We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.Comment: 32 pages, accepted for publication in MNRA

Here we propose a mechanism for efficiently growing intermediate mass black holes (IMBH) in discs around supermassive black holes. Stellar mass objects can efficiently agglomerate when facilitated by the gas disc. Stars, compact objects and binaries can migrate, accrete and merge within discs around supermassive black holes. While dynamical heating by cusp stars excites the velocity dispersion of nuclear cluster objects (NCOs) in the disc, gas in the disc damps NCO orbits. If gas damping dominates, NCOs remain in the disc with circularized orbits and large collision cross‐sections. IMBH seeds can grow extremely rapidly by collisions with disc NCOs at low relative velocities, allowing for super‐Eddington growth rates. Once an IMBH seed has cleared out its feeding zone of disc NCOs, growth of IMBH seeds can become dominated by gas accretion from the active galactic nucleus (AGN) disc. However, the IMBH can migrate in the disc and expand its feeding zone, permitting a super‐Eddington accretion rate to continue. Growth of IMBH seeds via NCO collisions is enhanced by a pile‐up of migrators. We highlight the remarkable parallel between the growth of IMBH in AGN discs with models of giant planet growth in protoplanetary discs. If an IMBH becomes massive enough it can open a gap in the AGN disc. IMBH migration in AGN discs may stall, allowing them to survive the end of the AGN phase and remain in galactic nuclei. Our proposed mechanisms should be more efficient at growing IMBH in AGN discs than the standard model of IMBH growth in stellar clusters. Dynamical heating of disc NCOs by cusp stars is transferred to the gas in an AGN disc helping to maintain the outer disc against gravitational instability. Model predictions, observational constraints and implications are discussed in a companion paper (Paper II).

Black hole mergers detectable with LIGO can occur in active galactic nucleus (AGN) disks. Here we parameterize the merger rates, the mass spectrum and the spin spectrum of black holes (BH) in AGN disks. The predicted merger rate spans ∼ 10 −4 − 10 4 Gpc −1 yr −1 , so upper limits from LIGO (< 212Gpc −1 yr −1 ) already constrain it. The predicted mass spectrum has the form of a broken power-law consisting of a pre-existing BH powerlaw mass spectrum and a harder powerlaw mass spectrum resulting from mergers. The predicted spin spectrum is multi-peaked with the evolution of retrograde spin BH in the gas disk playing a key role. We outline the large uncertainties in each of these LIGO observables for this channel and we discuss ways in which they can be constrained in the future.

Outward migration of low-mass planets has recently been shown to be a possibility in non-barotropic disks. We examine the consequences of this result in evolutionary models of protoplanetary disks. Planet migration occurs toward equilibrium radii with zero torque. These radii themselves migrate inwards because of viscous accretion and photoevaporation. We show that as the surface density and temperature fall the planet orbital migration and disk depletion timescales eventually become comparable, with the precise timing depending on the mass of the planet. When this occurs, the planet decouples from the equilibrium radius. At this time, however, the gas surface density is already too low to drive substantial further migration. A higher mass planet, of 10 M ⊕ , can open a gap during the late evolution of the disk, and stops migrating. Low-mass planets, with 1 or 0.1 M ⊕ , released beyond 1 AU in our models avoid migrating into the star. Our results provide support for the reduced migration rates adopted in recent planet population synthesis models.Subject headings:

Context. As accretion in protoplanetary disks is enabled by turbulent viscosity, the border between active and inactive (dead) zones constitutes a location where there is an abrupt change in the accretion flow. The gas accumulation that ensues triggers the Rossby wave instability, which in turn saturates into anticyclonic vortices. It has been suggested that the trapping of solids within them leads to a burst of planet formation on very short timescales. Aims. We study in the formation and evolution of the vortices in greater detail, focusing on the implications for the dynamics of embedded solid particles and planet formation. Methods. We performed two-dimensional global simulations of the dynamics of gas and solids in a non-magnetized thin protoplanetary disk with the Pencil code. We used multiple particle species of radius 1, 10, 30, and 100 cm. We computed the particles' gravitational interaction by a particle-mesh method, translating the particles' number density into surface density and computing the corresponding self-gravitational potential via fast Fourier transforms. The dead zone is modeled as a region of low viscosity. Adiabatic and locally isothermal equations of state are used. Results. The Rossby wave instability is triggered under a variety of conditions, thus making vortex formation a robust process. Inside the vortices, fast accumulation of solids occurs and the particles collapse into objects of planetary mass on timescales as short as five orbits. Because the drag force is size-dependent, aerodynamical sorting ensues within the vortical motion, and the first bound structures formed are composed primarily of similarly-sized particles. In addition to erosion due to ram pressure, we identify gas tides from the massive vortices as a disrupting agent of formed protoplanetary embryos. We find evidence that the backreaction of the drag force from the particles onto the gas modifies the evolution of the Rossby wave instability, with vortices being launched only at later times if this term is excluded from the momentum equation. Even though the gas is not initially gravitationally unstable, the vortices can grow to Q ≈ 1 in locally isothermal runs, which halts the inverse cascade of energy towards smaller wavenumbers. As a result, vortices in models without self-gravity tend to rapidly merge towards a m = 2 or m = 1 mode, while models with self-gravity retain dominant higher order modes (m = 4 or m = 3) for longer times. Non-selfgravitating disks thus show fewer and stronger vortices. We also estimate the collisional velocity history of the particles that compose the most massive embryo by the end of the simulation, finding that the vast majority of them never experienced a collision with another particle at speeds faster than 1 m s −1 . This result lends further support to previous studies showing that vortices provide a favorable environment for planet formation.

Many white dwarf stars show signs of having accreted smaller bodies, implying that they may host planetary systems. A small number of these systems contain gaseous debris discs, visible through emission lines. We report a stable 123.4-minute periodic variation in the strength and shape of the Ca ii emission line profiles originating from the debris disc around the white dwarf SDSS J122859.93+104032.9. We interpret this short-period signal as the signature of a solid-body planetesimal held together by its internal strength.

Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability in the astrophysical community. This discussion relies largely on how the KHI test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two dimensional Kelvin-Helmholtz instability. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of Smoothed Particle Hydrodynamics. We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.

Context. Centimeter and meter-sized solid particles in protoplanetary disks are trapped within long-lived, high-pressure regions, creating opportunities for collapse into planetesimals and planetary embryos. Aims. We aim to study the effect of the high-pressure regions generated in the gaseous disks by a giant planet perturber. These regions consist of gas retained in tadpole orbits around the stable Lagrangian points as a gap is carved, and the Rossby vortices launched at the edges of the gap. Methods. We performed global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk. We employed the Pencil code to solve the Eulerian hydro equations, tracing the solids with a large number of Lagrangian particles, usually 100 000. To compute the gravitational potential of the swarm of solids, we solved the Poisson equation using particle-mesh methods with multiple fast Fourier transforms. Results. Huge particle concentrations are seen in the Lagrangian points of the giant planet, as well as in the vortices they induce at the edges of the carved gaps. For 1 cm to 10 cm radii, gravitational collapse occurs in the Lagrangian points in less than 200 orbits. For 5 cm particles, a 2 M ⊕ planet is formed. For 10 cm, the final maximum collapsed mass is around 3 M ⊕ . The collapse of the 1 cm particles is indirect, following the timescale of gas depletion from the tadpole orbits. Vortices are excited at the edges of the gap, primarily trapping particles of 30 cm radii. The rocky planet that is formed is as massive as 17 M ⊕ , constituting a Super-Earth. Collapse does not occur for 40 cm onwards. By using multiple particle species, we find that gas drag modifies the streamlines in the tadpole region around the classical L4 and L5 points. As a result, particles of different radii have their stable points shifted to different locations. Collapse therefore takes longer and produces planets of lower mass. Three super-Earths are formed in the vortices, the most massive having 4.5 M ⊕ . Conclusions. A Jupiter-mass planet can induce the formation of other planetary embryos at the outer edge of its gas gap. Trojan Earth-mass planets are readily formed; although not existing in the solar system, might be common in the exoplanetary zoo.