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1.
The migration and growth of protoplanets in protostellar discs   总被引：1，自引：0，他引：1  
We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using three independent numerical codes.
A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-circular orbit after a characteristic viscous time‐scale of ∼104 initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is ∼5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planets of increasing mass.
Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc–protoplanet interactions during the late stages of giant planet formation.  相似文献   

2.
In this paper we develop further the model for the migration of planets introduced in Del Popolo et al. We first model the protoplanetary nebula as a time-dependent accretion disc, and find self-similar solutions to the equations of the accretion disc that give us explicit formulae for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc, and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parameter α . We find that planets that are embedded in planetesimal discs, having total mass of  10-4-0.1 M⊙  , can migrate inward a large distance for low values of α (e.g.,   α ≃10-3-10-2)  and/or large disc mass, and can survive only if the inner disc is truncated or because of tidal interaction with the star. Orbits with larger a are obtained for smaller values of the disc mass and/or for larger values of α . This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.  相似文献   

3.
Astronomical observations have shown that protoplanetary disks are dynamic objects through which mass is transported and accreted by the central star. This transport causes the disks to decrease in mass and cool over time, and such evolution is expected to have occurred in our own solar nebula. Age dating of meteorite constituents shows that their creation, evolution, and accumulation occupied several Myr, and over this time disk properties would evolve significantly. Moreover, on this timescale, solid particles decouple from the gas in the disk and their evolution follows a different path. It is in this context that we must understand how our own solar nebula evolved and what effects this evolution had on the primitive materials contained within it. Here we present a model which tracks how the distribution of water changes in an evolving disk as the water-bearing species experience condensation, accretion, transport, collisional destruction, and vaporization. Because solids are transported in a disk at different rates depending on their sizes, the motions will lead to water being concentrated in some regions of a disk and depleted in others. These enhancements and depletions are consistent with the conditions needed to explain some aspects of the chemistry of chondritic meteorites and formation of giant planets. The levels of concentration and depletion, as well as their locations, depend strongly on the combined effects of the gaseous disk evolution, the formation of rapidly migrating rubble, and the growth of immobile planetesimals. Understanding how these processes operate simultaneously is critical to developing our models for meteorite parent body formation in the Solar System and giant planet formation throughout the galaxy. We present examples of evolution under a range of plausible assumptions and demonstrate how the chemical evolution of the inner region of a protoplanetary disk is intimately connected to the physical processes which occur in the outer regions.  相似文献   

4.
E.W. Thommes  M.J. Duncan 《Icarus》2003,161(2):431-455
Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as “oligarchic growth.” Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼10 × minimum-mass) is required to produce giant planet core-sized bodies (∼10 M⊕) within the lifetime of the nebular gas (?10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of noninteracting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System’s two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.  相似文献   

5.
We explore the cross section of giant planet envelopes at capturing planetesimals of different sizes. For this purpose we employ two sets of realistic planetary envelope models (computed assuming for the protoplanetary nebula masses of 10 and 5 times the mass of the minimum mass solar nebula), account for drag and ablation effects and study the trajectories along which planetesimals move. The core accretion of these models has been computed in the oligarchic growth regime [Fortier, A., Benvenuto, O.G., Brunini, A., 2007. Astron. Astrophys. 473, 311-322], which has also been considered for the velocities of the incoming planetesimals. This regime predicts velocities larger that those used in previous studies of this problem. As the rate of ablation is dependent on the third power of velocity, ablation is more important in the oligarchic growth regime. We compute energy and mass deposition, fractional ablated masses and the total cross section of planets for a wide range of values of the critical parameter of ablation. In computing the total cross section of the planet we have included the contributions due to mass deposited by planetesimals moving along unbound orbits. Our results indicate that, for the case of small planetary cores and low velocities for the incoming planetesimals, ablation has a negligible impact on the capture cross section in agreement with the results presented in Inaba and Ikoma [Inaba, S., Ikoma, M., 2003. Astron. Astrophys. 410, 711-723]. However for the case of larger cores and high velocities of the incoming planetesimals as predicted by the oligarchic growth regime, we find that ablation is important in determining the planetary cross section, being several times larger than the value corresponding ignoring ablation. This is so regardless of the size of the incoming planetesimals.  相似文献   

6.
The existence of Uranus and Neptune presents severe difficulties for the core accretion model for the formation of ice giant planets. We suggest an alternative mechanism, namely disk instability leading to the formation of gas giant protoplanets, coagulation and settling of dust grains to form ice-rock cores at their centers, and photoevaporation of their gaseous envelopes by a nearby OB star, as a possible means of forming ice giant planets.  相似文献   

7.
In this paper we present a new semianalytical model of oligarchic growth of planets considering a distribution of planetesimal sizes, fragmentation of planetesimals in mutual collisions, sublimation of ices through the snow line, random velocities out of equilibrium and merging of planetary embryos. We show that the presence of several planetary embryos growing simultaneously at different locations in the protoplanetary disk affects the whole accretion history, specially for the innermost planets. The results presented here clearly indicate the relevance of considering a distribution of planetesimal sizes. Fragmentation occurring during planetesimal-planetesimal collisions represent only a marginal effect in shaping the surface density of solid material in the protoplanetary disc.  相似文献   

8.
We develop a simple model for computing planetary formation based on the core instability model for the gas accretion and the oligarchic growth regime for the accretion of the solid core. In this model several planets can form simultaneously in the disc, a fact that has important implications especially for the changes in the dynamic of the planetesimals and the growth of the cores since we consider the collision between them as a source of potential growth. The type I and type II migration of the embryos and the migration of the planetesimals due to the interaction with the disc of gas are also taken into account. With this model we consider different initial conditions to generate a variety of planetary systems and analyse them statistically. We explore the effects of using different type I migration rates on the final number of planets formed per planetary system such as on the distribution of masses and semimajor axis of extrasolar planets, where we also analyse the implications of considering different gas accretion rates. A particularly interesting result is the generation of a larger population of habitable planets when the gas accretion rate and type I migration are slower.  相似文献   

9.
Gas giant planets have been detected in orbit around an increasing number of nearby stars. Two theories have been advanced for the formation of such planets: core accretion and disk instability. Core accretion, the generally accepted mechanism, requires several million years or more to form a gas giant planet in a protoplanetary disk like the solar nebula. Disk instability, on the other hand, can form a gas giant protoplanet in a few hundred years. However, disk instability has previously been thought to be important only in relatively massive disks. New three-dimensional, "locally isothermal," hydrodynamical models without velocity damping show that a disk instability can form Jupiter-mass clumps, even in a disk with a mass (0.091 M middle dot in circle within 20 AU) low enough to be in the range inferred for the solar nebula. The clumps form with initially eccentric orbits, and their survival will depend on their ability to contract to higher densities before they can be tidally disrupted at successive periastrons. Because the disk mass in these models is comparable to that apparently required for the core accretion mechanism to operate, the models imply that disk instability could obviate the core accretion mechanism in the solar nebula and elsewhere.  相似文献   

10.
The gas giant planets’ formation processes in a viscously evolved protoplanetary disk are studied in the context of the core accretion model. In this paper, we follow the entire formation process of the core accretion model (the three stages). We find that the gas giant planets’ final masses and formation regions have strong dependence on the molecular cloud core’s properties (angular velocity \(\omega \) and mass \(M _{c d}\)) and the \(\alpha _{ \mathit{min} }\) parameter. We find and build the relationship between gas giant planets’ properties and molecular cloud core’s properties. In contrast to the previous works, we find that the formation process can be finished within the protoplanetary disk’s lifetime (4×106 yr) in our disk model. This is because the mass influx produced by the molecular cloud core can provide enough material to the protoplanetary disk. We also find that the gas giant planets’ final masses increase generally with the viscosity coefficient \(\alpha \). This is because most of the gas giant planet’s mass is captured during the rapid gas accretion phase (the third stage of the core accretion model), and furthermore the accretion of gas in this phase is dominated by the “gap limiting case”. And our numerical results can also be compared with the observed data of exoplanet systems.  相似文献   

11.

The sequence of evolution of the protoplanetary gas-and-dust disk around the parent star includes, according to modern concepts, its compression in the central plane and decay into separate dust condensations (clusters) due to the occurrence of various types of instabilities. The interaction of dust clusters of a fractal structure during their collisions is considered as a key mechanism for the formation and growth of primary solids, which serve as the basis for the subsequent formation of planetesimals and embryos of planets. Among the mechanisms contributing to the formation of planetesimals, an important place belongs, along with gravitational instability, hydrodynamic instabilities, in particular, the socalled streaming instability of the two-phase gas-dust layer due to its ability to concentrate dispersed particles in dense clots. In contrast to a number of existing models of streaming instability, in which dust particles are considered structurally compact and monodisperse, this paper proposes a more realistic model of polydisperse particles of fractal nature, forming dust clusters as a result of coagulation. The instability of the dust layer in the central plane of the protoplanetary disk under linear axisymmetric perturbations of its parameters is considered. A preliminary conclusion can be drawn that the proposed model of dust fractal aggregates of different scales increases the efficiency of linear growth of hydrodynamic instabilities, including the streaming instabilities associated with the difference between the velocities of the dust and gas phases.

  相似文献   

12.
In this paper we investigate both the global and the local hydrodynamics of axisymmetric accretion disks around young stellar objects under the simultaneous action of viscosity, self-gravity and pressure forces. For simplicity, we take for the global model a polytropic equation of state, make the infinitely thin disk approximation and characterize the surface density and temperature profiles in the disk as power laws in the radial distance r from the protostar. We solve the problem of the general density profile of a Keplerian disk showing that self-gravity could not be an important factor for the fast formation of the rocky cores of giant gaseous planets in our solar system. Under the hypothesis that the unperturbed rotation curve of the disk is nearly Keplerian throughout the radial extent, we can estimate with our polytropic model a lower limit for the resulting masses Md(r) of stable disks up to 100 AU. These masses are in the range of the so-called minimum mass solar nebular (d/Ms ≈ 0.01–0.02).By adopting a simplified viscosity model, where the height-integrated turbulent dynamical viscosity ν is a function of the surface density σ like η ∝ σΓ, we derive in the local shearing sheet model linearized evolution equations for small density perturbations describing both a diffusion process and the propagation of acoustic density waves. We solve a special initial value problem and calculate the appropriate Green's function. The analytical solutions so obtained describe in the case Γ < 0 the successive formation of quasi-stationary ring-shaped density structures in a disk with a definite mode of maximum instability, whereas in the case Γ > Γc the density wave equation describes the propagation of an “overstable” ring-shaped acoustic density wavelet to the outer ranges of the accretion disk. Whereas the group velocity of the wave packet is subsonic, the phase velocities of individual wave crests in the wave packet are supersonic. The mode of maximum instability, the growth rate and the number of growing waves in the wavelet are controlled by Γ and α. Our present knowledge concerning turbulent viscosity in protoplanetary disks is not sufficient to decide whether or not the case Γ > Γc is realized.The suggested structuring processes in the linear theory should initiate in the non-linear regime the formation of narrow ring-shaped density shock waves moving through the protoplanetary disk. These non-linear waves could produce extremely spatially and temporally heterogeneous temperature regions in the disk. We speculate that ring-shaped density waves, excited by inner boundary conditions and which have dominated the disk's evolution at early times, are responsible both for the fast growth of dust to planetesimals and at least for the rapid accretion of the rocky cores of giant gaseous planets in the protoplanetary accretion disk (shock wave trigger hypothesis). We derive provisional scaling rules for planetary systems regarding the spacing of orbits as a function of the mass ratio of the protoplanetary disk to the protostar. However, further analytical work and linear as well as nonlinear numerical simulations of density waves excited by inner boundary conditions are needed to consolidate the results and speculations of our linear wave mechanics in the future.  相似文献   

13.
We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary mass to see how they effect the resulting disk structure. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region.  相似文献   

14.
Adrián Brunini 《Icarus》2005,177(1):264-268
The sample of known exoplanets is strongly biased to masses larger than the ones of the giant gaseous planets of the Solar System. Recently, the discovery of two extrasolar planets of considerably lower masses around the nearby Stars GJ 436 and ρ Cancri was reported. They are like our outermost icy giants, Uranus and Neptune, but in contrast, these new planets are orbiting at only some hundredth of the Earth-Sun distance from their host stars, raising several new questions about their origin and constitution. Here we report numerical simulations of planetary accretion that show, for the first time through N-body integrations that the formation of compact systems of Neptune-like planets close to the hosts stars could be a common by-product of planetary formation. We found a regime of planetary accretion, in which orbital migration accumulates protoplanets in a narrow region around the inner edge of the nebula, where they collide each other giving rise to Neptune-like planets. Our results suggest that, if a protoplanetary solar environment is common in the Galaxy, the discovery of a vast population of this sort of ‘hot cores’ should be expected in the near future.  相似文献   

15.
J.A. Fernández  W.-H. Ip 《Icarus》1984,58(1):109-120
The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 108 years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.  相似文献   

16.
Giant planet formation process is still not completely understood. The current most accepted paradigm, the core instability model, explains several observed properties of the Solar System’s giant planets but, to date, has faced difficulties to account for a formation time shorter than the observational estimates of protoplanetary disks’ lifetimes, especially for the cases of Uranus and Neptune. In the context of this model, and considering a recently proposed primordial Solar System orbital structure, we performed numerical calculations of giant planet formation. Our results show that if accreted planetesimals follow a size distribution in which most of the mass lies in 30-100 m sized bodies, Jupiter, Saturn, Uranus and Neptune may have formed according to the nucleated instability scenario. The formation of each planet occurs within the time constraints and they end up with core masses in good agreement with present estimations.  相似文献   

17.
G.P. Horedt 《Icarus》1985,64(3):448-470
We derive first-order differential equations for the late stages of planetary accretion (planetesimal mass >1013 g). The effect of gravitational encounters, energy exchange, collisions, and gas drag has been included. Two simple models are discussed, namely, (i) when all planetesimals have the same mass and (ii) when there is one large planetesimal and numerous small planetesmals. Gravitational two-body encounters are modeled according to Chandrasekhar's classical theory from stellar dynamics. It is shown that the velocity increase due to mutual encounters can be modeled according to the simple theory of random flights. We find analytical equations for the average velocity decrease due to collisions. Gas drag, if present, is modeled in averaged form up to the first order in the eccentricities and inclinations of the planetesimals. Characteristic time scales for the formation of the terrestrial planets are found for the most favorable models to be of order 108 year. The calculated mass of rock and ice of the giant planets is too low as compared to the observed one. This difficulty of our model could be overcome by assuming a several times larger surface density, an enlarged accretion cross section, and gas accretion during the final stages of accretion of the solid cores of the giant planets. Analytical and numerical results are presebted, the evolutionary tracks showing satisfactory agreement with observations for some models.  相似文献   

18.
We have performed 8 numerical simulations of the final stages of accretion of the terrestrial planets, each starting with over 5× more gravitationally interacting bodies than in any previous simulations. We use a bimodal initial population spanning the region from 0.3 to 4 AU with 25 roughly Mars-mass embryos and an equal mass of material in a population of ∼1000 smaller planetesimals, consistent with models of the oligarchic growth of protoplanetary embryos. Given the large number of small planetesimals in our simulations, we are able to more accurately treat the effects of dynamical friction during the accretion process. We find that dynamical friction can significantly lower the timescales for accretion of the terrestrial planets and leads to systems of terrestrial planets that are much less dynamically excited than in previous simulations with fewer initial bodies. In addition, we study the effects of the orbits of Jupiter and Saturn on the final planetary systems by running 4 of our simulations with the present, eccentric orbits of Jupiter and Saturn (the EJS simulations) and the other 4 using a nearly circular and co-planar Jupiter and Saturn as predicted in the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465] (the CJS simulations). Our EJS simulations provide a better match to our Solar System in terms of the number and average mass of the final planets and the mass-weighted mean semi-major axis of the final planetary systems, although increased dynamical friction can potentially improve the fit of the CJS simulations as well. However, we find that in our EJS simulations, essentially no water-bearing material from the outer asteroid belt ends up in the final terrestrial planets, while a large amount is delivered in the CJS simulations. In addition, the terrestrial planets in the EJS simulations receive a late veneer of material after the last giant impact event that is likely too massive to reconcile with the siderophile abundances in the Earth's mantle, while the late veneer in the CJS simulations is much more consistent with geochemical evidence.  相似文献   

19.
Observational constraints on interior models of the giant planets indicate that these planets were all much hotter when they formed and they all have rock and/or ice cores of ten to thirty earth masses. These cores are probably soluble in the envelopes above, especially in Jupiter and Saturn, and are therefore likely to be primordial. They persist despite the continual upward mixing by thermally driven convection throughout the age of the solar system, because of the inefficiency of double-diffusive convection. Thus, these planets most probably formed by the hydrodynamic collapse of a gaseous envelope onto a core rather than by direct instability of the gaseous solar nebula. Recent calculations by Mizuno (1980, Prog. Theor. Phys.64, 544) show that this formation mechanism may explain the similarity of giant planet core masses. Problems remain however, and no current model is entirely satisfactory in explaining the properties of the giant planets and simultaneously satisfying the terrestrial planet constraints. Satellite systematics and protoplanetary disk nebulae are also discussed and related to formation conditions.  相似文献   

20.
In this paper we investigate the evolution of a pair of interacting planets – a Jupiter-mass planet and a Super-Earth with a mass of  5.5 M ⊕  – orbiting a Solar-type star and embedded in a gaseous protoplanetary disc. We focus on the effects of type I and II orbital migrations, caused by the planet–disc interaction, leading to the capture of the Super-Earth in first-order mean-motion resonances by the Jupiter. The stability of the resulting resonant system in which the Super-Earth is on the internal orbit relative to the Jupiter is studied numerically by means of full 2D hydrodynamical simulations. Our main aim is to determine the Super-Earth behaviour in the presence of the gas giant in the system. It is found that the Jupiter captures the Super-Earth into the interior 3:2 or 4:3 mean-motion resonance, and that the stability of such configurations depends on the initial positions of the planets and on the evolution of the eccentricity. If the initial separation of the orbits of the planets is larger than or close to that required for the exact resonance, the final outcome is the migration of the pair of planets at a rate similar to that of the gas giant, at least for the time of our simulations. Otherwise, we observe a scattering of the Super-Earth from the disc. The evolution of planets immersed in a gaseous disc is compared with their behaviour in the case of the classical three-body problem when the disc is absent.  相似文献   

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