arXiv subjects

Richard P. Nelson

Publications and source records attributed to Richard P. Nelson.

At least 91 records · Page 5Linked to original sources

arXiv2010

On the growth and orbital evolution of giant planets in layered protoplanetary disks

We present the results of hydrodynamic simulations of the growth and orbital evolution of giant planets embedded in a protoplanetary disk with a dead-zone. The aim is to examine to what extent the presence of a dead-zone affects the rates of mass accretion and migration for giant planets. We performed 3D numerical simulations using a grid-based hydrodynamics code. In these simulations of non-magnetised disks, the dead-zone is treated as a region where the vertical profile of the viscosity depends on the distance from the equatorial plane. We consider dead-zones with vertical sizes, H_dz, ranging from 0 to H_dz=2.3H, where H is the disk scale-height. For all models, the vertically integrated viscous stress, and the related mass flux through the disk, have the same value, such that the simulations test the dependence of planetary mass accretion and migration on the vertical distribution of the viscous stress. For each model, an embedded 30 earth-masses planet on a fixed circular orbit is allowed to accrete gas from the disk. Once the planet mass becomes equal to that of Saturn or Jupiter, we allow the planet orbit to evolve due to gravitational interaction with the disk. We find that the time scale over which a protoplanet grows to become a giant planet is essentially independent of the dead-zone size, and depends only on the total rate at which the disk viscously supplies material to the planet. For Saturn-mass planets, the migration rate depends only weakly on the size of the dead-zone for H_dz< 1.5H, but becomes slower when H_dz=2.3H. This effect is due to the desaturation of corotation torques which originate from residual material in the partial-gap region. For Jupiter-mass planets, there is a clear tendency for the migration to proceed more slowly as the size of the dead-zone increases.

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arXiv2010

An Investigation on the Morphological Structure of IC59: A New Type of Morphology of BRCs?

With references to recent observational results on the nebula IC59, we applied our previously developed Smoothed Particle Hydrodynamics (SPH) code which is based on Radiative Driven Implosion (RDI) model, to investigate the possible formation mechanism for the observed morphological structures of differently shaped BRCs. The simulation results confirmed the existence of the 4th type morphology of BRCs -- type M BRC. We are able to find the necessary condition for the appearance of the type M BRC based on the fact that the simulated physical properties of the cloud are consistent with observations on IC59. More importantly, the prospect of RDI triggered star formation by RDI model in all of the observed type M BRCs is ruthlessly eliminated.

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arXiv2009

Global MHD simulations of stratified and turbulent protoplanetary discs. II. Dust settling

The aim of this paper is to study the vertical profile of small dust particles in protoplanetary discs in which angular momentum transport is due to MHD turbulence driven by the magnetorotational instability. We consider particle sizes that range from approximately 1 micron up to a few millimeters.We use a grid--based MHD code to perform global two-fluid simulations of turbulent protoplanetary discs which contain dust grains of various sizes. In quasi--steady state, the gravitational settling of dust particles is balanced by turbulent diffusion. Simple and standard models of this process fail to describe accurately the vertical profile of the dust density. The disagreement is larger for small dust particles (of a few microns in size), especially in the disc upper layers ($Z>3H$, where $H$ is the scale-height). Here there can be orders of magnitude in the disagreement between the simple model predictions and the simulation results. This is because MHD turbulence is not homogeneous in accretion discs, since velocity fluctuations increase significantly in the disc upper layer where a strongly magnetized corona develops. We provide an alternative model that gives a better fit to the simulations. In this model, dust particles are diffused away from the midplane by MHD turbulence, but the diffusion coefficient varies vertically and is everywhere proportional to the square of the local turbulent vertical velocity fluctuations. The spatial distribution of dust particles can be used to trace the properties of MHD turbulence in protoplanetary discs, such as the amplitude of the velocity fluctuations. In the future, detailed and direct comparison between numerical simulations and observations should prove a useful tool for constraining the properties of turbulence in protoplanetary discs.

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arXiv2008

On the growth and stability of Trojan planets

We investigate the stability of those low-mass Trojan planets that form in a protoplanetary disc and subsequently accrete gas to become gas giants. We calculate their evolution before, during, and after gas disc dispersal. A two-dimensional hydrodynamics code combined with an N-body solver is used to evolve the system of disc and planets. Gas disc dispersal is simulated in a simple manner by assuming global exponential decay of the disc mass, leading to the stalling of migration after semi-major axes have approximately halved from their initial values. We consider Trojan pairs with different initial masses and gas accretion rates and gas disc models with different masses and viscosities. An N-body code, adapted to model disc forces, is used to examine large-scale migration and the formation of very short period Trojan planets. For each combination of planetary pair and disc model that we consider in our hydrodynamic simulations, each Trojan system remains stable before, during, and after disc dispersal. The long-term stability of these systems in the absence of gas is tested using N-body simulations, and all systems remain stable for those evolution times equal to 10^9 years. Eccentricities remain low (e<0.02) in all cases. Increases in the amplitude of libration about the L4/L5 Lagrange points accompany the inward migration, and during very large-scale migration Trojan systems may be disrupted prior to the onset of disc dispersal. The stability of Trojan pairs during rapid type I migration, during the transition to type II migration with the accompanying gap formation in the gas disc, and during gas loss when the disc disperses, indicates that isolated Trojan planet systems are very stable. If a common mechanism exists for their formation, we suggest they may be readily observed in nature.

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arXiv2008

Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc

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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arXiv2008

On the formation and migration of giant planets in circumbinary discs

We present the results of hydrodynamic simulations of the formation and subsequent orbital evolution of giant planets embedded in a circumbinary disc. We assume that a 20 earth masses core has migrated to the edge of the inner cavity formed by the binary where it remains trapped by corotation torques. This core is then allowed to accrete gas from the disc, and we study its orbital evolution as it grows in mass. For each of the two accretion time scales we considered, we performed three simulations. In two of the three simulations, we stop the accretion onto the planet once its mass becomes characteristic of that of Saturn or Jupiter. In the remaining case, the planet can accrete disc material freely in such a way that its mass becomes higher than Jupiter's. The simulations show different outcomes depending on the final mass m_p of the giant. For m_p=1 M_S (where M_S is Saturn's mass), we find that the planet migrates inward through its interaction with the disc until its eccentricity becomes high enough to induce a torque reversal. The planet then migrates outward, and the system remains stable on long time scales. For m_p > 1 M_J (where M_J is Jupiter's mass) we observed two different outcomes. In each case the planet enters the 4:1 resonance with the binary, and resonant interaction drives up the eccentricity of the planet until it undergoes a close encounter with the secondary star. The result can either be ejection from the system or scattering out into the disc followed by a prolonged period of outward migration. These results suggest that circumbinary planets are more likely to be quite common in the Saturn-mass range. Jupiter-mass circumbinary planets are likely to be less common because of their less stable evolution.

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arXiv2008

Turbulent transport and its effect on the dead zone in protoplanetary discs

Protostellar accretion discs have cool, dense midplanes where externally originating ionisation sources such as X-rays or cosmic rays are unable to penetrate. This suggests that for a wide range of radii, MHD turbulence can only be sustained in the surface layers where the ionisation fraction is sufficiently high. A dead zone is expected to exist near the midplane, such that active accretion only occurs near the upper and lower disc surfaces. Recent work, however, suggests that under suitable conditions the dead zone may be enlivened by turbulent transport of ions from the surface layers into the dense interior. In this paper we present a suite of simulations that examine where, and under which conditions, a dead zone can be enlivened by turbulent mixing. We use three-dimensional, multifluid shearing box MHD simulations, which include vertical stratification, ionisation chemistry, ohmic resistivity, and ionisation due to X-rays from the central protostar. We compare the results of the MHD simulations with a simple reaction-diffusion model. The simulations show that in the absence of gas-phase heavy metals, such as magnesium, turbulent mixing has essentially no effect on the dead zone. The addition of a relatively low abundance of magnesium, however, increases the recombination time and allows turbulent mixing of ions to enliven the dead zone completely beyond a distance of 5 AU from the central star, for our particular disc model. During the late stages of protoplanetary disc evolution, when small grains have been depleted and the disc surface density has decreased below its high initial value, the structure of the dead zone may be significantly altered by the action of turbulent transport.

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arXiv2008

Constraints on resonant-trapping for two planets embedded in a protoplanetary disc

We investigate the evolution of two-planet systems embedded in a protoplanetary disc, which are composed of a Jupiter-mass planet plus another body located further out in the disc. We consider outermost planets with masses ranging from 10 earth masses to 1 M_J. We also examine the case of outermost bodies with masses < 10 earth masses (M_E). Differential migration of the planets due to disc torques leads to different evolution outcomes depending on the mass of the outer protoplanet. For planets with mass < 3.5 M_E the type II migration rate of the giant exceeds the type I migration rate of the outer body, resulting in divergent migration. Outer bodies with masses in the range 3.5 < m_o < 20 M_E become trapped at the edge of the gap formed by the giant planet, because of corotation torques. Higher mass planets are captured into resonance with the inner planet. If 30 < m_o < 40 M_E or m_o=1 M_J, then the 2:1 resonance is established. If 80 < m_o < 100 M_E, the 3:2 resonance is favoured. Simulations of gas-accreting protoplanets of mass m_o > 20 M_E, trapped initially at the edge of the gap, or in the 2:1 resonance, also result in eventual capture in the 3:2 resonance as the planet mass grows to become close to the mass of Saturn. Our results suggest that there is a theoretical lower limit to the mass of an outer planet that can be captured into resonance with an inner Jovian planet, which is relevant to observations of extrasolar multiplanet systems. Furthermore, capture of a Saturn-like planet into the 3:2 resonance with a Jupiter-like planet is a very robust outcome of simulations. This result is relevant to recent scenarios of early Solar System evolution which require Saturn to have existed interior to the 2:1 resonance with Jupiter prior to the onset of the Late Heavy Bombardment.

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arXiv2007

On the evolution of multiple low mass planets embedded in a circumbinary disc

Previous work has shown that the tidal interaction between a binary system and a circumbinary disc leads to the formation of a large inner cavity in the disc. Subsequent formation and inward migration of a low mass planet causes it to become trapped at the cavity edge, where it orbits until further mass growth or disc dispersal. The question of how systems of multiple planets in circumbinary discs evolve has not yet been addressed. Here, we present a suite of simulations which study the evolution of pairs of planets migrating in the disc. We also present the results of hydrodynamic simulations of five-planet systems, and study their long term evolution after disc dispersal using a N-body code. For the two-planet simulations we assume that the innermost planet has migrated to the edge of the inner cavity and remains trapped there, and study the subsequent evolution of the system as the outermost planet migrates inward. We find that the outcomes largely depend on the mass ratio q=m_i/m_o, where m_i (m_o) is the mass of the innermost (outermost) planet. For q<1, planets usually undergo dynamical scattering or orbital exchange. For values of q>1 the systems reach equilibrium configurations in which the planets are locked into mean motion resonances, and remain trapped at the edge of the inner cavity without further migration. Most simulations of five-planet systems we performed resulted in collisions and scattering events, such that only a single planet remained in orbit about the binary. In one case however, a multiplanet resonant system was found to be dynamically stable over long time scales, suggesting that such systems may be observed in planet searches focussed on close binary systems.

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arXiv2007

Building Giant-Planet Cores at a Planet Trap

A well-known bottleneck for the core-accretion model of giant-planet formation is the loss of the cores into the star by Type-I migration, due to the tidal interactions with the gas disk. It has been shown that a steep surface-density gradient in the disk, such as the one expected at the boundary between an active and a dead zone, acts as a planet trap and prevents isolated cores from migrating down to the central star. We study the relevance of the planet trap concept for the accretion and evolution of systems of multiple planetary embryos/cores. We performed hydrodynamical simulations of the evolution of systems of multiple massive objects in the vicinity of a planet trap. The planetary embryos evolve in 3 dimensions, whereas the disk is modeled with a 2D grid. Synthetic forces are applied onto the embryos to mimic the damping effect that the disk has on their inclinations. Systems with two embryos tend to acquire stable, separated and non-migrating orbits, with the more massive embryo placed at the planet trap and the lighter one farther out in the disk. Systems of multiple embryos are intrinsically unstable. Consequently, a long phase of mutual scattering can lead to accreting collisions among embryos; some embryos are injected into the inner part of the disk, where they can be evacuated into the star by Type I migration. The system can resume a stable, non-migrating configuration only when the number of surviving embryos decreases to a small value (~2-4). This can explain the limited number of giant planets in our solar system. These results should apply in general to any case in which the Type-I migration of the inner embryo is prevented by some mechanism, and not solely to the planet trap scenario.

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arXiv2007

Can Terrestrial Planets Form in Hot-Jupiter Systems?

Models of terrestrial planet formation in the presence of a migrating giant planet have challenged the notion that hot-Jupiter systems lack terrestrial planets. We briefly review this issue and suggest that hot-Jupiter systems should be prime targets for future observational missions designed to detect Earth-sized and potentially habitable worlds.

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arXiv2007

On the migration of protoplanets embedded in circumbinary disks

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. 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 5, 10 and 20 Earth masses. 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 positve 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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arXiv2007

The effect of type I migration on the formation of terrestrial planets in hot-Jupiter systems

Context: Our previous models of a giant planet migrating through an inner protoplanet/planetesimal disk find that the giant shepherds a portion of the material it encounters into interior orbits, whilst scattering the rest into external orbits. Scattering tends to dominate, leaving behind abundant material that can accrete into terrestrial planets. Aims: We add to the possible realism of our model by simulating type I migration forces which cause an inward drift, and strong eccentricity and inclination damping of protoplanetary bodies. This extra dissipation might be expected to enhance shepherding at the expense of scattering, possibly modifying our previous conclusions. Methods: We employ an N-body code that is linked to a viscous gas disk algorithm capable of simulating: gas accretion onto the central star; gap formation in the vicinity of the giant planet; type II migration of the giant planet; type I migration of protoplanets; and the effect of gas drag on planetesimals. We use the code to re-run three scenarios from a previous work where type I migration was not included. Results: The additional dissipation introduced by type I migration enhances the inward shepherding of material but does not severely reduce scattering. We find that > 50% of the solids disk material still survives the migration in scattered exterior orbits: most of it well placed to complete terrestrial planet formation at < 3 AU. The shepherded portion of the disk accretes into hot-Earths, which survive in interior orbits for the duration of our simulations. Conclusions: Water-rich terrestrial planets can form in the habitable zones of hot-Jupiter systems and hot-Earths and hot-Neptunes may also be present. These systems should be targets of future planet search missions.

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arXiv2007

On the evolution of eccentric and inclined protoplanets embedded in protoplanetary disks

Young planets embedded in their protoplanetary disk interact gravitationally with it leading to energy and angular momentum exchange. This interaction determines the evolution of the planet through changes to the orbital parameters. We investigate changes in the orbital elements of a 20 Earth--mass planet due to the torques from the disk. We focus on the non-linear evolution of initially non-vanishing eccentricity $e$ and/or inclination $i$. We treat the disk as a two- or three-dimensional viscous fluid and perform hydrodynamical simulations with an embedded planet. We find rapid exponential decay of the planet orbital eccentricity and inclination for small initial values of $e$ and $i$, in agreement with linear theory. For larger values of $e > 0.1$ the decay time increases and the decay rate scales as $\dot{e} \propto e^{-2}$, consistent with existing theoretical models. For large inclinations ($i$ > 6 deg) the inclination decay rate shows an identical scaling $di/dt \propto i^{-2}$. We find an interesting dependence of the migration on the eccentricity. In a disk with aspect ratio $H/r=0.05$ the migration rate is enhanced for small non-zero eccentricities ($e < 0.1$), while for larger values we see a significant reduction by a factor of $\sim 4$. We find no indication for a reversal of the migration for large $e$, although the torque experienced by the planet becomes positive when $e \simeq 0.3$. This inward migration is caused by the persisting energy loss of the planet. For non gap forming planets, eccentricity and inclination damping occurs on a time scale that is very much shorter than the migration time scale. The results of non linear hydrodynamic simulations are in very good agreement with linear theory for small $e$ and $i$.

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arXiv2006

On the formation of terrestrial planets in hot-Jupiter systems

We present a series of calculations aimed at examining how an inner system of planetesimals/protoplanets, undergoing terrestrial planet formation, evolves under the influence of a giant planet undergoing inward type II migration through the region bounded between 5 - 0.1 AU. We find that > 60% of the solids disk survives by being scattered by the giant planet into external orbits. Planetesimals are scattered outward almost as efficiently as protoplanets, resulting in the regeneration of a solids disk where dynamical friction is strong and terrestrial planet formation is able to resume. A simulation extended for a few Myr after the migration of the giant planet halted at 0.1 AU, resulted in an apparently stable planet of ~ 2 Earth masses forming in the habitable zone. Migration-induced mixing of volatile-rich material from beyond the `snowline' into the inner disk regions means that terrestrial planets that form there are likely to be water-rich. We predict that hot--Jupiter systems are likely to harbor water-rich terrestrial planets in their habitable zones. These planets may be detected by future planet search missions.

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arXiv2006

Global MHD simulations of stratified and turbulent protoplanetary discs. I. Model properties

We present the results of global 3-D MHD simulations of stratified and turbulent protoplanetary disc models. The aim of this work is to develop thin disc models capable of sustaining turbulence for long run times, which can be used for on-going studies of planet formation in turbulent discs. The results are obtained using two codes written in spherical coordinates: GLOBAL and NIRVANA. Both are time--explicit and use finite differences along with the Constrained Transport algorithm to evolve the equations of MHD. In the presence of a weak toroidal magnetic field, a thin protoplanetary disc in hydrostatic equilibrium is destabilised by the magnetorotational instability (MRI). When the resolution is large enough (25 vertical grid cells per scale height), the entire disc settles into a turbulent quasi steady-state after about 300 orbits. Angular momentum is transported outward such that the standard alpha parameter is roughly 4-6*10^{-3}. We find that the initial toroidal flux is expelled from the disc midplane and that the disc behaves essentially as a quasi-zero net flux disc for the remainder of the simulation. As in previous studies, the disc develops a dual structure composed of an MRI--driven turbulent core around its midplane, and a magnetised corona stable to the MRI near its surface. By varying disc parameters and boundary conditions, we show that these basic properties of the models are robust. The high resolution disc models we present in this paper achieve a quasi--steady state and sustain turbulence for hundreds of orbits. As such, they are ideally suited to the study of outstanding problems in planet formation such as disc--planet interactions and dust dynamics.

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arXiv2006

On the ionisation fraction in protoplanetary disks III. The effect of X-ray flares on gas-phase chemistry

Context. Recent observations of the X-ray emission from T Tauri stars in the Orion nebula have shown that they undergo frequent outbursts in their X-ray luminosity. These X-ray flares are characterised by increases in luminosity by two orders of magnitude, a typical duration of less than one day, and a significant hardening of the X-ray spectrum. Aims. It is unknown what effect these X-ray flares will have on the ionisation fraction and dead-zone structure in protoplanetary disks. We present the results of calculations designed to address this question. Methods. We have performed calculations of the ionisation fraction in a standard $α$-disk model using two different chemical reaction networks. We include in our models ionisation due to X-rays from the central star, and calculate the time-dependent ionisation fraction and dead--zone structure for the inner 10 AU of a protoplanetary disk model. Results. We find that the disk response to X-ray flares depends on whether the plasma temperature increases during flares and/or whether heavy metals (such as magnesium) are present in the gas phase. Under favourable conditions the outer disk dead--zone can disappear altogether,and the dead-zone located between 0.5 < R < 2 AU can disappear and reappear in phase with the X-ray luminosity. Conclusions. X-ray flares can have a significant effect on the dead-zone structure in protoplanetary disks. Caution is required in interpreting this result as the duration of X-ray bursts is considerably shorter than the growth time of MHD turbulence due to the magnetorotational instability.

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arXiv2005

On the Ionisation Fraction in Protoplanetary Disks I: Comparing Different Reaction Networks

We calculate the ionisation fraction in protostellar disk models using a number of different chemical reaction networks, including gas-phase and gas-grain reaction schemes. The disk models we consider are conventional alpha-disks, which include viscous heating and radiative cooling. The primary source of ionisation is assumed to be X-ray irradiation from the central star. We consider a number of gas-phase chemical networks. In general we find that the simple models predict higher fractional ionisation levels and more extensive active zones than the more complex models. When heavy metal atoms are included the simple models predict that the disk is magnetically active throughout. The complex models predict that extensive regions of the disk remain magnetically uncoupled even with a fractional abundance of magnesium of 10(-8). The addition of submicron sized grains with a concentration of 10(-12) causes the size of the dead zone to increase dramatically for all kinetic models considered. We find that the simple and complex gas-grain reaction schemes agree on the size and structure of the resulting dead zone. We examine the effects of depleting the concentration of small grains as a crude means of modeling the growth of grains during planet formation. We find that a depletion factor of 10(-4) causes the gas-grain chemistry to converge to the gas-phase chemistry when heavy metals are absent. 10(-8) is required when magnesium is included. This suggests that efficient grain growth and settling will be required in protoplanetary disks, before a substantial fraction of the disk mass in the planet forming zone between 1 - 10 AU becomes magnetically active and turbulent.

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