The magnetic field of the planet-hosting star $τ$ Bootis

We have obtained high resolution spectropolarimetric data for the planet-hosting star $\tau$ Bootis, using the ESPaDOnS spectropolarimeter at CFHT. A weak but clear Stokes $V$ signature is detected on three of the four nights of June 2006 during which we have recorded data. This polarimetric signature indicates with no ambiguity the presence of a magnetic field at the star's surface, with intensity of just a few Gauss. The analysis of the photospheric lines of $\tau$ Boo at ultra-high signal-to-noise reveals the presence of an 18% relative differential rotation. Tentative Zeeman-Doppler imaging, using our spectropolarimetric observations covering only a fraction of the star's rotational phase, indicates a magnetic field with a dominant potential field component. The data are best fitted when a 3.1d period of modulation and an intermediate inclination are assumed. Considering the level of differential rotation of $\tau$ Boo, this implies a rotation period of 3.0d at the equator and of 3.7d at the pole, and a topology of the magnetic field where its main non-axisymmetric part is located at low latitudes. The planet is probably synchronised with the star's rotation at intermediate latitudes, while the non-axisymmetric part of the magnetic field seems located at lower latitudes. Our limited data do not provide sufficient constraints on the magnetic field to study a possible interaction of the planet with the star's magnetosphere. Investigating this issue will require data with much better phase coverage. Similar studies should also be performed for other stars hosting close-in giant planets.