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NASA NTRS1999

Turbulent Concentration of Chondrules: Size Distribution and Multifractal Scaling

Size-selective concentration of particles in 3D turbulence may be related to collection of chondrules and other constituents into primitive bodies in a weakly turbulent protoplanetary nebula. In the terrestrial planet region, both the characteristic size and narrow size distribution of chondrules are explained, whereas "fluffier" particles would be concentrated in lower density, or more intensely turbulent, regions of the nebula. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a dose tie to the turbulent cascade process. This scaling behavior allows predictions of the concentration probabilities to be made in the protoplanetary nebula, which are so large (> 10(exp 3) - 10(exp 4)) that further studies must be made of the role of mass loading.

Cuzzi, Jeffrey N.↗

NASA NTRS1998

Turbulence, Chondrules, and Planetesimals

It has been shown both numerically and experimentally that 3-D turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter, in "Chondrules and the protoplanetary disk" 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 = Re(nu)(sub m)/cH, where nu(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 > 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 ~ 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.

Cuzzi, Jeffrey↗

NASA NTRS1993

Solar Nebula Magnetohydrodynamic Dynamos: Kinematic Theory, Dynamical Constraints, and Magnetic Transport of Angular Momentum

A hydromagnetic dynamo provides the best mechanism for contemporaneously producing magnetic fields in a turbulent solar nebula. We investigate the solar nebula in the framework of a steady-state accretion disk model and establish the criteria for a viable nebular dynamo. We have found that typically a magnetic gap exists in the nebula, the region where the degree of ionization is too small for the magnetic field to couple to the gas. The location and width of this gap depend on the particular model; the supposition is that gaps cover different parts of the nebula at different evolutionary stages. We have found, from several dynamical constraints, that the generated magnetic field is likely to saturate at a strength equal to equipartition with the kinetic energy of turbulence. Maxwell stress arising from a large-scale magnetic field may significantly influence nebular structure, and Maxwell stress due to small-scale fields can actually dominate other stresses in the inner parts of the nebula. We also argue that the bulk of nebular gas, within the scale height from the midplane, is stable against Balbus-Hawley instability.

Stepinski, Tomasz F.↗

NASA NTRS1982

Nucleation and condensation in the primitive solar nebula

It is pointed out that the primitive solar nebula may be modeled using the frictionally induced transport theory of Lynden-Bell and Pringle (1974) if the principal frictional mechanism within the nebula is turbulent viscosity. The present investigation is concerned with the construction of a model of a section of the primitive solar nebula as a basis for the study of nucleation and condensation processes within this section. The construction involves a relatively simple application of the Lynden-Bell and Pringle theory subject to steady mass flow conditions. The calculations which are conducted in connection with the investigation indicate that by the time the gas in the primitive solar nebula has become sufficiently supercooled to nucleate condensation centers, several different compounds, including the magnesium silicates forsterite and enstatite (MgSiO3), will probably be able to condense on the growing condensation center.

Cameron, A. G. W.↗

NASA NTRS1989

Radial mixing of material in the asteroidal zone

The asteroid belt shows radial zoning of compositional structure. The most abundant types are successively S, C, and P types from the inner to the outer parts of the main belt, and D type in the Trojan clouds. This paper examines processes for producing this structure before, during, and after the accretion of asteroids. The initial structure is established by temperature and composition gradients in the turbulent solar nebula during the collapse of the presolar cloud. The radial scale of the zoning, comparable to the disk thickness, favors disk models with relatively low turbulent viscosity. Radial decay of solid bodies due to gas drag during settling to the central plane and planetesimal formation probably causes only a small degree of mixing, due to the systematic nature of drag-induced motions. The formation of Jupiter causes scattering of massive planetesimals from that planet's zone through the asteroid zone. The present random velocities of asteroids resulting from that stirring process are consistent with the radial scale of transitions between compositional types.

Ruzmaikina, T. V.↗

NASA NTRS1988

Comparisons of solar nebula models

The relationship between meteorites and solar nebulae is examined. Turbulent models of the solar nebulae are compared and discussed.

Weidenschilling, S. J.↗

DOE OSTI2026

Early Solar Wind and Dynamo Magnetic Field Topology Predictions for (16) Psyche and Other Asteroids

Abstract Asteroid (16) Psyche is a metal‐rich body that might record an ancient coherent magnetization if some relict crust or mantle is preserved. Herein, we use magnetohydrodynamic simulations to predict (16) Psyche's field topology for several distinct pathways: (i) an early solar wind‐induced magnetization imparted after a larger body was impacted, forming the present‐day asteroid, (ii) a core dynamo magnetization imparted in an asteroid that is either presently largely intact or was a rubble pile, and (iii) magnetization in the turbulent solar nebula disk. For pathway (i) we find the field to be predominantly dipolar and spin axis‐aligned. For pathway (ii) we find the field to be either dipolar and spin axis‐misaligned, or highly multipolar. We also find that (iii) a field produced earlier before the solar nebula cleared, would be highly multipolar. In cases (i) and (ii) we also place constraints on the field strength. Simple detection of a magnetic field without constraining its topology and temporal variability would be insufficient to confirm a remanent source, due to the influence of the present‐day solar wind, electromagnetic induction, and (16) Psyche's high obliquity. For sufficiently strong fields however, the field topology and orientation may reveal key observable consequences of the nature and history of (16) Psyche. Our framework is also broadly applicable to the study of magnetic fields from other asteroids.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2003

Hydrodynamic Instability and Enhanced Transport in Protoplanetary Nebulae

The nature of turbulence (and the enhanced transport it provides) is a key element to comprehend the dynamics, physics and chemistry of the protoplanetary nebulae and consequently the planet formation process. Early accretion disk models postulated the turbulent transport through the well-known "alpha-viscosity" model, introduced by Shakura and Sunyaev in 1973. Since then, the nature of the turbulence in disks has been a subject of investigation. In 1991, the rediscovery by Balbus and Hawley of Chandrasekhar's linear instability in magnetized disks was a breakthrough in the discipline. Unfortunately, the mechanisms leading to turbulence in non-magnetized disks, such as protoplanetary nebulae, remain poorly understood. We will present results from laboratory experiments along with analytical arguments showing that, despite skepticism in the Astrophysical community, differential rotation may indeed be sufficient to trigger and sustain turbulence. We will also propose an alternative viscosity prescription derived from both experiments and analysis.

Richard, Denis T.↗

NASA NTRS1988

The velocity structure and turbulence at the center of the Orion Nebula

Using the Coude Feed System of the Kitt Peak National Observatory at its highest possible dispersion and a CCD detector with wide dynamic range it was possible to examine in detail the radial and turbulent velocities of the Orion Nebula at the seeing limit. For the first time, multiple components of the spectral lines were resolved and the Gaussian profiles fit to them. Using four different observing runs, two circular areas 2 minutes in diameter were observed, the first centered on the theta sup 1 Orionis and the second centered on theta sup 2 Orionis. The velocity resolution of 1 km/s combined with the angular resolution of 2 seconds allowed observation in detail at line splitting as well as the location and measurement of high internal motions, about -50 km/s with respect to the bulk of ionized matter. Because over 900 different positions were measured, modern statistical techniques were used for the analysis of turbulence, so that the dispersion relation and the structure function could be calculated and compared with predictions of the Kolmogorov theory. The random motions showed correlation with spatial separation, as expected for turbulence; but comparison with predictions of the classical theory for nebular turbulence showed poor agreement. If Kolmogorov theory applies, then the energy must be input at many scales.

Castaneda, Hector O.↗

NASA NTRS1996

Planetesimal Formation in the Outer Solar Nebula

A numerical investigation of the orbital trajectories of individual particles in the turbulent outer solar nebula has been performed. The (spherical) particle consists of an unchanging mm-sized 'dust' core surrounded by an H2O ice mantle; the density of both core and mantle is 0.5 g/cm(exp 3). The simulations include the effects of H2O condensation from the gas phase, H2O sublimation from the particle surface, and collisional growth via particle collisions with a background distribution of small H2O grains. The model nebula is an azimuthally symmetric minimum-mass nebula of solar composition with a vertical (and radial) temperature gradient. Particle evolution follows a pattern. A particle starting out in a cool region grows via condensation and collisional accretion until it is large enough (decimeter- to meter-sized) to decouple somewhat from the turbulence. (This growth occurs on a timescale of several thousand years at 10 AU; at 30 AU, the timescale is approx. 104 years.) The particle then moves rapidly inward toward the sun due to secular gas drag forces, sublimates much of its icy mantle, and slows its inward migration as it gets caught up in the turbulence again (due to its now-smaller size) at the 'sublimation boundary,' where the ambient gas temperature is approx. 150 K. Such a process could, on a short timescale (i.e., a timescale much shorter than the nebular gas lifetime of approx. 106 yr), generate a population of decimeter- to meter-sized bodies which would then collisionally accrete to form planetesimals.

Supulver, K. D.↗

NASA NTRS1998

Mineralogic and Petrologic Studies of Meteorites and Lunar Samples

In the period named, P.I. Wood and his Research Associate M.I. Petaev published or submitted for publication the following papers and abstracts, which address the subjects: Simulation of melting-crystallization relationships in chondritic and achondritic igneous systems. METEOMOD: A numerical model for the calculation of melting-crystalyization relationships in meteoritic igneous systems. Secondary Ca-Fe-rich minerals in the Bali-like and Allende-like oxidized CV3 chondrites and Allende dark inclusions. Silica minerals in the Gibeon IVA iron meteorite. Drusy vugs in the Albion iron meteorite: Mineralogy and textures. Search for exsolved ferromagnesian olivines: A meteoritic survey. Cr-bearing minerals in the Gibeon IVA iron: Indicators of sulfur and oxygen fugacities in the parent body. Lunar Planet. Computer modelling of ordinary chondrite melting. Drusy vugs in the Albion iron meteorite: Early speculation on the origin. Also Processing of chondritic and planetary material in spiral density waves in the nebula. Chondrite formation by turbulence and shock in the solar nebula.

Wood, John A.↗

NASA NTRS1993

Magnetically controlled solar nebula

It is widely believed that a primordial solar nebula, the precursor of the Sun and its planetary system, could be best described in terms of an accretion disk. Such an accretion disk is though to be turbulent, and it is usually imagined that turbulent viscosity alone provides the torque responsible for the structure and the evolution of the nebula. However, it was found that an MHD dynamo operating in a turbulent nebula can contemporaneously produce magnetic fields capable of significantly altering or even dominating the total torque. Thus, it seems that no model of a viscous solar nebula is complete without taking magnetic fields into consideration. It was demonstrated that there are usually two distinct regions of nebular disk where a dynamo can operate: the inner region, where the magnetic field coupled to gas due to relatively high thermal ionization; and the outer region, where this coupling is achieved due to nonthermal ionization. Most models also show the existence of an intermediate region, 'the magnetic gap,' where neither thermal nor nonthermal sources can produce enough ionization to provide the necessary coupling between the magnetic field and the gas. The location and width of the gap change substantially from one model to another. At present, we can only estimate the strength of a generated magnetic field. It seems that a large-scale magnetic field is likely to be in the equipartition with the turbulent kinetic energy; however, the intense magnetic fluctuations may greatly exceed this equipartition strength on short time and length scales. To show how a dynamo-generated magnetic field changes the structure of a viscous nebula, we consider four nebula models extensively.

Stepinski, T. F.↗

NASA NTRS1995

A Numerical Turbulence Model for Multiphase Flows in the Protoplanetary Nebula

It is thought that planets form from solid particles in a flattened, rotating, 99% gaseous nebula. These grains gradually coagulate into millimeter-to-meter sized aggregates which settle toward the midplane of the nebula. It is widely believed that the resulting dense layer eventually becomes gravitationally unstable and collapses into 'planetesimals.' A new numerical model is presented to simulate the predominant processes (gravitation, vertical convection, and shear-driven turbulence) during the stage while the particulate material is still dispersed about the midplane of the nebula. In our previous work, particles were assumed to be spheres of a single radius; in the present work, particles are spheres of different radii. Results indicate that neither a broad nor a narrow distribution of particle sizes is likely to become gravitationally unstable.

Champney, Joelle M.↗

NASA NTRS2017

Planetesimals Born Big by Clustering Instability?

Roughly 100km diameter primitive bodies (today's asteroids and TNOs; [1]) are thought to be the end product of so-called "primary accretion". They dominated the initial mass function of planetesimals, and precipitated the onset of a subsequent stage, characterized by runaway gravitational effects, which proceeded onwards to planetary mass objects, some of which accreted massive gas envelopes. Asteroids are the parents of primitive meteorites; meteorite data suggest that asteroids initially formed directly from freelyfloating nebula particles in the mm-size range. Unfortunately, the process by which these primary 100km diameter planetesimals formed remains problematic. We review the most diagnostic primitive parent body observations, highlight critical aspects of the nebula context, and describe the issues facing various primary accretion models. We suggest a path forward that combines current scenarios of "turbulent concentration" (TC) and "streaming instabilities" (SI) into a triggered formation process we call clustering instability (CI). Under expected conditions of nebula turbulence, the success of these processes at forming terrestrial region (mostly silicate) planetesimals requires growth by sticking into aggregates in the several cm size range, at least, which is orders of magnitude more massive than allowed by current growth-by-sticking models using current experimental sticking parameters [2-4]. The situation is not as dire in the ice-rich outer solar system; however, growth outside of the snowline has important effects on growth inside of it [4] and at least one aspect of outer solar system planetesimals (high binary fraction) supports some kind of clustering instability.

Cuzzi, Jeffrey N.↗

NASA NTRS2017

Planetesimals Born Big by Clustering Instability?

Asteroids↗

NASA NTRS1978

Magnetic field in the primitive solar nebula

Carbonaceous chondrites have apparently been magnetized in their early history in magnetic fields with intensities of 0.1 to 10 G, but the origin of the magnetizing field has remained obscured. It is suggested that the magnetic field recorded in the remanence of carbonaceous chondrites may have been produced by a self-excited hydromagnetic dynamo in the gaseous preplanetary nebula from which the solar system is thought to have formed. Recently computed models for the evolution of the preplanetary nebula, consisting of turbulent and differentially rotating gaseous disks with characteristic radial scales of several AU, are used to demonstrate the feasibility of this hypothesis. The maximum field intensity that might be realized by the dynamo production process is estimated to be as high as 1 to 10 G, taking into account two dynamical mechanisms that limit the strength of the field (the Coriolis force and ambipolar diffusion).

Levy, E. H.↗

NASA NTRS1991

Aerodynamic and gasdynamic effects in cosmogony

An improved numerical code was constructed to model coagulation and settling of particles in disk nebula containing generic turbulence with arbitrary velocities in the gas. The turbulence is assumed to have a Kolmogorov eddy spectrum. Relative velocities of particles, which lead to collisions and possible coagulation, are computed as due all significant causes in their appropriate regimes: thermal motion, shear and inertial effects in turbulent eddies, and systematic motions due to settling and non-keplerian rotation of the gas. Significant improvements to this program were produced. One significant problem was the disparity of timescales for turbulent mixing and coagulation. To accurately compute the former, the timestep must be shorter than the smallest spatial scale (layer thickness) divided by the turbulent velocity. However, the size distribution often varies due to coagulation on much longer timescales. To minimize the computational overhead associated with collisions between particles of all sizes, a dual timestep was introduced. Collisional changes in the size distribution are computed once in every N substeps, where the substep is controlled by the turbulent diffusion velocity, and N is determined by the rate of collisions. This algorithm allowed simulations to be extended to longer times and later stages.

Weidenschilling, S. J.↗

NASA NTRS1987

Kinetics in a turbulent nebular cloud

Model calculations, which include the effects of turbulence during subsequent solar nebula evolution after the collapse of a cool interstellar cloud, can reconcile some of the apparent differences between physical parameters obtained from theory and the cosmochemical record. Two important aspects of turbulence in a protoplanetary cloud include the growth and transport of solid grains. While the physical effects of the process can be calculated and compared with the probable remains of the nebula formulation period, the more subtle effects on primitive grains and their survival in the cosmochemical record cannot be readily evaluated. The environment offered by the Space Station (or Space Shuttle) experimental facility can provide the vacuum and low gravity conditions for sufficiently long time periods required for experimental verification of these cosmochemical models.

Mackinnon, Ian D. R.↗