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ABSTRACT We study the evolution of eccentricity and inclination of massive planets in low-density cavities of protoplanetary discs using three-dimensional (3D) simulations. When the planet’s orbit is aligned with the equatorial plane of the disc, the eccentricity increases to high values of 0.7–0.9 due to the resonant interaction with the inner parts of the disc. For planets on inclined orbits, the eccentricity increases due to the Kozai–Lidov mechanism, where the disc acts as an external massive body, which perturbs the planet’s orbit. At small inclination angles, $${\lesssim}30^\circ$$, the resonant interaction with the inner disc strongly contributes to the eccentricity growth, while at larger angles, eccentricity growth is mainly due to the Kozai–Lidov mechanism. We conclude that planets inside low-density cavities tend to acquire high eccentricity if favourable conditions give sufficient time for growth. The final value of the planet’s eccentricity after the disc dispersal depends on the planet’s mass and the properties of the cavity and protoplanetary disc. 

Abstract Magnetospheric accretion models predict that matter from protoplanetary disks accretes onto stars via funnel flows, which follow stellar magnetic field lines and shock on the stellar surfaces 1–3 , leaving hot spots with density gradients 4–6 . Previous work has provided observational evidence of varying density in hot spots 7 , but these observations were not sensitive to the radial density distribution. Attempts have been made to measure this distribution using X-ray observations 8–10 ; however, X-ray emission traces only a fraction of the hot spot 11,12 and also coronal emission 13,14 . Here we report periodic ultraviolet and optical light curves of the accreting star GM Aurigae, which have a time lag of about one day between their peaks. The periodicity arises because the source of the ultraviolet and optical emission moves into and out of view as it rotates along with the star. The time lag indicates a difference in the spatial distribution of ultraviolet and optical brightness over the stellar surface. Within the framework of a magnetospheric accretion model, this finding indicates the presence of a radial density gradient in a hot spot on the stellar surface, because regions of the hot spot with different densities have different temperatures and therefore emit radiation at different wavelengths.