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.