Effect of disjoining pressure in a thin film equation with\ud non-uniform forcing

We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations and analytical considerations. The disjoining pressure has a regularizing influence on the evolution of the system and appears to select a single steady-state solution for fixed height boundary conditions; this is in contrast with the existence of a continuum of locally attracting solutions that exist in the absence of disjoining pressure for the same boundary conditions. We numerically implement matched asymptotics expansions to construct equilibrium solutions and also investigate how they behave as the disjoining pressure is sent to zero. Finally, we consider the effect of the competition between forcing and disjoining pressure on the coarsening dynamics of the thin film for fixed contact angle boundary conditions

Migration of Earth-size planets in 3D radiative discs

In this paper, we address the migration of small mass planets in 3D radiative disks. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs parameters for which outward migration has been shown in the range of $[5, 35]$ Earth masses, we find that the transition to inward migration occurs for masses in the range $[3, 5]$ Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modeling of the energy equation.Comment: 17 pages, 20 figures, accepted. MNRAS, 201

Meridional circulation of gas into gaps opened by giant planets in three-dimensional low-viscosity disks

We examine the gas circulation near a gap opened by a giant planet in a protoplanetary disk. We show with high resolution 3D simulations that the gas flows into the gap at high altitude over the mid-plane, at a rate dependent on viscosity. We explain this observation with a simple conceptual model. From this model we derive an estimate of the amount of gas flowing into a gap opened by a planet with Hill radius comparable to the scale-height of a layered disk (i. e. a disk with viscous upper layer and inviscid midplane). Our estimate agrees with modern MRI simulations(Gressel et al., 2013). We conclude that gap opening in a layered disk can not slow down significantly the runaway gas accretion of Saturn to Jupiter-mass planets.Comment: in press as a Note in Icaru

Gas accretion onto Jupiter mass planets in discs with laminar accretion flows

International audienceContext. Numerous studies have shown that a gap-forming Jovian mass planet embedded in a protoplanetary disc, in which a turbulent viscosity operates, can accrete gas efficiently through the gap, and for typical parameters it doubles its mass in ~0.1 Myr. The planet also migrates inwards on a timescale that is closely related to the local viscous evolution timescale, which is also typically 0.1 Myr. These timescales are short compared to protoplanetary disc lifetimes, and raise questions about the origins of the cold gas giant exoplanets that have been discovered in abundance. It is understood that protoplanetary discs are unlikely to be globally turbulent, and instead they may launch magnetised winds such that accretion towards the star occurs in laminar accretion flows located in narrow layers near the surfaces of the disc. Aims: The aim of this study is to examine the rate at which gas accretes onto Jovian mass planets that are embedded in layered protoplanetary discs, and to compare the results with those obtained for viscous models. Methods: We use 3D hydrodynamical simulations of planets embedded in protoplanetary discs, in which a constant radial mass flux towards the star of ṁ = 10−8 M⊙ yr−1 is sustained. We consider a classical viscous α disc model, and also models in which an external torque is applied in narrow surface layers to mimic the effects of a magnetised wind. The accreting layers have a variety of depths, as parameterised by their column densities ΣA, and we consider values of ΣA in the range 0.1−10 g cm−2. Results: The viscous disc model gives results in agreement with previous studies. In accord with our recent work that examines the migration of Jovian mass planets in layered models, we find the accretion rate onto the planet in the layered models crucially depends on the ability of the planet to block the wind-induced mass flow towards the star. For ΣA = 10 g cm−2, the planet torque can block the mass flow in disc, accretion onto the planet is slow, and a mass doubling time of 10 Myr is obtained. For ΣA = 0.1 g cm−2, the flow is not blocked, accretion is fast, and the mass doubling time is 0.2 Myr. Conclusions: Our results show that although the radial mass flow through the layered disc models is always 10−8 M⊙ yr−1, adopting different values of ΣA leads to very different gas accretion rates onto embedded gas giant planets

Controlling extended systems with spatially filtered, time-delayed feedback

We investigate a control technique for spatially extended systems combining spatial filtering with a previously studied form of time-delay feedback. The scheme is naturally suited to real-time control of optical systems. We apply the control scheme to a model of a transversely extended semiconductor laser in which a desirable, coherent traveling wave state exists, but is a member of a nowhere stable family. Our scheme stabilizes this state, and directs the system towards it from realistic, distant and noisy initial conditions. As confirmed by numerical simulation, a linear stability analysis about the controlled state accurately predicts when the scheme is successful, and illustrates some key features of the control including the individual merit of, and interplay between, the spatial and temporal degrees of freedom in the control.Comment: 9 pages REVTeX including 7 PostScript figures. To appear in Physical Review

Gas accretion onto Jupiter mass planets in discs with laminar accretion flows

(Abridged) Studies have shown that a Jovian mass planet embedded in a viscous protoplanetary disc (PPD) can accrete gas efficiently through the gap and doubles its mass in $\sim 0.1$ Myr. The planet also migrates inwards on a timescale of $\sim 0.1$ Myr. These timescales are short compared to PPD lifetimes, and raise questions about the origins of cold giant exoplanets. However, PPDs are unlikely to be globally turbulent, and instead they may launch magnetised winds such that accretion towards the star occurs in laminar accretion flows located in narrow layers near the surfaces of the disc. The aim of this study is to examine the rate at which gas accretes onto Jovian mass planets that are embedded in layered PPDs. We use 3D hydrodynamical simulations of planets embedded in PPDs, in which a constant radial mass flux towards the star of ${\dot m} = 10^{-8}$ M$_{\odot}$ yr$^{-1}$ is sustained. We consider a classical viscous alpha model, and also models in which an external torque is applied in narrow surface layers to mimic the effects of a magnetised wind. The accreting layers are parameterised by their column densities $\Sigma_{\rm A}$, and we consider values in the range 0.1 to 10 g cm$^{-2}$. The viscous model gives results in agreement with previous studies. We find the accretion rate onto the planet in the layered models crucially depends on the planet's ability to block the wind-induced mass flow. For $\Sigma_{\rm A}=10$ g cm$^{-2}$, the planet torque can block the mass flow through the disc, accretion onto the planet is slow, and a mass doubling time of 10 Myr is obtained. For $\Sigma_{\rm A}=0.1$ g cm$^{-2}$, accretion is fast and the mass doubling time is 0.2 Myr. Although the radial mass flow through the layered disc models is always $10^{-8}$ M$_{\odot}$ yr$^{-1}$, adopting different values of $\Sigma_{\rm A}$ leads to very different gas accretion rates onto gas giant planets.Comment: 14 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Stream Lifetimes Against Planetary Encounters

We study, both analytically and numerically, the perturbation induced by an encounter with a planet on a meteoroid stream. Our analytical tool is the extension of pik s theory of close encounters, that we apply to streams described by geocentric variables. The resulting formulae are used to compute the rate at which a stream is dispersed by planetary encounters into the sporadic background. We have verified the accuracy of the analytical model using a numerical test