Résumé
So far, surface magnetic fields have never been reported on Mira stars, while observational facilities allowing detection and measurement of weak surface fields through the Zeeman effect have become available. Then, in order to complete the knowledge of the magnetic field and of its influence during the transition from Asymptotic Giant Branch (AGB) to Planetary Nebulae (PN) stages, we have undertaken a search for magnetic fields at the surface of Miras. We present the first spectropolarimetric observations (performed with the Narval instrument at Télescope Bernard Lyot-TBL, Pic du Midi, France) of the S-type Mira star χ Cyg. We have detected a polarimetric signal in the Stokes V spectra and we have established its Zeeman origin. We claim that it is likely to be related to a weak magnetic field present at the photospheric level and in the lower part of the stellar atmosphere. The origin of this magnetic field is discussed in the framework of shock waves periodically propagating throughout the atmosphere of a Mira.