Two-dimensional models of layered protoplanetary discs - I. The ring instability (original) (raw)
Related papers
2005
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 in large regions of layered discs. Based on results obtained with the help of a simple 1-D hydrocode we identify these regions, and discuss conditions in which layered discs can give rise to FU~Orionis phenomena.
The dynamics of inner dead-zone boundaries in protoplanetary discs
Monthly Notices of the Royal Astronomical Society, 2012
In protoplanetary discs, the inner radial boundary between the MRI turbulent ('active') and MRI quiescent ('dead') zones plays an important role in models of the disc evolution and in some planet formation scenarios. In reality, this boundary is not well-defined: thermal heating from the star in a passive disc yields a transition radius close to the star (<0.1 au), whereas if the disc is already MRI active, it can self-consistently maintain the requisite temperatures out to a transition radius of roughly 1 au. Moreover, the interface may not be static; it may be highly fluctuating or else unstable. In this paper, we study a reduced model of the dynamics of the active/dead zone interface that mimics several important aspects of a real disc system. We find that MRI-transition fronts propagate inwards (a 'dead front' suppressing the MRI) if they are initially at the larger transition radius, or propagate outwards (an 'active front' igniting the MRI) if starting from the smaller transition radius. In both cases, the front stalls at a welldefined intermediate radius, where it remains in a quasi-static equilibrium. We propose that it is this new, intermediate stalling radius that functions as the true boundary between the active and dead zones in protoplanetary discs. These dynamics are likely implicated in observations of variable accretion, such as FU Ori outbursts, as well as in those planet formation theories that require the accumulation of solid material at the dead/active interface.
Magnetically driven accretion in protoplanetary discs
Monthly Notices of the Royal Astronomical Society, 2015
We characterize magnetically driven accretion at radii between 1 and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a minimum mass solar nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bimodality in the accretion process, with vertical magnetic fields aligned to the disc rotation supporting a strong laminar Maxwell stress that is absent if the field is anti-aligned. In the anti-aligned case, we instead find evidence for bursts of turbulent stress at 5-10 au, which we tentatively identify with the non-axisymmetric Hall-shear instability. The presence or absence of these bursts depends upon the details of the adopted chemical model, which suggests that appreciable regions of actual protoplanetary discs might lie close to the borderline between laminar and turbulent behaviour. Given the number of important control parameters that have already been identified in MHD models, quantitative predictions for disc structure in terms of only radius and accretion rate appear to be difficult. Instead, we identify robust qualitative tests of magnetically driven accretion. These include the presence of turbulence in the outer disc, independent of the orientation of the vertical magnetic fields, and a Hall-mediated bimodality in turbulent properties extending from the region of thermal ionization to 10 au.
Spiral-driven accretion in protoplanetary discs
Astronomy & Astrophysics, 2015
We numerically investigate the dynamics of a 2D non-magnetised protoplanetary disc surrounded by an inflow coming from an external envelope. We find that the accretion shock between the disc and the inflow is unstable, leading to the generation of largeamplitude spiral density waves. These spiral waves propagate over long distances, down to radii at least ten times smaller than the accretion shock radius. We measure spiral-driven outward angular momentum transport with 10 −4 α < 10 −2 for an inflow accretion rateṀ inf 10 −8 M yr −1. We conclude that the interaction of the disc with its envelope leads to long-lived spiral density waves and radial angular momentum transport with rates that cannot be neglected in young non-magnetised protostellar discs.
Evolution of protoplanetary discs driven by MHD turbulence and other agents
2004
Después de revisar el estado de nuestro conocimiento de cómo opera la inestabilidad magnetorotacional (MRI) en discos protoplanetarios, presentamos resultados preliminares sobre la evolución de tales sistemas, basándonos en la predicción de distribución espacial de torcas viscosas. Se construyen modelos unidimensionales de discos α para los discos protoplanetarios incorporando diferentes valores del parámetro α para reflejar los diferentes agentes que participan en la evolución de los discos. Tomamos en cuenta los efectos de viscosidad turbulenta debido a la MRI, de torcas de autogravedad (prescritas en términos de una viscosidad efectiva) y de otros agentes viscosos caracterizados por una eficiencia reducida. La estructura y evolución resultante para los discos es drásticamente diferente a la predicha por modelos de discos con α uniforme o por modelos de acreción en capas.
Modelling circumbinary protoplanetary disks
Astronomy & Astrophysics, 2015
Context. The Kepler mission's discovery of a number of circumbinary planets orbiting close (a p < 1.1 au) to the stellar binary raises questions as to how these planets could have formed given the intense gravitational perturbations the dual stars impart on the disk. The gas component of circumbinary protoplanetary disks is perturbed in a similar manner to the solid, planetesimal dominated counterpart, although the mechanism by which disk eccentricity originates differs. Aims. This is the first work of a series that aims to investigate the conditions for planet formation in circumbinary protoplanetary disks. Methods. We present a number of hydrodynamical simulations that explore the response of gas disks around two observed binary systems: Kepler-16 and Kepler-34. We probe the importance of disk viscosity, aspect-ratio, inner boundary condition, initial surface density gradient, and self-gravity on the dynamical evolution of the disk, as well as its quasi-steady-state profile. Results. We find there is a strong influence of binary type on the mean disk eccentricity,ē d , leading toē d = 0.02−0.08 for Kepler-16 andē d = 0.10−0.15 in Kepler-34. The value of α-viscosity has little influence on the disk, but we find a strong increase in mean disk eccentricity with increasing aspect-ratio due to wave propagation effects. The choice of inner boundary condition only has a small effect on the surface density and eccentricity of the disk. Our primary finding is that including disk self-gravity has little impact on the evolution or final state of the disk for disks with masses less than 12.5 times that of the minimum-mass solar nebula. This finding contrasts with the results of self-gravity relevance in circumprimary disks, where its inclusion is found to be an important factor in describing the disk evolution.
2006
We study the vertical settling of solid bodies in a turbulent protoplanetary disc. We consider the situation when the coupling to the gas is weak or equivalently when the particle stopping time τst due to friction with the gas is long compared to the orbital timescale Ω −1. An analytical model, which takes into account the stochastic nature of the sedimentation process using a Fokker-Planck equation for the particle distribution function in phase space, is used to obtain the vertical scale height of the solid layer as a function of the vertical component of the turbulent gas velocity correlation function and the particle stopping time. This is found to be of the same form as the relation obtained for strongly coupled particles in previous work. We compare the predictions of this model with results obtained from local shearing box MHD simulations of solid particles embedded in a vertically stratified disc in which there is turbulence driven by the MRI. We find that the ratio of the d...
2014
The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated by linear analysis. In the case where the dust to gas ratio is enhanced and turbulence is week, the instability grows, even in gravitationally stable disks, on a timescale of order 10 4−5 yr at a radius of order 100AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called "secular gravitational instability", which was investigated previously as an instability of dust in a fixed background gas flow. In this work, we solve the equations of motion for both gas and dust consistently and find that long-wavelength perturbations are stable, in contrast to the secular gravitational instability in the simplified treatment. This may indicate that we should not neglect small terms in equation of motion if the growth rate is small. The instability is expected to form ring structures in protoplanetary disks. The width of the ring formed at a radius of 100 AU is a few tens of AU. Therefore, the instability is a candidate for the formation mechanism of observed ring-like structures in disks. Another aspect of the instability is the accumulation of dust grains, and hence the instability may play an important role in the formation of planetesimals, rocky protoplanets, and cores of gas giants located at radii ∼100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.
The Evolution of Protoplanetary Disk Edges
The Astrophysical Journal, 2004
We investigate gap formation in gaseous protostellar disks by a planet in a circular orbit in the limit of low disk viscosity. This regime may be appropriate to an aging disk after the epoch of planet formation. We find that the distance of the planet to the gap outer boundary can be between the location of the m ¼ 2 and 1 outer Lindblad resonances. This distance is weakly dependent on both the planet's mass and disk viscosity. We find that the evolution of the disk edge takes place on two timescales. The first timescale is set by the spiral density waves driven by the planet. The second timescale depends on the viscosity of the disk. The disk approaches a state in which the outward angular momentum flux caused by the disk viscosity is balanced by the dissipation of spiral density waves that are driven at the Lindblad resonances. This occurs inefficiently, however, because of the extremely low gas density near the planet. We find that the distance between the planet and the peak density at the disk outer edge is only weakly dependent on the viscosity and planet mass; however, the ratio of the gas density near the planet to that in the disk (or the slope of density along the disk edge) is strongly dependent on both quantities. We find that the disk density profile along the edge scales approximately with the disk viscosity divided by the square of the planet mass. We account for this behavior with a simple scenario in which the dissipation of angular momentum from the spiral density waves is balanced against the diffusion in the steep edge of the disk.