arXiv subjects

Sijme-Jan Paardekooper

Publications and source records attributed to Sijme-Jan Paardekooper.

At least 19 recordsLinked to original sources

arXiv2026

Dust-driven vertical shear instability in an isothermal shearing box: I. Turbulence and gas dynamics without dust feedback

The classical vertical shear instability (VSI) is a baroclinic instability that arises from height-dependent azimuthal velocities and is a leading candidate for driving anisotropic turbulence in discs with extended vertical modes. The classical VSI requires fast cooling times and radial temperature gradients, which are absent in an isothermal stratified (barotropic) setup. We investigate the dust-driven vertical shear instability in an isothermal, stratified shearing box, where the VSI is generated by drag forces acting on the gas due to dust rather than radial thermal stratification. We construct two-fluid (gas+dust) vertically stratified equilibria including dust diffusion and use these profiles to initialise 2D (radial-vertical) hydrodynamical simulations with FARGO3D. To separate dust-driven vertical shear instability (DVSI) from drag instabilities, we employ a dust-analogue model in which dust-induced drag on the gas is prescribed as a time-invariant and height-dependent acceleration, such that the underlying spatial distribution of the dust is assumed to be constant. The DVSI grows from regions of strongest vertical shear away from the midplane, exciting predominantly radially short, vertically extended disturbances (large k_x/k_z) and producing banded structures in the perturbed azimuthal and vertical velocities during the linear phase. In the nonlinear regime, the instability saturates via a Kelvin-Helmholtz-like parasitic instability that breaks the coherent vertical-shear modes into smaller-scale eddies, which balance the growth of the vertically extended modes, driving sustained vertical stirring. Dust-driven vertical shear can drive anisotropic turbulence and vertical mixing in an isothermal model without invoking global thermal gradients and could play an important role in the stratified streaming instability.

astro-ph.EP↗

arXiv2026

A Comparative Study of the Streaming Instability: Unstratified Models with Marginally Coupled Grains

The streaming instability is a leading mechanism for concentrating solids and initiating planetesimal formation in protoplanetary disks. Although numerous studies have explored its linear growth, nonlinear evolution, and implications for planet formation, the diversity of numerical methods and dust treatments used across the literature has made it difficult to assess which features of the instability are physically robust and which arise from code-dependent choices. We present the first systematic comparison of seven hydrodynamic codes--spanning finite-volume and finite-difference schemes and modeling dust either as Lagrangian particles or as a pressureless fluid--applied to the unstratified streaming instability with a dimensionless stopping time of unity. All codes reproduce the characteristic sequence of exponential growth, filament formation, and turbulent saturation, demonstrating broad agreement in the qualitative behavior of the instability. Quantitatively, however, the dust model remains the dominant source of variation at moderate resolution: particle-based simulations reach higher peak densities and exhibit broader high-density tails than fluid-based models at $512^2$ resolution, although increasing the number of particles brings their initial maximum density evolution into close agreement with that of dust-fluid models. At $1024^2$, these differences diminish substantially, indicating better agreement of the saturated-state statistics across dust treatments. In terms of computational performance, most particle implementations suffer from imbalanced parallelized loads, while execution on a GPU is at least two to three times more energy efficient and scales better at higher resolutions than on CPUs. Given the intrinsic stochasticity of this nonlinear system, only statistical diagnostics remain meaningful across codes.

astro-ph.EP↗

arXiv2026

Hydrodynamical Simulations of Resonant Breaking in Multi-Planet Systems via Rebound Migration During Disk Dispersal

This study extends the investigation of rebound outward migration to multi-planet systems near an inner expanding disk cavity driven by stellar X-ray photoevaporation. Using 2D hydrodynamical simulations, we explore how systems of two and three planets that span masses from super-Earths to Jupiters evolve as the disk disperses from the inside out. Our results show that rebound migration can substantially reshape multi-planet architectures in the final stages of disk clearing. Owing to the strong, positive corotation torque exerted onto the planet near the cavity edge, divergent migration of the neighbouring planets can break resonant configurations and trigger dynamical instabilities, producing non-resonant orbits with widened period ratios. However, the outcome depends critically on planet mass and the disk dispersal timescale. In lower-mass disks where cavity expansion is too rapid, rebound migration is suppressed, and systems tend to preserve resonant chains. These findings suggest that the rebound mechanism can provide a compelling pathway to explain the prevalence of widely separated, non-resonant architecture observed in the exoplanet population.

astro-ph.EP↗

arXiv2025

Formation of cold giant planets around late M dwarfs via core accretion and the fate of inner rocky worlds

Modeling the formation of cold giant planets around M dwarfs is difficult because their disks may not contain enough solids to form massive cores and because forming giants are expected to migrate inward through disk interactions. It is also unclear whether inner rocky planets can survive in systems hosting a cold giant, with implications for the habitability of close-in worlds. We investigated the conditions that allow giant planets to form at 1-3 au around a 0.1 M$_\odot$ star and explored when a close-in rocky planet can survive. We perform N-body simulations in which embryos grow through pebble and gas accretion in a disk with a local turbulent viscosity of $α_t = 10^{-4}$. Planet-disk interactions are included using a prescription that triggers outward migration when the planet-to-star mass ratio ($q$) exceeds 0.002. We find that a cold giant can form even in a disk with an initial pebble mass of 6 M$_\oplus$ if the disk gas mass is 10$\%$ of the stellar mass. This requires a compact 20 au disk with a dense inner region set by $α_g = 10^{-4}$, the assembly of a $\sim$5 M$_\oplus$ core within 1 Myr, and a disk lifetime of 10 Myr. A close-in rocky planet can survive if it reaches the inner cavity before the outer body becomes a giant. Thus, giant planet formation around very low-mass stars does not require high dust masses as previously thought. A combination of planet-planet collisions, efficient pebble accretion, and a long disk lifetime plays a key role in enabling the formation of cold giant planets with masses between those of Saturn and Jupiter.

astro-ph.EP↗

arXiv2025

New migration patterns in high planet-star mass ratio systems in disks with low viscosity

Migration of giant planets remains a complex topic. While significant progress has been made for high-viscosity disks, the migration of planets with large planet-star mass ratios in low-viscosity environments is still not fully understood. We study the migration of such planets in disks with $α= 10^{-4}$ and derive analytical prescriptions applicable across stellar masses, from Sun-like stars to M dwarfs. Using hydrodynamical simulations with FARGO3D, we explored planets with mass ratios $10^{-3} < q < 2 \times 10^{-2}$ under different disk conditions, varying gas surface density, scale height, and density slope. Our results show a migration reversal at $ q \approx 0.002$, with outward migration for $ q > 0.002$. For planets undergoing outward migration, the migration speed depends on the unperturbed local gas density. In most cases, outward migration is sustained by a positive torque related to planetary eccentricities below $ e < 0.2$. However, for certain disk parameters, planets with $ q > 0.01$ reach higher eccentricities ($0.2 < e < 0.45$), leading to stalled migration. Our findings suggest that outward migration is a viable mechanism for massive planets in low-viscosity disks, which has implications for the formation and distribution of super-Jupiter planets around Sun-like stars and planets more massive than Neptune around very low-mass stars. Given the challenges in detecting such planets, improving our theoretical understanding of their migration is essential for interpreting exoplanet demographics and guiding future observational efforts.

astro-ph.EP↗

arXiv2025

Hydrodynamical Simulations of Planet Rebound Migration in Photo-evaporating Disks

This study investigates the orbital migration of a planet located near the truncated edge of protoplanetary disks, induced by X-ray photo-evaporation originating from the central star. The combined effects of turbulent viscous accretion and stellar X-ray photo-evaporation give rise to the formation of a cavity in the central few astronomical units in disks. Once the cavity is formed, the outer disk experiences rapid mass loss and the cavity expands inside out. We have conducted 2D hydrodynamical simulations of planet-disk interaction for various planet masses and disk properties. Our simulations demonstrate that planets up to about Neptune masses experience a strong positive corotation torque along the cavity edge that leads to sustained outward migration -- a phenomenon previously termed {\it rebound} migration. Rebound migration is more favorable in disks with moderate stellar photo-evaporation rates of ${\sim}10^{-8} ~ \rm M_{\odot}\,yr^{-1}$. Saturn-mass planets only experience inward migration due to significant gas depletion in their co-orbital regions. In contrast, Jupiter-mass planets are found to undergo modest outward migration as they cause the residual disk to become eccentric. This work presents the first 2D hydrodynamical simulations that confirm the existence and viability of rebound outward migration during the inside-out clearing in protoplanetary disks.

astro-ph.EP↗

arXiv2025

Halting the migration of super-Earths by efficient gap opening in radiative, low viscosity disks

While planet migration has been extensively studied for classical viscous disks, planet-disk interaction in nearly inviscid disks has mostly been explored with greatly simplified thermodynamics. In such environments, motivated by models of wind-driven accretion disks, even Earth-mass planets located interior to 1 au can significantly perturb the disk, carving gaps and exciting vortices on their edges. Both processes are influenced by radiative transfer, which can both drive baroclinic forcing and influence gap opening. We perform a set of high-resolution radiation hydrodynamics simulations of planet-disk interaction in the feedback and gap-opening regimes, aiming to understand the role of radiation transport in the migration of super-Earth-mass planets representative of the observed exoplanet population. We find that radiative cooling drives baroclinic forcing during multiple stages of the planet's migration in the feedback regime (~1.5 M_earth), significantly delaying the onset of vortex formation at the gap edge but ultimately resulting in type-III runaway migration episodes. For super-thermal-mass planets (~6.7 M_earth), radiative cooling is fundamentally linked to the gap opening process, with the planet stalling instead of undergoing vortex-assisted migration as expected from isothermal or adiabatic models. This stalling of migration can only be captured when treating radiative effects, and since it affects super-thermal-mass planets its implications for both the final configuration of planetary systems and population synthesis modeling are potentially huge. Combining our findings with previous related studies, we present a map of migration regimes for radiative, nearly-inviscid disks, with the cooling-mediated gap-opening regime playing a central role in determining the planet's orbital properties.

astro-ph.EP↗

arXiv2025

Nonlinear Evolution of the Unstratified Polydisperse Dust Settling Instability

Context. The Dust Settling Instabilty (DSI) is a member of the Resonant Drag Instabilities (RDI) family, and is thus related to the Streaming Instability (SI). Linear calculations found that the unstratified monodisperse DSI has growth rates much higher than the SI even with lower initial dust to gas ratios. However, recent nonlinear investigation found no evidence of strong dust clumping at the saturation level. Aims. To investigate the nonlinear saturation of the mono- and polydisperse DSI. We examine the convergence behaviour wrt. both the numerical resolution and the number of species. By characterising the morphology of the dust evolution triggered by the DSI, we can shed more light on its role in planetesimal formation. Methods. We perform a suite of 2D shearing box hydro simulations with the code Idefix, both in the mono- and polydisperse regimes. We focus on the time evolution of the maximum dust density, noting the time at which the instability is triggered, as well as analyse the morphology of the resultant structure. Results. In our monodisperse simulations, the maximum dust density increases and the instability saturates earlier with higher spatial resolution, with no signs of convergence. The polydisperse simulations do seem to converge with the number of species and produce maximum dust densities that are comparable to, albeit lower than, the monodisperse simulations. Different dust species tend to form adjacent but separate dust filaments, which may have implications on dust growth and further clumping. Conclusions. The monodisperse DSI produces dust structure at densities high enough that likely leads to clumping. The polydisperse DSI produces lower but comparable dust densities. Our idealised treatment suggests that the DSI is important for planetesimal formation, as it suffers less than the SI from including a dust size distribution.

astro-ph.EP↗

arXiv2025

Resonant drag instabilities for polydisperse dust. II. The streaming and settling instabilities

Dust grains embedded in gas flow give rise to a class of hydrodynamic instabilities, called resonant drag instabilities. These instabilities have predominantly been studied for single grain sizes, in which case they are found to grow fast. Nonlinear simulations indicate that strong dust overdensities can form, aiding the formation of planetesimals. In reality, however, there is going to be a distribution of dust sizes, which potentially has important consequences. We study two different resonant drag instabilities, the streaming instability and the settling instability, taking into account a continuous spectrum of grain sizes, to determine whether these instabilities survive in the polydisperse regime and how the resulting growth rates compare to the monodisperse case. We solve the linear equations for a polydisperse fluid in an unstratified shearing box to recover the streaming instability and, for approximate stratification, the settling instability, in all cases focusing on small dust-to-gas ratios. Size distributions of realistic width turn the singular perturbation of the monodisperse limit into a regular perturbation due to the fact that the backreaction on the gas involves an integration over the resonance. The contribution of the resonance to the integral can be negative, as in the case of the streaming instability, which as a result does not survive in the polydisperse regime, or positive, which is the case in the settling instability. The latter therefore has a polydisperse counterpart, with growth rates that can be comparable to the monodisperse case. Wide size distributions in almost all cases remove the resonant nature of drag instabilities. This can lead to reduced growth, as is the case in large parts of parameter space for the settling instability, or complete stabilisation, as is the case for the streaming instability.

astro-ph.EP↗

arXiv2025

Resonant Drag Instabilities for Polydisperse Dust, I. The Acoustic Resonant Drag Instability

Dust grains embedded in gas flow give rise to a class of hydrodynamic instabilities that can occur whenever there exists a relative velocity between gas and dust. These instabilities have predominantly been studied for single grain sizes, for which a strong interaction can be found between drifting dust and a travelling gas wave, leading to fast-growing perturbations (growth rates $\propto \sqrtμ$) even at small dust-to-gas ratios $μ$. They are called resonant drag instabilities. We focus on the acoustic resonant drag instability, which is potentially important in AGB star outflows, around supernova remnants and star clusters in starburst galaxies. We study the acoustic resonant drag instability, taking into account a continuous spectrum of grain sizes, to determine whether it survives in the polydisperse regime and how the resulting growth rates compare to the monodisperse case. We solve the linear equations for a polydisperse fluid for the acoustic drag instability, focusing on small dust-to-gas ratios. Size distributions of realistic width turn the fast-growing perturbations $\propto \sqrtμ$ of the monodisperse limit into slower growing perturbations $\propto μ$ due to the fact that the backreaction on the gas involves an integration over the resonance. Furthermore, the large wave numbers that grow fastest in the monodisperse regime are stabilized by a size distribution, severely limiting the growth rates in the polydisperse regime. The acoustic resonant drag instability turns from a singularly perturbed problem in $μ$ in the monodisperse limit into a regular perturbation for a sufficiently wide size distribution. It can still grow exponentially in the polydisperse regime, but at a slower pace compared to the single size case.

astro-ph.GA↗

arXiv2025

Polydisperse Formation of Planetesimals: The dust size distribution in clumps

The streaming instability is an efficient method for overcoming the barriers to planet formation in protoplanetary discs. The streaming instability has been extensively modelled by hydrodynamic simulations of gas and a single dust size. However, more recent studies considering a more realistic case of a particle size distribution show that this will significantly decrease the growth rate of the instability. We follow up on these studies by evaluating the polydisperse streaming instability, looking at the non-linear phase of the instability at the highest density regions, and investigating the dust size distribution in the densest dust structures. We employ 2D hydrodynamic simulations in an unstratified shearing box with multiple dust species representing an underlying continuous dust size spectrum using FARGO3D. To calculate the drag force on the gas due to a continuous dust size distribution, we apply the Gauss-Legendre quadrature method in dust size space. This method converges faster with the number of dust species than the usual uniform sampling method. The polydisperse streaming instability is less efficient than its monodisperse counterpart in generating dense clumps that could collapse into planetesimals. In the densest dust structure, the larger dust sizes are more abundant because they are less coupled to the gas and, therefore, can clump together more than the smaller dust grains. This trend is broken at the largest dust size due to size-dependent spatial segregation of the highest-density regions, where particles with the largest Stokes numbers are located just outside the densest areas of the combined dust species. This is observed as a peak in the size distribution at the densest regions, which could relate to the size distribution that ends up in the planetesimal after collapse and can mimic the size distribution of dust growth.

astro-ph.EP↗

arXiv2024

Buoyancy torques prevent low-mass planets from stalling in low-turbulence radiative disks

Low-mass planets migrating inwards in laminar protoplanetary disks (PPDs) experience a dynamical corotation torque, which is expected to slow down migration to a stall. However, baroclinic effects can reduce or even reverse this effect, leading to rapid inward migration. In the radiatively inefficient inner disk, one such mechanism is the buoyancy response of the disk to an embedded planet. Recent work has suggested that radiative cooling can quench this response, but for parameters that are not necessarily representative of the inner regions of PPDs. We perform global three dimensional inviscid radiation hydrodynamics simulations of planet-disk interaction to investigate the effect of radiative cooling on the buoyancy-driven torque in a more realistic disk model. We find that the buoyancy response exerts a negative dynamical corotation torque -- albeit partially damped due to radiative cooling -- resulting in sustained, rapid inward migration. Models that adopt a local cooling prescription significantly overestimate the impact of the buoyancy response, highlighting the importance of a realistic treatment of radiation transport that includes radiative diffusion. Our results suggest that low-mass planets should migrate inwards faster than has been previously expected in radiative disks, with implications for the formation and orbital distribution of super-Earths and sub-Neptunes at intermediate distances from their host stars, unless additional physical processes that can slow down migration are considered.

astro-ph.EP↗

arXiv2024

Migration of low-mass planets in inviscid disks: the effect of radiation transport on the dynamical corotation torque

Low-mass planets migrate in the type-I regime. In the inviscid limit, the contrast between the vortensity trapped inside the planet's corotating region and the background disk vortensity leads to a dynamical corotation torque, which is thought to slow down inward migration. We investigate the effect of radiative cooling on low-mass planet migration using inviscid 2D hydrodynamical simulations. We find that cooling induces a baroclinic forcing on material U-turning near the planet, resulting in vortensity growth in the corotating region, which in turn weakens the dynamical corotation torque and leads to 2-3x faster inward migration. This mechanism is most efficient when cooling acts on a timescale similar to the U-turn time of material inside the corotating region, but is nonetheless relevant for a substantial radial range in a typical disk (5-50 au). As the planet migrates inwards, the contrast between the vortensity inside and outside the corotating region increases and partially regulates the effect of baroclinic forcing. As a secondary effect, we show that radiative damping can further weaken the vortensity barrier created by the planet's spiral shocks, supporting inward migration. Finally, we highlight that a self-consistent treatment of radiative diffusion as opposed to local cooling is critical in order to avoid overestimating the vortensity growth and the resulting migration rate.

astro-ph.EP↗

arXiv2024

Stability of Dusty Rings in Protoplanetary Discs

Dust rings in protoplanetary discs are often observed in thermal dust emission and could be favourable environments for planet formation. While dust rings readily form in gas pressure maxima, their long-term stability is key to both their observability and potential to assist in planet formation. We investigate the stability of the dust ring generated by interactions of a protoplanetary disc with a Neptune sized planet and consider its possible long term evolution using the FARGO3D Multifluid code. We look at the onset of the Rossby Wave Instability (RWI) and compare how the addition of dust in a disc can alter the stability of the gas phase. We find that with the addition of dust, the rings generated by planet disc interactions are more prone to RWI and can cause the gas phase to become unstable. The instability is shown to occur more easily for higher Stokes number dust, as it accumulates into a more narrow ring which triggers the RWI, while the initial dust fraction plays a more minor role in the stability properties. We show that the dusty RWI generates vortices that collect dust in their cores, which could be sites for further planetesimal formation. We conclude that the addition of dust can cause a ring in a protoplanetary disc to become more prone to instability leading to a different long term evolution compared to gas only simulations of the RWI.

astro-ph.EP↗

arXiv2023

Buoyancy response of a disk to an embedded planet: a cross-code comparison at high resolution

In radiatively inefficient, laminar protoplanetary disks, embedded planets can excite a buoyancy response as gas gets deflected vertically near the planet. This results in vertical oscillations that drive a vortensity growth in the planet's corotating region, speeding up inward migration in the type-I regime. We present a comparison between PLUTO/IDEFIX and FARGO3D using 3D, inviscid, adiabatic numerical simulations of planet-disk interaction that feature the buoyancy response of the disk, and show that PLUTO/IDEFIX struggle to resolve higher-order modes of the buoyancy-related oscillations, weakening vortensity growth and the associated torque. We interpret this as a drawback of total-energy-conserving, finite-volume schemes. Our results indicate that a very high resolution or high-order scheme is required in shock-capturing codes in order to adequately capture this effect.

astro-ph.EP↗

arXiv2022

Planet-Disk Interactions

Planet-disk interactions, where an embedded massive body interacts gravitationally with the protoplanetary disk it was formed in, can play an important role in reshaping both the disk and the orbit of the planet. Spiral density waves are launched into the disk by the planet, which, if they are strong enough, can lead to the formation of a gap. Both effects are observable with current instruments. The back-reaction of perturbations induced in the disk, both wave-like and non-wavelike, is a change in orbital elements of the planet. The efficiency of orbital migration is a long-standing problem in planet formation theory. We discuss recent progress in planet-disk interactions for different planet masses and disk parameters, in particular the level of turbulence, and progress in modeling observational signatures of embedded planets.

astro-ph.EP↗

arXiv2022

Single Fluid vs. Multifluid: Comparison between single fluid and multifluid dust models for disc planet interactions

Recent observations of substructures such as dust gaps and dust rings in protoplanetary discs have highlighted the importance of including dust into purely gaseous disc models. At the same time, computational difficulties arise with the standard models of simulating the dust and gas separately. These include the cost of accurately simulating the interactions between well coupled dust and gas and issues of dust concentration in areas below resolution of the gas phase. We test a single fluid approach, that incorporates the terminal velocity approximation valid for small particles, which can overcome these difficulties, through modification of FARGO3D. We compare this single fluid model with a multifluid model for a variety of planet masses. We find differences in the dust density distribution in all cases. For high-mass, gap-opening planets we find differences in the amplitude of the resulting dust rings, which we attribute to the failure of the terminal velocity approximation around shocks. For low-mass planets, both models agree everywhere except in the corotation region, where the terminal velocity approximation shows overdense dust lobes. We tentatively interpret these as dusty equivalents of thermal lobes seen in non-isothermal simulations with thermal diffusion, but more work is necessary to confirm this. At the same resolution, the computational time for the terminal velocity approximation model is significantly less than a two fluid model. We conclude that the terminal velocity approximation is a valuable tool for modelling a protoplanetary disc but that care should be taken when shocks are involved.

astro-ph.EP↗

arXiv2022

Dynamics of Dusty Vortices II: Stability of 2D dust laden vortices

Vortices have long been speculated to play a role in planet formation, via the collection of dust in the pressure maxima that arise at the cores of vortices in protoplanetary discs. The question remains however: as dust collects in the core of a vortex, when does that vortex remain stable and able to collect further dust, and when and why does it break up? We study this question by running high resolution 2D simulations of dust laden vortices. By using the terminal velocity approximation in a local shearing box it was possible to efficiently run simulations of back-reacting dust in a gas at high resolution. Our results show how the stability of 2D dust laden vortices in protoplanetary discs depends on their size relative to the disc scale height, as well as the dust coupling. We find small vortices with semiminor axis much smaller than the scale height to be stable for the duration of the simulations ($t>2000$ orbits). Larger vortices, with semiminor axis smaller than but of order of the scale height, exhibit a drag instability after undergoing a long period of contraction where the core becomes progressively more dust rich. The lifetime of these vortices depends on the dust size, with larger dust grains causing the instability to occur sooner. For the size ranges tested in this paper, $μ$m to mm sized grains, vortices survived for several hundreds of orbits. The result implies that the stability of vortices formed by vertical shear instability and zombie vortex instability, or the breakup of larger vortices through hydrodynamic instabilities, is affected by the presence of dust in the disc. The lifetimes observed in this paper, while shortened by the presence of dust for larger vortices, were still long enough to lead to considerable dust enrichment in the vortex cores.

astro-ph.EP↗