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Pollux is considered as an archetype of a giant star hosting a planet: itsradial velocity (RV) presents sinusoidal variations with a period of about 590d, which have been stable for more than 25 years. Using ESPaDOnS and Narval wehave detected a weak (sub-gauss) magnetic field at the surface of Pollux andfollowed up its variations with Narval during 4.25 years, i.e. more than fortwo periods of the RV variations. The longitudinal magnetic field is found tovary with a sinusoidal behaviour with a period close to that of the RVvariations and with a small shift in phase. We then performed a Zeeman Dopplerimaging (ZDI) investigation from the Stokes V and Stokes I least-squaresdeconvolution (LSD) profiles. A rotational period is determined, which isconsistent with the period of variations of the RV. The magnetic topology isfound to be mainly poloidal and this component almost purely dipolar. The meanstrength of the surface magnetic field is about 0.7 G. As an alternative to thescenario in which Pollux hosts a close-in exoplanet, we suggest that themagnetic dipole of Pollux can be associated with two temperature andmacroturbulent velocity spots which could be sufficient to produce the RVvariations. We finally investigate the scenarii of the origin of the magneticfield which could explain the observed properties of Pollux.

Pollux: a stable weak dipolar magnetic field but no planet ?