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ABSTRACT We carry out hydrodynamical simulations to study the eccentricity growth of a 1–30 Jupiter mass planet located inside the fixed cavity of a protoplanetary disc. The planet exchanges energy and angular momentum with the disc at resonant locations, and its eccentricity grows due to Lindblad resonances. We observe several phases of eccentricity growth where different eccentric Lindblad resonances dominate from 1:3 up to 3:5. The maximum values of eccentricity reached in our simulations are 0.65–0.75. We calculate the eccentricity growth rate for different planet masses and disc parameters and derive analytical dependencies on these parameters. We observe that the growth rate is proportional to both the planet’s mass and the characteristic disc mass for a wide range of parameters. In a separate set of simulations, we derived the width of the 1:3 Lindblad resonance. 

ABSTRACT We present results of global 3D magnetohydrodynamic simulations of accretion on to magnetized stars where both the magnetic and rotational axes of the star are tilted about the rotational axis of the disc. We observed that initially the inner parts of the disc are warped, tilted, and precess due to the magnetic interaction between the magnetosphere and the disc. Later, larger tilted discs form with the size increasing with the magnetic moment of the star. The normal vector to the discs are tilted at different angles, from ∼5°–10° up to ∼30°–40°. Small tilts may result from the winding of the magnetic field lines about the rotational axis of the star and the action of the magnetic force which tends to align the disc. Another possible explanation is the magnetic Bardeen–Petterson effect in which the disc settles in the equatorial plane of the star due to precessional and viscous torques in the disc. Tilted discs slowly precess with the time-scale of the order of ∼50 Keplerian periods at the reference radius (∼3 stellar radii). Our results can be applied to different types of stars where signs of tilted discs and/or slow precession have been observed.