We investigate the evolution of two-planet systems embedded in a protoplanetary disc, which are composed of a Jupiter-mass planet plus another body located further out in the disc. We consider outermost planets with masses ranging from 10 earth masses to 1 M_J. We also examine the case of outermost bodies with masses < 10 earth masses (M_E). Differential migration of the planets due to disc torques leads to different evolution outcomes depending on the mass of the outer protoplanet. For planets with mass < 3.5 M_E the type II migration rate of the giant exceeds the type I migration rate of the outer body, resulting in divergent migration. Outer bodies with masses in the range 3.5 < m_o < 20 M_E become trapped at the edge of the gap formed by the giant planet, because of corotation torques. Higher mass planets are captured into resonance with the inner planet. If 30 < m_o < 40 M_E or m_o=1 M_J, then the 2:1 resonance is established. If 80 < m_o < 100 M_E, the 3:2 resonance is favoured. Simulations of gas-accreting protoplanets of mass m_o > 20 M_E, trapped initially at the edge of the gap, or in the 2:1 resonance, also result in eventual capture in the 3:2 resonance as the planet mass grows to become close to the mass of Saturn. Our results suggest that there is a theoretical lower limit to the mass of an outer planet that can be captured into resonance with an inner Jovian planet, which is relevant to observations of extrasolar multiplanet systems. Furthermore, capture of a Saturn-like planet into the 3:2 resonance with a Jupiter-like planet is a very robust outcome of simulations. This result is relevant to recent scenarios of early Solar System evolution which require Saturn to have existed interior to the 2:1 resonance with Jupiter prior to the onset of the Late Heavy Bombardment.
Local three-dimensional shearing box simulations of the compressible coupled dust-gas equations are used in the fluid approximation to study the evolution of different initial vortex configurations in a protoplanetary disc and their dust-trapping capabilities. The initial conditions for the gas are derived from an analytic solution to the compressible Euler equation and the continuity equation. The solution is valid if there is a vacuum outside the vortex. In the simulations the vortex is either embedded in a hot corona, or it is extended in a cylindrical fashion in the vertical direction. Bot…
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. We study the accumulations in the stable Lagrangian points of a giant planet, as well as in the Rossby vortices launched at the edges of the gap it carves. We employ the Pencil Code, tracing the solids with a large number of interacting Lagrangian particles, usually 100,000. For particles of 1 cm to 10 cm radii, gravitational collapse occurs in the Lagrangian points in less than 200 orbits. For 5 cm…
Mean-motion resonances (MMRs) are likely to play an important role both during and after the lifetime of a protostellar gas disk. We study the dynamical evolution and stability of planetary systems containing two giant planets on circular orbits near a 2:1 resonance and closer. We find that by having the outer planet migrate inward, the two planets can capture into either the 2:1, 5:3, or 3:2 MMR. We use direct numerical integrations of ~1000 systems in which the planets are initially locked into one of these resonances and allowed to evolve for up to ~10^7 yr. We find that the final eccentric…
We study the efficiency of the noble gases sequestration by the ion H3+ in the form of XH3+ complexes (with X = argon, krypton or xenon) in gas phase conditions similar to those encountered during the cooling of protoplanetary disks, at the epoch of icy planetesimals formation. We show that XH3+ complexes form very stable structures in the gas phase and that their binding energies are much higher than those involved in the structures of X-H2O hydrates or pure X-X condensates. This implies that, in presence of H3+ ions, argon, krypton or xenon are likely to remain sequestrated in the form of XH…
In the borders of the dead zones of protoplanetary disks, the inflow of gas produces a local density maximum that triggers the Rossby wave instability. The vortices that form are efficient in trapping solids. We aim to assess the possibility of gravitational collapse of the solids within the Rossby vortices. We perform global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk with the Pencil code. We use multiple particle species of radius 1, 10, 30, and 100 cm. The dead zone is modeled as a region of low viscosity. The Rossby v…
We present new results related to the coupled evolution of a two giant planet system embedded in a protoplanetary disk, in which a Saturn mass protoplanet is trapped in an outer mean motion resonance with a Jupiter mass protoplanet. The gaps opened in the disk by the two planets overlap, therefore the two planet system exchanges angular momentum with the disk at the inner planet's Inner Lindblad Resonances (ILRs) and at the outer planet Outer Lindblad Resonances (OLRs). Since the torques are proportional to the square of the planet masses, and since the inner planet is about three times more m…
We present a mechanism related to the migration of giant protoplanets embedded in a protoplanetary disc whereby a giant protoplanet is caught up, before having migrated all the way to the central star, by a lighter outer giant protoplanet. This outer protoplanet may get captured into the 2:3 resonance with the more massive one, in which case the gaps that the two planets open in the disc overlap. Two effects arise, namely a squared mass weighted torque imbalance and an increased mass flow through the overlapping gaps from the outer disc to the inner disc, which both play in favour of an outwar…
We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow. The simulations are done in a local coordinate frame comoving with the gas in Keplerian rotation. Periodic boundary conditions are used in all directions, and vertical gravity is not applied to the gas. Using a two-fluid approach, small dust grains of various sizes (with friction times up to $\varOmega_0 τ_{\rm f}=0.02$) are allowed to move under the influence of friction with t…
In the simulation of protoplanetary disc with a power law density profile a disc instability is detected. The instability arises only with a power law profile and is affected by power index. Thus the impact of initial density profile is large within the employed numerical model.
We calculate global $m=1$ modes with low pattern speed corresponding to introducing a finite eccentricity into a protoplanetary disc. We consider disc models which are either isolated or contain one or two protoplanets orbiting in an inner cavity. Global modes that are strongly coupled to inner protoplanets are found to have disc orbits which tend to have apsidal lines antialigned with respect to those of the inner protoplanets. Other modes corresponding to free disc modes may be global over a large range of length scales and accordingly be long lived. We consider the motion of a protoplanet i…
The continuous spectra of the substars with surrounding protoplanetary disks were calculated. The results reveal that protoplanetary disc average temperature decreases to 3 K during the period of 5 Myr for substars with masses 0.01M_{Sun} and during the period of 160 Myr for substars with masses 0.08M_{Sun}. Estimations of protoplanetary discs flux maximum depending on the substar mass at the age of 1 Myr are: 4.6 kJy (for 0.01M_{Sun}) and 3.4 MJy (for 0.08M_{Sun}). Maximum of protoplanetary disc radiation before it reaches the temperature of the cosmic microwave background changes within the …
We investigate numerically the orbital evolution of massive extrasolar planets within central cavities of their parent protoplanetary discs. Assuming that they arrive at the inner edge of the disc due to type II migration, we show that they spiral further in. We find that in magnetospheric cavities more massive planets stop migrating at a larger distance from the edge of the disc. This effect may qualitatively explain the correlation between masses and orbital periods found for massive planets with P shorter than 5 days.
(abridged) We analyse the evolution of the fractional ionisation in a steady-state protoplanetary disc with a vertical temperature gradient and with gas-grain chemistry including surface reactions. The ionisation due to stellar X-rays, stellar and interstellar UV radiation, cosmic rays and radionuclide decay is taken into account. Using our reduction schemes as a tool for the analysis, we isolate small sets of chemical reactions that reproduce the evolution of the ionisation degree at representative disc locations with an accuracy of 50%-100%. Column densities of key molecules are calculated a…
We study the effect of an imposed vertical magnetic field on the turbulent mass diffusion properties of magnetorotational turbulence in protoplanetary discs. It is well-known that the effective viscosity generated by the turbulence depends strongly on the magnitude of such an external field. In this letter we show that the turbulent diffusion of the flow also grows, but that the diffusion coefficient does not rise with increasing vertical field as fast as the viscosity does. The vertical Schmidt number, i.e. the ratio between viscosity and vertical diffusion, can be close to 20 for high field …
Using a local model Gammie (2001) has shown that accretion discs with cooling times t_cool <= 3/Omega fragment into gravitationally bound objects, while those with cooling times t_cool > 3/Omega evolve into a quasi-steady state. We use three-dimensional smoothed particle hydrodynamic simulations of protoplanetary accretion discs to test if the local results hold globally. We find that for disc masses appropriate for T Tauri discs, the fragmentation boundary still occurs at a cooling time close to t_cool = 3/Omega. For more massive discs, which are likely to be present at an earlier stage of th…
We study the migration of solid bodies in turbulent protoplanetary accretion discs by means of global MHD simulations. The bodies range in size from 5 centimetres up to 1 metre, and so include objects whose migration is expected to be the most rapid due to gas drag interaction with the disc. As they drift inward through the disc, some of them are trapped in regions where gas pressure maxima are created by long lived anticyclonic vortices. This accumulation is very efficient, locally increasing the dust--to--gas ratio by a factor > 100 in some cases. We discuss the possible implications of this…
We consider two protoplanets gravitationally interacting with each other and a protoplanetary disc. The two planets orbit interior to a tidally maintained disc cavity while the disc interaction indices inward migration. When the migration is slow enough, the more rapidly migrating outer protoplanet approaches and becomes locked in a 2:1 commensurability with the inner one. This is maintained in subsequent evolution. We study this evolution using a simple anaytic model, full hydrodynamic 2D simulations of the disc planet system and longer time N body integrations incorporating simple prescripti…
We study axisymmetric models of layered protoplanetary discs taking radiative transfer effects into account, and allowing for a residual viscosity in the dead zone. We also explore the effect of different viscosity prescriptions. In addition to the ring instability reported in the first paper of the series we find an oscillatory instability of the dead zone, accompanied by variations of the accretion rate onto the central star. We provide a simplified analytical description explaining the mechanism of the oscillations. Finally, we find that the residual viscosity enables stationary accretion i…
In this paper, we present mean gas and dust opacities relevant to the physical conditions typical of protoplanetary discs. As the principal absorber for temperatures below ~1,500 K, we consider spherical and aggregate dust particles of various sizes, chemical structure, and porosity, consisting of ice, organics, troilite, silicates, and iron. For higher temperatures, ions, atoms, molecules, and electrons are included as the main opacity sources. Rosseland and Planck mean opacities are calculated for temperatures between 5 K and 10,000 K and gas densities ranging from 10^{-18} g/ccm to 10^{-7} …
We consider the dynamics of dust and gas during the clearing of protoplanetary discs. We work within the context of a photoevaporation/viscous model for the evolution of the gas disc, and use a two-fluid model to study the dynamics of dust grains as the gas disc is cleared. Small (<~10um) grains remain well-coupled to the gas, but larger (~1mm) grains are subject to inward migration from large radii (~50AU), suggesting that the time-scale for grain growth in the outer disc is ~10^4-10^5yr. We describe in detail the observable appearance of discs during clearing, and find that pressure gradient…
In this work we use the radiation hydrodynamic code TRAMP to perform a two-dimensional axially symmetric model of the layered disc. Using this model we follow the accumulation of mass in the dead zone due to the radially varying accretion rate. We found a new type of instability which causes the dead zone to split into rings. This "ring instability" works due to the positive feedback between the thickness of the dead zone and the mass accumulation rate. We give an analytical description of this instability, taking into account non-zero thickness of the dead zone and deviations from the Kepleri…
The most intriguing question related to the chemical evolution of protoplanetary disks is the genesis of pre-biotic organic molecules in the planet-forming zone. In this contribution we briefly review current observational knowledge of physical structure and chemical composition of disks and discuss whether organic molecules can be present in large amounts at the verge of planet formation. We predict that some molecules, including CO-bearing species such as H$_2$CO, can be underabundant in inner regions of accreting protoplanetary disks around low-mass stars due to the high-energy stellar radi…
More than 30 extra-solar Jupiter-like planets have shorter periods than the planet Mercury. It is generally accepted that they formed further out, and migrated inwards. In order to be driven by tidal torques from the gaseous disc, the disc exterior to the planet had to contain about a planetary mass. The fact that the planets stopped migrating means that their outer disc was removed. We suggest that the outer disc was accreted by the planet. In this scenario, the endgame is a race. The planet survives if it accretes its outer disc before being accreted by the star. The winner is determined sol…
It has already been shown, using a local model, that accretion discs with cooling times t_cool <= 3 Omega^-1 fragment into gravitationally bound objects, while those with cooling times t_cool > 3 Omega^-1 evolve into a quasi-steady state. We present results of three-dimensional simulations that test if the local result still holds globally. We find that the fragmentation boundary is close to that determined using the local model, but that fragmentation may occur for longer cooling times when the disc is more massive or when the mass is distributed in such a way as to make a particular region o…
We present the results of three-dimensional numerical simulations that include the effects of hydrodynamical forces and gas drag upon an evolving dusty gas disk. We briefly describe a new parallel, two phase numerical code based upon the smoothed particle hydrodynamics (SPH) technique in which the gas and dust phases are represented by two distinct types of particles. We use the code to follow the dynamical evolution of a population of grains in a gaseous protoplanetary disk in order to understand the distribution of grains of different sizes within the disk. Our ``grains'' range from metre to…
