetic field amplitudes. We show that angle preservation in Möbius transformations can reveal circular, elliptical, or linear polarization in magnetic field perturbations.