arXiv subjects

Jeffrey N. Cuzzi

Publications and source records attributed to Jeffrey N. Cuzzi.

At least 19 recordsLinked to original sources

arXiv2026

Evidence For Turbulent Concentration In Particle-Laden Midplane Layers of Planet-Forming Disks

We investigate the axisymmetric, weakly turbulent state of settled particle layers in a model of a globally laminar protoplanetary disk. We focus on conditions in which the large-scale axisymmetric filaments associated with the streaming instability (SI) either cannot form or have not developed yet. We observe small-scale particle clumping consistent with turbulent concentration (TC), in which particle-rich filaments align with regions of high gas strain rate and enclose gas-only voids exhibiting coherent vorticity. Across a range of particle Stokes numbers, St$_K$ ($0.01-0.04$) -- defined as stopping times relative to the Keplerian frequency -- effective Stokes number within particle voids, St$_ω$, defined instead using local gas vorticity, collapses to values in the range $\sim 0.4-0.7$ for the St$_K$ considered. These values lie close to critical turbulent Stokes numbers associated with maximal clustering intermittency identified in statistical studies of TC. A timescale comparison reveals that in simulations with midplane particle-to-gas density ratios below unity and St$_K \ll 1$, SI growth rates are 1 - 2 orders of magnitude slower than turbulent overturn frequencies at the large-eddy scale, which appears to rule out SI as the primary driver of turbulence here. Instead, we suggest the Symmetric Instability (SymI) may be responsible. We show for our St$_K$ that TC is a persistent feature of our turbulent particle layers, and conclude that small scale particle density fluctuations exceeding the Roche density within large-scale axisymmetric SI filaments reported in the literature are also expressions of TC operating on top of the slightly elevated background particle densities within those large-scale structures.

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arXiv2024

Length and Velocity Scales in Protoplanetary Disk Turbulence

In the theory of protoplanetary disk turbulence, a widely adopted \emph{ansatz}, or assumption, is that the turnover frequency of the largest turbulent eddy, $Ω_L$, is the local Keplerian frequency $Ω_K$. In terms of the standard dimensionless Shakura-Sunyaev $α$ parameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by $\sqrtαH$ and $\sqrtαc$, in which $H$ and $c$ are the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as Vertical Shear Instability. Here we explore the more general case where $Ω_L\geΩ_K$ and show that under these conditions, the characteristic length and velocity scales are respectively $\sqrt{α/R'}H$ and $\sqrt{αR'}c$, where $R'\equiv Ω_L/Ω_K$ is twice the Rossby number. It follows that $α=\alphat/R'$, where $\sqrt{\alphat} c$ is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For $R'>1$ the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation.

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arXiv2023

A recent impact origin of Saturn's rings and mid-sized moons

We simulate the collision of precursor icy moons analogous to Dione and Rhea as a possible origin for Saturn's remarkably young rings. Such an event could have been triggered a few hundred million years ago by resonant instabilities in a previous satellite system. Using high-resolution smoothed particle hydrodynamics simulations, we find that this kind of impact can produce a wide distribution of massive objects and scatter material throughout the system. This includes the direct placement of pure-ice ejecta onto orbits that enter Saturn's Roche limit, which could form or rejuvenate rings. In addition, fragments and debris of rock and ice totalling more than the mass of Enceladus can be placed onto highly eccentric orbits that would intersect with any precursor moons orbiting in the vicinity of Mimas, Enceladus, or Tethys. This could prompt further disruption and facilitate a collisional cascade to distribute more debris for potential ring formation, the re-formation of the present-day moons, and evolution into an eventual cratering population of planeto-centric impactors.

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arXiv2022

Global Modeling of Nebulae With Particle Growth, Drift, and Evaporation Fronts. II. The Influence of Porosity on Solids Evolution

Incremental particle growth in turbulent protoplanetary nebulae is limited by a combination of barriers that can slow or stall growth. Moreover, particles that grow massive enough to decouple from the gas are subject to inward radial drift which could lead to the depletion of most disk solids before planetesimals can form. Compact particle growth is probably not realistic. Rather, it is more likely that grains grow as fractal aggregates which may overcome this so-called radial drift barrier because they remain more coupled to the gas than compact particles of equal mass. We model fractal aggregate growth and compaction in a viscously evolving solar-like nebula for a range of turbulent intensities $α_{\rm{t}} = 10^{-5}-10^{-2}$. We do find that radial drift is less influential for porous aggregates over much of their growth phase; however, outside the water snowline fractal aggregates can grow to much larger masses with larger Stokes numbers more quickly than compact particles, leading to rapid inward radial drift. As a result, disk solids outside the snowline out to $\sim 10-20$ AU are depleted earlier than in compact growth models, but outside $\sim 20$ AU material is retained much longer because aggregate Stokes numbers there remain lower initially. Nevertheless, we conclude even fractal models will lose most disk solids without the intervention of some leap-frog planetesimal forming mechanism such as the Streaming Instability (SI), though conditions for the SI are generally never satisfied, except for a brief period %for a brief stage around $\sim 0.2$ Myr at the snowline for $α_{\rm{t}}=10^{-5}$.

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arXiv2022

Global Modeling of Nebulae With Particle Growth, Drift, and Evaporation Fronts. III. Redistribution of Refractories and Volatiles

Formation of the first planetesimals remains an unsolved problem. Growth by sticking must initiate the process, but multiple studies have revealed a series of barriers that can slow or stall growth, most of them due to nebula turbulence. In a companion paper, we study the influence of these barriers on models of fractal aggregate and solid, compact particle growth in a viscously evolving solar-like nebula for a range of turbulent intensities $α_{\rm{t}} = 10^{-5}-10^{-2}$. Here, we examine how disk composition in these same models changes with time. We find that advection and diffusion of small grains and vapor, and radial inward drift for larger compact particles and fractal aggregates, naturally lead to diverse outcomes for planetesimal composition. Larger particles can undergo substantial inward radial migration due to gas drag before being collisionally fragmented or partially evaporating at various temperatures. This leads to enhancement of the associated volatile in both vapor inside, and solids outside, their respective evaporation fronts, or ``snowlines''. In cases of lower $α_{\rm{t}}$, we see narrow belts of volatile or supervolatile material develop in the outer nebula, which could be connected to the bands of ``pebbles" seen by ALMA. Volatile bands, which migrate inwards as the disk cools, can persist over long timescales as their gas phase continues to advect or diffuse outward across its evaporation front. These belts could be sites where supervolatile-rich planetesimals form, such as the rare CO-rich and water-poor comets; giant planets formed just outside the H$_2$O snowline may be enhanced in water.

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arXiv2022

Depletion of Moderately Volatile Elements by Open-System loss in the Early Solar Nebula

Rocky bodies of the inner solar system display a systematic depletion of the "Moderately Volatile Elements" (MVEs) that correlates with the expected condensation temperature of their likely host materials under protoplanetary nebula conditions. In this paper, we present and test a new hypothesis in which open system loss processes irreversibly remove vaporized MVEs from high nebula altitudes, leaving behind the more refractory solids residing much closer to the midplane. The MVEs irreversibly lost from the nebula through these open system loss processes are then simply unavailable for condensation onto planetesimals forming even much later, after the nebula cooled, overcoming a critical difficulty encountered by previous models of this type. We model open system loss processes operating at high nebula altitudes, such as resulting from disk winds flowing out of the system entirely, or layered accretion directly onto the young sun. We find that mass loss rates higher than found in typical T-Tauri disk winds, lasting short periods of time, are most satisfactory, pointing to multiple intense early outburst stages. Using our global nebula model, incorporating realistic particle growth and inward drift for solids, we constrain how much the MVE depletion signature in the inner region is diluted by the drift of undepleted material from the outer nebula. We also find that a significant irreversible loss of the common rock-forming elements (Fe, Mg, Si) can occur, leading to a new explanation of another longstanding puzzle of the apparent "enhancement" in the relative abundance of highly refractory elements in chondrites.

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arXiv2020

The Saturn Ring Skimmer Mission Concept: The next step to explore Saturn's rings, atmosphere, interior, and inner magnetosphere

The innovative Saturn Ring Skimmer mission concept enables a wide range of investigations that address fundamental questions about Saturn and its rings, as well as giant planets and astrophysical disk systems in general. This mission would provide new insights into the dynamical processes that operate in astrophysical disk systems by observing individual particles in Saturn's rings for the first time. The Ring Skimmer would also constrain the origin, history, and fate of Saturn's rings by determining their compositional evolution and material transport rates. In addition, the Ring Skimmer would reveal how the rings, magnetosphere, and planet operate as an inter-connected system by making direct measurements of the ring's atmosphere, Saturn's inner magnetosphere and the material owing from the rings into the planet. At the same time, this mission would clarify the dynamical processes operating in the planet's visible atmosphere and deep interior by making extensive high-resolution observations of cloud features and repeated measurements of the planet's extremely dynamic gravitational field. Given the scientific potential of this basic mission concept, we advocate that it be studied in depth as a potential option for the New Frontiers program.

astro-ph.IM↗

arXiv2020

Streaming Instability in Turbulent Protoplanetary Disks

The streaming instability for solid particles in protoplanetary disks is re-examined assuming the familiar alpha ($α$) model for isotropic turbulence. Turbulence always reduces the growth rates of the streaming instability relative to values calculated for globally laminar disks. While for small values of the turbulence parameter, $α< 10^{-5}$, the wavelengths of the fastest-growing disturbances are small fractions of the local gas vertical scale height $H$, we find that for moderate values of the turbulence parameter, i.e., $α\sim 10^{-5}-10^{-3}$, the lengthscales of maximally growing disturbances shift toward larger scales, approaching $H$. At these moderate turbulent intensities and for local particle to gas mass density ratios $ε< 0.5$, the vertical scales of the most unstable modes begin to exceed the corresponding radial scales so that the instability appears in the form of vertically oriented sheets extending well beyond the particle scale height. We find that for hydrodynamical turbulent disk models reported in the literature, with $α= 4\times 10^{-5} - 5\times 10^{-4}$, together with state of the art global evolution models of particle growth, the streaming instability is predicted to be viable within a narrow triangular patch of $α$--$τ_s$ parameter space centered on Stokes numbers, $τ_s \sim 0.01$ and $α\sim 4\times 10^{-5}$ and, further, exhibits growth rates on the order of several hundred to thousands of orbit times for disks with 1 percent ($Z= 0.01$) cosmic solids abundance or metallicity. Our results are consistent with, and place in context, published numerical studies of streaming instabilities.

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arXiv2020

Cascade Model for Planetesimal Formation by Turbulent Clustering

We use a newly developed cascade model of turbulent concentration of particles in protoplanetary nebulae to calculate several properties of interest to the formation of primitive planetesimals and to the meteorite record. The model follows, and corrects, calculations of the primary planetesimal Initial Mass Function (IMF) by Cuzzi et al. (2010), in which an incorrect cascade model was used. Here we use the model of Hartlep et al. (2017), which has been validated against several published numerical simulations of particle concentration in turbulence. We find that, for a range of nebula and particle properties, planetesimals may be "born big", formed as sandpiles with diameters in the 10-100 km range, directly from freely floating particles. The IMFs have a modal nature, with a well-defined peak rather than a powerlaw size dependence. Predictions for the inner and outer nebula behave similarly in these regards, and observations of inner and outer nebula primitive bodies support such modal IMFs. Also, we present predictions of local particle concentrations on several lengthscales in which particles "commonly" find themselves, which have significance for meteoritical observations of the redox state and isotopic fractionation in regions of chondrule formation. An important difference between these results, and those of Cuzzi et al. (2010), is that particle growth-by-sticking must proceed to at least the 1-few cm radius range for the IMF and meteoritical properties to be most plausibly satisfied. That is, as far as the inner nebula goes, the predominant "particles" must be aggregates of chondrules (or chondrule-size precursors) rather than individual chondrules themselves.

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arXiv2018

Witnessing Planetary Systems in the Making with the Next Generation Very Large Array

The discovery of thousands of exoplanets over the last couple of decades has shown that the birth of planets is a very efficient process in nature. Theories invoke a multitude of mechanisms to describe the assembly of planets in the disks around pre-main-sequence stars, but observational constraints have been sparse on account of insufficient sensitivity and resolution. Understanding how planets form and interact with their parental disk is crucial also to illuminate the main characteristics of a large portion of the full population of planets that is inaccessible to current and near-future observations. This White Paper describes some of the main issues for our current understanding of the formation and evolution of planets, and the critical contribution expected in this field by the Next Generation Very Large Array.

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arXiv2017

Formulas for Radial Transport in Protoplanetary Disks

Quantification of the radial transport of gaseous species and solid particles is important to many applications in protoplanetary disk evolution. An especially important example is determining the location of the water snow lines in a disk, which requires computing the rates of outward radial diffusion of water vapor and the inward radial drift of icy particles; however, the application is generalized to evaporation fronts of all volatiles. We review the relevant formulas using a uniform formalism. This uniform treatment is necessary because the literature currently contains at least six mutually exclusive treatments of radial diffusion of gas, only one of which is correct. We derive the radial diffusion equations from first principles, using Fick's law. For completeness, we also present the equations for radial transport of particles. These equations may be applied to studies of diffusion of gases and particles in protoplanetary and other accretion disks.

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arXiv2017

Scale Dependence of Multiplier Distributions for Particle Concentration, Enstrophy and Dissipation in the Inertial Range of Homogeneous Turbulence

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into sub-volumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, $Re$, finding good agreement with the asymptotic, infinite $Re$ inertial range theory of Zaichik and Alipchenkov [New Journal of Physics 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

physics.flu-dyn↗

arXiv2016

Critical layers and protoplanetary disk turbulence

A linear analysis of the zombie vortex instability is performed in a stratified shearing sheet setting for three model barotropic shear flows. The linear analysis is done by utilizing a Green's function formulation to resolve the critical layers of the associated normal-mode problem. The instability is the result of a resonant interaction between a Rossby wave and a gravity wave which we refer to as Z-modes. The associated critical layer is the location where the Doppler shifted frequency of a distant Rossby wave equals the local Brunt-Vaisala frequency. The minimum required Rossby number for instability, Ro= 0.2, is confirmed for parameter values reported in the literature. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The zombie vortex instability is examined in a jet model, finding that the instability can occur for Ro= 0.05. Nonlinear vorticity forcing due to unstable Z-modes is shown to result in the creation of a jet flow at the critical layer emerging as the result of the competition between the vertical lifting of perturbation radial vorticity and the radial transport of perturbation vertical vorticity. We find that the picture of this instability leading to a form of nonlinearly driven self-replicating pattern of creation and destruction is warranted: a parent jet spawns a growing child jet at associated critical layers. A mature child jet creates a next generation of child jets at associated critical layers while simultaneously destroying its parent jet via the Rossby wave instability.

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arXiv2015

Global Modeling of Nebulae with Particle Growth, Drift and Evaporation Fronts. I: Methodology and Typical Results

We model particle growth in a turbulent, viscously evolving protoplanetary nebula, incorporating sticking, bouncing, fragmentation, and mass transfer at high speeds. We treat small particles using a moments method and large particles using a traditional histogram binning, including a probability distribution function of collisional velocities. The fragmentation strength of the particles depends on their composition (icy aggregates are stronger than silicate aggregates). The particle opacity, which controls the nebula thermal structure, evolves as particles grow and mass redistributes. While growing, particles drift radially due to nebula headwind drag. Particles of different compositions evaporate at "evaporation fronts" (EFs) where the midplane temperature exceeds their respective evaporation temperatures. We track the vapor and solid phases of each component, accounting for advection and radial and vertical diffusion. We present characteristic results in evolutions lasting $2 \times 10^5$ years. In general, (a) mass is transferred from the outer to inner nebula in significant amounts, creating radial concentrations of solids at EFs, (b) particle sizes are limited by a combination of fragmentation, bouncing, and drift, (c) "lucky" large particles never represent a significant amount of mass, and (d) restricted radial zones just outside each EF become compositionally enriched in the associated volatiles. We point out implications for mm-submm SEDs and inference of nebula mass, radial banding, the role of opacity on new mechanisms for generating turbulence, enrichment of meteorites in heavy oxygen isotopes, variable and nonsolar redox conditions, primary accretion of silicate and icy planetesimals, and the makeup of Jupiter's core.

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arXiv2015

Observing Planetary Rings with JWST: Science Justification and Observation Requirements

The James Webb Space Telescope (JWST) will provide unprecedented opportunities to observe the rings and small satellites in our solar system, accomplishing three primary objectives: 1) discovering new rings and moons, 2) unprecedented spectroscopy, and 3) time-domain observations. We give details on these science objectives and describe requirements that JWST must fulfill in order to accomplish the science objectives

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arXiv2015

New Paradigms For Asteroid Formation

Asteroids and meteorites provide key evidence on the formation of planetesimals in the Solar System. Asteroids are traditionally thought to form in a bottom-up process by coagulation within a population of initially km-scale planetesimals. However, new models challenge this idea by demonstrating that asteroids of sizes from 100 to 1000 km can form directly from the gravitational collapse of small particles which have organised themselves in dense filaments and clusters in the turbulent gas. Particles concentrate passively between eddies down to the smallest scales of the turbulent gas flow and inside large-scale pressure bumps and vortices. The streaming instability causes particles to take an active role in the concentration, by piling up in dense filaments whose friction on the gas reduces the radial drift compared to that of isolated particles. In this chapter we review new paradigms for asteroid formation and compare critically against the observed properties of asteroids as well as constraints from meteorites. Chondrules of typical sizes from 0.1 to 1 mm are ubiquitous in primitive meteorites and likely represent the primary building blocks of asteroids. Chondrule-sized particles are nevertheless tightly coupled to the gas via friction and are therefore hard to concentrate in large amounts in the turbulent gas. We review recent progress on understanding the incorporation of chondrules into the asteroids, including layered accretion models where chondrules are accreted onto asteroids over millions of years. We highlight in the end ten unsolved questions in asteroid formation where we expect that progress will be made over the next decade.

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arXiv2015

The Gravitational instability of solids assisted by gas drag: slowing by turbulent mass diffusivity

The Goldreich and Ward (1973) (axisymmetric) gravitational instability of a razor thin particle layer occurs when the Toomre parameter $Q_T \equiv c_p Ω_0 / πG Σ_p < 1$ ($c_p$ being the particle dispersion velocity). Ward(1976,2000) extended this analysis by adding the effect of gas drag upon particles and found that even when $Q_T > 1$, sufficiently long waves were always unstable. Youdin (2005a,b) carried out a detailed analysis and showed that the instability allows chondrule-sized ($\sim 1 $ mm) particles to undergo radial clumping with reasonable growth times even in the presence of a moderate amount of turbulent stirring. The analysis of Youdin includes the role of turbulence in setting the thickness of the dust layer and in creating a turbulent particle pressure in the momentum equation. However, he ignores the effect of turbulent mass diffusivity on the disturbance wave. Here we show that including this effect reduces the growth-rate significantly, by an amount that depends on the level of turbulence, and reduces the maximum intensity of turbulence the instability can withstand by 1 to 3 orders of magnitude. The instability is viable only when turbulence is extremely weak and the solid to gas surface density of the particle layer is considerably enhanced over minimum-mass-nebula values. A simple mechanistic explanation of the instability shows how the azimuthal component of drag promotes instability while the radial component hinders it. A gravito-diffusive overstability is also possible but never realized in the nebula models.

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arXiv2015

The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas

Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, $J_t$, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas as a separate parameter. An ordinary differential equation model is developed which takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit $J_t \to 0$, collapse time equals sedimentation time. As $J_t$ increases, the collapse time decreases roughly linearly with $J_t$ until $J_t \gtrsim 0.4$ when it becomes approximately equal to the dynamical time.

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