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Eiichiro Kokubo - One of the best experts on this subject based on the ideXlab platform.
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Ejection of close-in super-Earths around low-mass stars in the giant impact stage
'EDP Sciences', 2020Co-Authors: Yuji Matsumoto, Shoichi Oshino, Eiichiro Kokubo, Masashi OmiyaAbstract:Context. Earth-sized planets were observed in close-in orbits around M dwarfs. While more and more planets are expected to be uncovered around M dwarfs, theories of their formation and dynamical evolution are still in their infancy. Aims. We investigate the giant impact stage for the growth of Protoplanets, which includes strong scattering around low-mass stars. The aim is to clarify whether strong scattering around low-mass stars affects the orbital and mass distributions of the planets. Methods. We performed an N-body simulation of Protoplanets by systematically surveying the parameter space of the stellar mass and surface density of Protoplanets. Results. We find that Protoplanets are often ejected after twice or three times the close-scattering around late M dwarfs. The ejection sets the upper limit of the largest planet mass. By adopting the surface density that linearly scales with the stellar mass, we find that as the stellar mass decreases, less massive planets are formed in orbits with higher eccentricities and inclinations. Under this scaling, we also find that a few close-in Protoplanets are generally ejected. Conclusions. The ejection of Protoplanets plays an important role in the mass distribution of super-Earths around late M dwarfs. The mass relation of observed close-in super-Earths and their central star mass is reproduced well by ejection
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merging criteria for giant impacts of Protoplanets
The Astrophysical Journal, 2012Co-Authors: Hidenori Genda, Eiichiro Kokubo, Shigeru IdaAbstract:At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized Protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of Protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding Protoplanets always merge. However, recent impact simulations have shown that collisions among Protoplanets are not always merging events, that is, two colliding Protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step toward studying the effects of such imperfect accretion of Protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky Protoplanets. Using the smoothed particle hydrodynamic method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of Protoplanets, γ, the total mass of two Protoplanets, M T, the impact angle, θ, and the impact velocity, v imp. We investigated the critical impact velocity, v cr, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, v cr/v esc, depends on γ and θ, but does not depend on M T, where v esc is the two-body escape velocity. We derived a simple formula for v cr/v esc as a function of γ and θ (Equation (16)), and applied it to the giant impact events obtained by N-body calculations in the previous studies. We found that 40% of these events should not be merging events.
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merging criteria for giant impacts of Protoplanets
arXiv: Earth and Planetary Astrophysics, 2011Co-Authors: Hidenori Genda, Eiichiro Kokubo, Shigeru IdaAbstract:At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized Protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of Protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding Protoplanets always merge. However, recent impact simulations have shown that collisions among Protoplanets are not always merging events, that is, two colliding Protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step towards studying the effects of such imperfect accretion of Protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky Protoplanets. Using the smoothed particle hydrodynamic (SPH) method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of Protoplanets, $\gamma$, the total mass of two Protoplanets, $M_{\rm T}$, the impact angle, $\theta$, and the impact velocity, $v_{\rm imp}$. We investigated the critical impact velocity, $v_{\rm cr}$, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, $v_{\rm cr}/v_{\rm esc}$, depends on $\gamma$ and $\theta$, but does not depend on $M_{\rm T}$, where $v_{\rm esc}$ is the two-body escape velocity. We derived a simple formula for $v_{\rm cr}/v_{\rm esc}$ as a function of $\gamma$ and $\theta$, and applied it to the giant impact events obtained by \textit{N}-body calculations in the previous studies. We found that 40% of these events should not be merging events.
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gas accretion onto a protoplanet and formation of a gas giant planet
Monthly Notices of the Royal Astronomical Society, 2010Co-Authors: Masahiro N. Machida, Shu-ichiro Inutsuka, Eiichiro Kokubo, Tomoaki MatsumotoAbstract:We investigate gas accretion on to a protoplanet, by considering the thermal effect of gas in three-dimensional hydrodynamical simulations, in which the wide region from a protoplanetary gas disc to a Jovian radius planet is resolved using the nested grid method. We estimate the mass accretion rate and growth time-scale of gas giant planets. The mass accretion rate increases with protoplanet mass for Mp M cri, where Mcri ≡ 0.036 MJup(ap/1au) 0.75 , and MJup and ap are the Jovian mass and the orbital radius, respectively. This accretion rate is typically two orders of magnitude smaller than that in two-dimensional simulations. The growth time-scale of a gas giant planet or the time-scale of the gas accretion on to the protoplanet is about 10 5 yr, that is two orders of magnitude shorter than the growth time-scale of the solid core. The thermal effects barely affect the mass accretion rate because the gravitational energy dominates the thermal energy around the protoplanet. The mass accretion rate obtained in our local simulations agrees quantitatively well with those obtained in global simulations with coarser spatial resolution. The mass accretion rate is mainly determined by the protoplanet mass and the property of the protoplanetary disc. We find that the mass accretion rate is correctly calculated when the Hill or Bondi radius is sufficiently resolved. Using the oligarchic growth of Protoplanets, we discuss the formation time-scale of gas giant planets.
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formation of terrestrial planets from Protoplanets under a realistic accretion condition
The Astrophysical Journal, 2010Co-Authors: Eiichiro Kokubo, Hidenori GendaAbstract:The final stage of terrestrial planet formation is known as the giant impact stage where Protoplanets collide with one another to form planets. So far this stage has been mainly investigated by N-body simulations with an assumption of perfect accretion in which all collisions lead to accretion. However, this assumption breaks for collisions with high velocity and/or a large impact parameter. We derive an accretion condition for protoplanet collisions in terms of impact velocity and angle and masses of colliding bodies, from the results of numerical collision experiments. For the first time, we adopt this realistic accretion condition in N-body simulations of terrestrial planet formation from Protoplanets. We compare the results with those with perfect accretion and show how the accretion condition affects terrestrial planet formation. We find that in the realistic accretion model about half of collisions do not lead to accretion. However, the final number, mass, orbital elements, and even growth timescale of planets are barely affected by the accretion condition. For the standard protoplanetary disk model, typically two Earth-sized planets form in the terrestrial planet region over about 108 yr in both realistic and perfect accretion models. We also find that for the realistic accretion model, the spin angular velocity is about 30% smaller than that for the perfect accretion model, which is as large as the critical spin angular velocity for rotational instability. The spin angular velocity and obliquity obey Gaussian and isotropic distributions, respectively, independently of the accretion condition.
Richard P Nelson - One of the best experts on this subject based on the ideXlab platform.
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three dimensional simulations of multiple Protoplanets embedded in a protostellar disc
arXiv: Astrophysics, 2008Co-Authors: P Cresswell, Richard P NelsonAbstract:Protoplanet eccentricities of e >~ H/r can slow or reverse migration, but previous 2D studies have shown that gravitational scattering cannot maintain significant planet eccentricities against disc-induced damping. We simulate the evolution of low-mass protoplanetary swarms in three dimensions. The aim is to examine both protoplanet survival rates and the dynamical structure of the resulting planetary systems, and to compare them with 2D simulations. We present results from a 3D hydrodynamic simulation of eight Protoplanets embedded in a protoplanetary disc. We also present a suite of simulations performed using an N-body code, modified to include prescriptions for planetary migration and for eccentricity and inclination damping. These prescriptions were obtained by fitting analytic formulae to hydrodynamic simulations of planets embedded in discs with initially eccentric and/or inclined orbits. As was found in two dimensions, differential migration produces groups of Protoplanets in stable, multiple mean-motion resonances that migrate in lockstep, preventing prolonged periods of gravitational scattering. In almost all simulations, this leads to large-scale migration of the protoplanet swarm into the central star in the absence of a viable stopping mechanism. The evolution involves mutual collisions, occasional instances of large-scale scattering, and the frequent formation of the long-lived, co-orbital planet systems that arise in > 30% of all runs. Disc-induced damping overwhelms eccentricity and inclination growth due to planet-planet interactions. Co-orbital planets are a natural outcome of dynamical relaxation in a strongly dissipative environment, and if observed in nature would imply that such a period of evolution commonly arises during planetary formation.
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three dimensional simulations of multiple Protoplanets embedded in a protostellar disc
Astronomy and Astrophysics, 2008Co-Authors: P Cresswell, Richard P NelsonAbstract:Context. Theory predicts that low-mass Protoplanets in a protostellar disc migrate into the central star on a time scale that is short compared with the disc lifetime or the giant planet formation time scale. Protoplanet eccentricities of e ≥ H/r can slow or reverse migration, but previous 2D studies of multiple Protoplanets embedded in a protoplanetary disc have shown that gravitational scattering cannot maintain significant planet eccentricities against disc-induced damping. The eventual fate of these systems was migration into the central star. Aims. Here we simulate the evolution of low-mass protoplanetary swarms in three dimensions. The aim is to examine both protoplanet survival rates and the dynamical structure of the resulting planetary systems, and to compare them with 2D simulations. Methods. We present results from a 3D hydrodynamic simulation of eight Protoplanets embedded in a protoplanetary disc. We also present a suite of simulations performed using an N-body code, modified to include prescriptions for planetary migration and for eccentricity and inclination damping. These prescriptions were obtained by fitting analytic formulae to hydrodynamic simulations of planets embedded in discs with initially eccentric and/or inclined orbits. Results. As was found in two dimensions, differential migration produces groups of Protoplanets in stable, multiple mean-motion resonances that migrate in lockstep, preventing prolonged periods of gravitational scattering. In almost all simulations, this leads to large-scale migration of the protoplanet swarm into the central star in the absence of a viable stopping mechanism. The evolution involves mutual collisions, occasional instances of large-scale scattering, and the frequent formation of the long-lived, co-orbital planet systems that arise in >30% of all runs. Conclusions. Disc-induced damping overwhelms eccentricity and inclination growth due to planet-planet interactions, leading to large-scale migration of protoplanet swarms. Co-orbital planets are a natural outcome of dynamical relaxation in a strongly dissipative environment, and if observed in nature would imply that such a period of evolution commonly arises during planetary formation.
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on the migration of Protoplanets embedded in circumbinary disks
Astronomy and Astrophysics, 2007Co-Authors: A Pierens, Richard P NelsonAbstract:Aims. We present the results of hydrodynamical simulations of low mass Protoplanets embedded in circumbinary accretion disks. The aim is to examine the migration and long term orbital evolution of the Protoplanets, in order to establish the stability properties of planets that form in circumbinary disks. Methods. Simulations were performed using a grid-based hydrodynamics code. First we present a set of calculations that study how a binary interacts with a circumbinary disk. We evolve the system for ~ 10 5 binary orbits, which is the time needed for the system to reach a quasi-equilibrium state. From this time onward the apsidal lines of the disk and the binary are aligned, and the binary eccentricity remains essentially unchanged with a value of e b ~ 0.08. Once this stationary state is obtained, we embed a low mass protoplanet in the disk and let it evolve under the action of the binary and disk forces. We consider Protoplanets with masses of m p = 5, 10 and 20 $M_\oplus$. Results. In each case, we find that inward migration of the protoplanet is stopped at the edge of the tidally truncated cavity formed by the binary. This effect is due to positive corotation torques, which can counterbalance the net negative Lindblad torques in disk regions where the surface density profile has a sufficiently large positive gradient. Halting of migration occurs in a region of long-term stability, suggesting that low mass circumbinary planets may be common, and that gas giant circumbinary planets should be able to form in circumbinary disks.
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on the orbital evolution of low mass Protoplanets in turbulent magnetised disks
Astronomy and Astrophysics, 2005Co-Authors: Richard P NelsonAbstract:We present the results of MHD simulations of low mass Protoplanets interacting with turbulent, magnetised protostellar disks. We calculate the orbital evolution of planetesimals and Protoplanets with masses in the range 0 ≤ m p < 30 M ○+ . The disk models are cylindrical models with toroidal net-flux magnetic fields, having aspect ratio H/r = 0.07 and effective viscous stress parameter α 5 × 10 -3 . A significant result is that the m p = 0 planetesimals, and Protoplanets of all masses considered, undergo stochastic migration due to gravitational interaction with turbulent density fluctuations in the disk. For simulation run times currently feasible (covering between 100-150 planet orbits), the stochastic migration dominates over type I migration for many models. Fourier analysis of the torques experienced by Protoplanets indicates that the torque fluctuations contain components with significant power whose time scales of variation are similar to the simulation run times, These long term torque fluctuations in part explain the dominance of stochastic torques in the models, and may provide a powerful means of counteracting the effects of type I migration acting on some planets in turbulent disks. The effect of superposing type I migration torques appropriate for laminar disks on the stochastic torques was examined. This analysis predicts that a greater degree of inward migration should occur than was observed in the MHD simulations. This may be a first hint that type I torques are modified in a turbulent disk, but the results are not conclusive on this matter. The turbulence is found to be a significant source of eccentricity driving, with the planetesimals attaining eccentricities in the range 0.02 ≤ e < 0.14 during the simulations. The eccentricity evolution of the Protoplanets shows strong dependence on the protoplanet mass. Protoplanets with mass m p = 1 M ○+ attained eccentricities in the range 0.02 < e ≤ 0.08. Those with m p = 10 M ○+ reached 0.02 < e ≤ 0.03. This trend is in basic agreement with a model in which eccentricity growth arises because of turbulent forcing, and eccentricity damping occurs through interaction with disk material at coorhilal Lindblad resonances. These results are significant for the theory of planet formation. Stochastic migration may provide a means of preventing at least some planetary cores from migrating into the central star due to type I migration before they become gas giants. The growth of planetary cores may he enhanced hy preventing isolation during planetesimal accretion. The excitation of eccentricity by the turbulence, however, may act to reduce the growth rates of planetary cores during the runaway and oligarchic growth stages, and may cause collisions between planetesimals to he destructive rather than accumulative.
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models of accreting gas giant Protoplanets in protostellar disks
Astronomy and Astrophysics, 2005Co-Authors: John C B Papaloizou, Richard P NelsonAbstract:We present evolutionary models of gas giant planets forming in protoplanetary disks. We first consider protoplanet models that consist of solid cores surrounded by hydrostatically supported gaseous envelopes that are in contact with the boundaries of their Hill spheres, and accrete gas from the surrounding disk. We neglect planetesimal accretion, and suppose that the luminosity arises from gas accretion alone. This generally occurs on a long time scale which may be comparable to the protostellar disk lifetime. We classify these models as being of type A, and follow their quasi static evolution until the point of rapid gas accretion is reached. We consider a second class of protoplanet models that have not hitherto been considered. These models have a free surface, their energy supply is determined by gravitational contraction, and mass accretion from the protostellar disk that is assumed to pass through a circumplanetary disk. An evolutionary sequence is obtained by specifying the accretion rate that the protostellar disk is able to supply. We refer to these models as being of type B. An important result is that these protoplanet models contract quickly to a radius ∼2 × 10 10 cm and are able to accrete gas from the disk at any reasonable rate that may be supplied without any consequent expansion (e.g. a Jupiter mass in ∼few ×10 3 years, or more slowly if so constrained by the disk model). We speculate that the early stages of gas giant planet formation proceed along evolutionary paths described by models of type A, but at the onset of rapid gas accretion the protoplanet contracts interior to its Hill sphere, making a transition to an evolutionary path described by models of type B, receiving gas through a circumplanetary disk that forms within its Hill sphere, which is in turn fed by the surrounding protostellar disk. We consider planet models with solid core masses of 5 and 15 M⊕, and consider evolutionary sequences assuming different amounts of dust opacity in the gaseous envelope. The initial protoplanet mass doubling time scale is very approximately inversely proportional to the magnitude of this opacity. Protoplanets with 5 M⊕ cores, and standard dust opacity require ∼3 × 10 8 years to grow to a Jupiter mass, longer than reasonable disk life-times. A model with 1% of standard dust opacity requires ∼3 × 10 6 years. Rapid gas accretion in both these cases ensues once the planet mass exceeds � 18 M⊕, with substantial time spent in that mass range. Protoplanets with 15 M⊕ cores grow to a Jupiter mass in ∼3 × 10 6 years if standard dust opacity is assumed, and in ∼10 5 years if 1% of standard dust opacity is adopted. In these cases, the planet spends substantial time with mass between 30−40 M⊕ before making the transition to rapid gas accretion. We emphasize that these growth times apply to the gas accretion phase and not to the prior core formation phase. According to the usual theory of protoplanet migration, although there is some dependence on disk parameters, migration in standard model disks is most effective in the mass range where the transition from type A to type B occurs. This is also the transitional regime between type I and type II migration. If a mechanism prevents the type I migration of low mass Protoplanets, they could then undergo a rapid inward migration at around the transitional mass regime. Such Protoplanets would end up in the inner regions of the disk undergoing type II migration and further accretion potentially becoming sub Jovian close orbiting planets. Noting that more dusty and higher mass cores spend more time at a larger transitional mass that in general favours more rapid migration, such planets are more likely to become close orbiters. We find that the luminosity of the forming Protoplanets during the later stages of gas accretion is dominated by the circumplane- tary disk and protoplanet-disk boundary layer. For final accretion times for one Jupiter mass in the range 10 5−6 y, the luminosities are in the range ∼10 −(3−4) Land the characteristic temperatures are in the range 1000−2000 K. However, the luminosity may reach ∼10 −1.5 Lfor shorter time periods at the faster rates of accretion that could be delivered by the protoplanetary disk.
Shigeru Ida - One of the best experts on this subject based on the ideXlab platform.
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eccentricity evolution through accretion of Protoplanets
arXiv: Earth and Planetary Astrophysics, 2015Co-Authors: Yuji Matsumoto, Makiko Nagasawa, Shigeru IdaAbstract:Most of super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity ("escape eccentricities"). If orbital instability followed by giant impacts among Protoplanets that have migrated from outer region is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the {\it in situ} accretion model has not been studied in detail. Here, we investigate the eccentricity evolution through {\it N}-body simulations. We have found that the merged planets tend to have much smaller eccentricities than the escape eccentricities due to very efficient collision damping. If the protoplanet orbits are initially well separated and their eccentricities are securely increased, an inner protoplanet collides at its apocenter with an outer protoplanet at its pericenter. The eccentricity of the merged body is the smallest for such configuration. Orbital inclinations are also damped by this mechanism and planets tend to share a same orbital plane, which is consistent with {\it Kepler} data. Such efficient collision damping is not found when we start calculations from densely packed orbits of the Protoplanets. If the Protoplanets are initially in the mean-motion resonances, which corresponds to well separated orbits, the {\it in situ} accretion model well reproduces the features of eccentricities and inclinations of multiple super-Earths/Earth systems discovered by RV and {\it Kepler} surveys.
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merging criteria for giant impacts of Protoplanets
The Astrophysical Journal, 2012Co-Authors: Hidenori Genda, Eiichiro Kokubo, Shigeru IdaAbstract:At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized Protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of Protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding Protoplanets always merge. However, recent impact simulations have shown that collisions among Protoplanets are not always merging events, that is, two colliding Protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step toward studying the effects of such imperfect accretion of Protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky Protoplanets. Using the smoothed particle hydrodynamic method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of Protoplanets, γ, the total mass of two Protoplanets, M T, the impact angle, θ, and the impact velocity, v imp. We investigated the critical impact velocity, v cr, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, v cr/v esc, depends on γ and θ, but does not depend on M T, where v esc is the two-body escape velocity. We derived a simple formula for v cr/v esc as a function of γ and θ (Equation (16)), and applied it to the giant impact events obtained by N-body calculations in the previous studies. We found that 40% of these events should not be merging events.
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merging criteria for giant impacts of Protoplanets
arXiv: Earth and Planetary Astrophysics, 2011Co-Authors: Hidenori Genda, Eiichiro Kokubo, Shigeru IdaAbstract:At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized Protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of Protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding Protoplanets always merge. However, recent impact simulations have shown that collisions among Protoplanets are not always merging events, that is, two colliding Protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step towards studying the effects of such imperfect accretion of Protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky Protoplanets. Using the smoothed particle hydrodynamic (SPH) method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of Protoplanets, $\gamma$, the total mass of two Protoplanets, $M_{\rm T}$, the impact angle, $\theta$, and the impact velocity, $v_{\rm imp}$. We investigated the critical impact velocity, $v_{\rm cr}$, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, $v_{\rm cr}/v_{\rm esc}$, depends on $\gamma$ and $\theta$, but does not depend on $M_{\rm T}$, where $v_{\rm esc}$ is the two-body escape velocity. We derived a simple formula for $v_{\rm cr}/v_{\rm esc}$ as a function of $\gamma$ and $\theta$, and applied it to the giant impact events obtained by \textit{N}-body calculations in the previous studies. We found that 40% of these events should not be merging events.
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formation of terrestrial planets from Protoplanets ii statistics of planetary spin
The Astrophysical Journal, 2007Co-Authors: Eiichiro Kokubo, Shigeru IdaAbstract:The final stage of terrestrial planet formation is known as the giant impact stage, where Protoplanets collide with one another to form planets. The initial spin state of terrestrial planets is determined at this stage. We statistically investigate the spin parameters of terrestrial planets assembled from Protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of Protoplanets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We find that the spin angular velocity of the planets is well expressed by a Gaussian distribution, and their obliquity is well expressed by an isotropic distribution. The typical spin angular velocity is given by the critical spin angular velocity for rotational instability under the assumption of perfect accretion in collisions. We show the dependencies of the spin parameters on the initial protoplanet system parameters. The initial orbital separation and velocity anisotropy of Protoplanets barely affect the spin parameters. The bulk density of Protoplanets does not affect the obliquity distribution, while the spin angular velocity increases with the bulk density.
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formation of terrestrial planets from Protoplanets i statistics of basic dynamical properties
The Astrophysical Journal, 2006Co-Authors: Eiichiro Kokubo, Junko Kominami, Shigeru IdaAbstract:The final stage of terrestrial planet formation is known as the giant impact stage, where Protoplanets collide with one another to form planets. As this process is stochastic, in order to clarify it, it is necessary to quantify it statistically. We investigate this final assemblage of terrestrial planets from Protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of Protoplanets. We systematically change the surface density, surface density profile, and orbital separation of the initial protoplanet system, and the bulk density of Protoplanets, while the initial system radial range is fixed at 0.5-1.5 AU. For each initial condition, we perform 20 runs, and from their results we derive the statistical properties of the assembled planets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We show the dependences of the masses and orbital elements of planets on the initial protoplanet system parameters and give their simple empirical fits. The number of planets slowly decreases as the surface density of the initial Protoplanets increases, while the masses of individual planets increase almost linearly. For a steeper surface density profile, large planets tend to form closer to the star. For the parameter ranges that we test, the basic structure of planetary systems depends only slightly on the initial distribution of Protoplanets and the bulk density as long as the total mass is fixed.
Matthew R. Bate - One of the best experts on this subject based on the ideXlab platform.
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migration of Protoplanets with surfaces through discs with steep temperature gradients
Monthly Notices of the Royal Astronomical Society, 2011Co-Authors: Matthew R. Bate, Ben A AyliffeAbstract:We perform three-dimensional self-gravitating radiative transfer simulations of protoplanet migration in circumstellar discs to explore the impact upon migration of the radial temperature profiles in these discs. We model Protoplanets with masses ranging between 10–100 M⊕, in discs with surface density profiles of Σ∝r−1/2, and temperature profiles of the form T∝r−β, where β ranges 0–2. We find that steep (β > 1) temperature profiles lead to outward migration of low-mass Protoplanets in interstellar grain opacity discs, but in more optically thin discs the migration is always inwards. The trend in migration rates with changing β obtained from our models shows good agreement with those obtained using recent analytic descriptions which include consideration of the coorbital torques and their saturation. We find that switching between two models of the protoplanet, one in which accretion acts by evacuating gas and one in which gas piles up on a surface to form an atmosphere, leads to a small shift in the migration rates. If comparing these models in discs with conditions which lead to a marginally inward migration, the small shift can lead to outward migration. However, the direction and speed of migration is dominated by disc conditions rather than by the specific prescription used to model the flow near the protoplanet.
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migration of Protoplanets with surfaces through discs with steep temperature gradients
arXiv: Earth and Planetary Astrophysics, 2011Co-Authors: Matthew R. Bate, Ben A AyliffeAbstract:We perform three-dimensional self-gravitating radiative transfer simulations of protoplanet migration in circumstellar discs to explore the impact upon migration of the radial temperature profiles in these discs. We model Protoplanets with masses ranging between 10-100 M\bigoplus, in discs with surface density profiles of {\Sigma} \varpropto r^-1/2, and temperature profiles of the form T \varpropto r^-{\beta}, where {\beta} ranges 0-2. We find that steep ({\beta} > 1) temperature profiles lead to outward migration of low mass Protoplanets in interstellar grain opacity discs, but in more optically thin discs the migration is always inwards. The trend in migration rates with changing {\beta} obtained from our models shows good agreement with those obtained using recent analytic descriptions which include consideration of the co-orbital torques and their saturation. We find that switching between two models of the protoplanet, one in which accretion acts by evacuating gas and one in which gas piles up on a surface to form an atmosphere, leads to a small shift in the migration rates. If comparing these models in discs with conditions which lead to a marginally inward migration, the small shift can lead to outward migration. However, the direction and speed of migration is dominated by disc conditions rather than by the specific prescription used to model the flow near the protoplanet.
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planet migration self gravitating radiation hydrodynamical models of Protoplanets with surfaces
arXiv: Earth and Planetary Astrophysics, 2010Co-Authors: Ben A Ayliffe, Matthew R. BateAbstract:We calculate radial migration rates of Protoplanets in laminar minimum mass solar nebula discs using three-dimensional self-gravitating radiation hydrodynamical (RHD) models. The Protoplanets are free to migrate, whereupon their migration rates are measured. For low mass Protoplanets (10-50 M_\oplus) we find increases in the migration timescales of up to an order of magnitude between locally-isothermal and RHD models. In the high-mass regime the migration rates are changed very little. These results are arrived at by calculating migration rates in locally-isothermal models, before sequentially introducing self-gravity, and radiative transfer, allowing us to isolate the effects of the additional physics. We find that using a locally-isothermal equation of state, without self-gravity, we reproduce the migration rates obtained by previous analytic and numerical models. We explore the impact of different protoplanet models, and changes to their assumed radii, upon migration. The introduction of self-gravity gives a slight reduction of the migration rates, whilst the inertial mass problem, which has been proposed for high mass Protoplanets with circumplanetary discs, is reproduced. Upon introducing radiative transfer to models of low mass Protoplanets (\approx 10 M_\oplus), modelled as small radius accreting point masses, we find outward migration with a rate of approximately twice the analytic inward rate. However, when modelling such a protoplanet in a more realistic manner, with a surface which enables the formation of a deep envelope, this outward migration is not seen.
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circumplanetary disc properties obtained from radiation hydrodynamical simulations of gas accretion by Protoplanets
arXiv: Earth and Planetary Astrophysics, 2009Co-Authors: Ben A Ayliffe, Matthew R. BateAbstract:We investigate the properties of circumplanetary discs formed in three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by Protoplanets. We determine disc sizes, scaleheights, and density and temperature profiles for different protoplanet masses, in solar nebulae of differing grain opacities. We find that the analytical prediction of circumplanetary disc radii in an evacuated gap (R_Hill/3) from Quillen & Trilling (1998) yields a good estimate for discs formed by high mass Protoplanets. The radial density profiles of the circumplanetary discs may be described by power-laws between r^-2 and r^-3/2. We find no evidence for the ring-like density enhancements that have been found in some previous models of circumplanetary discs. Temperature profiles follow a ~r^-7/10 power-law regardless of protoplanet mass or nebula grain opacity. The discs invariably have large scaleheights (H/r > 0.2), making them thick in comparison with their encompassing circumstellar discs, and they show no flaring.
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Gas accretion on to planetary cores: three-dimensional self-gravitating radiation hydrodynamical calculations
Monthly Notices of the Royal Astronomical Society, 2009Co-Authors: Benjamin Ayliffe, Matthew R. BateAbstract:We present results from three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by planetary cores. In some cases, the accretion flow is resolved down to the surface of the solid core – the first time such simulations have been performed. We investigate the dependence of the gas accretion rate upon the planetary core mass, and the surface density and opacity of the encompassing protoplanetary disc. Accretion of planetesimals is neglected. We find that high-mass Protoplanets are surrounded by thick circumplanetary discs during their gas accretion phase but, contrary to locally isothermal calculations, discs do not form around accreting Protoplanets with masses 50M⊕ when radiation hydrodynamical simulations are performed, even if the grain opacity is reduced from interstellar values by a factor of 100. We find that the opacity of the gas plays a large role in determining the accretion rates for low-mass planetary cores. For example, reducing the opacities from interstellar values by a factor of 100 leads to roughly an order of magnitude increase in the accretion rates for 10–20 M⊕ Protoplanets. The dependence on opacity becomes less important in determining the accretion rate for more massive cores where gravity dominates the effects of thermal support and the protoplanet is essentially accreting at the runaway rate. Increasing the core mass from 10 to 100 M⊕ increases the accretion rate by a factor of ≈50 for interstellar opacities. Beyond ∼100 M⊕, the ability of the protoplanetary disc to supply material to the accreting protoplanet limits the accretion rate, independent of the opacity. Finally, for low-mass planetary cores (20M⊕), we obtain accretion rates that are in agreement with previous one-dimensional quasi-static models. This indicates that three-dimensional hydrodynamical effects may not significantly alter the gas accretion time-scales that have been obtained from quasi-static models.
Masahiro N. Machida - One of the best experts on this subject based on the ideXlab platform.
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gas accretion onto a protoplanet and formation of a gas giant planet
Monthly Notices of the Royal Astronomical Society, 2010Co-Authors: Masahiro N. Machida, Shu-ichiro Inutsuka, Eiichiro Kokubo, Tomoaki MatsumotoAbstract:We investigate gas accretion on to a protoplanet, by considering the thermal effect of gas in three-dimensional hydrodynamical simulations, in which the wide region from a protoplanetary gas disc to a Jovian radius planet is resolved using the nested grid method. We estimate the mass accretion rate and growth time-scale of gas giant planets. The mass accretion rate increases with protoplanet mass for Mp M cri, where Mcri ≡ 0.036 MJup(ap/1au) 0.75 , and MJup and ap are the Jovian mass and the orbital radius, respectively. This accretion rate is typically two orders of magnitude smaller than that in two-dimensional simulations. The growth time-scale of a gas giant planet or the time-scale of the gas accretion on to the protoplanet is about 10 5 yr, that is two orders of magnitude shorter than the growth time-scale of the solid core. The thermal effects barely affect the mass accretion rate because the gravitational energy dominates the thermal energy around the protoplanet. The mass accretion rate obtained in our local simulations agrees quantitatively well with those obtained in global simulations with coarser spatial resolution. The mass accretion rate is mainly determined by the protoplanet mass and the property of the protoplanetary disc. We find that the mass accretion rate is correctly calculated when the Hill or Bondi radius is sufficiently resolved. Using the oligarchic growth of Protoplanets, we discuss the formation time-scale of gas giant planets.
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Gas Accretion onto a Protoplanet and Formation of a Gas Giant Planet
Monthly Notices of the Royal Astronomical Society, 2010Co-Authors: Masahiro N. Machida, Eiichiro Kokubo, Shu-ichiro InutsukaAbstract:We investigate gas accretion onto a protoplanet, by considering the thermal effect of gas in three-dimensional hydrodynamical simulations, in which the wide region from a protoplanetary gas disk to a Jovian radius planet is resolved using the nested-grid method. We estimate the mass accretion rate and growth timescale of gas giant planets. The mass accretion rate increases with protoplanet mass for M_p M_cri, where M_cri = 0.036 M_Jup (a_p/1AU)^0.75, and M_Jup and a_p are the Jovian mass and the orbital radius, respectively. The growth timescale of a gas giant planet or the timescale of the gas accretion onto the protoplanet is about 10^5 yr, that is two orders of magnitude shorter than the growth timescale of the solid core. The thermal effects barely affect the mass accretion rate because the gravitational energy dominates the thermal energy around the protoplanet. The mass accretion rate obtained in our local simulations agrees quantitatively well with those obtained in global simulations with coarser spatial resolution. The mass accretion rate is mainly determined by the protoplanet mass and the property of the protoplanetary disk. We find that the mass accretion rate is correctly calculated when the Hill or Bondi radius is sufficiently resolved. Using the oligarchic growth of Protoplanets, we discuss the formation timescale of gas giant planets.
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thermal effects of circumplanetary disc formation around proto gas giant planets
Monthly Notices of the Royal Astronomical Society, 2009Co-Authors: Masahiro N. MachidaAbstract:The formation of a circumplanetary disc and accretion of angular momentum on to a protoplanetary system are investigated using three-dimensional hydrodynamical simulations. The local region around a protoplanet in a protoplanetary disc is considered with sufficient spatial resolution: the region from outside the Hill sphere to the Jovian radius is covered by the nested-grid method. To investigate the thermal effects of the circumplanetary disc, various equations of state are adopted. Large thermal energy around the protoplanet slightly changes the structure of the circumplanetary disc. Compared with a model adopting an isothermal equation of state, in a model with an adiabatic equation of state, the protoplanet's gas envelope extends farther, and a slightly thick disc appears near the protoplanet. However, different equations of state do not affect the acquisition process of angular momentum for the protoplanetary system. Thus, the specific angular momentum acquired by the system is fitted as a function only of the protoplanet's mass. A large fraction of the total angular momentum contributes to the formation of the circumplanetary disc. The disc forms only in a compact region in very close proximity to the protoplanet. Adapting the results to the Solar system, the proto-Jupiter and Saturn have compact discs in the region of r < 21r Jup (r < 0.028 r H,Jup ) and r < 66r Sat (r < 0.061r H,sat ), respectively, where r Jup (r H,Jup ) and r Sat (r H.Sat ) are the Jovian and Satumian (Hill) radius, respectively. The surface density has a peak in these regions due to the balance between centrifugal force and gravity of the protoplanet. The size of these discs corresponds well to the outermost orbit of regular satellites around Jupiter and Saturn. Regular satellites may form in such compact discs around proto-gas giant planets.
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angular momentum accretion onto a gas giant planet
arXiv: Astrophysics, 2008Co-Authors: Masahiro N. Machida, Shu-ichiro Inutsuka, Eiichiro Kokubo, Tomoaki MatsumotoAbstract:We investigate the accretion of angular momentum onto a protoplanet system using three-dimensional hydrodynamical simulations. We consider a local region around a protoplanet in a protoplanetary disk with sufficient spatial resolution. We describe the structure of the gas flow onto and around the protoplanet in detail. We find that the gas flows onto the protoplanet system in the vertical direction crossing the shock front near the Hill radius of the protoplanet, which is qualitatively different from the picture established by two-dimensional simulations. The specific angular momentum of the gas accreted by the protoplanet system increases with the protoplanet mass. At Jovian orbit, when the protoplanet mass M_p is M_p 1 M_J. The stronger dependence of the specific angular momentum on the protoplanet mass for M_p < 1 M_J is due to thermal pressure of the gas. The estimated total angular momentum of a system of a gas giant planet and a circumplanetary disk is two-orders of magnitude larger than those of the present gas giant planets in the solar system. A large fraction of the total angular momentum contributes to the formation of the circumplanetary disk. We also discuss the satellite formation from the circumplanetary disk.
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Angular Momentum Accretion onto a Gas Giant Planet
The Astrophysical Journal, 2008Co-Authors: Masahiro N. Machida, Shu-ichiro Inutsuka, Eiichiro Kokubo, Tomoaki MatsumotoAbstract:We investigate the accretion of angular momentum onto a protoplanet system using three-dimensional hydrodynamical simulations. We consider a local region around a protoplanet in a protoplanetary disk with sufficiently high spatial resolution. We describe the structure of the gas flow onto and around the protoplanet in detail. We find that the gas flows onto the protoplanet system in the vertical direction, crossing the shock front near the Hill radius of the protoplanet, which is qualitatively different from the picture established by two-dimensional simulations. The specific angular momentum of the gas accreted by the protoplanet system increases with the protoplanet's mass. At a Jovian orbit, when the protoplanet's mass Mp is Mp 1MJup, where MJup is the Jovian mass, the specific angular momentum increases as j ∝ Mp. On the other hand, it increases as j ∝ Mp2/3 when the protoplanet's mass is Mp 1MJup. The stronger dependence of the specific angular momentum on the protoplanet's mass for Mp 1MJup is due to the thermal pressure of the gas. The estimated total angular momentum of a system of a gas giant planet and a circumplanetary disk is 2 orders of magnitude larger than those of the present gas giant planets in the solar system. A large fraction of the total angular momentum contributes to the formation of the circumplanetary disk. We also discuss the formation of satellites from the circumplanetary disk.
