Surface magnetism of cool stars
O. Kochukhov, P. Petit, K.G. Strassmeier, T.A. Carroll, R. Fares, C.P., Folsom, S.V. Jeffers, H. Korhonen, J.D. Monnier, J. Morin, L. Rosen, R.M., Roettenbacher, D. Shulyak

TL;DR
This paper reviews recent advances in detecting and characterizing magnetic fields on cool stars, highlighting techniques, challenges, and key findings from surface magnetic studies and their implications.
Contribution
It provides a comprehensive summary of current methods and results in direct magnetic field measurements and surface inhomogeneity analysis of cool stars.
Findings
Progress in magnetic field topology mapping techniques
Application of polarisation data and intensity spectra analysis
Controversial results in magnetic field measurements
Abstract
Magnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet their direct detection and characterisation is notoriously difficult, requiring high-quality observations and advanced analysis techniques. Significant progress has been recently achieved by several types of direct magnetic field studies on the surfaces of cool active stars. In particular, complementary techniques of the field topology mapping with polarisation data and total magnetic flux measurements from intensity spectra have been systematically applied to different classes of active stars leading to interesting and occasionally controversial results. In this paper we summarise the current status of direct magnetic field studies of cool stars, and investigations of surface inhomogeneities caused by the field, based on the material presented at the Cool Stars 19…
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