Spectropolarimetric measurements of magnetic Ap and Bp stars in all four Stokes parameters

In this paper we begin an exploration of the potential of spectral line Zee man linear and circular polarization signatures for reconstructing the surf ace magnetic field topologies of magnetic Ap and Bp stars. We present our f irst observational results, which include the very first high-quality measu rements of stellar Zeeman spectral line linear polarization ever obtained. Using the new MuSiCoS spectropolarimeter at the Pic du Midi Observatory, ov er 360 spectra were obtained, in circular or linear polarization, of 14 mag netic Ap/Bp stars and six calibration objects. Zeeman circular polarization signatures are detected in most single lines in essentially all spectra of magnetic Ap stars, with typical relative amplitudes of a few per cent. Lin ear polarization Zeeman signatures are unambiguously detected in individual strong, magnetically sensitive lines in outstanding spectra of five object s. However, linear polarization is generally not detected in individual str ong lines in our much more common moderate signal-to-noise ratio (S/N) spec tra, and is essentially never detected in weak lines. In order to overcome the limitations imposed by the S/N ratio and the inherent weakness of linea r polarization Zeeman signatures, we exploit the information contained in t he many lines in our spectra by using the least-squares deconvolution (LSD) technique. Using LSD, mean linear polarization signatures are consistently detected within the spectral lines of 10 of our 14 programme stars. These mean linear polarization signatures are very weak, with typical amplitudes 10-20 times smaller than those of the associated mean circular polarization signatures. For 11 stars full or partial rotational phase coverage has been obtained in the Stokes I and V or the Stokes I, V, Q and U parameters. The rotational modulation of the LSD mean signatures is reported for these objects. Measur ements of the longitudinal field and net linear polarization obtained from these LSD profiles show they are consistent with existing comparable data, and provide constraints on magnetic field models which are at least as powe rful as any other data presently available. To illustrate the new information available from these data sets, we compar e for four stars the observed Stokes profiles with those predicted by magne tic field models published previously in the literature. Important and some times striking differences between the observed and computed profiles indic ate that the Zeeman signatures presented here contain important new informa tion about the structure of the magnetic fields of Ap and Bp stars capable of showing the limitations of the best magnetic field models currently avai lable.