REBOUND is a new multi-purpose N-body code which is freely available under an open-source license. It was designed for collisional dynamics such as planetary rings but can also solve the classical N-body problem. It is highly modular and can be customized easily to work on a wide variety of different problems in astrophysics and beyond. REBOUND comes with three symplectic integrators: leap-frog, the symplectic epicycle integrator (SEI) and a Wisdom-Holman mapping (WH). It supports open, periodic and shearing-sheet boundary conditions. REBOUND can use a Barnes-Hut tree to calculate both selfgravity and collisions. These modules are fully parallelized with MPI as well as OpenMP. The former makes use of a static domain decomposition and a distributed essential tree. Two new collision detection modules based on a plane-sweep algorithm are also implemented. The performance of the plane-sweep algorithm is superior to a tree code for simulations in which one dimension is much longer than the other two and in simulations which are quasi-two dimensional with less than one million particles. In this work, we discuss the different algorithms implemented in REBOUND, the philosophy behind the code's structure as well as implementation specific details of the different modules. We present results of accuracy and scaling tests which show that the code can run efficiently on both desktop machines and large computing clusters.

We present Atacama Large Millimeter and Submillimeter Array observations of the protoplanetary disk around the Herbig Ae star HD 163296 that trace the spatial distribution of millimeter-sized particles and cold molecular gas on spatial scales as small as 25 astronomical units (A.U.). The image of the disk recorded in the 1.3 mm continuum emission reveals three dark concentric rings that indicate the presence of dust depleted gaps at about 60, 100, and 160 A.U. from the central star. The maps of the 12 CO, 13 CO, and C 18 O J ¼ 2 − 1 emission do not show such structures but reveal a change in the slope of the radial intensity profile across the positions of the dark rings in the continuum image. By comparing the observations with theoretical models for the disk emission, we find that the density of CO molecules is reduced inside the middle and outer dust gaps. However, in the inner ring there is no evidence of CO depletion. From the measurements of the dust and gas densities, we deduce that the gas-to-dust ratio varies across the disk and, in particular, it increases by at least a factor 5 within the inner dust gap compared to adjacent regions of the disk. The depletion of both dust and gas suggests that the middle and outer rings could be due to the gravitational torque exerted by two Saturn-mass planets orbiting at 100 and 160 A.U. from the star. On the other hand, the inner dust gap could result from dust accumulation at the edge of a magnetorotational instability dead zone, or from dust opacity variations at the edge of the CO frost line. Observations of the dust emission at higher angular resolution and of molecules that probe dense gas are required to establish more precisely the origins of the dark rings observed in the HD 163296 disk.

Recent Atacama Large Millimeter and Submillimeter Array (ALMA) observations of the protoplanetary disk around the Herbig Ae star HD 163296 revealed three depleted dust gaps at 60, 100, and 160 au in the 1.3 mm continuum as well as CO depletion in the middle and outer dust gaps. However, no CO depletion was found in the inner dust gap. To examine the planet-disk interaction model, we present results of 2D two fluid (gas + dust) hydrodynamic simulations coupled with 3D radiative transfer simulations. To fit the high gas-to-dust ratio of the first gap, we find that the Shakura-Sunyaev viscosity parameter α must be very small ( 10 4  -) in the inner disk. On the other hand, a relatively large α ( 7.5 10 3´-) is required to reproduce the dust surface density in the outer disk. We interpret the variation of α as an indicator of the transition from an inner dead zone to the outer magnetorotational instability (MRI) active zone. Within ∼100 au, the HD 163296 disk's ionization level is low, and non-ideal magnetohydrodynamic effects could suppress the MRI, so the disk can be largely laminar. The disk's ionization level gradually increases toward larger radii, and the outermost disk (r 300 > au) becomes turbulent due to MRI. Under this condition, we find that the observed dust continuum and CO gas line emissions can be reasonably fit by three half-Jovian-mass planets (0.46, 0.46, and M 0.58 J ) at 59, 105, and 160 au, respectively.