Diagnosing large-scale stellar magnetic fields using PCA on spectropolarimetric data

Insights on stellar surface large-scale magnetic field topologies are usually drawn by applying Zeeman-Doppler-Imaging (ZDI) to the observed spectropolarimetric time series. However, ZDI requires experience for reliable results to be reached and is based on a number of prior assumptions that may not be valid, e.g., when the magnetic topology is evolving on timescales comparable to or shorter than the time span over which observations are collected. In this paper, we present a method based on Principal Component Analysis (PCA) applied to circularly polarised (Stokes~$V$) line profiles of magnetic stars to retrieve the main characteristics of the parent large-scale magnetic topologies, like for instance, the relative strength of the poloidal and toroidal components, and the degree of axisymmetry of the dominant field component and its complexity (dipolar or more complex). We show that this method can also be used to diagnose the temporal variability of the large-scale magnetic field. Performing best for stars with moderate projected equatorial velocities hosting relatively simple magnetic field topologies, this new method is simpler than ZDI, making it convenient to rapidly diagnose the main characteristics of the large-scale fields of non-degenerate stars and to provide insights into the temporal evolution of the field topology.