arXiv subjects

Arnaud Pierens

Publications and source records attributed to Arnaud Pierens.

At least 37 records · Page 2Linked to original sources

arXiv2016

Planet Formation Imager (PFI): science vision and key requirements

The Planet Formation Imager (PFI) project aims to provide a strong scientific vision for ground-based optical astronomy beyond the upcoming generation of Extremely Large Telescopes. We make the case that a breakthrough in angular resolution imaging capabilities is required in order to unravel the processes involved in planet formation. PFI will be optimised to provide a complete census of the protoplanet population at all stellocentric radii and over the age range from 0.1 to about 100 Myr. Within this age period, planetary systems undergo dramatic changes and the final architecture of planetary systems is determined. Our goal is to study the planetary birth on the natural spatial scale where the material is assembled, which is the "Hill Sphere" of the forming planet, and to characterise the protoplanetary cores by measuring their masses and physical properties. Our science working group has investigated the observational characteristics of these young protoplanets as well as the migration mechanisms that might alter the system architecture. We simulated the imprints that the planets leave in the disk and study how PFI could revolutionise areas ranging from exoplanet to extragalactic science. In this contribution we outline the key science drivers of PFI and discuss the requirements that will guide the technology choices, the site selection, and potential science/technology tradeoffs.

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arXiv2016

Mapping CO Gas in the GG Tauri A Triple System with 50 AU Spatial Resolution

We aim to unveil the observational imprint of physical mechanisms that govern planetary formation in the young, multiple system GG Tau A. We present ALMA observations of $^{12}$CO and $^{13}$CO 3-2 and 0.9 mm continuum emission with 0.35" resolution. The $^{12}$CO 3-2 emission, found within the cavity of the circumternary dust ring (at radius $< 180$ AU) where no $^{13}$CO emission is detected, confirms the presence of CO gas near the circumstellar disk of GG Tau Aa. The outer disk and the recently detected hot spot lying at the outer edge of the dust ring are mapped both in $^{12}$CO and $^{13}$CO. The gas emission in the outer disk can be radially decomposed as a series of slightly overlapping Gaussian rings, suggesting the presence of unresolved gaps or dips. The dip closest to the disk center lies at a radius very close to the hot spot location at $\sim250-260$~AU. The CO excitation conditions indicate that the outer disk remains in the shadow of the ring. The hot spot probably results from local heating processes. The two latter points reinforce the hypothesis that the hot spot is created by an embedded proto-planet shepherding the outer disk.

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arXiv2015

Fast migration of low-mass planets in radiative discs

Low-mass planets are known to undergo Type I migration and this process must have played a key role during the evolution of planetary systems. Analytical formulae for the disc torque have been derived assuming that the planet evolves on a fixed circular orbit. However, recent work has shown that in isothermal discs, a migrating protoplanet may also experience dynamical corotation torques that scale with the planet drift rate. The aim of this study is to examine whether dynamical corotation torques can also affect the migration of low-mass planets in non-isothermal discs. We performed 2D radiative hydrodynamical simulations to examine the orbital evolution outcome of migrating protoplanets as a function of disc mass. We find that a protoplanet can enter a fast migration regime when it migrates in the direction set by the entropy-related horseshoe drag and when the Toomre stability parameter is less than a threshold value below which the horseshoe region contracts into a tadpole-like region. In that case, an underdense trapped region appears near the planet, with an entropy excess compared to the ambient disc. If the viscosity and thermal diffusivity are small enough so that the entropy excess is conserved during migration, the planet then experiences strong corotation torques arising from the material flowing across the planet orbit. During fast migration, we observe that a protoplanet can pass through the zero-torque line predicted by static torques. We also find that fast migration may help in disrupting the mean-motion resonances that are formed by convergent migration of embryos.

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arXiv2015

Accretion of Uranus and Neptune from inward-migrating planetary embryos blocked by Jupiter and Saturn

Reproducing Uranus and Neptune remains a challenge for simulations of solar system formation. The ice giants' peculiar obliquities suggest that they both suffered giant collisions during their formation. Thus, there must have been an epoch of accretion dominated by collisions among large planetary embryos in the primordial outer solar system. We test this idea using N-body numerical simulations including the effects of a gaseous protoplanetary disk. One strong constraint is that the masses of the ice giants are very similar -- the Neptune/Uranus mass ratio is $\sim1.18$. We show that similar-size ice giants do indeed form by collisions between planetary embryos beyond Saturn. The fraction of successful simulations varies depending on the initial number of planetary embryos in the system, their individual and total masses. Similar-sized ice giants are consistently reproduced in simulations starting with 5-10 planetary embryos with initial masses of $\sim$3-6 ${\rm M_\oplus}$. We conclude that accretion from a population of planetary embryos is a plausible scenario for the origin of Uranus and Neptune.

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arXiv2015

Gas giant planets as dynamical barriers to inward-migrating super-Earths

Planets of 1-4 times Earth's size on orbits shorter than 100 days exist around 30-50% of all Sun-like stars. In fact, the Solar System is particularly outstanding in its lack of "hot super-Earths" (or "mini-Neptunes"). These planets -- or their building blocks -- may have formed on wider orbits and migrated inward due to interactions with the gaseous protoplanetary disk. Here, we use a suite of dynamical simulations to show that gas giant planets act as barriers to the inward migration of super-Earths initially placed on more distant orbits. Jupiter's early formation may have prevented Uranus and Neptune (and perhaps Saturn's core) from becoming hot super-Earths. Our model predicts that the populations of hot super-Earth systems and Jupiter-like planets should be anti-correlated: gas giants (especially if they form early) should be rare in systems with many hot super-Earths. Testing this prediction will constitute a crucial assessment of the validity of the migration hypothesis for the origin of close-in super-Earths.

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arXiv2014

Hot super-Earths and giant planet cores from different migration histories

Planetary embryos embedded in gaseous protoplanetary disks undergo Type I orbital migration. Migration can be inward or outward depending on the local disk properties but, in general, only planets more massive than several $M_\oplus$ can migrate outward. Here we propose that an embryo's migration history determines whether it becomes a hot super-Earth or the core of a giant planet. Systems of hot super-Earths (or mini-Neptunes) form when embryos migrate inward and pile up at the inner edge of the disk. Giant planet cores form when inward-migrating embryos become massive enough to switch direction and migrate outward. We present simulations of this process using a modified N-body code, starting from a swarm of planetary embryos. Systems of hot super-Earths form in resonant chains with the innermost planet at or interior to the disk inner edge. Resonant chains are disrupted by late dynamical instabilities triggered by the dispersal of the gaseous disk. Giant planet cores migrate outward toward zero-torque zones, which move inward and eventually disappear as the disk disperses. Giant planet cores migrate inward with these zones and are stranded at ~1-5 AU. Our model reproduces several properties of the observed extra-solar planet populations. The frequency of giant planet cores increases strongly when the mass in solids is increased, consistent with the observed giant exoplanet - stellar metallicity correlation. The frequency of hot super-Earths is not a function of stellar metallicity, also in agreement with observations. Our simulations can reproduce the broad characteristics of the observed super-Earth population.

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arXiv2014

Outward migration of Jupiter and Saturn in 3:2 or 2:1 resonance in radiative disks: implications for the Grand Tack and Nice models

Embedded in the gaseous protoplanetary disk, Jupiter and Saturn naturally become trapped in 3:2 resonance and migrate outward. This serves as the basis of the Grand Tack model. However, previous hydrodynamical simulations were restricted to isothermal disks, with moderate aspect ratio and viscosity. Here we simulate the orbital evolution of the gas giants in disks with viscous heating and radiative cooling. We find that Jupiter and Saturn migrate outward in 3:2 resonance in modest-mass ($M_{disk} \approx M_{MMSN}$, where MMSN is the "minimum-mass solar nebula") disks with viscous stress parameter $α$ between $10^{-3}$ and $10^{-2} $. In disks with relatively low-mass ($M_{disk} \lesssim M_{MMSN}$) , Jupiter and Saturn get captured in 2:1 resonance and can even migrate outward in low-viscosity disks ($α\le 10^{-4}$). Such disks have a very small aspect ratio ($h\sim 0.02-0.03$) that favors outward migration after capture in 2:1 resonance, as confirmed by isothermal runs which resulted in a similar outcome for $h \sim 0.02$ and $α\le 10^{-4}$. We also performed N-body runs of the outer Solar System starting from the results of our hydrodynamical simulations and including 2-3 ice giants. After dispersal of the gaseous disk, a Nice model instability starting with Jupiter and Saturn in 2:1 resonance results in good Solar Systems analogs. We conclude that in a cold Solar Nebula, the 2:1 resonance between Jupiter and Saturn can lead to outward migration of the system, and this may represent an alternative scenario for the evolution of the Solar System.

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arXiv2014

Disruption of co-orbital (1:1) planetary resonances during gas-driven orbital migration

Planets close to their stars are thought to form farther out and migrate inward due to angular momentum exchange with gaseous protoplanetary disks. This process can produce systems of planets in co-orbital (Trojan or 1:1) resonance, in which two planets share the same orbit, usually separated by 60 degrees. Co-orbital systems are detectable among the planetary systems found by the Kepler mission either directly or by transit timing variations. However, no co-orbital systems have been found within the thousands of Kepler planets and candidates. Here we study the orbital evolution of co-orbital planets embedded in a protoplanetary disk using a grid-based hydrodynamics code. We show that pairs of similar-mass planets in co-orbital resonance are disrupted during large-scale orbital migration. Destabilization occurs when one or both planets is near the critical mass needed to open a gap in the gaseous disk. A confined gap is opened that spans the 60 degree azimuthal separation between planets. This alters the torques imparted by the disk on each planet -- pushing the leading planet outward and the trailing planet inward -- and disrupts the resonance. The mechanism applies to systems in which the two planets' masses differ by a factor of two or less. In a simple flared disk model the critical mass for gap opening varies from a few Earth masses at the inner edge of the disk to 1 Saturn-mass at 5 AU. A pair of co-orbital planets with masses in this range that migrates will enter a region where the planets are at the gap-opening limit. At that point the resonance is disrupted. We therefore predict an absence of planets on co-orbital configurations with masses in the super-Earth to Saturn mass range with similar masses.

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arXiv2013

Making giant planet cores: convergent migration and growth of planetary embryos in non-isothermal discs

Earth-mass bodies are expected to undergo Type I migration directed either inward or outward depending on the thermodynamical state of the protoplanetary disc. Zones of convergent migration exist where the Type I torque cancels out. We study the evolution of multiple protoplanets of a few Earth masses embedded in a non-isothermal protoplanetary disc. The protoplanets are located in the vicinity of a convergence zone located at the transition between two different opacity regimes. Inside the convergence zone, Type I migration is directed outward and outside the zone migration is directed inward. We used a grid-based hydrodynamical code that includes radiative effects. We performed simulations varying the initial number of embryos and tested the effect of including stochastic forces to mimic the effects resulting from turbulence. We also performed N-body runs calibrated on hydrodynamical calculations to follow the evolution on Myr timescales. For a small number of initial embryos (N = 5-7) and in the absence of stochastic forcing, the population of protoplanets migrates convergently toward the zero-torque radius and forms a stable resonant chain that protects embryos from close encounters. In systems with a larger initial number of embryos, or in which stochastic forces were included, these resonant configurations are disrupted. This in turn leads to the growth of larger cores via a phase of giant impacts, after which the system settles to a new stable resonant configuration. Giant planets cores with masses of 10 Earth masses formed in about half of the simulations with initial protoplanet masses of m_p = 3 Earth masses but in only 15% of simulations with m_p = 1 Earth mass. This suggests that if ~2-3 Earth mass protoplanets can form in less than ~1 Myr, convergent migration and giant collisions can grow giant planet cores at Type I migration convergence zones.

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arXiv2013

Making systems of Super Earths by inward migration of planetary embryos

Using N-body simulations with planet-disk interactions, we present a mechanism capable of forming compact systems of hot super Earths such as Kepler 11. Recent studies show that outward migration is common in the inner parts of radiative disks. However we show that two processes naturally tip the balance in favor of inward migration. First the corotation torque is too weak to generate outward migration for planetary embryos less massive than $4\mearth$. Second, system of multiple embryos generate sustained non-zero eccentricities that damp the corotation torque and again favor inward migration. Migration and accretion of planetary embryos in realistic disks naturally produce super Earths in resonant chains near the disk inner edge. Their compact configuration is similar to the observed systems.

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arXiv2013

Migration and gas accretion scenarios for the Kepler 16, 34 and 35 circumbinary planets

Several circumbinary planets have been detected by the Kepler mission. Recent work has emphasized the difficulty of forming these planets at their observed locations. It has been suggested that these planets formed further out in their discs and migrated in to locations where they are observed. We examine the orbital evolution of planets embedded in circumbinary disc models for the three systems Kepler-16, Kepler-34 and Kepler-35. The aims are: to explore the plausibility of a formation scenario in which cores form at large distances from the binaries and undergo inward migration and gas accretion as the gas disc disperses; to determine which sets of disc parameters lead to planets whose final orbits provide reasonable fits to the observed systems. We performed simulations of a close binary system interacting with circumbinary discs with differing aspect ratios, and viscous stress parameters. Once the binary+disc system reaches quasi-equilibrium we embed a planet in the disc and examine its evolution under the action of binary and disc forces. We consider fully-formed planets with masses equal to those inferred from Kepler data, and low-mass cores that migrate and accrete gas while the gas disc is being dispersed. A typical outcome for all systems is stalling of inward migration as the planet enters the inner cavity formed by the binary system. The circumbinary disc becomes eccentric and the disc eccentricity forces the planet into a noncircular orbit. For each of the Kepler-16b, Kepler-34b and Kepler-35b systems we obtain planets whose parameters agree reasonably well with the observational data. The simulations presented here provide support for a formation scenario in which a core forms, migrates inward and accretes gas, but accurate fitting of the observed Kepler systems is likely to require disc models that are significantly more sophisticated in terms of their input physics.

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arXiv2013

Convergence zones for Type I migration: an inward shift for multiple planet systems

Earth-mass planets embedded in gaseous protoplanetary disks undergo Type I orbital migration. In radiative disks an additional component of the corotation torque scaling with the entropy gradient across the horseshoe region can counteract the general inward migration, Type I migration can then be directed either inward or outward depending on the local disk properties. Thus, special locations exist in the disk toward which planets migrate in a convergent way. Here we present N-body simulations of the convergent migration of systems of low-mass (M=1-10 m_earth) planets. We show that planets do not actually converge in convergence zones. Rather, they become trapped in chains of mean motion resonances (MMRs). This causes the planets' eccentricities to increase to high enough values to affect the structure of the horseshoe region and weaken the positive corotation torque. The zero-torque equilibrium point of the resonant chain of planets is determined by the sum of the attenuated corotation torques and unattenuated differential Lindblad torques acting on each planet. The effective convergence zone is shifted inward. Systems with several planets can experience stochastic migration as a whole due to continuous perturbations from planets entering and leaving resonances.

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arXiv2011

Two phase, inward-then-outward migration of Jupiter and Saturn in the gaseous Solar Nebula

It has recently been shown that the terrestrial planets and asteroid belt can be reproduced if the giant planets underwent an inward-then-outward migration (the "Grand Tack"; Walsh et al 2011). Inward migration occurs when Jupiter opens a gap and type II migrates inward. The planets "tack" and migrate outward when Saturn reaches the gap-opening mass and is caught in the 3:2 resonance with Jupiter. The aim is to test the viability of the Grand Tack model and to study the dynamical evolution of Jupiter and Saturn during their growth from 10 Earth masses cores. We have performed numerical simulations using a grid-based hydrodynamical code. Most of our simulations assume an isothermal equation of state for the disk but a subset use a fully-radiative version of the code. For an isothermal disk the two phase migration of Jupiter and Saturn is very robust and independent of the mass-growth history of these planets provided the disk is cool enough. For a radiative disk the we find some outcomes with two phase migrations and others with more complicated behavior. We construct a simple, 1-D model of an evolving viscous disk to calculate the evolution of the disk's radiative properties: the disk transitions from radiative to isothermal from its outermost regions inward in time. We show that a two-phase migration is a natural outcome at late times even under the limiting assumption that isothermal conditions are required. Thus, our simulations provide strong support for the Grand Tack scenario.

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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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arXiv2009

A local prescription for the softening length in self-gravitating gaseous discs

In 2D-simulations of self-gravitating gaseous discs, the potential is often computed in the framework of "softened gravity" initially designed for N-body codes. In this special context, the role of the softening length LAMBDA is twofold: i) to avoid numerical singularities in the integral representation of the potential (i.e., arising when the relative separation vanishes), and ii) to acount for stratification of matter in the direction perpendicular to the disc mid-plane. So far, most studies have considered LAMBDA as a free parameter and various values or formulae have been proposed without much mathematical justification. In this paper, we demonstrate by means of a rigorous calculus that it is possible to define LAMBDA such that the gravitational potential of a flat disc coincides at order zero with that of a geometically thin disc of the same surface density. Our prescription for LAMBDA, valid in the local, axisymmetric limit, has the required properties i) and ii). It is mainly an analytical function of the radius and disc thickness, and is sensitive to the vertical stratification. For mass density profiles considered (namely, profiles expandable over even powers of the altitude), we find that LAMBDA : i) is independant of the numerical mesh, ii) is always a fraction of the local thickness H, iii) goes through a minimum at the singularity (i.e., at null separation), and iv) is such that 0.13 < LAMBDA/H < 0.29 typically (depending on the separation and on density profile). These results should help us to improve the quality of 2D- and 3D-simulations of gaseous discs in several respects (physical realism, accuracy, and computing time).

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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

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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