arXiv subjects

Leonardo Krapp

Publications and source records attributed to Leonardo Krapp.

17 recordsLinked to original sources

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

Not Just Gas: How Solid-Driven Torques Shaped the Migration of the Galilean Moons

Surviving rapid inward orbital migration is a crucial aspect of formation models for the Jupiter's Galilean moons. The primary aim of this study is to investigate the orbital migration of the Galilean moons by incorporating self-consistent solid dynamics in circumjovian disk models. We perform two-fluid simulations using the FARGO3D code on a 2D polar grid. The simulations model a satellite with the mass of a proto-moon, Europa, or Ganymede interacting with a circumjovian disk. The dust component, coupled to the gas via a drag force, is characterized by the dust-to-gas mass ratio ($ε$) and the Stokes number ($T_s$). The effect of solids fundamentally alter the satellites' evolution. We identify a vast parameter space where migration is slowed, halted, robustly reversed -leading to outward migration-, or significantly accelerated inward. The migration rate is dependent on satellite mass, providing a natural source of differential migration. Solid dynamics provides a robust and self-consistent mechanism that fundamentally alters the migration of the Galilean moons, potentially addressing the long-standing migration catastrophe. This mechanism critically affects the survival of satellites and could offer a viable physical process to explain the establishment of resonances through differential migration. These findings establish that solid torques are a critical, non-negligible factor in shaping the final architecture of satellite systems.

astro-ph.EP↗

arXiv2024

A thermodynamic criterion for the formation of Circumplanetary Disks

The formation of circumplanetary disks is central to our understanding of giant planet formation, influencing their growth rate during the post-runaway phase and observability while embedded in protoplanetary disks. We use 3D global multifluid radiation hydrodynamics simulations with the FARGO3D code to define the thermodynamic conditions that enable circumplanetary disk formation around Jovian planets on wide orbits. Our simulations include stellar irradiation, viscous heating, static mesh refinement, and active calculation of opacity based on evolving dust fluids. We find a necessary condition for the formation of circumplanetary disks in terms of a mean cooling time: when the cooling time is at least one order of magnitude shorter than the orbital time scale, the specific angular momentum of the gas is nearly Keplerian at scales of $R_{\rm{Hill}}/3$. We show that the inclusion of multifluid dust dynamics favors rotational support because dust settling produces an anisotropic opacity distribution that favors rapid cooling. In all our models with radiation hydrodynamics, specific angular momentum decreases as time evolves in agreement with the formation of an inner isentropic envelope due to compressional heating. The isentropic envelope can extend up to $R_{\rm{Hill}}/3$ and shows negligible rotational support. Thus, our results imply that young gas giant planets may host spherical isentropic envelopes, rather than circumplanetary disks.

astro-ph.EP↗

arXiv2024

Dust rings trap protoplanets on eccentric orbits and get consumed by them

We study the orbital evolution and mass growth of protoplanets with masses $M \in [0.1-8]$~M$_\oplus$ in the vicinity of a dusty ring, using three-dimensional numerical simulations with a two-fluid model and nested-meshes. We find two stable, eccentric orbits that lock the planet in the ring vicinity, thereby inhibiting its migration and allowing it to accrete dust from the ring. One of these orbits has an eccentricity comparable to the aspect ratio of the gaseous disc and has its periastron within the ring, enabling intermittent accretion during each pass. The other orbit has a smaller eccentricity and an apoastron slightly inside the ring. A planet locked at the outer orbit efficiently accretes from the ring and can reach the critical mass for runaway gas accretion on timescales $\gtrsim 10^5$ yr (for a 10~M$_\oplus$ dust ring at 10~au) while a planet locked at the inner orbit has a slower growth and might not supersede the super-Earth stage over the disc lifetime. While in our runs a low-mass embryo forming within the ring eventually joins the outer orbit, it is likely that the path taken depends on the specific details of the ring. The trapping on the outer orbit arises from an intermittent, strong thermal force at each passage through the ring, where the accretion rate spikes. It is insensitive to uncertainties that plague models considering planets trapped on circular orbits in rings. It is highly robust and could allow a growing planet to follow an expanding ring over large distances.

astro-ph.EP↗

arXiv2024

A Fast second-order solver for stiff multifluid dust and gas hydrodynamics

We present MDIRK: a Multifluid second-order Diagonally-Implicit Runge-Kutta method to study momentum transfer between gas and an arbitrary number ($N$) of dust species. The method integrates the equations of hydrodynamics with an Implicit Explicit (IMEX) scheme and solves the stiff source term in the momentum equation with a diagonally-implicit asymptotically stable Runge-Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with $\mathcal{O}(N)$ operations, instead of standard matrix inversion, which is $\mathcal{O}(N)^3$. Therefore the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multi-fluid dusty Jeans instability, and a steady-state gas-dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order asymptotically stable multifluid methods.

physics.comp-ph↗

arXiv2024

A solution for the density dichotomy problem of Kuiper Belt objects with multi-species streaming instability and pebble accretion

Kuiper belt objects show an unexpected trend, whereby large bodies have increasingly higher densities, up to five times greater than their smaller counterparts. Current explanations for this trend assume formation at constant composition, with the increasing density resulting from gravitational compaction. However, this scenario poses a timing problem to avoid early melting by decay of $^{26}$Al. We aim to explain the density trend in the context of streaming instability and pebble accretion. Small pebbles experience lofting into the atmosphere of the disk, being exposed to UV and partially losing their ice via desorption. Conversely, larger pebbles are shielded and remain more icy. We use a shearing box model including gas and solids, the latter split into ices and silicate pebbles. Self-gravity is included, allowing dense clumps to collapse into planetesimals. We find that the streaming instability leads to the formation of mostly icy planetesimals, albeit with an unexpected trend that the lighter ones are more silicate-rich than the heavier ones. We feed the resulting planetesimals into a pebble accretion integrator with a continuous size distribution, finding that they undergo drastic changes in composition as they preferentially accrete silicate pebbles. The density and masses of large KBOs are best reproduced if they form between 15 and 22\,AU. Our solution avoids the timing problem because the first planetesimals are primarily icy, and $^{26}$Al is mostly incorporated in the slow phase of silicate pebble accretion. Our results lend further credibility to the streaming instability and pebble accretion as formation and growth mechanisms.

astro-ph.EP↗

arXiv2023

Dust Dynamics in Hall-effected Protoplanetary Disks. I. Background Drift Hall Instability

Recent studies have shown that the large-scale gas dynamics of protoplanetary disks (PPDs) are controlled by non-ideal magneto-hydrodynamics (MHD), but how this influences dust dynamics is not fully understood. To this end, we investigate the stability of dusty, magnetized disks subject to the Hall effect, which applies to planet-forming regions of PPDs. We find a novel Background Drift Hall Instability (BDHI) that may facilitate planetesimal formation in Hall-effected disk regions. Through a combination of linear analysis and nonlinear simulations, we demonstrate the viability and characteristics of BDHI. We find it can potentially dominate over the classical streaming instability (SI) and standard MHD instabilities at low dust-to-gas ratios and weak magnetic fields. We also identify magnetized versions of the classic SI, but these are usually subdominant. We highlight the complex interplay between magnetic fields and dust-gas dynamics in PPDs, underscoring the need to consider non-ideal MHD like the Hall effect in the broader narrative of planet formation.

astro-ph.EP↗

arXiv2023

RAM: Rapid Advection Algorithm on Arbitrary Meshes

The study of many astrophysical flows requires computational algorithms that can capture high Mach number flows, while resolving a large dynamic range in spatial and density scales. In this paper we present a novel method, RAM: Rapid Advection Algorithm on Arbitrary Meshes. RAM is a time-explicit method to solve the advection equation in problems with large bulk velocity on arbitrary computational grids. In comparison with standard up-wind algorithms, RAM enables advection with larger time steps and lower truncation errors. Our method is based on the operator splitting technique and conservative interpolation. Depending on the bulk velocity and resolution, RAM can decrease the numerical cost of hydrodynamics by more than one order of magnitude. To quantify the truncation errors and speed-up with RAM, we perform one and two-dimensional hydrodynamics tests. We find that the order of our method is given by the order of the conservative interpolation and that the effective speed up is in agreement with the relative increment in time step. RAM will be especially useful for numerical studies of disk-satellite interaction, characterized by high bulk orbital velocities, and non-trivial geometries. Our method dramatically lowers the computational cost of simulations that simultaneously resolve the global disk and well inside the Hill radius of the secondary companion.

astro-ph.IM↗

arXiv2023

On the Origin of Dust Structures in Protoplanetary Disks: Constraints from the Rossby Wave Instability

High resolution sub-mm observations of protoplanetary disks with ALMA have revealed that dust rings are common in large, bright disks. The leading explanation for these structures is dust-trapping in a local gas pressure maximum, caused by an embedded planet or other dynamical process. Independent of origin, such dust traps should be stable for many orbits to collect significant dust. However, ring-like perturbations in gas disks are also known to trigger the Rossby Wave Instability (RWI). We investigate whether axisymmetric pressure bumps can simultaneously trap dust and remain stable to the RWI. The answer depends on the thermodynamic properties of pressure bumps. For isothermal bumps, dust traps are RWI-stable for widths from ${\sim}1$ to several gas scale-heights. Adiabatic dust traps are stable over a smaller range of widths. For temperature bumps with no surface density component, however, all dust traps tend to be unstable. Smaller values of disk aspect ratio allow stable dust trapping at lower bump amplitudes and over a larger range of widths. We also report a new approximate criterion for RWI. Instability occurs when the radial oscillation frequency is $\lesssim75$\% of the Keplerian frequency, which differs from the well-known Lovelace necessary (but not sufficient) criterion for instability. Our results can guide ALMA observations of molecular gas by constraining the resolution and sensitivity needed to identify the pressure bumps thought to be responsible for dust rings.

astro-ph.EP↗

arXiv2022

Substructures in protoplanetary disks imprinted by compact planetary systems

The substructures observed in protoplanetary disks may be the signposts of embedded planets carving gaps or creating vortices. The inferred masses of these planets often fall in the Jovian regime despite their low abundance compared to lower-mass planets, partly because previous works often assume that a single substructure (a gap or vortex) is caused by a single planet. In this work, we study the possible imprints of compact systems composed of Neptune-like planets ($\sim10-30\;M_\oplus$) and show that long-standing vortices are a prevalent outcome when their inter-planetary separation ($Δa$) falls below $\sim8$ times $H_{\rm p}$ -- the average disk's scale height at the planets locations. In simulations where a single planet is unable to produce long-lived vortices, two-planet systems can preserve them for at least $5,000$ orbits in two regimes: i) fully-shared density gaps with elongated vortices around the stable Lagrange points $L_4$ and $L_5$ for the most compact planet pairs ($Δa \lesssim 4.6\; H_{\rm p}$); ii) partially-shared gaps for more widely spaced planets ($Δa \sim 4.6 - 8\;H_{\rm p}$) forming vortices in a density ring between the planets through the Rossby wave instability. The latter case can produce vortices with a wide range of aspect ratios down to $\sim3$ and can occur for planets captured into the 3:2 (2:1) mean-motion resonances for disk's aspects ratios of $h\gtrsim 0.033$ ($h\gtrsim 0.057$). We suggest that their long lifetimes are sustained by the interaction of spiral density waves launched by the neighboring planets. Overall, our results show that distinguishing imprint of compact systems with Neptune-mass planets are long-lived vortices inside the density gaps, which in turn are shallower than single-planet gaps for a fixed gap width.

astro-ph.EP↗

arXiv2022

The 3D dust and opacity distribution of protoplanets in multi-fluid global simulations

The abundance and distribution of solids inside the Hill sphere are central to our understanding of the giant planet dichotomy. Here, we present a three-dimensional characterization of the dust density, mass flux, and mean opacities in the envelope of sub-thermal and super-thermal mass planets. We simulate the dynamics of multiple dust species in a global protoplanetary disk model accounting for dust feedback. We find that the meridional flows do not effectively stir dust grains at scales of the Bondi sphere. Thus the dust-settling driven by the stellar gravitational potential sets the latitudinal dust density gradient within the planet envelope. Not only does the planet's potential enhance this gradient, but also the spiral wakes serve as another source of asymmetry. These asymmetries substantially alter the inferred mean Rosseland and Planck opacities. In cases with the moderate-to-strong dust settling, the opacity gradient can range from a few percent to more than two orders of magnitude between the mid-plane and the polar regions of the Bondi sphere. Finally, we show that this strong latitudinal opacity gradient can introduce a transition between optically thick and thin regimes at the scales of the planet envelope. We suggest that this transition is likely to occur when the equilibrium scale height of hundred-micron-sized particles is smaller than the Hill radius of the forming planet. This work calls into question the adoption of a constant opacity derived from well-mixed distributions and demonstrates the need for global radiation hydrodynamics models of giant planet formation which account for dust dynamics.

astro-ph.EP↗

arXiv2020

Dust Settling Instability in Protoplanetary Discs

The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on previous linear analyses by including particle size distributions and performing a detailed study of the amount of background turbulence needed to stabilize the DSI. When including binned size distributions, the DSI often produces converged growth rates with fewer bins than the standard SI. With background turbulence, we find that the most favorable conditions for DSI growth are weak turbulence, characterized by $α\lesssim 10^{-6}$ with intermediate-sized grains that settle from one gas scale-height. These conditions could arise during a sudden decrease in disc turbulence following an accretion outburst. Ignoring background turbulence, we performed a parameter survey of local 2D DSI simulations. Particle clumping was either weak or occurred slower than particles settle. Clumping was reduced by a factor of two in a comparison 3D simulation. Overall, our results strongly disfavor the hypothesis that the DSI significantly promotes planetesimal formation. Non-linear simulations of the DSI with different numerical methods could support or challenge these findings.

astro-ph.EP↗

arXiv2019

Predicting the observational signature of migrating Neptune-sized planets in low-viscosity disks

The migration of planetary cores embedded in a protoplanetary disk is an important mechanism within planet-formation theory, relevant for the architecture of planetary systems. Consequently, planet migration is actively discussed, yet often results of independent theoretical or numerical studies are unconstrained due to the lack of observational diagnostics designed in light of planet migration. In this work we follow the idea of inferring the migration behavior of embedded planets by means of the characteristic radial structures that they imprint in the disk's dust density distribution. We run hydrodynamical multifluid simulations of gas and several dust species in a locally isothermal $α$-disk in the low-viscosity regime ($α=10^{-5}$) and investigate the obtained dust structures. In this framework, a planet of roughly Neptune mass can create three (or more) rings in which dust accumulates. We find that the relative spacing of these rings depends on the planet's migration speed and direction. By performing subsequent radiative transfer calculations and image synthesis we show that - always under the condition of a near-inviscid disk - different migration scenarios are, in principle, distinguishable by long-baseline, state-of-the-art ALMA observations.

astro-ph.EP↗

arXiv2019

Asymptotically stable numerical method for multispecies momentum transfer: gas and multifluid-dust test suite and implementation in FARGO3D

We present an asymptotically and unconditionally stable numerical method to account for the momentum transfer between multiple species. Momentum is conserved to machine precision. This implies that the asymptotic equilibrium corresponds to the velocity of the center of mass. Aimed at studying dust dynamics, we implement this numerical method in the publicly available code FARGO3D. To validate our implementation, we develop a test suite for an arbitrary number of species, based on analytical or exact solutions of problems related to perfect damping, damped sound waves, shocks, local and global gas-dust radial drift in a disk and, linear streaming instability. In particular, we obtain first-order, steady-state solutions for the radial drift of multiple dust species in protoplanetary disks, in which the pressure gradient is not necessarily small. We additionally present non-linear shearing-box simulations of the streaming instability and compare them with previous results obtained with Lagrangian particles. We successfully validate our implementation by recovering the solutions from the test suite to second- and first-order accuracy in space and time, respectively. From this, we conclude that our scheme is suitable, and very robust, to study the self-consistent dynamics of several fluids. In particular, it can be used for solving the collisions between gas and dust in protoplanetary disks, with any degree of coupling.

astro-ph.EP↗

arXiv2019

Streaming Instability for Particle-Size Distributions

The streaming instability is thought to play a central role in the early stages of planet formation by enabling the efficient bypass of a number of barriers hindering the formation of planetesimals. We present the first study exploring the efficiency of the linear streaming instability when a particle-size distribution is considered. We find that, for a given dust-to-gas mass ratio, the multi-species streaming instability grows on timescales much longer than those expected when only one dust species is involved. In particular, distributions that contain close-to-order-unity dust-to-gas mass ratios lead to unstable modes that can grow on timescales comparable, or larger, with those of secular instabilities. We anticipate that processes leading to particle segregation and/or concentration can create favourable conditions for the instability to grow fast. Our findings may have important implications for a large number of processes in protoplanetary disks that rely on the streaming instability as usually envisioned for a unique dust species. Our results suggest that the growth rates of other resonant-drag-instabilities may also decrease considerably when multiple species are considered.

astro-ph.EP↗

arXiv2019

Dust segregation in Hall-dominated turbulent protoplanetary disks

Imaging of the dust continuum emitted from disks around nearby protostars reveals diverse substructure. In recent years, theoretical efforts have been intensified to investigate how far the intrinsic dynamics of protoplanetary disks (PPDs) can lead to such features. Turbulence in the realm of non-ideal magnetohydrodynamics (MHD) is one candidate for explaining the generation of zonal flows which can lead to local dust enhancements. Adopting a radially varying cylindrical disk model, and considering combinations of vertical and azimuthal initial net flux, we perform 3D non-ideal MHD simulations aimed at studying self-organization induced by the Hall effect in turbulent PPDs. To this end, new modules have been incorporated into the NIRVANA-III and FARGO3D MHD codes. We moreover include dust grains, treated in the fluid approximation, in order to study their evolution subject to the emerging zonal flows. In the regime of a dominant Hall effect, we robustly obtain large-scale organized concentrations in the vertical magnetic field that remain stable for hundreds of orbits. For disks with vertical initial net flux alone, we confirm the presence of zonal flows and vortices that introduce regions of super-Keplerian gas flow. Including a moderately strong net-azimuthal magnetic flux can significantly alter the dynamics, partially preventing the self-organization of zonal flows. For plasma beta-parameters smaller than 50, large-scale, near-axisymmetric structures develop in the vertical magnetic flux. In all cases, we demonstrate that the emerging features are capable of accumulating dust grains for a range of Stokes numbers.

astro-ph.EP↗

arXiv2018

Characterizing the variable dust permeability of planet-induced gaps

Aerodynamic theory predicts that dust grains in protoplanetary disks will drift radially inward on comparatively short timescales. In this context, it has long been known that the presence of a gap opened by a planet can alter the dust dynamics significantly. In this paper, we carry out a systematic study employing long-term numerical simulations aimed at characterizing the critical particle-size for retention outside a gap as a function of particle size and for various key parameters defining the protoplanetary disk model. To this end, we perform multifluid hydrodynamical simulations in two dimensions, including different dust species, which we treat as pressureless fluids. We initialize the dust outside of the planet's orbit and study under which conditions dust grains are able to cross the gap carved by the planet. In agreement with previous work, we find that the permeability of the gap depends both on dust dynamical properties and the gas disk structure: while small dust follows the viscously accreting gas through the gap, dust grains approaching a critical size are progressively filtered out. Moreover, we introduce and compute a depletion factor that enables us to quantify the way in which higher viscosity, smaller planet mass, or a more massive disk can shift this critical size to larger values. Our results indicate that gap-opening planets may act to deplete the inner reaches of protoplanetary disks of large dust grains -- potentially limiting the accretion of solids onto forming terrestrial planets.

astro-ph.EP↗