Abstract

Magnetic fields play a fundamental role for the interior and atmospheric properies of M dwarfs and greatly influence terrestrial planets orbiting in the habitable zones of these low-mass stars. Determination of the strength and topology of magnetic fields, both on stellar surfaces and throughout the extended stellar magnetospheres, is a key ingredient for advancing stellar and planetary sciences. In this talk I will review modern methods of magnetic field measurements applied to M dwarfs, with an emphasis on direct diagnostics based on interpretation of the Zeeman effect signatures in high-resolution intensity and polarisation spectra. I will summarise results of field strength measurements using Zeeman broadening analyses as well as information on global magnetic geometries inferred from spectropolarimetric observations. The emerging understanding of complex, multi-scale nature of M-dwarf magnetic fields will be discussed in the context of theoretical models of hydromagnetic dynamos and stellar interior structure altered by magnetic fields.