We present the first three-dimensional magnetohydrodynamic (MHD) simulations of a circumbinary disk surrounding an equal mass binary. The binary maintains a fixed circular orbit of separation a. As in previous hydrodynamical simulations, strong torques by the binary can maintain a gap of radius 2a. Streams curve inward from r 2a toward the binary; some of their mass passes through the inner boundary, while the remainder swings back out to the disk. However, we also find that near its inner edge the disk develops both a strong m = 1 asymmetry and growing orbital eccentricity. Because the MHD stresses introduce more matter into the gap, the total torque per unit disk mass is 14 times larger than found previously. The inner boundary accretion rate per unit disk mass is 40 times greater than found from previous hydrodynamical calculations. The implied binary shrinkage rate is determined by a balance between the rate at which the binary gains angular momentum by accretion and loses it by gravitational torque. The large accretion rate brings these two rates nearly into balance, but in net, we find that ȧ/a < 0, and its magnitude is about 2.7 times larger than predicted by the earlier hydrodynamic simulations. If the binary comprises two massive black holes, the accretion rate may be great enough

Gap clearing by giant planets has been proposed to explain the optically thin cavities observed in many protoplanetary disks. How much material remains in the gap determines not only how detectable young planets are in their birth environments, but also how strong co-rotation torques are, which impacts how planets can survive fast orbital migration. We determine numerically how the average surface density inside the gap, Σ gap , depends on planet-to-star mass ratio q, Shakura-Sunyaev viscosity parameter α, and disk height-to-radius aspect ratio h/r. Our results are derived from our new GPU-accelerated Lagrangian hydrodynamical code PEnGUIn, and are verified by independent simulations with ZEUS90. For Jupiter-like planets, we find Σ gap ∝ q −2.2 α 1.4 (h/r) 6.6 , and for near brown dwarf masses, Σ gap ∝ q −1 α 1.3 (h/r) 6.1 . Surface density contrasts inside and outside gaps can be as large as 10 4 , even when the planet does not accrete. We derive a simple analytic scaling, Σ gap ∝ q −2 α 1 (h/r) 5 , that compares reasonably well to empirical results, especially at low Neptune-like masses, and use discrepancies to highlight areas for progress.

Following Paper I we investigate the properties of atmospheres that form around small protoplanets embedded in a protoplanetary disc by conducting hydrodynamical simulations. These are now extended to three dimensions, employing a spherical grid centred on the planet. Compression of gas is shown to reduce rotational motions. Contrasting the 2D case, no clear boundary demarcates bound atmospheric gas from disc material; instead, we find an open system where gas enters the Bondi sphere at high latitudes and leaves through the midplane regions, or, vice versa, when the disc gas rotates sub-Keplerian. The simulations do not converge to a time-independent solution; instead, the atmosphere is characterized by a time-varying velocity field. Of particular interest is the timescale to replenish the atmosphere by nebular gas, t replenish . It is shown that the replenishment rate, M atm /t replenish , can be understood in terms of a modified Bondi accretion rate, ∼R 2 Bondi ρ gas v Bondi , where v Bondi is set by the Keplerian shear or the magnitude of the sub-Keplerian motion of the gas, whichever is larger. In the inner disk, the atmosphere of embedded protoplanets replenishes on a timescale that is shorter than the Kelvin-Helmholtz contraction (or cooling) timescale. As a result, atmospheric gas can no longer contract and the growth of these atmospheres terminates. Future work must confirm whether these findings continue to apply when the (thermodynamical) idealizations employed in this study are relaxed. But if shown to be broadly applicable, replenishment of atmospheric gas provides a natural explanation for the preponderance of gas-rich but rock-dominant planets like super-Earths and mini-Neptunes.

Gaseous disks have been proposed as a mechanism for facilitating mergers of binary black holes. We explore circumbinary disk systems to determine the evolution of the central binary. To do so, we perform 3D, hydrodynamic, locally isothermal simulations of circumbinary disks on a Cartesian grid. We focus on binaries of equal mass ratios on fixed circular orbits. To investigate the orbital evolution of the binary, we examine the various torques exerted on the system. For the case where the disk plane and binary orbital plane are aligned, we find that the total torque is positive so that the semi-major axis of the binary increases. For the misaligned case, we run simulations with the binary orbital plane and disk midplane misaligned by 45 • and find the same results -the binary grows. The timescale for the circumbinary disk to realign to the plane of the binary is consistent with the global viscous timescale of the disk.

When an accretion disk surrounds a binary rotating in the same sense, the binary exerts strong torques on the gas. Analytic work in the 1D approximation indicated that these torques sharply diminish or even eliminate accretion from the disk onto the binary. However, recent 2D and 3D simulational work has shown at most modest diminution. We present new MHD simulations demonstrating that for binaries with mass ratios of 1 and 0.1 there is essentially no difference between the accretion rate at large radius in the disk and the accretion rate onto the binary. To resolve the discrepancy with earlier analytic estimates, we identify the small subset of gas trajectories traveling from the inner edge of the disk to the binary and show how the full accretion rate is concentrated onto them as a result of stream-disk shocks driven by the binary torques.

We study the properties of the turbulence driven by the magnetorotational instability (MRI) in a stratified shearing box with outflow boundary conditions and an equation of state determined by self-consistent dissipation and radiation losses. A series of simulations with increasing resolution are performed within a fixed computational box. We achieve numerical convergence with respect to radial and azimuthal resolution. As vertical resolution is improved, the ratio of stress to pressure increases slowly, but the absolute levels of both the stress and the pressure increase noticeably. These results are in contrast with those of previous work on unstratified shearing boxes, in which improved resolution caused a diminution in the magnetic field strength. We argue that the persistence of strong magnetic field at higher resolution found in the stratified case is due to buoyancy. In addition, we find that the time-averaged vertical correlation length of the magnetic field near the disk midplane is ≃ 3 times larger than found in previous unstratifed simulations, decreasing slowly with improved vertical resolution. We further show that the undulatory Parker instability drives the magnetic field upwelling at several scaleheights from the midplane that is characteristic of stratified MHD-turbulent disks.

Characterizing turbulence in protoplanetary disks is crucial for understanding how they accrete and spawn planets. Recent measurements of spectral line broadening promise to diagnose turbulence, with different lines probing different depths. We use three-dimensional local hydrodynamic simulations of cooling, self-gravitating disks to resolve how motions driven by "gravito-turbulence" vary with height. We find that gravito-turbulence is practically as vigorous at altitude as at depth. Even though gas at altitude is much too rarefied to be itself self-gravitating, it is strongly forced by self-gravitating overdensities at the midplane. The long-range nature of gravity means that turbulent velocities are nearly uniform vertically, increasing by just a factor of two from midplane to surface, even as the density ranges over nearly three orders of magnitude. The insensitivity of gravito-turbulence to height contrasts with the behavior of disks afflicted by the magnetorotational instability (MRI); in the latter case, noncircular velocities increase by at least a factor of 15 from midplane to surface, with various non-ideal effects only magnifying this factor. The distinct vertical profiles of gravito-turbulence versus MRI turbulence may be used in conjunction with measurements of non-thermal linewidths at various depths to identify the source of transport in protoplanetary disks.

In the core accretion paradigm of planet formation, gas giants only form a massive atmosphere after their progenitors exceeded a threshold mass: the critical core mass. Most (exo)planets, being smaller and rock/ice-dominated, never crossed this line. Nevertheless, they were massive enough to attract substantial amounts of gas from the disc, while their atmospheres remained in pressure-equilibrium with the disc. Our goal is to characterise the hydrodynamical properties of the atmospheres of such embedded planets and their implication for their (long-term) evolution. In this paper -the first in series -we start to investigate the properties of an isothermal and inviscid flow past a small, embedded planet by conducting local, 2D hydrodynamical simulations. Using the pluto code we confirm that the flow is steady and bound. This steady outcome is most apparent for the log-polar grid (with the grid spacing proportional to the distance from the planet). For low-mass planets, Cartesian grids are somewhat less efficient as they have difficulty to follow the circular, large speeds in the deep atmosphere. Relating the amount of rotation to the gas fraction of the atmosphere, we find that more massive atmospheres rotate faster -a finding consistent with Kelvin's circulation theorem. Rotation therefore limits the amount of gas that planets can acquire from the nebula. Dependent on the Toomre-Q parameter of the circumstellar disc, the planet's atmosphere will reach Keplerian rotation before self-gravity starts to become important.