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In order to complete the knowledge of the magnetic field and of its influenceduring the transition from Asymptotic Giant Branch to Planetary Nebulae stages,we have undertaken a search for magnetic fields at the surface of Mira stars.We used spectropolarimetric observations, collected with the Narval instrumentat TBL, in order to detect - with Least Squares Deconvolution method - a Zeemansignature in the visible part of the spectrum. We present the firstspectropolarimetric observations of the S-type Mira star chi Cyg, performedaround its maximum light. We have detected a polarimetric signal in the StokesV spectra and we have established its Zeeman origin. We claim that it is likelyto be related to a weak magnetic field present at the photospheric level and inthe lower part of the stellar atmosphere. We have estimated the strength of itslongitudinal component to about 2-3 Gauss. This result favors a 1/r law for thevariation of the magnetic field strength across the circumstellar envelope ofchi Cyg. This is the first detection of a weak magnetic field at the stellarsurface of a Mira star and we discuss its origin in the framework of shockwaves periodically propagating throughout the atmosphere of these radiallypulsating stars. At the date of our observations of chi Cyg, the shock wavereaches its maximum intensity, and it is likely that the shock amplifies a weakstellar magnetic field during its passage through the atmosphere. Without suchan amplification by the shock, the magnetic field strength would have been toolow to be detected. For the first time, we also report strong Stokes Q and Usignatures (linear polarization) centered onto the zero velocity (i.e., at theshock front position). They seem to indicate that the radial direction would befavored by the shock during its propagation throughout the atmosphere.

Search for surface magnetic fields in Mira stars. First detection in chi Cyg