arXiv subjects

F. S. Masset

Publications and source records attributed to F. S. Masset.

16 recordsLinked to original sources

arXiv2025

Dust-void evolution driven by turbulent dust flux can induce runaway migration of Earth-mass planets

Torques from asymmetric dust structures (so-called dust-void and filamentary structures) formed around low-mass planets embedded in a non turbulent dust-gas disk can exceed the torques produced by the gas disk component, then governing the planet's orbital dynamics. Here, we investigate how these structures (hence the dust torque) change when the effect of turbulent dust diffusion and dust feedback are included, and the direct implications on the migration of Earth-like planets. Using the \textsc{Fargo3D} code, we perform 2D and 3D multifluid hydrodynamic simulations, focusing on a non-migrating planet with the mass $M_p=1.5\,M_\oplus$ in 2D and on migrating planets with $M_p\in[1.5,12]\,M_\oplus$ in 3D. We vary the $δ$-dimensionless diffusivity parameter in the range $[0,3\times10^{-3}]$ and consider three different Stokes numbers $\mathrm{St}=\{0.04,0.26,0.55\}$, which are representative of the gas, transitional and gravity-dominated regimes, respectively. In our 2D models, we find that turbulent diffusion of dust prevents the formation of the dust-void and filamentary structures when $δ>3\times10^{-4}$. Otherwise, dust structures survive turbulent diffusion flow. However, dust and total torques become positive only in transitional and gravity-dominated regimes. In our 3D models, we find that the dust-void is drastically modified and the high-density ring-shaped barrier delineating the dust-void disappears if $δ\gtrsim10^{-4} $, due to the effect of dust turbulent diffusion along with the back-reaction of the dust. For all values of $δ$, the filament in front of the planet is replaced by a low-density trench. Remarkably, as we allow the planets to migrate, the evolving dust-void can drive either runaway migration or outward (inward) oscillatory-torque migration. Our study thus suggests that low-mass Earth-like planets can undergo runaway migration in dusty disks.

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arXiv2024

Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion

Pebbles drifting past a disk-embedded low-mass planet develop asymmetries in their distribution and exert a substantial gravitational torque on the planet, thus modifying its migration rate. Our aim is to assess how the distribution of pebbles and the resulting torque change in the presence of pebble accretion, focusing on its 2D regime. First, we performed 2D high-resolution multi-fluid simulations with Fargo3D but found that they are impractical for resolving pebble accretion due to the smoothing of the planetary gravitational potential. To remove the smoothing and directly trace pebbles accreted by the planet, we developed a new code, Deneb, which evolves an ensemble of pebbles, represented by Lagrangian superparticles, in a steady-state gaseous background. For small and moderate Stokes numbers, St $\lesssim 0.1$, pebble accretion creates two underdense regions with a front-rear asymmetry with respect to the planet. The underdensity trailing the planet is more extended. The resulting excess of pebble mass in front of the planet then makes the pebble torque positive and capable of outperforming the negative gas torque. Pebble accretion thus enables outward migration (previously thought to occur mainly for St $\gtrsim 0.1$) in a larger portion of the parameter space. It occurs for the planet mass $M_{pl}\lesssim3\,M_{\oplus}$ and for all the Stokes numbers considered in our study, St $\in$ [$10^{-2}, 0.785$], assuming a pebble-to-gas mass ratio of $Z = 0.01$. If some of the observed planets underwent outward pebble-driven migration during their accretion, the formation sites of their progenitor embryos could have differed greatly from the usual predictions of planet formation models. To enable an update of the respective models, we provide a scaling law for the pebble torque that can be readily incorporated in N-body simulations.

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arXiv2024

A close pair of orbiters embedded in a gaseous disk: the repulsive effect

We develop a theoretical framework and use two-dimensional hydrodynamical simulations to study the repulsive effect between two close orbiters embedded in an accretion disk. We consider orbiters on fixed Keplerian orbits with masses low enough to open shallow gaps. The simulations indicate that the repulsion is larger for more massive orbiters and decreases with the orbital separation and the disk's viscosity. We use two different assumptions to derive theoretical scaling relations for the repulsion. A first scenario assumes that each orbiter absorbs the angular momentum deposited in its horseshoe region by the companion's wake. A second scenario assumes that the corotation torques of the orbiters are modified because the companion changes the underlying radial gradient of the disk surface density. We find a substantial difference between the predictions of these two scenarios. The first one fails to reproduce the scaling of the repulsion with the disk viscosity and generally overestimates the strength of the repulsion. The second scenario, however, gives results that are broadly consistent with those obtained in the simulations.

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arXiv2023

On the interaction of pebble accreting embryos with the gaseous disc: importance of thermal forces

A planetary embryo embedded in a gaseous disc can grow by pebble accretion while subjected to a gravitational force from the disc that changes its orbital elements. Usually, that force is considered to arise from the Lindblad and corotation resonances with the embryo. However, more important contributions exist for low-mass planets. Radiative thermal diffusion in the vicinity of embryos yields an additional contribution to the disc's force that damps the eccentricity and inclination much more vigorously than the resonant interaction with the disc, and that in general induces fast inward migration. In addition, the irradiation of the disc by a hot embryo gives rise to an additional contribution that excites eccentricity and inclination, and induces outward migration. Which of the two contributions dominates depends on the embryo's luminosity. We assess the importance of these contributions (termed thermal forces) on the dynamics and growth of a set of pebble-accreting embryos initially of Martian mass, by means of N-body simulations that include analytic expressions for the disc's force. We find very different outcomes for the embryos subjected to thermal forces and those subjected only to resonant forces. Importantly, we find that the median final mass of the embryos subjected to thermal forces is nearly independent of the metallicity, whereas this mass roughly scales with the metallicity when they are subjected only to resonant forces. These results can be explained by the strong damping of eccentricity and inclination at low metallicity, which enhances the embryos' accretion efficiency.

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arXiv2023

Evolution of the eccentricity and inclination of low-mass planets subjected to thermal forces: a numerical study

By means of three dimensional, high resolution hydrodynamical simulations we study the orbital evolution of weakly eccentric or inclined low-mass protoplanets embedded in gaseous discs subject to thermal diffusion. We consider both non-luminous planets, and planets that also experience the radiative feedback from their own luminosity. We compare our results to previous analytical work, and find that thermal forces (the contribution to the disc's force arising from thermal effects) match those predicted by linear theory within $\sim 20$%. When the planet's luminosity exceeds a threshold found to be within $10$% of that predicted by linear theory, its eccentricity and inclination grow exponentially, whereas these quantities undergo a strong damping below this threshold. In this regime of low luminosity indeed, thermal diffusion cools the surroundings of the planet and allows gas to accumulate in its vicinity. It is the dynamics of this gas excess that contributes to damp eccentricity and inclination. The damping rates obtained can be up to $h^{-1}$ times larger than those due to the resonant interaction with the disc, where $h$ is the disc's aspect ratio. This suggests that models that incorporate planet-disc interactions using well-known formulae based on resonant wave-launching to describe the evolution of eccentricity and inclination underestimate the damping action of the disc on the eccentricity and inclination of low-mass planets by an order of magnitude.

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arXiv2019

Thermal torque effects on the migration of growing low-mass planets

As planets grow the exchange of angular momentum with the gaseous component of the protoplanetary disc produces a net torque resulting in a variation of the semi-major axis of the planet. For low-mass planets not able to open a gap in the gaseous disc this regime is known as type I migration. Pioneer works studied this mechanism in isothermal discs finding fast inward type I migration rates that were unable to reproduce the observed properties of extrasolar planets. In the last years, several improvements have been made in order to extend the study of type I migration rates to non-isothermal discs. Moreover, it was recently shown that if the planet's luminosity due to solid accretion is taken into account, inward migration could be slowed down and even reversed. In this work, we study the planet formation process incorporating, and comparing, updated type I migration rates for non-isothermal discs and the role of planet's luminosity over such rates. We find that the latter can have important effects on planetary evolution, producing a significant outward migration for the growing planets.

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arXiv2017

Gap formation by inclined massive planets in locally isothermal three-dimensional discs

We study gap formation in gaseous protoplanetary discs by a Jupiter mass planet. The planet's orbit is circular and inclined relative to the midplane of the disc. We use the impulse approximation to estimate the gravitational tidal torque between the planet and the disc, and infer the gap profile. For low-mass discs, we provide a criterion for gap opening when the orbital inclination is $\leq 30^{\circ}$. Using the FARGO3D code, we simulate the disc response to an inclined massive planet. The dependence of the depth and width of the gap obtained in the simulations on the inclination of the planet is broadly consistent with the scaling laws derived in the impulse approximation. Although we mainly focus on planets kept on fixed orbits, the formalism permits to infer the temporal evolution of the gap profile in cases where the inclination of the planet changes with time. This study may be useful to understand the migration of massive planets on inclined orbit, because the strength of the interaction with the disc depends on whether a gap is opened or not.

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arXiv2012

On type-I migration near opacity transitions. A generalized Lindblad torque formula for planetary population synthesis

We give an expression for the Lindblad torque acting on a low-mass planet embedded in a protoplanetary disk that is valid even at locations where the surface density or temperature profile cannot be approximated by a power law, such as an opacity transition. At such locations, the Lindblad torque is known to suffer strong deviation from its standard value, with potentially important implications for type I migration, but the full treatment of the tidal interaction is cumbersome and not well suited to models of planetary population synthesis. The expression that we propose retains the simplicity of the standard Lindblad torque formula and gives results that accurately reproduce those of numerical simulations, even at locations where the disk temperature undergoes abrupt changes. Our study is conducted by means of customized numerical simulations in the low-mass regime, in locally isothermal disks, and compared to linear torque estimates obtained by summing fully analytic torque estimates at each Lindblad resonance. The functional dependence of our modified Lindblad torque expression is suggested by an estimate of the shift of the Lindblad resonances that mostly contribute to the torque, in a disk with sharp gradients of temperature or surface density, while the numerical coefficients of the new terms are adjusted to seek agreement with numerics. As side results, we find that the vortensity related corotation torque undergoes a boost at an opacity transition that can counteract migration, and we find evidence from numerical simulations that the linear corotation torque has a non-negligible dependency upon the temperature gradient, in a locally isothermal disk.

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arXiv2009

On the horseshoe drag of a low-mass planet. I - Migration in isothermal disks

We investigate the unsaturated horseshoe drag exerted on a low-mass planet by an isothermal gaseous disk. In the globally isothermal case, we use a formal- ism, based on the use of a Bernoulli invariant, that takes into account pressure effects, and that extends the torque estimate to a region wider than the horse- shoe region. We find a result that is strictly identical to the standard horseshoe drag. This shows that the horseshoe drag accounts for the torque of the whole corotation region, and not only of the horseshoe region, thereby deserving to be called corotation torque. We find that evanescent waves launched downstream of the horseshoe U-turns by the perturbations of vortensity exert a feed-back on the upstream region, that render the horseshoe region asymmetric. This asymmetry scales with the vortensity gradient and with the disk's aspect ratio. It does not depend on the planetary mass, and it does not have any impact on the horseshoe drag. Since the horseshoe drag has a steep dependence on the width of the horseshoe region, we provide an adequate definition of the width that needs to be used in horseshoe drag estimates. We then consider the case of locally isothermal disks, in which the tempera- ture is constant in time but depends on the distance to the star. The horseshoe drag appears to be different from the case of a globally isothermal disk. The difference, which is due to the driving of vortensity in the vicinity of the planet, is intimately linked to the topology of the flow. We provide a descriptive inter- pretation of these effects, as well as a crude estimate of the dependency of the excess on the temperature gradient.

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arXiv2009

On the horseshoe drag of a low-mass planet. II Migration in adiabatic disks

We evaluate the horseshoe drag exerted on a low-mass planet embedded in a gaseous disk, assuming the disk's flow in the coorbital region to be adiabatic. We restrict this analysis to the case of a planet on a circular orbit, and we assume a steady flow in the corotating frame. We also assume that the corotational flow upstream of the U-turns is unperturbed, so that we discard saturation effects. In addition to the classical expression for the horseshoe drag in barotropic disks, which features the vortensity gradient across corotation, we find an additional term which scales with the entropy gradient, and whose amplitude depends on the perturbed pressure at the stagnation point of the horseshoe separatrices. This additional torque is exerted by evanescent waves launched at the horseshoe separatrices, as a consequence of an asymmetry of the horseshoe region. It has a steep dependence on the potential's softening length, suggesting that the effect can be extremely strong in the three dimensional case. We describe the main properties of the coorbital region (the production of vortensity during the U-turns, the appearance of vorticity sheets at the downstream separatrices, and the pressure response), and we give torque expressions suitable to this regime of migration. Side results include a weak, negative feed back on migration, due to the dependence of the location of the stagnation point on the migration rate, and a mild enhancement of the vortensity related torque at large entropy gradient.

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arXiv2006

On the migration of protogiant solid cores

The increase of computational resources has recently allowed high resolution, three dimensional calculations of planets embedded in gaseous protoplanetary disks. They provide estimates of the planet migration timescale that can be compared to analytical predictions. While these predictions can result in extremely short migration timescales for cores of a few Earth masses, recent numerical calculations have given an unexpected outcome: the torque acting on planets with masses between 5 M_Earth and 20 M_Earth is considerably smaller than the analytic, linear estimate. These findings motivated the present work, which investigates existence and origin of this discrepancy or ``offset'', as we shall call it, by means of two and three dimensional numerical calculations. We show that the offset is indeed physical and arises from the coorbital corotation torque, since (i) it scales with the disk vortensity gradient, (ii) its asymptotic value depends on the disk viscosity, (iii) it is associated to an excess of the horseshoe zone width. We show that the offset corresponds to the onset of non-linearities of the flow around the planet, which alter the streamline topology as the planet mass increases: at low mass the flow non-linearities are confined to the planet's Bondi sphere whereas at larger mass the streamlines display a classical picture reminiscent of the restricted three body problem, with a prograde circumplanetary disk inside a ``Roche lobe''. This behavior is of particular importance for the sub-critical solid cores (M <~ 15 M_Earth) in thin (H/r <~0.06) protoplanetary disks. Their migration could be significantly slowed down, or reversed, in disks with shallow surface density profiles.

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arXiv2006

Disk-Planet Interactions During Planet Formation

The discovery of close orbiting extrasolar giant planets led to extensive studies of disk planet interactions and the forms of migration that can result as a means of accounting for their location. Early work established the type I and type II migration regimes for low mass embedded planets and high mass gap forming planets respectively. While providing an attractive means of accounting for close orbiting planets intially formed at several AU, inward migration times for objects in the earth mass range were found to be disturbingly short, making the survival of giant planet cores an issue. Recent progress in this area has come from the application of modern numerical techniques which make use of up to date supercomputer resources. These have enabled higher resolution studies of the regions close to the planet and the initiation of studies of planets interacting with disks undergoing MHD turbulence. This work has led to indications of how the inward migration of low to intermediate mass planets could be slowed down or reversed. In addition, the possibility of a new very fast type III migration regime, that can be directed inwards or outwards, that is relevant to partial gap forming planets in massive disks has been investigated.

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arXiv2003

Runaway migration and the formation of hot Jupiters

[Abridged] We evaluate the coorbital corotation torque on a migrating protoplanet. The coorbital torque is assumed to come from orbit crossing fluid elements which exchange angular momentum with the planet when they execute a U-turn at the end of horseshoe streamlines. When the planet migrates inward, the fluid elements of the inner disk undergo one such exchange as they pass to the outer disk. The angular momentum they gain is removed from the planet, and this corresponds to a negative contribution to the corotation torque, which scales with the drift rate. In addition, the material trapped in the coorbital region drifts radially with the planet giving a positive contribution to the corotation torque, which also scales with the drift rate. These two contributions do not cancel out if the coorbital region is depleted, in which case there is a net corotation torque which scales with the drift rate and the mass deficit in the coorbital region, and which has same sign as the drift rate. This leads to a positive feedback on the migrating planet. In particular, if the coorbital mass deficit is larger than the planet mass, the migration rate undergoes a runaway which can vary the protoplanet semi-major axis by 50% over a few tens of orbits. This can happen only if the planet mass is sufficient to create a dip or gap in its surrounding region, and if the surrounding disk mass is larger than the planet mass. This typically corresponds to planet masses in the sub-Saturnian to Jovian mass range embedded in massive protoplanetary disks. Runaway migration is a good candidate to account for the orbital characteristics of close orbiting giant planets, most of which have sub-Jovian masses. Further, we show that in the runaway regime, migration can be directed outwards.

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arXiv2002

On the Spiral Structure of NGC 2915 and Dark Matter

NGC 2915 is a blue compact dwarf galaxy embedded in an extended, low surface brightness HI disk exhibiting a two-armed spiral structure and a central bar-like component. Commonly accepted mechanisms are unable to explain the existence of these patterns and Bureau et al. proposed disk dark matter (scaling with the HI distribution) or a rotating triaxial dark halo as alternative solutions. In an attempt to explore these mechanisms, hydrodynamical simulations were run for each case and compared to observations using customized column density and kinematic constraints. The spiral structure can be accounted for both by an unseen bar or triaxial halo, the former fitting the observations slightly better. However, the large bar mass or halo pattern frequency required make it unlikely that the spiral wave is driven by an external perturber. In particular, the spin parameter is much higher than predicted by current cold dark matter (CDM) structure formation scenarios. The massive disk models show that when the observed gas surface density is scaled up by a factor about 10, the disk develops a spiral structure resembling closely the observed one, in perturbed density as well as perturbed velocity. This is consistent with more limited studies in other galaxies and suggests that the disk of NGC 2915 contains much more mass than is visible, tightly linked to the neutral hydrogen. A classic (quasi-)spherical halo is nevertheless still required, as increasing the disk mass further to fit the circular velocity curve would make the disk violently unstable. Scaling the observed surface density profile by an order of magnitude brings the disk and halo masses to comparable values within the disk radius.

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arXiv2002

The co-orbital corotation torque in a viscous disk: numerical simulations

The torque felt by a non-accreting protoplanet on a circular orbit embedded in a uniform surface density protoplanetary disk is analyzed by means of time-dependent numerical simulations. Varying the viscosity enables one to disentangle the Lindblad torque (which is independent of viscosity) from the corotation torque, which saturates at low viscosity and is unsaturated at high viscosity. The dependence of the corotation torque upon the viscosity and upon the width of the librating zone is compared with previous analytical expressions, and shown to be in agreement with those. The effect of the potential smoothing respectively on the Lindblad torque and on the corotation torque is investigated, and the question of whether 3D effects and their impact on the total torque sign and magnitude can be modeled by an adequate smoothing prescription in a 2D simulation is addressed. As a side result, this study shows that the total torque acting on a Neptune-sized protoplanet is positive in a sufficiently thin, viscous disk (H/r < 4%, α> 10^-2), but the inward migration time of smaller bodies is still very short, making it unlikely that they reach the torque reversal mass before having migrated all the way to the central object.

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arXiv2002

On the coorbital corotation torque in a viscous disk and its impact on planetary migration

We evaluate the coorbital corotation torque on a planet on a fixed circular orbit embedded in a viscous protoplanetary disk, for the case of a steady flow in the planet frame. This torque can be evaluated just from the flow properties at the separatrix between the librating (horseshoe) and circulating streamlines. A stationary solution is searched for the flow in the librating region. When used to evaluate the torque exerted by the circulating material of the outer and inner disk on the trapped material of the librating region, this solution leads to an expression of the coorbital corotation torque in agreement with previous estimates. An analytical expression is given for the corotation torque as a function of viscosity. Lastly, we show that additional terms in the torque expression can play a crucial role. In particular, they introduce a coupling with the disk density profile perturbation (the `dip' which surrounds the planet) and add to the corotation torque a small, positive fraction of the one-sided Lindblad torque. As a consequence, the migration could well be directed outwards in very thin disks (aspect ratio smaller than a few percent). This 2D analysis is especially relevant for mildly embedded protoplanets (sub-Saturn sized objects).

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