Marina M. Romanova

We investigate the Type I migration of planets in low-density cavities and inner discs of strongly magnetized young stars using global three-dimensional (3D) magnetohydrodynamic (MHD) simulations, where the strong magnetic field carves the low-density cavity. Simulations show that a planet in the cavity migrates inwards up to the radius at which the outer Lindblad resonances are inside the cavity. At smaller radii, the migration stalls. The migration is faster if a star accretes in the unstable regime where the temporary tongues penetrate the magnetosphere. If a planet is in a highly inclined orbit, it interacts with the disc, and the eccentricity increases due to the Kozai-Lydov mechanism. A planet may stop or reverse its migration in the inner disc before entering the cavity. The magnetosphere interacts with the inner disc, changing its density distribution such that migration slows down or is even reversed. A tilted magnetosphere also excites density and bending waves in the disc, which may slow down migration and also increase the inclination and eccentricity of the planet. When a planet reaches the disc-cavity boundary, it is typically trapped at the boundary by asymmetric corotation torque. A planet moves together with the boundary when the cavity expands. Overall, a magnetized star provides an environment for slow or reverse migration.

We investigate the origin of photometric variability in the classical T Tauri star TW Hya by comparing light curves obtained by TESS and ground-based telescopes with light curves created using three-dimensional (3D) magnetohydrodynamic (MHD) simulations. TW Hya is modeled as a rotating star with a dipole magnetic moment, slightly tilted about the rotational axis. We observed that for various model parameters, matter accretes in the unstable regime and produces multiple hot spots on the star's surface, which leads to stochastic-looking light curves similar to the observed ones. Wavelet and Fourier spectra of observed and modeled light curves show multiple quasiperiodic oscillations (QPOs) with quasiperiods from less than 0.1 to 9 days. Models show that variation in the strength and tilt of the dipole magnetosphere leads to different periodograms, where the period of the star may dominate or be hidden. The amplitude of QPOs associated with the stellar period can be smaller than that of other QPOs if the tilt of the dipole magnetosphere is small and when the unstable regime is stronger. In models with small magnetospheres, the short-period QPOs associated with rotation of the inner disc dominate and can be mistaken for a stellar period. We show that longer-period (5-9 days) QPOs can be caused by waves forming beyond the corotation radius.

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.

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.

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.

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 spots⁷, 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.

We present results of global three-dimensional (3D) magnetohydrodynamic (MHD) simulations of accretion onto 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 process 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 degrees up to 30-40 degrees. 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 (approx. 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.

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.

Inward migration of low-mass planets and embryos of giant planets can be stopped at the disc–cavity boundaries due to co-orbital corotation torque. We performed the first global three-dimensional (3D) simulations of planet migration at the disc–cavity boundary, and have shown that the boundary is a robust trap for low-mass planets and embryos. A protoplanetary disc may have several such trapping regions at various distances from the star, such as at the edge of the stellar magnetosphere, the inner edge of the dead zone, the dust-sublimation radius and the snow lines. Corotation traps located at different distances from a star, and moving outward during the disc dispersal phase, may possibly explain the observed homogeneous distribution of low-mass planets with distance from their host stars.

Inward migration of low-mass planets and embryos of giant planets can be stopped at the disc-cavity boundaries due to co-orbital corotation torque. We performed the first global three-dimensional (3D) simulations of planet migration at the disc-cavity boundary, and have shown that the boundary is a robust trap for low-mass planets and embryos. A protoplanetary disc may have several such trapping regions at various distances from the star, such as at the edge of the stellar magnetosphere, the inner edge of the dead zone, the dust-sublimation radius and the snow lines. Corotation traps located at different distances from a star, and moving outward during the disc dispersal phase, may possibly explain the observed homogeneous distribution of low-mass planets with distance from their host stars.