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Register a new userHow initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non viscous SPH simulations
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Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one protoplanet, to evaluate the effectiveness of the accretion disc in the protoplanet dragging towards the central star, as a function of the mass of the planet itself, of disc tangential kinematics. To this purpose, the SPH scheme is considered suitable to study the roles of turbulence, kinematic and boundary conditions, due to its intrinsic advective turbulence, especially in 2D and in 3D codes. Simulations are performed both in disc sub-Keplerian and in Keplerian kinematic conditions as a parameter study of protoplanetary migration if moderate and consistent deviations from Keplerian Kinematics occur. Our results show migration times of a few orbital periods for Earth-like planets in sub-Keplerian conditions, while for Jupiter-like planets estimates give that about $10^4$ orbital periods are needed to half the orbital size. Timescales of planet migration are strongly dependent on the relative position of the planet with respect to the shock region near the centrifugal barrier of the disc flow.
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One class of protoplanetary disc models, the X-wind model, predicts strongly subkeplerian orbital gas velocities, a configuration that can be sustained by magnetic tension. We investigate disc-planet interactions in these subkeplerian discs, focusing on orbital migration for low-mass planets and gap formation for high-mass planets. We use linear calculations and nonlinear hydrodynamical simulations to measure the torque and look at gap formation. In both cases, the subkeplerian nature of the disc is treated as a fixed external constraint. We show that, depending on the degree to which the disc is subkeplerian, the torque on low-mass planets varies between the usual Type I torque and the one-sided outer Lindblad torque, which is also negative but an order of magnitude stronger. In strongly subkeplerian discs, corotation effects can be ignored, making migration fast and inward. Gap formation near the planets orbit is more difficult in such discs, since there are no resonances close to the planet accommodating angular momentum transport. In stead, the location of the gap is shifted inwards with respect to the planet, leaving the planet on the outside of a surface density depression. Depending on the degree to which a protoplanetary disc is subkeplerian, disc-planet interactions can be very different from the usual Keplerian picture, making these discs in general more hazardous for young planets.
We study the numerical convergence of hydrodynamical simulations of self-gravitating accretion discs, in which a simple cooling law is balanced by shock heating. It is well-known that there exists a critical cooling time scale for which shock heating can no longer compensate for the energy losses, at which point the disc fragments. The numerical convergence of previous results of this critical cooling time scale was questioned recently using Smoothed Particle Hydrodynamics (SPH). We employ a two-dimensional grid-based code to study this problem, and find that for smooth initial conditions, fragmentation is possible for slower cooling as the resolution is increased, in agreement with recent SPH results. We show that this non-convergence is at least partly due to the creation of a special location in the disc, the boundary between the turbulent and the laminar region, when cooling towards a gravito-turbulent state. Converged results appear to be obtained in setups where no such sharp edges appear, and we then find a critical cooling time scale of ~ 4 $Omega^{-1}$, where $Omega$ is the local angular velocity.
We calculate the chemical evolution of protoplanetary disks considering radial viscous accretion, vertical turbulent mixing and vertical disk winds. We study the effects on the disk chemical structure when different models for the formation of molecular hydrogen on dust grains are adopted. Our gas-phase chemistry is extracted from the UMIST Database for Astrochemistry (Rate06) to which we have added detailed gas-grain interactions. We use our chemical model results to generate synthetic near- and mid-infrared LTE line emission spectra and compare these with recent Spitzer observations. Our results show that if H2 formation on warm grains is taken into consideration, the H2O and OH abundances in the disk surface increase significantly. We find the radial accretion flow strongly influences the molecular abundances, with those in the cold midplane layers particularly affected. On the other hand, we show that diffusive turbulent mixing affects the disk chemistry in the warm molecular layers, influencing the line emission from the disk and subsequently improving agreement with observations. We find that NH3, CH3OH, C2H2 and sulphur-containing species are greatly enhanced by the inclusion of turbulent mixing. We demonstrate that disk winds potentially affect the disk chemistry and the resulting molecular line emission in a similar manner to that found when mixing is included.
The nature and rate of (viscous) angular momentum transport in protoplanetary discs (PPDs) has important consequences for the formation process of planetary systems. While accretion rates onto the central star yield constraints on such transport in the inner regions of a PPD, empirical constraints on viscous spreading in the outer regions remain challenging to obtain. Here we demonstrate a novel method to probe the angular momentum transport at the outer edge of the disc. This method applies to PPDs that have lost a significant fraction of their mass due to thermal winds driven by UV irradiation from a neighbouring OB star. We demonstrate that this external photoevaporation can explain the observed depletion of discs in the 3-5 Myr old $sigma$ Orionis region, and use our model to make predictions motivating future empirical investigations of disc winds. For populations of intermediate-age PPDs, in viscous models we show that the mass flux outwards due to angular momentum redistribution is balanced by the mass-loss in the photoevaporative wind. A comparison between wind mass-loss and stellar accretion rates therefore offers an independent constraint on viscous models in the outer regions of PPDs.
The streaming instability is a popular candidate for planetesimal formation by concentrating dust particles to trigger gravitational collapse. However, its robustness against physical conditions expected in protoplanetary disks is unclear. In particular, particle stirring by turbulence may impede the instability. To quantify this effect, we develop the linear theory of the streaming instability with external turbulence modelled by gas viscosity and particle diffusion. We find the streaming instability is sensitive to turbulence, with growth rates becoming negligible for alpha-viscosity parameters $alpha gtrsim mathrm{St} ^{1.5}$, where $mathrm{St}$ is the particle Stokes number. We explore the effect of non-linear drag laws, which may be applicable to porous dust particles, and find growth rates are modestly reduced. We also find that gas compressibility increase growth rates by reducing the effect of diffusion. We then apply linear theory to global models of viscous protoplanetary disks. For minimum-mass Solar nebula disk models, we find the streaming instability only grows within disk lifetimes beyond $sim 10$s of AU, even for cm-sized particles and weak turbulence ($alphasim 10^{-4}$). Our results suggest it is rather difficult to trigger the streaming instability in non-laminar protoplanetary disks, especially for small particles.
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