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We use numerical simulations of circumplanetary disks to determine the boundary between disks that are radially truncated by the tidal potential and those where gas escapes the Hill sphere. We consider a model problem, in which a coplanar circumplanetary disk is resupplied with gas at an injection radius smaller than the Hill radius. We evolve the disk using thePhantomsmoothed particle hydrodynamics code until a steady state is reached. We find that the most significant dependence of the truncation boundary is on the disk aspect ratioH/R. Circumplanetary disks are efficiently truncated forH/R≲ 0.2. ForH/R≃ 0.3, up to about half of the injected mass, depending on the injection radius, flows outward through the decretion disk and escapes. As expected from analytic arguments, the conditions (H/Rand Shakura–Sunyaevα) required for tidal truncation are independent of planet mass. A simulation with largerα= 0.1 shows stronger outflow than one withα= 0.01, but the dependence on transport efficiency is less important than variations ofH/R. Our results suggest two distinct classes of circumplanetary disks: tidally truncated thin disks with dust-poor outer regions, and thicker actively decreting disks with enhanced dust-to-gas ratios. Applying our results to the PDS 70 c system, we predict a largely truncated circumplanetary disk, but it is possible that enough mass escapes to support an outward flow of dust that could explain the observed disk size.

 

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.

 

Mutually misaligned circumbinary planets may form in a warped or broken gas disk or from later planet–planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semimajor axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect—it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.

 

While giant planet occurrence rates increase with stellar mass, occurrence rates of close-in super-Earths decrease. This is in contradiction to the expectation that the total mass of the planets in a system scale with the protoplanetary disc mass and hence the stellar mass. Since the snow line plays an important role in the planet formation process, we examine differences in the temperature structure of protoplanetary gas discs around stars of different mass. Protoplanetary discs likely contain a dead zone at the mid-plane that is sufficiently cold and dense for the magneto-rotational instability to be suppressed. As material builds up, the outer parts of the dead zone may be heated by self-gravity. The temperature in the disc can be below the snow line temperature far from the star and in the inner parts of a dead zone. The inner icy region has a larger radial extent around smaller mass stars. The increased mass of solid icy material may allow for the in situ formation of larger and more numerous planets close to a low-mass star. Super-Earths that form in the inner icy region may have a composition that includes a significant fraction of volatiles.

 

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.

 

We present hydrodynamical simulations to model the accretion flow from a polar circumbinary disc on to a high eccentricity (e = 0.78) binary star system with near unity mass ratio (q = 0.83), as a model for binary HD 98800 BaBb. We compare the polar circumbinary disc accretion flow with the previously studied coplanar case. In the coplanar case, the circumbinary disc becomes eccentric and the accretion alternates from being dominant on to one binary member to the other. For the polar disc case involving a highly eccentric binary, we find that the circumbinary disc retains its initially low eccentricity and that the primary star accretion rate is always about the same as the secondary star accretion rate. Recent observations of the binary HD 98800 BaBb, which has a polar circumbinary disc, have been used to determine the value of the $\rm H\,\alpha$ flux from the brighter component. From this value, we infer that the accretion rate is much lower than for typical T Tauri stars. The eccentric orbit of the outer companion HD 98800 A increases the accretion rate on to HD 98800 B by ∼20 per cent after each periastron passage. Our hydrodynamical simulations are unable to explain such a low accretion rate unless the disc viscosity parameter is very small, α < 10−5. Additional observations of this system would be useful to check on this low accretion rate.

 

ABSTRACT The core accretion model of giant planet formation has been challenged by the discovery of recycling flows between the planetary envelope and the disc that can slow or stall envelope accretion. We carry out 3D radiation hydrodynamic simulations with an updated opacity compilation to model the proto-Jupiter’s envelope. To isolate the 3D effects of convection and recycling, we simulate both isolated spherical envelopes and envelopes embedded in discs. The envelopes are heated at given rates to achieve steady states, enabling comparisons with 1D models. We vary envelope properties to obtain both radiative and convective solutions. Using a passive scalar, we observe significant mass recycling on the orbital time-scale. For a radiative envelope, recycling can only penetrate from the disc surface until ∼0.1–0.2 planetary Hill radii, while for a convective envelope, the convective motion can ‘dredge up’ the deeper part of the envelope so that the entire convective envelope is recycled efficiently. This recycling, however, has only limited effects on the envelopes’ thermal structure. The radiative envelope embedded in the disc has identical structure as the isolated envelope. The convective envelope has a slightly higher density when it is embedded in the disc. We introduce a modified 1D approach which can fully reproduce our 3D simulations. With our updated opacity and 1D model, we recompute Jupiter’s envelope accretion with a 10 M⊕ core, and the time-scale to runaway accretion is shorter than the disc lifetime as in prior studies. Finally, we discuss the implications of the efficient recycling on the observed chemical abundances of the planetary atmosphere (especially for super-Earths and mini-Neptunes).