We present the first maps of the surface magnetic fields of a pre-main sequence binary system. Spectropolarimetric observations of the young, 18 Myr, HD 155555 (V824 Ara, G5IV + K0IV) system were obtained at the Anglo-Australian Telescope in 2004 and 2007. Both datasets are analysed using a new binary Zeeman Doppler imaging (ZDI) code. This allows us to simultaneously model the contribution of each component to the observed circularly polarised spectra. Stellar brightness maps are also produced for HD 155555 and compared to previous Doppler images. Our radial magnetic maps reveal a complex surface magnetic topology with mixed polarities at all latitudes. We find rings of azimuthal field on both stars, most of which are found to be non-axisymmetric with the stellar rotational axis. We also examine the field strength and the relative fraction of magnetic energy stored in the radial and azimuthal field components at both epochs. A marked weakening of the field strength of the secondary star is observed between the 2004 and 2007 epochs. This is accompanied by an apparent shift in the location of magnetic energy from the azimuthal to radial field. We suggest that this could be indicative of a magnetic activity cycle. We use the radial magnetic maps to extrapolate the coronal field (by assuming a potential field) for each star individually - at present ignoring any possible interaction. The secondary star is found to exhibit an extreme tilt (~75 deg) of its large scale magnetic field to that of its rotation axis for both epochs. The field complexity that is apparent in the surface maps persists out to a significant fraction of the binary separation. Any interaction between the fields of the two stars is therefore likely to be complex also. Modelling this would require a full binary field extrapolation.
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