We study dust capture by vortices and its long-term consequences in global two-fluid inviscid disk simulations using a new polar grid code RoSSBi that allows to model the background gas flow with very high stability and accuracy thanks to a well-balanced scheme. We perform the longest integrations so far, several hundred disk orbits, at the highest resolution attainable in global simulations of disks with dust, namely 2048x4096 grid points. This allows to study the dust evolution well beyond vortex dissipation. We vary a wide range of parameters, most notably the dust-to-gas ratio in the initial setup varies in the range 10 −3 to 0.1. Irrespective of the initial dust-to-gas ratio we find rapid concentration of the dust inside vortices, reaching dust-to-gas ratios of order unity inside the vortex. We present an analytical model that describes very well the dust capture process inside vortices, finding consistent results for all dust-to-gas ratios. A vortex streaming instability develops which causes invariably vortex destruction. After vortex dissipation large-scale dust-rings encompassing a disk annulus form in most cases, which sustain very high dust concentration, approaching ratios of order unity. The rings are long livedlasting as long as the duration of the simulations. They also develop a streaming instability, which manifests itself in eddies at various scales within which the dust forms compact high density clumps. Such clumps would be unstable to gravitational collapse in absence of strong dissipation by viscous forces. When vortices are particularly long lived, rings do not form but dust clumps inside vortices become then long lived features and would likely undergo collapse by gravitational instability. Rings encompass almost an Earth mass of solid material, while even larger masses of dust do accumulate inside vortices in the earlier stage. We argue that rapid planetesimal formation would occur in the dust clumps inside the vortices as well as in the post-vortex ring. Planetesimals would have a wide range of sizes given the turbulent nature of the density fluctuations, with potentially important implications for the formation of terrestrial planets as well as for the cores of gas giants. Even higher resolution will be needed to study robustly the streaming instability in the rings as well as in the low Stokes number regime, while self-gravity will be added in the future to explore the eventual collapse of the dust clumps.

Aims. We determine the size, structure, and evolution of persistent vortices in 2D and inviscid Keplerian flows. Methods. A Gaussian model of the vortices is built and compared with numerical solutions issued from non-linear hydrodynamical simulations. Test vortices are also produced using a fiducial method based on the Rossby wave instability to help explore the vortex parameters. Numerical simulations are performed using a second order finite volume method. We assume a perfect-gas law and a non-homentropic adiabatic flow.Results. The new model nicely fits the numerical vortex solution. In the vortex centre it is consistent with existing models, whereas in the outer regions it enables the vortex to be connected with the background flow. Two families of vortices can be distinguished following the importance of the compressional effects. The model also permitted a new class of vortices to be discovered corresponding to huge perturbations of pressure and density and whose radial sizes are significantly larger than the disk scale height, in contrast with the standard way to define the maximum vortex size. Conclusions. Our Gaussian model of the vortex solutions of the 2D Euler's equations is a useful tool for studying vortex properties. Among the large number of vortex solutions, the possible existence of giant vortices could open interesting perspectives in planetary formation, particularly during the building stage of the giant gas planets.

We exploit our formula for the gravitational potential of finite size, power-law disks to derive a general expression linking the mass of the black hole in active galactic nuclei (AGN), the mass of the surrounding disk, its surface density profile (through the power index s), and the differential rotation law. We find that the global rotation curve v(R) of the disk in centrifugal balance does not obey a power law of the cylindrical radius R (except in the confusing case s = −2 that mimics a Keplerian motion), and discuss the local velocity index. This formula can help to understand how, from position-velocity diagrams, mass is shared between the disk and the black hole. To this purpose, we checked the idea by generating a sample of synthetic data with different levels of Gaussian noise, added in radius. It turns out that, when observations are spread over a large radial domain and exhibit low dispersion (standard deviation σ 10% typically), the disk properties (mass and s-parameter) and black hole mass can be deduced from a non linear fit of kinematic data plotted on a (R, Rv 2 )-diagram. For σ 10%, masses are estimated fairly well from a linear regression (corresponding to the zeroth-order treatment of the formula), but the power index s is no longer accessible. We have applied the model to 7 AGN disks whose rotation has already been probed through water maser emission. For NGC 3393 and UGC 3789, the masses seem well constrained through the linear approach. For IC 1481, the power-law exponent s can even be deduced. Because the model is scale-free, it applies to any kind of star/disk system. Extension to disks around young stars showing deviation from Keplerian motion is thus straightforward.

We study the evolution of planet-induced vortices in radially stratified disks, with initial conditions allowing for radial buoyancy. For this purpose we run global two-dimensional hydrodynamical simulations, using the PLUTO code. Planet-induced vortices are a product of the Rossby wave instability (RWI) triggered in the edges of a planetary gap. In this work we assess the influence of radial buoyancy for the development of the vortices. We found that radial buoyancy leads to smoother planetary gaps, which generates weaker vortices. This effect is less pronounced for locally isothermal and quasi-isothermal (very small cooling rate) disks. We observed the formation of two generations of vortices. The first generation of vortices is formed in the outer wall of the planetary gap. The merged primary vortex induces accretion, depleting the mass on its orbit. This process creates a surface density enhancement beyond the primary vortex position. The second generation of vortices arise in this surface density enhancement, indicating that the bump in this region is sufficient to trigger the RWI. The merged secondary vortex is a promising explanation for the location of the vortex in the Oph IRS 48 system. Finally, we observed a nonmonotonic behavior for the vortex lifetimes as a function of the thermal relaxation timescale, agreeing with previous studies. The birth times of the secondary vortices also display a nonmonotonic behavior, which is correlated with the growth time of the primary vortex and its induced accretion.