We report results of a spectropolarimetric and photometric monitoring of the weak-line T Tauri stars (wTTSs) V819 Tau and V830 Tau within the MaTYSSE programme, involving the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. At ~3 Myr, both stars dissipated their discs recently and are interesting objects for probing star and planet formation. Profile distortions and Zeeman signatures are detected in the unpolarized and circularly-polarized lines, whose rotational modulation we modelled using tomographic imaging, yielding brightness and magnetic maps for both stars. We find that the large-scale magnetic fields of V819 Tau and V830 Tau are mostly poloidal and can be approximated at large radii by 350-400 G dipoles tilted at ~30 degrees to the rotation axis. They are significantly weaker than the field of GQ Lup, an accreting classical T Tauri star (cTTS) with similar mass and age which can be used to compare the magnetic properties of wTTSs and cTTSs. The reconstructed brightness maps of both stars include cool spots and warm plages. Surface differential rotation is small, typically ~4.4x smaller than on the Sun, in agreement with previous results on wTTSs. Using our Doppler images to model the activity jitter and filter it out from the radial velocity (RV) curves, we obtain RV residuals with dispersions of 0.033 and 0.104 km/s for V819 Tau and V830 Tau respectively. RV residuals suggest that a hot Jupiter may be orbiting V830 Tau, though additional data are needed to confirm this preliminary result. We find no evidence for close-in giant planet around V819 Tau.
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