Instability In Protoplanetary Discs Research Articles

THE ROLE OF PEBBLE FRAGMENTATION IN PLANETESIMAL FORMATION. II. NUMERICAL SIMULATIONS

ABSTRACT Some scenarios for planetesimal formation go through a phase of collapse of gravitationally bound clouds of millimeter- to centimeter-size pebbles. Such clouds can form, for example, through the streaming instability in protoplanetary disks. We model the collapse process with a statistical model to obtain the internal structure of planetesimals with solid radii between 10 and 1000 km. During the collapse, pebbles collide, and depending on their relative speeds, collisions have different outcomes. A mixture of particle sizes inside a planetesimal leads to better packing capabilities and higher densities. In this paper we apply results from new laboratory experiments of dust aggregate collisions (presented in a companion paper) to model collision outcomes. We find that the internal structure of a planetesimal is strongly dependent on both its mass and the applied fragmentation model. Low-mass planetesimals have no/few fragmenting pebble collisions in the collapse phase and end up as porous pebble piles. The number of fragmenting collisions increases with increasing cloud mass, resulting in wider particle size distributions and higher density. The collapse is nevertheless “cold” in the sense that collision speeds are damped by the high collision frequency. This ensures that a significant fraction of large pebbles survive the collapse in all but the most massive clouds. Our results are in broad agreement with the observed increase in density of Kuiper Belt objects with increasing size, as exemplified by the recent characterization of the highly porous comet 67P/Churyumov–Gerasimenko.

IONIZATION AND DUST CHARGING IN PROTOPLANETARY DISKS

ABSTRACT Ionization–recombination balance in dense interstellar and circumstellar environments is a key factor for a variety of important physical processes, such as chemical reactions, dust charging and coagulation, coupling of the gas with magnetic field, and development of instabilities in protoplanetary disks. We determine a critical gas density above which the recombination of electrons and ions on the grain surface dominates over the gas-phase recombination. For this regime, we present a self-consistent analytical model, which allows us to calculate exactly the abundances of charged species in dusty gas, without making assumptions on the grain charge distribution. To demonstrate the importance of the proposed approach, we check whether the conventional approximation of low grain charges is valid for typical protoplanetary disks, and discuss the implications for dust coagulation and development of the “dead zone” in the disk. The presented model is applicable for arbitrary grain-size distributions and, for given dust properties and conditions of the disk, has only one free parameter—the effective mass of the ions, shown to have a small effect on the results. The model can be easily included in numerical simulations following the dust evolution in dense molecular clouds and protoplanetary disks.

Toroidal vortices and the conglomeration of dust into rings in protoplanetary discs

Abstract We identify a new hydrodynamical instability in protoplanetary discs that may arise due to variations in the dust-to-gas ratio and may lead to concentration of dust grains within a disc. The instability can arise due to dust settling, which produces a vertical compositional entropy gradient. The entropy gradient drives a baroclinic instability that is capable of creating toroidal gas vortices that gather dust into rings. Such dust rings are potentially observable via continuum emission of the dust or scattered light. Indeed, this instability may offer an explanation for the rings recently observed in the discs around the young stars HL Tau and TW Hya that does not rely on clearing by protoplanets. The instability may also have wider ramifications, potentially aiding dust agglomeration, altering the radial migration of larger planetesimals, and modifying angular momentum transport within a disc.

SIGNATURES OF PLANETS AND PROTOPLANETS IN THE GALACTIC CENTER: A CLUE TO UNDERSTANDING THE G2 CLOUD?

Several hundred young stars lie in the innermost parsec of our Galaxy. The supermassive black hole (SMBH) might capture planets orbiting these stars and bring them onto nearly radial orbits. The same fate might occur to planetary embryos (PEs), i.e., protoplanets born from gravitational instabilities in protoplanetary disks. In this paper, we investigate the emission properties of rogue planets and PEs in the Galactic center. In particular, we study the effects of photoevaporation caused by the ultraviolet background. Rogue planets can hardly be detected by current or forthcoming facilities, unless they are tidally disrupted and accrete onto the SMBH. In contrast, photoevaporation of PEs (especially if the PE is being tidally stripped) might lead to a recombination rate as high as s?1, corresponding to a Brackett- luminosity erg s?1, very similar to the observed luminosity of the dusty object G2. We critically discuss the possibility that G2 is a rogue PE, and the major uncertainties of this model.

TWO-COMPONENT SECULAR GRAVITATIONAL INSTABILITY IN A PROTOPLANETARY DISK: A POSSIBLE MECHANISM FOR CREATING RING-LIKE STRUCTURES

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 $\sim$100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.

Dust and gas mixtures with multiple grain species – a one-fluid approach

We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalising the approach developed in Laibe & Price (2014a). A generalisation for continuous dust distributions as well as analytic approximations for strong drag regimes are also provided. This formalism lays the foundation for numeri- cal simulations of dust populations in a wide range of astrophysical systems while avoiding limitations associated with a multiple-fluid treatment. The usefulness of the formalism is illustrated on a series of analytical problems, namely the dustybox, dustyshock and dustywave problems as well as the radial drift of grains and the streaming instability in protoplanetary discs. We find physical effects specific to the presence of several dust phases and multiple drag timescales, including non-monotonic evolution of the differential velocity between phases and increased efficiency of the linear growth of the streaming instability. Interestingly, it is found that under certain conditions, large grains can migrate outwards in protoplanetary discs. This may explain the presence of small pebbles at several hundreds of astronomical units from their central star.

Early evolution of clumps formed via gravitational instability in protoplanetary discs: precursors of Hot Jupiters?

Although it is fairly established that Gravitational Instability (GI) should occur in the early phases of the evolution of a protoplanetary disc, the fate of the clumps resulting from disc fragmentation and their role in planet formation is still unclear. In the present study we investigate semi-analytically their evolution following the contraction of a synthetic population of clumps with varied initial structure and orbits coupled with the surrounding disc and the central star. Our model is based on recently published state-of-the-art 3D collapse simulations of clumps with varied thermodynamics. Various evolutionary mechanisms are taken into account, and their effect is explored both individually and in combination with others: migration and tidal disruption, mass accretion, gap opening and disc viscosity. It is found that, in general, at least 50 per cent of the initial clumps survive tides, leaving behind potential gas giant progenitors after ˜105 yr of evolution in the disc. The rest might either be disrupted or produce super-Earths and other low-mass planets provided that a solid core can be assembled on a sufficiently short time-scale, a possibility that we do not address in this paper. Extrapolating to million year time-scales, all our surviving protoplanets would lead to close-in gas giants. This outcome might in part reflect the limitations of the migration model adopted, and is reminiscent of the analogous result found in core-accretion models in absence of fine-tuning of the migration rate. Yet it suggests that a significant fraction of the clumps formed by GI could be the precursors of Hot Jupiters.

Fully compressible simulations of the baroclinic instability in protoplanetary disks

The occurrence of the baroclinic instability in protoplanetary disks is investigated using fully compressible numerical simulations. We study the role of disk stratification and heat transfer in the development of the instability. Vortices are found to form whatever the importance of the stratification but to grow and persist only when the disk is not stably stratified. In the presence of thermal diffusion the baroclinic instability leads to hollow vortices that decays into transient vortical structures.

The Rossby wave instability in protoplanetary disks

The Rossby wave instability has been proposed as a mechanism to transport angular momentum in the dead zone of protoplanetary disks and to form vortices. These vortices are of particular interest to concentrate solids in their centres and eventually to form planetesimals. Here we summarize some recent results concerning the growth and structure of this instability in radially and vertically stratified disks, its saturation and non-linear evolution. We also discuss the concentration of solids in the Rossby vortices including vertical settling.

The Short Circuit Instability in Protoplanetary Disks: Processing high temperature minerals

We introduce a magneto-hydrodynamic instability which occurs, among other locations, in the inner, hot regions of protoplanetary disks, and which alters the way in which resistive dissipation of magnetic energy into heat proceeds. This instability can be likened to both an electrical short circuit and lightning, as it concentrates the dissipation of magnetic energy by means of the enhanced release of free electrons. This instability can generate very high temperatures, making it an excellent candidate for thermally pro- cessing protoplanetary disk solids, from annealing silicates to melting chondrules or even CAIs.

Conditions of Gravitational Instability in Protoplanetary Disks

Abstract Gravitational instability is one of the considerable mechanisms to explain the formation of giant planets. We have studied the gravitational stability in protoplanetary disks around a protostar. The temperature and Toomre's $ Q$ value were calculated by assuming local equilibrium between viscous heating and radiative cooling (local thermal equilibrium). We assumed a constant $ \alpha$ viscosity and used a cooling function with realistic opacity. Then, we derived the critical surface density, $ \Sigma_{\rm {c}}$ , that is needed in order for a disk to become gravitationally unstable as a function of $ r$ . This critical surface density, $ \Sigma _{\rm c}$ , is strongly affected by the temperature dependence of the opacity. At a radius of $ r_{\rm c}$$ \sim$ 20 AU, where ices form, the value of $ \Sigma _{\rm c}$ changes discontinuously by one order of magnitude. This $ \Sigma _{\rm c}$ is determined only by a local thermal process and the criterion of gravitational instability. By comparing a given surface density profile with $ \Sigma _{\rm c}$ , one can discuss the gravitational instability of protoplanetary disks. As an example, we discuss the gravitational instability of two semianalytic models for protoplanetary disks. One is a steady state accretion disk, which is realized after viscous evolution. The other is a disk that has the same angular-momentum distribution as its parent cloud core, which corresponds to the disk that has just formed. As a result, it is found that the disk tends to become gravitationally unstable for $ r$$ \ge$$ r_{\rm c}$ because ices make the disk temperature low. In a region closer to the protostar than $ r_{\rm c}$ , it is difficult for a typical protoplanetary disk to fragment because of the high temperature and the large Coriolis force. Based on this result, we conclude that fragmentation near the central star is possible, but difficult.

Hall diffusion and the magnetorotational instability in protoplanetary discs

The destabilising effect of Hall diffusion in a Keplerian disc allows the MRI to occur for much lower ionisation levels than would otherwise be possible. However, simulations suggest that the consequences for the saturated state are not as significant as suggested by the linear instability. Close inspection reveals that that the simulations have not yet probed the Hall-dominated regime. Here we revisit the effect of Hall diffusion on the MRI and the implications for the extent of MHD turbulence in protoplanetary discs. We conduct a local stability analysis for a vertical, weak magnetic field subject to axisymmetric perturbations with a vertical wave vector. The diffusivity dependence is presented using analytic expressions and contours in the eta_H - eta_P plane for the maximum growth rate and corresponding wave number, the upper cut-off for unstable wave numbers, and the loci that divide the plane into regions of different characteristic behaviour. In the highly-diffusive limit the magnetic field decouples from the fluid perturbations and the diffusive MRI reduces to a diffusive plane-parallel shear instability with effective shear rate 1.5 Omega. We give analytic expressions for the growth rate and wave number of the most unstable mode. Finally, we illustrate the critical effect of Hall diffusion on the extent of dead zones in protoplanetary discs by applying a local stability criterion to a simple model of the minimum-mass solar nebula at 1 au, including x-ray and cosmic-ray ionisation and a population of 1 micron grains. Hall diffusion increases or decreases the MRI-active column density by an order of magnitude or more, depending on whether B is parallel or antiparallel to the rotation axis, respectively. Existing estimates of the depth of magnetically active layers in protoplanetary discs are likely to be wildly inaccurate. [Abridged]

The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks. IV. Simulations with Envelope Irradiation

It is generally thought that protoplanetary disks embedded in envelopes are more massive and thus more suscep- tible to gravitational instabilities (GIs) than exposed disks. We present three-dimensional radiative hydrodynamic simulationsof protoplanetarydiskswiththepresenceof envelopeirradiation.Foradiskwitharadiusof 40AUanda mass of 0.07 Maround a young star of 0.5 M� , envelope irradiation tends to weaken and even suppress GIs as the irradiating flux is increased. The global mass transport induced by GIs is dominated by lower order modes, and irradiation preferentially suppresses higher order modes. As a result, gravitational torques and mass inflow rates are actually increased bymild irradiation. None of the simulations producedense clumps or rapid cooling byconvection, arguing against direct formation of giant planets by disk instability, at least in irradiated disks. However, dense gas rings andradial mass concentrationsare produced,and these mightbeconduciveto accelerated planetary coreforma- tion. Preliminary results from a simulation of a massive embedded disk with physical characteristics similar to one of thedisksintheembeddedsourceL1551IRS5indicatealongradiativecoolingtimeandnofragmentation.TheGIsin this disk are dominated by global two- and three-armed modes. Subject headingg accretion,accretiondisks — hydrodynamics — instabilities — planetarysystems:formation — planetary systems: protoplanetary disks

Magnetorotational instability in protoplanetary discs: the effect of dust grains

We investigate the linear growth and vertical structure of the MRI in protoplanetary discs when dust grains are well mixed with the gas over the entire disc thickness. All the grains have the same radius (a = 0.1, 1 or 3 micron) and constitute 1 % of the total mass of the gas. Solutions are obtained at R = 5 and 10 AU for a minimum-mass solar nebula model and different choices of the initially vertical magnetic field strength (B), configuration of the diffusivity tensor and grain sizes. We find that when no grains are present, or they are > 1 micron, the midplane remains magnetically coupled for B up to a few gauss at both radii. In contrast, when a population of small grains (a = 0.1 micron) is present, the disc is magnetically inactive for z/H 5, ambipolar diffusion is severe and prevents the field from coupling to the gas for all B. Hall diffusion is dominant for a wide range of field strengths at both radii when dust grains are present. The growth rate, wavenumber and range of magnetic field strengths for which MRI-unstable modes exist are all drastically diminished when dust grains are present, particularly when they are small (a ~ 0.1 micron). We conclude that in protoplanetary discs, the magnetic field is able to couple to the gas and shear over a wide range of fluid conditions even when small dust grains are well mixed with the gas. Despite the low magnetic coupling, MRI modes grow for an extended range of magnetic field strengths and Hall diffusion largely determines the properties of the perturbations in the inner regions of the disc (abridged).

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Nonlinear Saturation and Particle Concentration

We present simulations of the nonlinear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian timescale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random walk, depends strongly on their stopping time and on the solids-to-gas ratio of the background state, but diffusion is generally modest, particularly for tightly coupled solids. Angular momentum transport is too weak and of the wrong sign to influence stellar accretion. Self-gravity and collisions will be needed to determine the relevance of particle overdensities for planetesimal formation.

The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks. III. Simulations with Radiative Cooling and Realistic Opacities

This paper presents a fully three-dimensional radiative hydrodymanics simulation with realistic opacities for a gravitationally unstable 0.07 M☉ disk around a 0.5 M☉ star. We address the following aspects of disk evolution: the strength of gravitational instabilities under realistic cooling, mass transport in the disk that arises from GIs, comparisons between the gravitational and Reynolds stresses measured in the disk and those expected in an α-disk, and comparisons between the SED derived for the disk and SEDs derived from observationally determined parameters. The mass transport in this disk is dominated by global modes, and the cooling times are too long to permit fragmentation for all radii. Moreover, our results suggest a plausible explanation for the FU Ori outburst phenomenon.

Erratum: "The Effects of Metallicity and Grain Size on Gravitational Instabilities in Protoplanetary Disks" ([URL ADDRESS="/cgi-bin/resolve?2006ApJ...636L.149C" STATUS="OKAY"]ApJ 636, L149 [2006][/URL

We have found that the total cumulative radiative energy losses shown in Figure 2 of the above-mentioned Letter were computed for only half the disk. This caused the final global cooling times tcool in the eighth column of the original Table 1 to be too large by a factor of 2. Proper values of tcool are given in the revised Table 1 below. To be more consistent with what the Letter states, we now use instantaneous values for both the total internal energy and the final total net cooling rates to compute final tcool’s, instead of averaging the loss rates over an interval of time at the end of the calculations before dividing, as was done in the Letter. We also take this opportunity to make a few other inconsequential corrections to the fourth column of the table. In addition to the changes to Table 1, the approximate initial tcool relation in the fourth paragraph of § 3.2 becomes to within tens t ∼ Z/Z cool , of percent. Despite the corrections, our conclusions in the Letter remain unchanged. Most importantly, the final tcool’s vary with metallicity and are still too long for disk fragmentation to occur with our equation of state over the range of Z examined. We regret any inconvenience our errors may have caused.

The Effects of Metallicity and Grain Size on Gravitational Instabilities in Protoplanetary Disks

Observational studies show that the probability of finding gas giant planets around a star increases with the star's metallicity. Our latest simulations of disks undergoing gravitational instabilities (GIs) with realistic radiative cooling indicate that protoplanetary disks with lower metallicity generally cool faster and thus show stronger overall GI activity. More importantly, the global cooling times in our simulations are too long for disk fragmentation to occur, and the disks do not fragment into dense protoplanetary clumps. Our results suggest that direct gas giant planet formation via disk instabilities is unlikely to be the mechanism that produced most observed planets. Nevertheless, GIs may still play an important role in a hybrid scenario, compatible with the observed metallicity trend, where structure created by GIs accelerates planet formation by core accretion.

Two-dimensional models of layered protoplanetary discs - I. The ring instability

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 find 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 the non-zero thickness of the dead zone and deviations from the Keplerian rotational velocity. The analytical model agrees reasonably well with the results of numerical simulations. Finally, we speculate concerning the possible role of the ring instability in protoplanetary discs and in the formation of planets.

Magnetorotational instability in protoplanetary discs

We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionized, stratified accretion discs. The magnetic field is initially vertical and dust grains are assumed to have settled towards the mid-plane, so charges are carried by electrons and ions only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionization, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low-conductivity discs. Moreover, no evidence was found of a low-limit field strength below which unstable modes do not exist. For the minimum-mass solar nebula model, incorporating cosmic ray ionization, perturbations grow at 1 au for B ≤ 8 G. For a significant subset of these strengths (200 mG ≤ B ≤ 5 G), the maximum growth rate is of the order of the ideal magnetohydrodynamic (MHD) rate (0.75 Ω). Hall conductivity modifies the structure and growth rate of global unstable modes at 1 au for all magnetic field strengths that support MRI. As a result, at this radius, modes obtained with a full conductivity tensor grow faster and are active over a more extended cross-section of the disc than perturbations in the ambipolar diffusion limit. For relatively strong fields (e.g. B ≥ 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B ≤ 2 G. For strong fields, perturbations exhibit a kink at the height where X-ray ionization becomes active. Finally, for R = 5 au (10 au), unstable modes exist for B ≤ 800 mG (B ≤ 250 mG) and the maximum growth rate is close to the ideal-MHD rate for 20 ≤ B ≤ 500 mG (2 ≤ B ≤ 50 mG). Similarly, perturbations incorporating Hall conductivity have a higher wavenumber and grow faster than solutions in the ambipolar diffusion limit for B ≤ 100 mG (B ≤ 10 mG). Unstable modes grow even at the mid-plane for B ≥ 100 mG (B ∼ 1 mG), but for weaker fields, a small dead region exists. This study shows that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 au for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 au, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability and more generally in studies of the dynamics of astrophysical discs.