In this paper we investigate the possibility of a migration-induced resonance locking in systems containing three planets, namely an Earth analog, a super-Earth and a gas giant. The planets have been listed in order of increasing orbital periods. All three bodies are embedded in a locally isothermal gaseous disc and orbit around a solar mass star. We are interested in answering the following question: Will the low-mass planets form the same resonant structures with each other in the vicinity of the gas giant as in the case when the gas giant is absent? When there is no gas giant in the system, it has been already shown that if the two low-mass planets undergo a convergent differential migration, they will capture each other in a mean-motion resonance. For the choices of disc parameters and planet masses made in this paper, the formation of the 5:4 resonance in the absence of the Jupiter has been observed. In this work we add a gas giant on the most external orbit of the system in such a way that its differential migration is convergent with the low-mass planets. We show that the result of this set-up is the speeding up of the migration of the super-Earth and, after that, all three planets become locked in a triple mean-motion resonance. However, this resonance is not maintained due to the low-mass planet eccentricity excitation, a fact that leads to close encounters between planets and eventually to the ejection from the internal orbits of one or both low-mass planets.
It has recently been shown that the terrestrial planets and asteroid belt can be reproduced if the giant planets underwent an inward-then-outward migration (the "Grand Tack"; Walsh et al 2011). Inward migration occurs when Jupiter opens a gap and type II migrates inward. The planets "tack" and migrate outward when Saturn reaches the gap-opening mass and is caught in the 3:2 resonance with Jupiter. The aim is to test the viability of the Grand Tack model and to study the dynamical evolution of Jupiter and Saturn during their growth from 10 Earth masses cores. We have performed numerical simulat…
As planets grow the exchange of angular momentum with the gaseous component of the protoplanetary disc produces a net torque resulting in a variation of the semi-major axis of the planet. For low-mass planets not able to open a gap in the gaseous disc this regime is known as type I migration. Pioneer works studied this mechanism in isothermal discs finding fast inward type I migration rates that were unable to reproduce the observed properties of extrasolar planets. In the last years, several improvements have been made in order to extend the study of type I migration rates to non-isothermal d…
The regular satellites found around Neptune ($\approx 17~M_{\Earth}$) and Uranus ($\approx 14.5~M_{\Earth}$) suggest that past gaseous circumplanetary disks may have co-existed with solids around sub-Neptune-mass protoplanets ($< 17~M_{\Earth}$). These disks have been shown to be cool, optically thin, quiescent, with low surface density and low viscosity. Numerical studies of the formation are difficult and technically challenging. As an introductory attempt, three-dimensional global simulations are performed to explore the formation of circumplanetary disks around sub-Neptune-mass protoplanet…
We study gap formation in gaseous protoplanetary discs by a Jupiter mass planet. The planet's orbit is circular and inclined relative to the midplane of the disc. We use the impulse approximation to estimate the gravitational tidal torque between the planet and the disc, and infer the gap profile. For low-mass discs, we provide a criterion for gap opening when the orbital inclination is $\leq 30^{\circ}$. Using the FARGO3D code, we simulate the disc response to an inclined massive planet. The dependence of the depth and width of the gap obtained in the simulations on the inclination of the pla…
We investigate the unsaturated horseshoe drag exerted on a low-mass planet by an isothermal gaseous disk. In the globally isothermal case, we use a formal- ism, based on the use of a Bernoulli invariant, that takes into account pressure effects, and that extends the torque estimate to a region wider than the horse- shoe region. We find a result that is strictly identical to the standard horseshoe drag. This shows that the horseshoe drag accounts for the torque of the whole corotation region, and not only of the horseshoe region, thereby deserving to be called corotation torque. We find that ev…
Massive planetary cores embedded in protoplanetary discs are believed to accrete extended atmospheres, providing a pathway to forming gas giants and gas-rich super-Earths. The properties of these atmospheres strongly depend on the nature of the coupling between the atmosphere and the surrounding disc. We examine the formation of gaseous envelopes around massive planetary cores via three-dimensional inviscid and isothermal hydrodynamic simulations. We focus the changes in the envelope properties as the core mass varies from low (sub-thermal) to high (super-thermal) values, a regime relevant to …
Embedded in the gaseous protoplanetary disk, Jupiter and Saturn naturally become trapped in 3:2 resonance and migrate outward. This serves as the basis of the Grand Tack model. However, previous hydrodynamical simulations were restricted to isothermal disks, with moderate aspect ratio and viscosity. Here we simulate the orbital evolution of the gas giants in disks with viscous heating and radiative cooling. We find that Jupiter and Saturn migrate outward in 3:2 resonance in modest-mass ($M_{disk} \approx M_{MMSN}$, where MMSN is the "minimum-mass solar nebula") disks with viscous stress parame…
We fit an isothermal oscillatory density model of Neptune's protoplanetary disk to the surviving regular satellites and its innermost ring and we determine the radial scale length of the disk, the equation of state and the central density of the primordial gas, and the rotational state of the Neptunian nebula. Neptune's regular moons suffered from the retrograde capture of Triton that disrupted the system. Some moons may have been ejected, while others may have survived inside their potential minima. For this reason, the Neptunian nebula does not look like any of the nebulae that we modeled pr…
We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal effects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs Type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, usin…
Low-mass objects embedded in isothermal protoplanetary discs are known to suffer rapid inward Type I migration. In non-isothermal discs, recent work has shown that a decreasing radial profile of the disc entropy can lead to a strong positive corotation torque which can significantly slow down or reverse Type I migration in laminar viscous disc models. It is not clear however how this picture changes in turbulent disc models. The aim of this study is to examine the impact of turbulence on the torque experienced by a low-mass planet embedded in a non-isothermal protoplanetary disc. We particular…
Several observations of transition discs show lopsided dust-distributions. A potential explanation is the formation of a large-scale vortex acting as a dust-trap at the edge of a gap opened by a giant planet. Numerical models of gap-edge vortices have thus far employed locally isothermal discs, but the theory of this vortex-forming or `Rossby wave' instability was originally developed for adiabatic discs. We generalise the study of planetary gap stability to non-isothermal discs using customised numerical simulations of disc-planet systems where the planet opens an unstable gap. We include in …
The core accretion hypothesis posits that planets with significant gaseous envelopes accreted them from their protoplanetary discs after the formation of rocky/icy cores. Observations indicate that such exoplanets exist at a broad range of orbital radii, but it is not known whether they accreted their envelopes in situ, or originated elsewhere and migrated to their current locations. We consider the evolution of solid cores embedded in evolving viscous discs that undergo gaseous envelope accretion in situ with orbital radii in the range $0.1-10\rm au$. Additionally, we determine the long-term …
In view of the many recent observations conducted by ALMA and SPHERE, it is becoming clear that protoplanetary disks form planets in narrow annular gaps at various distances from the central protostars before these protostars are actually fully formed and the gaseous disks have concluded their accretion/dispersal processes. This is in marked contrast to the many multi-planet exoplanetary systems that do not conform to this pristine picture. This major discrepancy calls for an explanation. We provide such an explanation in this work, based on analytical solutions of the cylindrical isothermal L…
The recent discoveries of circumbinary planets by $\it Kepler$ raise questions for contemporary planet formation models. Understanding how these planets form requires characterizing their formation environment, the circumbinary protoplanetary disc, and how the disc and binary interact and change as a result. The central binary excites resonances in the surrounding protoplanetary disc that drive evolution in both the binary orbital elements and in the disc. To probe how these interactions impact binary eccentricity and disc structure evolution, N-body smooth particle hydrodynamics (SPH) simulat…
It is believed that large-scale horseshoe-like brightness asymmetries found in dozens of transitional protoplanetary discs are caused by anticyclonic vortices. These vortices can play a key role in planet formation, as mm-sized dust -- the building blocks of planets -- can be accumulated inside them. Anticyclonic vortices are formed by the Rossby wave instability, which can be excited at the gap edges opened by a giant planet or at sharp viscosity transitions of accretionally inactive regions. It is known that vortices are prone to stretching and subsequent dissolution due to disc self-gravity…
We describe a new mechanism that leads to the destabilisation of non-axisymmetric waves in astrophysical discs with an imposed radial temperature gradient. This might apply, for example, to the outer parts of protoplanetary discs. We use linear density wave theory to show that non-axisymmetric perturbations generally do not conserve their angular momentum in the presence of a forced temperature gradient. This implies an exchange of angular momentum between linear perturbations and the background disc. In particular, when the disturbance is a low-frequency trailing wave and the disc temperature…
Gas rich dusty circumstellar discs observed around young stellar objects are believed to be the birthplace of planets and planetary systems. Recent observations revealed that large-scale horseshoe-like brightness asymmetries are present in dozens of transitional protoplanetary discs. Theoretical studies suggest that these brightness asymmetries bf could be caused by large-scale anticyclonic vortices triggered by the Rossby Wave Instability (RWI), which can be excited at the edges of the accretionally inactive region, the dead zone edge. Since vortices may play a key role in planet formation, i…
We study the dynamical evolution of Jupiter and Saturn embedded in a gaseous, solar-nebula-type disc by means of hydrodynamics simulations with the FARGO2D1D code. We study the evolution for different initial separations of the planets' orbits, Delta a_SJ , to investigate whether they become captured in mean motion resonance (MMR) and the direction of the subsequent migration of the planet (inward or outward). We also provide an assessment of the planet's orbital dynamics at different epochs of Saturn's growth. We find that the evolution of initially compact orbital configurations is dependent…
We perform hydrodynamical simulations of the accretion of pebbles and rocks onto protoplanets of a few hundred kilometres in radius, including two-way drag force coupling between particles and the protoplanetary disc gas. Particle streams interacting with the gas far out within the Hill sphere of the protoplanet spiral into a prograde circumplanetary disc. Material is accreted onto the protoplanet due to stirring by the turbulent surroundings. We speculate that the trend for prograde rotation among the largest asteroids is primordial and that protoplanets accreted 10%-50% of their mass from pe…
1-3 per cent of white dwarfs are orbited by planetary dusty debris detectable as infrared emission in excess above the white dwarf flux. In a rare subset of these systems, a gaseous disc component is also detected via emission lines of the Ca II 8600Å triplet, broadened by the Keplerian velocity of the disc. We present the first statistical study of the fraction of debris discs containing detectable amounts of gas in emission at white dwarfs within a magnitude and signal-to-noise limited sample. We select 7705 single white dwarfs spectroscopically observed by the Sloan Digital Sky Survey (SDSS…
A thin gaseous disc with an almost keplerian angular velocity profile, bounded by a free surface and rotating around point-mass gravitating object is nearly spectrally stable. Despite that the substantial transient growth of linear perturbations measured by the evolution of their acoustic energy is possible. This fact is demonstrated for the simple model of a non-viscous polytropic thin disc of a finite radial size where the small adiabatic perturbations are considered as a linear combination of neutral modes with a corotational radius located beyond the outer boundary of the flow.
This is the second of two papers where we study additional analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. In a first Paper, hydrodynamics equations were solved for the equilibrium and perturbed configurations and a wave-like equation for the gas perturbed specific mass was deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. In this paper, two other general cases of exponents, including a polytropic case, are solve…
Abstract This is the first of two papers where we study analytical solutions of a bidimensional low mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corres…
We present the detection of an unusually large transient gas absorption in several ionized species in the debris disc star HD 37306 using high-resolution optical spectra. We have been analysing a large sample of debris discs searching for circumstellar gas absorptions aiming to determine the frequency of gas in debris discs. HD 37306 stood out showing remarkably broad absorptions superimposed onto several photospheric Ca ii, Fe ii and Ti ii lines. The observed absorptions, unlike typical exocometary transits, lasted for at least eight days. Here we analyse simultaneous spectroscopic and photom…
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…
