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We describe the first grid-based simulations of the polar alignment of a circumbinary disc. We simulate the evolution of an inclined disc around an eccentric binary using the grid-based code athena++ . The use of a grid-based numerical code allows us to explore lower disc viscosities than have been examined in previous studies. We find that the disc aligns to a polar orientation when the α viscosity is high, while discs with lower viscosity nodally precess with little alignment over 1000 binary orbital periods. The time-scales for polar alignment and disc precession are compared as a function of disc viscosity, and are found to be in agreement with previous studies. At very low disc viscosities (e.g. α = 10−5), anticyclonic vortices are observed along the inner edge of the disc. These vortices can persist for thousands of binary orbits, creating azimuthally localized overdensities and multiple pairs of spiral arms. The vortex is formed at ∼3–4 times the binary semimajor axis, close to the inner edge of the disc, and orbits at roughly the local Keplerian speed. The presence of a vortex in the disc may play an important role in the evolution of circumbinary systems, such as driving episodic accretion and accelerating the formation of polar circumbinary planets.

 

A test particle orbit around an eccentric binary has two stationary states in which there is no nodal precession: coplanar and polar. Nodal precession of a misaligned test particle orbit centres on one of these stationary states. A low-mass circumbinary disc undergoes the same precession and moves towards one of these states through dissipation within the disc. For a massive particle orbit, the stationary polar alignment occurs at an inclination less than 90°, which is the prograde-polar stationary inclination. A sufficiently high angular momentum particle has an additional higher inclination stationary state, the retrograde-polar stationary inclination. Misaligned particle orbits close to the retrograde-polar stationary inclination are not nested like the orbits close to the other stationary points. We investigate the evolution of a gas disc that begins close to the retrograde-polar stationary inclination. With hydrodynamical disc simulations, we find that the disc moves through the unnested crescent shape precession orbits and eventually moves towards the prograde-polar stationary inclination, thus increasing the parameter space over which circumbinary discs move towards polar alignment. If protoplanetary discs form with an isotropic orientation relative to the binary orbit, then polar discs may be more common than coplanar discs around eccentric binaries, even for massive discs. This has implications for the alignment of circumbinary planets.

 

ABSTRACT Recent ALMA molecular line observations have revealed 3D gas velocity structure in protoplanetary discs, shedding light on mechanisms of disc accretion and structure formation. (1) By carrying out viscous simulations, we confirm that the disc’s velocity structure differs dramatically using vertical stress profiles from different accretion mechanisms. Thus, kinematic observations tracing flows at different disc heights can potentially distinguish different accretion mechanisms. On the other hand, the disc surface density evolution is mostly determined by the vertically integrated stress. The sharp disc outer edge constrained by recent kinematic observations can be caused by a radially varying α in the disc. (2) We also study kinematic signatures of a young planet by carrying out 3D planet–disc simulations. The relationship between the planet mass and the ‘kink’ velocity is derived, showing a linear relationship with little dependence on disc viscosity, but some dependence on disc height when the planet is massive (e.g. 10MJ). We predict the ‘kink’ velocities for the potential planets in DSHARP discs. At the gap edge, the azimuthally averaged velocities at different disc heights deviate from the Keplerian velocity at similar amplitudes, and its relationship with the planet mass is consistent with that in 2D simulations. After removing the planet, the azimuthally averaged velocity barely changes within the viscous time-scale, and thus the azimuthally averaged velocity structure at the gap edge is due to the gap itself and not directly caused to the planet. Combining both axisymmetric kinematic observations and the residual ‘kink’ velocity is needed to probe young planets in protoplanetary discs.