After our recent discovery of four magnetic Herbig stars, we have decided to study in detail one of them, HD 200775, to determine if its magnetic topology is similar to that of the main sequence magnetic stars. With this aim, we monitored this star in Stokes I and V over more than two years, using the new spectropolarimeters ESPaDOnS at CFHT, and Narval at TBL. Using our data, we find that HD 200775 is a double-lined spectroscopic binary system, whose secondary seems similar, in temperature, to the primary. We determine the luminosity ratio of the system, and using the luminosity of the system found in literature, we derive the luminosity of both stars. From our measurements of the radial velocities of both stars we determine the ephemeris and the orbital parameters of the system. We have fitted 30 Stokes V profiles simultaneously, using a chi2 minimisation method, with a decentered-dipole model. The best-fit model provides a rotation period of 4.3281 d an inclination angle of 60 degrees, and a magnetic obliquity angle of 125 degrees. The polar strength of the magnetic dipole field is 1000 G, which is decentered by 0.05 R* from the center of the star. The derived magnetic field model is qualitatively identical to those commonly observed in the Ap/Bp stars, which bring strong argument in favour of the fossil field hypothesis, to explain the origin of the magnetic fields in the main sequence Ap/Bp stars. Our determination of the inclination of the rotation axis leads to a radius of the primary which is smaller than that derived from the HR diagram position. This can be explained by a larger intrinsic luminosity of the secondary relative to the primary, due to a larger circumstellar extinction of the secondary relative to the primary.
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