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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Size-Selective Concentration of Chondrules and Other Small Particles in Protoplanetary Nebula Turbulence

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive bodY precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region. both the characteristic size and size distribution of chondrules are explained. "Fluffier" particles would be concentrated in nebula regions which were at a lower density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (less than 10(exp 5)) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.

Cuzzi, Jeffrey N.↗
NASA NTRS2015

Preferrential Concentration of Particles in Protoplanetary Nebula Turbulence

Preferential concentration in turbulence is a process that causes inertial particles to cluster in regions of high strain (in-between high vorticity regions), with specifics depending on their stopping time or Stokes number. This process is thought to be of importance in various problems including cloud droplet formation and aerosol transport in the atmosphere, sprays, and also in the formation of asteroids and comets in protoplanetary nebulae. In protoplanetary nebulae, the initial accretion of primitive bodies from freely-floating particles remains a problematic subject. Traditional growth-by-sticking models encounter a formidable "meter-size barrier" [1] in turbulent nebulae. One scenario that can lead directly from independent nebula particulates to large objects, avoiding the problematic m-km size range, involves formation of dense clumps of aerodynamically selected, typically mm-size particles in protoplanetary turbulence. There is evidence that at least the ordinary chondrite parent bodies were initially composed entirely of a homogeneous mix of such particles generally known as "chondrules" [2]. Thus, while it is arcane, turbulent preferential concentration acting directly on chondrule size particles are worthy of deeper study. Here, we present the statistical determination of particle multiplier distributions from numerical simulations of particle-laden isotopic turbulence, and a cascade model for modeling turbulent concentration at lengthscales and Reynolds numbers not accessible by numerical simulations. We find that the multiplier distributions are scale dependent at the very largest scales but have scale-invariant properties under a particular variable normalization at smaller scales.

protoplanetary nebulae↗
NASA NTRS1994

Turbulent diffusion and concentration of chondrules in the protoplanetary nebula

Turbulence is known to possess structure on many scales. The largest or integral scale L is usually taken to be the largest dimension of the system. Two different turbulent regimes are likely to be of importance. Early stage convective turbulence in a hot nebula probably extends over the entire nebula scale height, and probably has typical eddy frequency comparable to the orbit frequency. At a later stage, midplane shear layer turbulence can be driven by the presence of a differently rotating, densely settled particle layer, with different length and timescales.

Cuzzi, J. N.↗
NASA NTRS1994

Turbulent Diffusion and Concentration of "Chondrules" in the Protoplanetary Nebula

Turbulence is known to possess structure on many scales. The largest or integral scale L is usually taken to be the largest relevant dimension of the system; for the nebula as a whole, it would be on the order of a vertical gas scale height H approximately 0.1R where R is the distance from the sun. Turbulent kinetic energy cascades towards smaller scales; for fully developed, homogeneous turbulence, the turbulent kinetic energy peaks at the integral scale and is distributed within its "inertial range" according to the Kolmogorov energy spectrum dE(k) = E(sub 0)(kL)(sup -5/3)dk where k is the wavenumber or inverse wavelength. The smallest scale in a turbulent regime is the Kolmogorov scale (n)(sometimes referred to as the inner scale). On this scale, molecular viscosity can dissipate turbulent kinetic energy . Turbulent flows are characterized by their Reynolds number Re = UL/v, where U is a characteristic velocity scale and v is molecular viscosity. More energetic (higher Re) flows drive turbulence to smaller Kolmogorov scales: n = LRe(sup -3/4). Two different turbulent regimes are likely to be of importance; early stage convective turbulence in a hot nebula probably extends over the entire nebula scale height, and probably has typical eddy frequency comparable to the orbit frequency. At a later stage, midplane shear layer turbulence can be driven by the presence of a differentially rotating, densely settled particle layer, with different length and time scales.

Cuzzi, Jeffrey N.↗
NASA NTRS1985

Evolution of Grains in a Turbulent Solar Nebula

Planetesimal formation by gravitational instability of a dust layer requires a nonturbulent solar nebula. The assumption that the solar nebula is a turbulent, convective accretion disk is explored. Self consistent models of a convective disk depend on high opacity of the disk material, which must be provided by grains. Grain coagulation is implied by the requirement of forming planetesimals, as the turbulent velocities (approx. 1/3 sound speed) in the accretion disk would disrupt any dust layer. Collisional coagulation could form large planetesimals, simultaneously leaving a sufficient fraction of matter in small grains to maintain the nebula's opacity. Or, coagulation of grains into small (approx. cm) aggregates could lower the opacity enough for turbulence to decay. The evolution of a population of grains in a turbulent solar nebula is calculated numerically.

Weidenschilling, S. J.↗
NASA NTRS2003

Blowing in the Wind: II. Creation and Redistribution of Refractory Inclusions in a Turbulent Protoplanetary Nebula

Ca-Al rich refractory mineral inclusions (CAIs) found at 1-6% mass fraction in primitive chondrites appear to be 1-3 million years older than the dominant (chondrule) components which were accreted into the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the sun. We reassess the situation in terms of a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can overwhelm inward drift, and prevent significant numbers of CAI-size particles from being lost into the sun for times on the order of 10(exp 6) years. CAIs can form early, when the inner nebula was hot, and persist in sufficient abundance to be incorporated into primitive planetesimals at a much later time. Small (less than or approx. equal to 0.1 mm diameter) CAIs persist for longer times than large (greater than or approx. equal to 5mm diameter ones). To obtain a quantitative match t o the observed volume fractions of CAIs in chondrites, another process must be allowed for: a substantial enhancement of the inner hot nebula in silicate-forming material, which we suggest was caused by rapid inward drift of meter-sized objects. This early in nebula history, the drifting rubble would have a carbon content probably an order of magnitude larger than even the most primitive (CI) carbonaceous chondrites. Abundant carbon in the evaporating material would help keep the nebula oxygen fugacity low, plausably solar, as inferred for the formation environment of CAIs. The associated production of a larger than canonical amount of CO2 might also play a role in mass-independent fractionation of oxygen isotopes, leaving the gas rich in l60 as inferred from CAIs and other high temperature condensates.

Cuzzi, Jeffrey N.↗
NASA NTRS2003

Blowing in the Wind: II. Creation and Redistribution of Refractory Inclusions in a Turbulent Protoplanetary Nebula

Ca-A1 rich refractory mineral inclusions (CAIs) found at 1-6% mass fraction in primitive chondrites appear to be 1-3 million years older than the dominant (chondrule) components which were accreted into the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the sun. We reassess the situation in terms of a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can overwhelm inward drift, and prevent significant numbers of CAI-size particles from being lost into the sun for times on the order of 10(exp 6) years. CAIs can form early, when the inner nebula was hot, and persist in sufficient abundance to be incorporated into primitive planetesimals at a much later time. Small (less than or approximately 0.1 mm diameter) CAIs persist for longer times than large (greater than or approximately 5mm diameter ones. To obtain a quantitative match to the observed volume fractions of CAIs in chondrites, another process must be allowed for: a substantial enhancement of the inner hot nebula in silicate-forming material, which we suggest was caused by rapid inward drift of meter-sized objects. This early in nebula history, the drifting rubble would have a carbon content probably an order of magnitude larger than even the most primitive (CI) carbonaceous chondrites. Abundant carbon in the evaporating material would help keep the nebula oxygen fugacity low, plausibly solar; as inferred for the formation environment of CAIs. The associated production of a larger than canonical amount of CO2 might also play a role in mass-independent fractionation of oxygen isotopes, leaving the gas rich in O-16 as inferred from CAIs and other high temperature condensates.

Cuzzi, Jeffrey N.↗
NASA NTRS2003

Blowing in the Wind: I. Velocities of Chondrule-sized Particles in a Turbulent Protoplanetary Nebula

Small but macroscopic particles - chondrules, higher temperature mineral inclusions, metal grains, and their like - dominate the fabric of primitive meteorites. The properties of these constituents, and their relationship to the fine dust grains which surround them, suggest that they led an extended existence in a gaseous protoplanetary nebula prior to their incorporation into their parent primitive bodies. In this paper we explore in some detail the velocities acquired by such particles in a turbulent nebula. We treat velocities in inertial space (relevant to diffusion), velocities relative to the gas and entrained microscopic dust (relevant to accretion of dust rims), and velocities relative to each other (relevant to collisions). We extend previous work by presenting explicit, closed-form solutions for the magnitude and size dependence of these velocities in this important particle size regime, and compare these expressions with new numerical calculations. The magnitude and size dependence of these velocities have immediate applications to chondrule and CAI rimming by fine dust, and to their diffusion in the nebula, which we explore separately.

Cuzzi, Jeffrey N.↗
NASA NTRS2003

Blowing in the Wind: Velocities of Chondrule-Sized Particles in a Turbulent Protoplanetary Nebula - 1

Small but macroscopic particles-chondrules, higher temperature mineral inclusions, metal grains and their like-dominate the fabric of primitive meteorites. The properties of these constituents, and their relationship to the fine dust grains which surround them, suggest that they led an extended existence in a gaseous protoplanetary nebula prior to their incorporation into their parent primitive bodies. In this paper we explore in some detail the velocities acquired by such particles in a turbulent nebula. We treat velocities in inertial space (relevant to diffusion), velocities relative to the gas entrained microscopic dust (relevant to accretion of dust rims), and velocities relative to each other (relevant to collisions). We extend previous work by presenting explicit, closed-form solutions for the magnitude and size dependence of these velocities in this important particle size regime, and we compare these expressions with new numerical calculations. The magnitude and size dependence of these velocities have immediate applications to chondrule and CAI rimming by fine dust and to their diffusion in the nebula, which we explore separately.

Cuzzi, Jeffrey N.↗
NASA NTRS2017

Aggregates: The Fundamental Building Blocks of Planetesimals?

The initial accretion of primitive asteroids (meteorite parent bodies) from freely-floating nebula particles remains problematic. Traditional growth-by-sticking models in turbulent nebulae encounter a formidable "meter-size barrier" due to both drift and destruction, or even a mmtocmsize "bouncing" barrier. Even if growth by sticking could somehow breach these barriers (perhaps if the actual sticking or strength is larger than current estimates, which are based on pure ice or pure silicate), turbulent nebulae present further obstacles through the 1-10km size range. On the other hand, nonturbulent nebulae form large asteroids too quickly to explain long spreads in formation times, or the dearth of melted asteroids. Thus, the intensity of nebula turbulence (or "alpha ") is critical to the entire process. Theoretical understanding of nebula turbulence continues to evolve; while recent models of MRI (magneticallydriven) turbulence favor lowornoturbulence environments, purely hydrodynamic turbulence is making a comeback with three recently discovered mechanisms generating turbulence of moderate which do not rely on magnetic fields at all.

Cuzzi, J. N.↗
NASA NTRS1984

Evolution of grains in a turbulent solar nebula

In the present computation of the evolution of grain size distribution in a turbulent disk for turbulent solar nebula models, using realistic collisional outcomes and strengths of grain aggregates, the half space above the central plane of the disk is divided into a series of levels. At each level, the size distribution is represented by the population of a series of discrete size bins, each spanning an order of magnitude in mass. Coagulation, erosion, or disruption, occur for various combinations of relative particle sizes and velocities, together with assumed material strength, based on experimental impact data. The calculation is one-dimensional, in that it is performed at a single radial location in the disk.

Weidenschilling, S. J.↗
NASA NTRS1987

Accumulation of solid bodies in the solar nebula

Current theories on the accretion of the planets from the solar nebula are reviewed. The settling of solid material to the central plane of the nebula and the formation of planetesimals is reviewed for both the case of a laminar nebula and a turbulent nebula. The advances that have been made in understanding the accumulation of the terrestrial and giant planets in the solar nebula are reviewed along with the remaining problems.

Weidenschilling, S. J.↗
NASA NTRS2003

Creation and Distribution of CAIs in the Protoplanetary Nebula

CaAl rich refractory mineral inclusions (CAIs) found at 1 - 10% mass fraction in primitive chondrites appear to be several million years older than the dominant (chondrule) components in the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the sun. We assess a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can prevent significant numbers of CAI-size particles from being lost into the sun for times of 1 - 3 x 10(exp 6) years. To match the CAI abundances quantitatively, we advocate an enhancement of the inner hot nebula in silicate-forming material, due to rapid inward migration of very primitive, silicate and carbon rich, meter-sized objects. 'Combustion' of the carbon into CO would make the CAI formation environment more reduced than solar, as certain observations imply. Abundant CO might also play a role in mass-independent chemical fractionation of oxygen isotopes as seen in CAIs and associated primitive, high-temperature condensates.

Cuzzi, J. N.↗
NASA NTRS1998

Planetesimal Formation in the Protoplanetary Nebula

In this talk we will address two distinct phases of planetesimal formation, each of which is fundamentally dependent upon the coupled interactions of particles and turbulent nebula gas. It has been shown both numerically and experimentally that 3-D (three dimensional) turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Rev(sub m)/cH, where v(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha is greater than 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C is approximately equal to 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation. Once large particles (meter-size mass equivalent) reach the midplane, perhaps in the form of dense aggregates of the sort formed in 3D turbulence, they remain stable against gravitational instability but might grow rapidly by accretion of their drifting neighbors, depending on the level of global turbulence.

Cuzzi, Jeffrey N.↗
NASA NTRS1988

Rapid formation of Jupiter by diffuse redistribution of water vapor in the solar nebula

In the present, water-vapor diffusive redistribution and condensation model of solid material abundance enhancement in the solar nebula's Jupiter-formation region, the assumed turbulent nebula temperatures decrease inversely with radial distance from the center, and time-scales are set by turbulent viscosities. The length scale for condensation of diffusively-transported water vapor is about 0.4 AU, and the surface density of ice in the Jupiter-formation zone undergoes enhancement by a factor of as much as 75; this surface density enhancement is enough to precipitate the rapid accretion of planetesimals into a solid core.

Stevenson, David J.↗
NASA NTRS1990

Dynamo magnetic field-induced angular momentum transport in protostellar nebulae - The 'minimum mass' protosolar nebula

Magnetic torques can produce angular momentum redistribution in protostellar nebulas. Dynamo magnetic fields can be generated in differentially rotating and turbulent nebulas and can be the source of magnetic torques that transfer angular momentum from a protostar to a disk, as well as redistribute angular momentum within a disk. A magnetic field strength of 100-1000 G is needed to transport the major part of a protostar's angular momentum into a surrounding disk in a time characteristic of star formation, thus allowing formation of a solar-system size protoplanetary nebula in the usual 'minimum-mass' model of the protosolar nebula. This paper examines the possibility that a dynamo magnetic field could have induced the needed angular momentum transport from the proto-Sun to the protoplanetary nebula.

Stepinski, T. F.↗
NASA NTRS1996

Vortices and Planetesimals

How planetesimals form in a turbulent nebula is a key question for planetary formation. This paper investigates the interaction of the solid particles with the giant vortices, suspected to survive during many rotation periods in the protoplanetary disks. Such vortices could have an origin similar to that of the coherent structures of the 2D turbulence. It is found that these vortices can capture and concentrate large amounts of the solid particles. The strong efficiency of this mechanism make them the most favorable places where to form the planetesimals. A conclusion which holds even if their lifetime is assumed much shorter than expected.

Barge, P.↗