Disc instability (DI) is a model aimed at explaining the formation of companions through the fragmentation of the circumstellar gas disc. Furthermore, DI could explain the formation of part of the observed exoplanetary population. We aim to provide a new comprehensive global model for the formation of companions via DI. The latter leads for the companions to orbital migration and damping of the eccentricities and inclinations. As it evolves, the disc is continuously monitored for self-gravity and fragmentation. When the conditions are satisfied, one (or several) clumps are inserted. The evolution of the clumps is then followed in detail. We showcased the model by performing a number of simulations for various initial conditions, from simple non-fragmenting systems to complex systems with many fragments. We confirm that the DIPSY model is a comprehensive and versatile global model of companion formation via DI. It enables studies of the formation of companions with planetary to low stellar masses around primaries with final masses that range from the brown dwarf to the B-star regime. We conclude that it is necessary to consider the many interconnected processes such as gas accretion, orbital migration, and N-body interactions, as they strongly influence the inferred population of forming objects. It is also clear that model assumptions play a key role in the determination of the systems undergoing formation.
(abridged) Aims: We present new results exhibiting a subcritical baroclinic instability (SBI) in local shearing box models. We describe the 2D and 3D behaviour of this instability using numerical simulations and we present a simple analytical model describing the underlying physical process. Results: A subcritical baroclinic instability is observed in flows stable for the Solberg-Hoiland criterion using local simulations. This instability is found to be a nonlinear (or subcritical) instability, which cannot be described by ordinary linear approaches. It requires a radial entropy gradient weakl…
Recent results by Martin et al. (2014) showed in 3D SPH simulations that tilted discs in binary systems can be unstable to the development of global, damped Kozai-Lidov (KL) oscillations in which the discs exchange tilt for eccentricity. We investigate the linear stability of KL modes for tilted inviscid discs under the approximations that the disc eccentricity is small and the disc remains flat. By using 1D equations, we are able to probe regimes of large ratios of outer to inner disc edge radii that are realistic for binary systems of hundreds of AU separations and are not easily probed by m…
The Rossby wave instability (RWI) is a promising mechanism for producing large-scale vortices in protoplanetary discs. The instability operates around a density bump in the disc, and the resulting vortices may facilitate planetesimal formation and angular momentum transfer in the disc dead zone. Most previous works on the RWI deal with two-dimensional (height-integrated) discs. However, vortices may have different dynamical behaviours in 3D than in 2D. Recent numerical simulations of the RWI in 3D global discs by Meheut et al. have revealed intriguing vertical structure of the vortices, includ…
Planetary systems form in gas-dust protoplanetary discs via the growth of solid bodies. In this paper, we show that the most intriguing stage of such growth --- namely, the transformation of 1-10 m boulders into kilometre-sized planetesimals --- can be explained by a mechanism of gravitational instability. The present work focused on the origin of self-gravitating clumps in which planetesimal formation could take place. Our computer simulations demonstrated that such clumps of gas and boulders formed due to the development of a two-phase instability. This instability revealed a so-called 'mutu…
We consider the evolution of accretion discs that contain some turbulence within a disc dead zone, a region about the disc midplane of a disc that is not sufficiently ionised for the magneto-rotational instability (MRI) to drive turbulence. In particular, we determine whether additional sources of turbulence within a dead zone are capable of suppressing gravo-magneto (GM) disc outbursts that arise from a rapid transition from gravitationally produced to MRI produced turbulence. With viscous $α$ disc models we consider two mechanisms that may drive turbulence within the dead zone. First, we exa…
Protoplanetary discs should exhibit a weak vertical variation in their rotation profiles. Typically this `vertical shear' issues from a baroclinic effect driven by the central star's radiation field, but it might also arise during the launching of a magnetocentrifugal wind. As a consequence, protoplanetary discs are subject to a hydrodynamical instability, the `vertical shear instability' (VSI), whose breakdown into turbulence could transport a moderate amount of angular momentum and facilitate, or interfere with, the process of planet formation. Magnetic fields may suppress the VSI, however, …
We carry out global three-dimensional radiation hydrodynamical simulations of self-gravitating accretion discs to determine if, and under what conditions, a disc may fragment to form giant planets. We explore the parameter space (in terms of the disc opacity, temperature and size) and include the effect of stellar irradiation. We find that the disc opacity plays a vital role in determining whether a disc fragments. Specifically, opacities that are smaller than interstellar Rosseland mean values promote fragmentation (even at small radii, R < 25AU) since low opacities allow a disc to cool quick…
Observations with the Atacama Large Millimeter/Submillimeter array (ALMA) have dramatically improved our understanding of the site of exoplanet formation: protoplanetary discs. However, many basic properties of these discs are not well-understood. The most fundamental of these is the total disc mass, which sets the mass budget for planet formation. Discs with sufficiently high masses can excite gravitational instability and drive spiral arms that are detectable with ALMA . Although spirals have been detected in ALMA observations of the dust , their association with gravitational instability, a…
We present the first detection of the 13C17O J=3-2 transition toward the HL Tau protoplanetary disc. We find significantly more gas mass (at least a factor of ten higher) than has been previously reported using C18O emission. This brings the observed total disc mass to 0.2 M, which we consider to be a conservative lower limit. Our analysis of the Toomre Q profile suggests that this brings the disc into the regime of gravitational instability. The radial region of instability (50-110 au) coincides with the location of a proposed planet-carved gap in the dust disc and a spiral in the gas. We, th…
Fragmentation of rotating gaseous systems via gravitational instability is believed to be a crucial mechanism in several astrophysical processes, such as formation of planets in protostellar discs, of molecular clouds in galactic discs, and of stars in molecular clouds. Gravitational instability is fairly well understood for infinitesimally thin discs. However, the thin-disc approximation is not justified in many cases, and it is of general interest to study the gravitational instability of rotating fluids with different degrees of rotation support and stratification. We derive dispersion rela…
Context: Around 30 per cent of the observed exoplanets that orbit M dwarf stars are gas giants that are more massive than Jupiter. These planets are prime candidates for formation by disc instability. Aims: We want to determine the conditions for disc fragmentation around M dwarfs and the properties of the planets that are formed by disc instability. Methods: We performed hydrodynamic simulations of M dwarf protostellar discs in order to determine the minimum disc mass required for gravitational fragmentation to occur. Different stellar masses, disc radii, and metallicities were considered. Th…
Damping of the previously discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is studied using the local approach to dynamics of gas-dust perturbations in the limit of the small dust fraction. Turbulence in a disc is represented by the effective viscosity and diffusivity in equations of motion for gas and dust, respectively. In the standard case of the Schmidt number (ratio of the effective viscosity to diffusivity) Sc = 1, the reduced description of RDI in terms of the inertial wave (IW) and the streaming dust wave (SDW) falling in resonance with each other rev…
In the present study, we addressed the question of how the growth rate of the magnetorotational instability is modified when the radial component of the stellar dipole magnetic field is taken into account in addition to the vertical component. Considering a fiducial radius in the disc where diamagnetic currents are pronounced, we carried out a linear stability analysis to obtain the growth rates of the magnetorotational instability for various parameters such as the ratio of the radial-to-vertical component and the gradient of the magnetic field, the Alfvenic Mach number and the diamagnetizati…
Warped accretion discs of low viscosity are prone to hydrodynamic instability due to parametric resonance of inertial waves as confirmed by local simulations. Global simulations of warped discs, using either smoothed particle hydrodynamics (SPH) or grid-based codes, are ubiquitous but no such instability has been seen. Here we utilize a hybrid Godunov-type Lagrangian method to study parametric instability in global simulations of warped Keplerian discs at unprecedentedly high resolution (up to 120 million particles). In the global simulations, the propagation of the warp is well described by t…
We study drag-driven instability in a protoplanetary disc consisting of a layer of single-sized dust particles which are coupled to the magnetized gas aerodynamically and the particle-to-gas feedback is included. We find a dispersion relation for axisymmetric linear disturbances and growth rate of the unstable modes are calculated numerically. While the secular gravitational instability in the absence of particle-to-gas feedback predicts the dust layer is unstable, magnetic fields significantly amplifies the instability if the Toomre parameter for the gas component is fixed. We also show that …
Circumplanetary discs can be linearly unstable to the growth of disc tilt in the tidal potential of the star-planet system. We use three-dimensional hydrodynamical simulations to characterize the disc conditions needed for instability, together with its long term evolution. Tilt growth occurs for disc aspect ratios, evaluated near the disc outer edge, of $H/r\gtrsim 0.05$, with a weak dependence on viscosity in the wave-like regime of warp propagation. Lower mass giant planets are more likely to have circumplanetary discs that satisfy the conditions for instability. We show that the tilt insta…
The Rossby wave instability, associated with density bumps in differentially rotating discs, may arise in several different astrophysical contexts, such as galactic or protoplanetary discs. While the linear phase of the instability has been well studied, the nonlinear evolution and especially the saturation phase remain poorly understood. In this paper, we test the non-linear saturation mechanism analogous to that derived for wave-particle interaction in plasma physics. To this end we perform global numerical simulations of the evolution of the instability in a two-dimensional disc. We confirm…
Streaming instability is a privileged channel to bridge the gap between collisional growth of dust grains and planetesimal formation triggered by gravity. This instability is thought to develop through its secular mode, which is long-time growing and may not develop easily in real discs. We address this point by revisiting its perturbation analysis. A third-order expansion with respect to the Stokes number reveals important features over-looked so far. The secular mode can be stable. Epicycles can be unstable, more resistant to viscosity and are identified by Green's function analysis as promi…
Streaming instability is a powerful mechanism which concentrates dust grains in pro- toplanetary discs, eventually up to the stage where they collapse gravitationally and form planetesimals. Previous studies inferred that it should be ineffective in viscous discs, too efficient in inviscid discs, and may not operate in local pressure maxima where solids accumulate. From a linear analysis of stability, we show that streaming instability behaves differently inside local pressure maxima. Under the action of the strong differential advection imposed by the bump, a novel unstable mode develops and …
The origin of turbulence in accretion discs is still not fully understood. While the magneto-rotational instability is considered to operate in sufficiently ionized discs, its role in the poorly ionized protoplanetary disc is questionable. Recently, the vertical shear instability (VSI) has been suggested as a possible alternative. Our goal is to study the characteristics of this instability and the efficiency of angular momentum transport, in extended discs, under the influence of radiative transport and irradiation from the central star. We use multi-dimensional hydrodynamic simulations to mo…
The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite differences in the radial direction and spectral collocation in the vertical direction. RWI modes are calculated subject to different upper disc boundary conditions. These include free surface, solid boundaries and variable vertical domain size. Boundary conditions that oppose vertical motion increase the instability growth rate by a few per cent. The magnitude of …
We present the results of 2D and 3D hydrodynamic simulations of idealized protoplanetary discs that examine the formation and evolution of vortices by the vertical shear instability (VSI). In agreement with recent work, we find that discs with radially decreasing temperature profiles and short thermal relaxation time-scales, are subject to the axisymmetric VSI. In three dimensions, the resulting velocity perturbations give rise to quasi-axisymmetric potential vorticity perturbations that break-up into discrete vortices, in a manner that is reminiscent of the Rossby wave instability. Discs with…
In this paper, we investigate whether overdensity formation via streaming instability is consistent with recent multi-wavelength ALMA observations in the Lupus star forming region. We simulate the local action of streaming instability in 2D using the code ATHENA, and examine the radiative properties at mm wavelengths of the resulting clumpy dust distribution by focusing on two observable quantities: the optically thick fraction $ff$ (in ALMA band 6) and the spectral index $α$ (in bands 3-7). By comparing the simulated distribution in the $ff-α$ plane before and after the action of streaming in…
Streaming instabilities in weakly ionized protoplanetary discs: the Ambipolar Streaming Instability (AmSI)
Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS（波尔多天体物理实验室，波尔多大学，法国国家科学研究中心）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
We carry out three dimensional SPH simulations to show that a migrating giant planet strongly suppresses the spiral structure in self-gravitating discs. We present mock ALMA continuum observations which show that in the absence of a planet, spiral arms due to gravitational instability are easily observed. Whereas in the presence of a giant planet, the spiral structures are suppressed by the migrating planet resulting in a largely axisymmetric disc with a ring and gap structure. Our modelling of the gas kinematics shows that the planet's presence could be inferred, for example, using optically …
Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and ultimately modify the global disc properties. We use a local model of an eccentric disc, derived in a companion paper, to compute the nonlinear vertical ("breathing mode") oscillations of the disc. We then analyse their linear stability to locally axisymmetric disturbances for any disc eccentricity and eccentricity gradient using a numerical Floquet method. In the …
We identify a new hydrodynamical instability in protoplanetary discs that may arise due to variations in the dust-to-gas ratio and may lead to concentration of dust grains within a disc. The instability can arise due to dust settling, which produces a vertical compositional entropy gradient. The entropy gradient drives a baroclinic instability that is capable of creating toroidal gas vortices that gather dust into rings. Such dust rings are potentially observable via continuum emission of the dust or scattered light. Indeed, this instability may offer an explanation for the rings recently obse…
(Abridged) We analyse the stability and evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are power-law functions of cylindrical radius. We employ two different hydrodynamic codes to perform 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the viscosity. We present a stability analysis of the problem that we use to interpret …
We investigate streaming instability using two-fluid approximation (neutral gas and dust) in a quasi-global, unstratified protoplanetary disc, with the help of PIERNIK code. We compare amplification rate of the eigen-mode in numerical simulations, with the corresponding growth resulting from the linear stability analysis of full system of Euler's equation including aerodynamic drag. Following Youdin & Goodman (2005) we show that (1) rapid dust clumping occurs due to the difference in azimuthal velocities of gas and dust, coupled by the drag force, (2) initial density perturbations are amplifie…
We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a "vertical-shear instability", which recent nonlinear simulations have shown to drive hydrodynamic activity in the MRI-stable regions of protoplanetary discs. We first revisit locally isothermal discs using the quasi-global reduced model derived by Nelson et al. (2013). This analysis is then extended to global axisymmetric perturbations in a cylindrical domain. We also derive and study a reduced model describin…
Giant planet formation in the core accretion (CA) paradigm is predicated by the formation of a core, assembled by the coagulation of grains and later by planetesimals within a protoplanetary disc. In contrast, in the disc instability paradigm, giant planet formation is believed to be independent of core formation: massive self-gravitating gas fragments cool radiatively and collapse as a whole. We show that giant planet formation in the disc instability model may be also enhanced by core formation for reasons physically very similar to the CA paradigm. In the model explored here, efficient grai…
We study the effect of large-scale magnetic fields on the non-axisymmetric Rossby wave instability (RWI) in accretion discs. The instability develops around a density bump, which is likely present in the transition region between the active zone and dead zone of protoplanetary discs. Previous works suggest that the vortices resulting from the RWI may facilitate planetesimal formation and angular momentum transport. We consider discs threaded by a large-scale poloidal magnetic field, with a radial field component at the disc surface. Such field configurations may lead to the production of magne…
The recently discovered resonant drag instability of dust settling in protoplanetary disc is considered as the mode coupling of subsonic gas-dust mixture perturbations. This mode coupling is coalescence of two modes with nearly equal phase velocities: the first mode is inertial wave having positive energy, while the second mode is a settling dust wave (SDW) having negative energy as measured in the frame of gas environment being at rest in vertical hydrostatic equilibrium. SDW is a trivial mode produced by the bulk settling of dust, which transports perturbations of dust density. The phase vel…
