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NASA NTRS1996

Protoplanetary Formation and the FU Orionis Outburst

The following three publications which reference the above grant from the NASA Origins of Solar Systems program are attached and form the final technical report for this project. The research involved comparisons of the spectral energy distributions of FU Orionis objects with theoretical models and associated studies of the structure of the outbursting accretion disks, as well as related studies on the effects of magnetic fields in disks, which will lead in the future to models of FU Orionis outbursts which include the effects of magnetic fields. The project was renewed under a new grant NAGW-4456, entitled 'Effects of FU Orionis Outbursts on Protoplanetary Disks'. Work now being prepared for publication deals more specifically with the issue of the effects of the outbursts on protoplanetary formation. Models of the spectral energy distribution of FU Orionis stars. A simple model of a buoyant magnetic dynamo in accretion disks and a numerical study of magnetic buoyancy in an accretion disk have been submitted.

Bodenheimer, P. H.↗

NASA NTRS1999

Hubble Space Telescope observations of Orion Nebula, Helix Nebula, and NGC 6822

This grant covered the major part of the work of the Principal Investigator and his collaborators as a Guaranteed Time Observer on the Hubble Space Telescope. The work done naturally divided itself into two portions the first being study of nebular objects and the second investigation of the interstellar medium between stars. The latter investigation was pursued through a contract with Princeton University, with Professor Lyman Spitzer as the supervising astronomer, assisted by Dr. Ed Fitzpatrick. Following the abrupt death of Professor Spitzer, his responsibilities were shifted to Dr. Fitzpatrick. When Dr. Fitzpatrick relocated to Villanova University the concluding work on that portion of this grant was concluded under a direct service arrangement. This program has been highly successful and the resulting publications in scientific journals are listed below. To the scientist, this is the bottom line, so that I shall simply try to describe the general nature of what was accomplished. There were three nebular programs conducted, one on the Orion Nebula, the second on the Helix Nebula, and the third on NGC 6822. The largest program was that on the Orion Nebula. This involved both HST observations and supporting groundbased observations obtained with a variety of instruments, including the Coude Feed Telescope at the Kitt Peak National observatory in Arizona, the Cerro Tololo observatory in Chile, and the Keck Observatory on Mauna Kea, Hawaii. Moreover, considerable theoretical modeling was done and all of the data analysis was performed at the Rice University in Houston, except for the PI's period of sabbatical leave (6-96 through 7-97) when he was based at the Max Planck Institute for Astronomy in Heidelberg, Germany. The Orion Nebula program was the most productive part, resulting in numerous papers, but more important in the discovery of a new class of objects, for which we coined the name "proplyds". The proplyds are protoplanetary disks surrounding very young stars still in the process of creation. The Orion Nebula is the residual material from a burst of star formation that occurred about 300,000 years ago. Each of these new stars has a surrounding disk of protoplanetary material. The same physics that renders the Nebula so highly visible means that the proto-planetary disks are also quite visible. With the wisdom of hindsight, we now see that this was to be expected and that we should have been searching specifically for this type of object. The discovery of these objects and their subsequent detailed investigation has lead to an accurate assessment of the frequency of protoplanetary disks in young stars and determination of the likelihood of survival of these disks into an era where planets actually form.

Spitzer, Lyman↗

NASA NTRS2001

Vorticity Transport and Wave Emission in the Protoplanetary Nebula

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler/Energy equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the nebula to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived using the simulation data and compared with analytical dispersion relations from the linearized Euler/Energy equations.

Davis, S. S.↗

NASA NTRS1990

Generation of dynamo magnetic fields in thin Keplerian disks

The combined action of nonuniform rotation and helical convection in protoplanetary disks, in the Galaxy, or in accretion disks surrounding black holes and other compact objects, enables an alpha-omega dynamo to generate a large-scale magnetic field. In this paper, the properties of such magnetic fields are investigated using a two-dimensional, partially numerical method. The structures of the lowest-order steady state and oscillatory modes are calculated for two kinds of external boundary conditions. A quadruple, steady state, highly localized mode is the most easily excited for low values of the dynamo number. The results indicate that, except under special conditions, disk dynamo modes tend to consist of relatively localized rings structures. For large values of the dynamo number, the magnetic field consists of a number of quasi-independent, spatially localized modes generated in various concentric rings filling the disk inward of a dynamo generation 'front'.

Stepinski, T. F.↗

NASA NTRS2000

Computing Needs for Astrobiology: Models of Planetary Formation

Theories of planet formation indicate that a diverse range of physical and chemical processes determine the characteristics of a planetary system. Extensive numerical modeling is required to understand how planetary systems form, and to make quantitative assessments of the factors which determine the masses, spacings and volatile compound inventories of planets and small bodies within a planetary system. Fluid flow problems associated with the formation and evolution of protoplanetary disks include specific local calculations to provide physical insight, which are best performed on workstations, and large multifaceted simulations which require supercomputers with large memories. Formation and early growth of planetesimals display a similar range of computational requirements. Modeling the late stages of planetary accumulation is very CPU intensive, as it requires following a simple system of approx. hundreds of bodies for millions of dynamical (orbital) times. These varied computational needs could be met in the most cost-effective manner by a diverse set of computers, including workstations for individual PI's and dedicated time on various types of supercomputers which are specialized for differing tasks.

Lissauer, Jack J.↗

NASA NTRS2019

Revolutionizing our Understanding of the Solar System via Sample Return from Mercury

Data from Mariner 10, MESSENGER, and ground-based telescopic observations have facilitated great advancements towards understanding the geochemistry, geology, internal structure, exosphere, and magnetosphere of Mercury. However, there are critical science questions that can be only addressed via examination of a sample in Earth-based laboratories, where numerous highly sensitive analytical measurements are possible. Collecting a sample from the surface of Mercury and bringing it to Earth for in-depth analysis would allow for transformative Solar System science to be conducted, examining aspects of our Solar System such as the evolution of the protoplanetary disk, space weathering on airless bodies, the geochemical behavior of elements at extreme conditions, and the origin and distribution of volatiles across the terrestrial planets. Furthermore, our knowledge of Mercury’s differentiation and geochemical processes, chronology and geologic evolution, tectonism and geomechanical properties, and past and ongoing magnetism would be greatly advanced via analysis of a sample from Mercury. Although there are ample challenges and knowledge gaps associated with sample return from Mercury in terms of both spacecraft requirements and material requirements for curatorial facilities, a sample from the planet would be an invaluable scientific resource for generations to come, enabling the most sophisticated measurements to be brought to bear for decades and helping to truly unlock the mysteries of our Solar System.

Vander Kaaden, Kathleen E.↗

NASA NTRS1994

Gravitational instabilities in a proto-planetary disk including the effects of magnetic fields

We investigate the gravitational instability of a thin, Keplerian protoplanetary disk including the effects of a largely azimuthal magnetic field. The model follows that of our previous work (Noh, Vishniac, & Cochran 1991) except for the inclusion of a magnetic field. The disk is assumed to consist of neutral and ionized gas and neutral dust which are coupled by gravity and friction. The growth rates and eigenfunctions are calculated numerically using nonaxisymmetric linear perturbation methods. The results show that the growth rate has a maximum at some intermediate azimuthal number m, but for each value of m it is reduced relative to the unmagnetized case. The effects of the magnetic field appear more strongly on small scales. As the strength of the equilibrium magnetic field increases the growth rates decrease, and the maximum instability occurs at a lower value on m due to the increasing magnetic pressure. The response of each component to the magnetic field is discussed using the behavior of the eigenfunctions in the radial direction. With the inclusion of the magnetic field, the effects of the ionization fraction and friction on the growth rates also appear to be important for high m modes. Increasing the ionization fraction or the friction suppresses instability, but only slightly changes the maximally unstable azimuthal scales. The enhanced growth rates due to a dust component for which thermal pressure is negligible are somewhat reduced by the inclusion of a magnetic field. The effects of different boundary conditions (reflecting and transmitting) on the growth rates are also shown.

Noh, Hyerim↗

NASA NTRS2014

Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk-a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies-the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as 'primitive' bodies). One implication of the truncation mechanism proposed in Walsh et al. is the scattering of primitive planetesimals onto planet-crossing orbits during the formation of the planets. We find here that the planets will accrete on order 1-2% of their total mass from these bodies. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. The radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system. However, we find that a truncated disk leads to formation timescales more rapid than suggested by radiometric chronometers. In particular, the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. This is at odds with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with those constraints.

Planetary dynamics↗

NASA NTRS1995

Evolution of magnetized protoplanetary disks

We investigate the global evolution of a turbulent protoplanetary disk in its viscous stage, incorporating the effects of Maxwell stress due to a large-scale magnetic field permeating disk. We assume that the viscous stress is given by an alpha model. A magnetic field is produced contemporaneously by an alpha omega dynamo mechanism and the resultant Maxwell stress assists the viscous stress in providing the means for disk evolution. The aim of this work is to compare the evolution of magnetized and nonmagnetized disks driven by turbulent viscosity of the same magnitude and thus assess the effects of a self-generated magnetic field on the structure and dynamical evolution of protoplanetary disks. Two illustrative examples corresponding to two different initial conditions are considered: a high-mass case that starts with a disk of 0.245 solar mass and angular momentum of 5.6 x 10(exp 52)g sq cm/s, and a low-mass that case starts with a disk of 0.11 solar mass and angular momentum of 1.8 x 10(exp 52)g sq cm/s. For each of these two cases the radial development of a disk is calculated numerically assuming a fiducial value of the dimensionless viscosity parameter alpha(sub ss) = 0.01, as well as alpha(sub ss) = 2 x 10(exp -3). In all cases the central star has a mass equal to 1 solar mass. The most striking feature of magnetized disk evolution is the presence of the surface density bulge located in the region of the disk where the dynamo mechanism cannot support a magnetic field. The bulge persists for a time of the order of 10(exp 5)-10(exp 6) yr. The presence and persistence of the surface density bulge may have important implications for the process of planet formation and the overall characteristics of resultant planetary systems.

Reyes-Ruiz, Mauricio↗

NASA NTRS2012

Coordinated Oxygen Isotopic and Petrologic Studies of CAIS Record Varying Composition of Protosolar

Ca-, Al-rich inclusions (CAIs) record the O-isotope composition of Solar nebular gas from which they grew [1]. High spatial resolution O-isotope measurements afforded by ion microprobe analysis across the rims and margin of CAIs reveal systematic variations in (Delta)O-17 and suggest formation from a diversity of nebular environments [2-4]. This heterogeneity has been explained by isotopic mixing between the O-16-rich Solar reservoir [6] and a second O-16-poor reservoir (probably nebular gas) with a "planetary-like" isotopic composition [e.g., 1, 6-7], but the mechanism and location(s) where these events occur within the protoplanetary disk remain uncertain. The orientation of large and systematic variations in (Delta)O-17 reported by [3] for a compact Type A CAI from the Efremovka reduced CV3 chondrite differs dramatically from reports by [4] of a similar CAI, A37 from the Allende oxidized CV3 chondrite. Both studies conclude that CAIs were exposed to distinct, nebular O-isotope reservoirs, implying the transfer of CAIs among different settings within the protoplanetary disk [4]. To test this hypothesis further and the extent of intra-CAI O-isotopic variation, a pristine compact Type A CAI, Ef-1 from Efremovka, and a Type B2 CAI, TS4 from Allende were studied. Our new results are equally intriguing because, collectively, O-isotopic zoning patterns in the CAIs indicate a progressive and cyclic record. The results imply that CAIs were commonly exposed to multiple environments of distinct gas during their formation. Numerical models help constrain conditions and duration of these events.

Simon, Justin I.↗

NASA NTRS2016

The Formation of Nucleobases from the Irradiation of Purine in Astophysical Ices and Comparisons with Meteorites.

N-heterocycles have been identified in meteorites and their extraterrestrial origins are suggested by isotopic ratio measurements. Although small N- heterocycles have not been detected in the interstellar medium (ISM), recent experiments in our lab have shown that the irradiation of the aromatic molecules like benzene (C6H6) and naphthalene (C10H8) in mixed molecular ices leads to the formation of O- and N-heterocyclic molecules. Among the class of N-heterocycles are the nucleobases, which are of astrobiological interest because they are the information bearing units of DNA and RNA. Nucleobases have been detected in meteorites [3-5], with isotopic signatures that are also consistent with an extraterrestrial origin. Three of the biologically relevant nucleobases (uracil, cytosine, and guanine) have a pyrimidine core structure while the remaining two (adenine and guanine) possess a purine core. Previous experiments in our lab have demonstrated that all of the bio-logical nucleobases (and numerous other molecules) with a pyrimidine core structure can be produced by irradiating pyrimidine in mixed molecular ices of several compositions [6-8]. In this work, we study the formation of purine-based molecules, including the nucleobases adenine, and guanine, from the ultraviolet (UV) irradiation of purine in ices consisting mixtures of H2O and NH3 at low temperature. The experiments are designed to simulate the astrophysical conditions under which these species may be formed in dense molecular clouds, protoplanetary disks, or on the surfaces of icy bodies in planetary systems.

Astrochemistry↗

NASA NTRS1987

Numerical solution of the radiation transport equation in disk geometry

An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

Spagna, George F., Jr.↗

NASA NTRS2003

Protoplanetary Nebula Evolution using the Beta Viscosity Model

The evolutionary dynamics of a protoplanetary disk is an important component of the planet formation process. In particular, the dynamic and thermodynamic field plays a critical role in chemical evolution, the migration of dust particles in the nebula, and the radial transport of meteoritic components. The dynamic evolution is investigated using analytical solutions of the surface density transport equations using a turbulence model based on hydrodynamic generation of turbulence. It captures the major properties of the disk including region of separation between radial inflow and-outflow and the evolution of the central plane temperature. The analytical formulas are compared with available numerical solutions based on the alpha viscosity model. The beta viscosity model, heretofore used for steady-state disks, is shown to be a useful approximation for unsteady problems.

Davis, Sanford S.↗

NASA NTRS2003

Mixing and Transport in the Solar Nebula

Boss & Vanhala (2000, 2001) prepared reviews of triggered collapse and injection models, using Prudence Foster's finite differences code at very high spatial resolution (440 x 1440 cells) to demonstrate the convergence of the R-T fingers in triggered injection models. A two dimensional hydrodynamical calculation with unprecedentedly high spatial resolution (960 x 2880 zones, or almost 3 million grid points) demonstrated that it suitable shock front can both trigger the collapse of an otherwise stable presolar cloud, and inject shock front particles into the collapsing cloud through the formation of what become Rayleigh-Taylor fingers of compressed fluid layers falling into the gravitational potential well of the growing protostar. These calculations suggest that heterogeneity derived from these R-T fingers will persist down to the scale of their injection onto the surface of the solar nebula. Haghighipour developed a numerical code capable of calculating the orbital evolution of dust grains of varied sizes in a gaseous nebula, subject to Epstein and Stokes drag as well as the self-gravity of the disk. In collaboration with the PI and George W. Wetherill, Haghighipour has been involved in development of a new idea on the possibility of rapid formation of ice giant planets via the disk instability mechanism. Haghighipour studied the stability of a five-body system consisting of the Sun and four protoplanets by numerically integrating their equations of motions. Using Levison and Duncan s SWIFT integrator, Haghighipour showed that, depending on the orbital parameters of the bodies, such a system can be stable for 0.1-10 Myr. Time periods of 1 Myr or more are long enough to be consistent with the time scale proposed for the formation of giant planets by the disk instability mechanism and the photoevaporation of the gaseous envelopes of the outermost protoplanets by a nearby OB star, resulting in the formation of ice giant planets. The PI has used his three dimensional models of marginally gravitationally unstable disks to study the preservation of isotopic heterogeneity in evolving protoplanetary disks. Such heterogeneity might arise from the infall onto the disk s surface of solids processed in the X-wind region of the disk, or derived from stellar nucleosynthesis and injected by R-T fingers. The technique used consists of solving a color equation, identical to the gas continuity equation, which follows the time evolution in three space dimensions of an arbitrarily placed initial color field, i.e., a dye inserted the disk. The models show that significant concentrations of color could persist for time periods of about a thousand years or more, even in the most dynamically active region of such a disk. Such a time period might be long enough for solids to coagulate and grow to significant sizes while retaining the isotopic signature of their birth region in the nebula.

Boss, Alan P.↗

NASA NTRS1996

Global Evolution of Solid Matter in Turbulent Protoplanetry Disks: Aerodynamics of Solid Particles - Part 1

The problem of planetary system formation and its subsequent character can only be addressed by studying the global evolution of solid material entrained in gaseous protoplanetary disks. We start to investigate this problem by considering the space-time development of aerodynamic forces that cause solid particles to decouple from the gas. The aim of this work is to demonstrate that only the smallest particles are attached to the gas, or that the radial distribution of the solid matter has no momentary relation to the radial distribution of the gas. We present the illustrative example wherein a gaseous disk of 0.245 solar mass and angular momentum of 5.6 x 10(exp 52) g/sq cm/s is allowed to evolve due to turbulent viscosity characterized by either alpha = 10(exp -2) or alpha = 10(exp -3). The motion of solid particles suspended in a viscously evolving gaseous disk is calculated numerically for particles of different sizes. In addition we calculate the global evolution of single-sized, noncoagulating particles. We find that particles smaller than 0.1 cm move with the gas; larger particles have significant radial velocities relative to the gas. Particles larger than 0.1 cm but smaller than 10(exp 3) cm have inward radial velocities much larger than the gas, whereas particles larger than 10(exp 4) cm have inward velocities much smaller than the gas. A significant difference in the form of the radial distribution of solids and the gas develops with time. It is the radial distribution of solids, rather than the gas, that determines the character of an emerging planetary system.

Stepinski, T. F.↗

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 NTRS2011

The Transitional Protoplanetary Disk Frequency as a Function of Age: Disk Evolution in the Coronet Cluster, Taurus, and Other 1--8 Myr-old Regions

We present Spitzer 3.6-24 micron photometry and spectroscopy for stars in the 1-3 Myr-old Coronet Cluster, expanding upon the survey of Sicilia-Aguilar et al. (2008). Using sophisticated radiative transfer models, we analyze these new data and those from Sicilia-Aguilar et al. (2008) to identify disks with evidence for substantial dust evolution consistent with disk clearing: transitional disks. We then analyze data in Taurus and others young clusters - IC 348, NGC 2362, and eta Cha -- to constrain the transitional disk frequency as a function of time. Our analysis confirms previous results finding evidence for two types of transitional disks -- those with inner holes and those that are homologously depleted. The percentage of disks in the transitional phase increases from approx.15-20% at 1-2 Myr to > 50% at 5-8 Myr; the mean transitional disk lifetime is closer to approx. 1 Myr than 0.1-0.5 Myr, consistent with previous studies by Currie et al. (2009) and Sicilia-Aguilar et al. (2009). In the Coronet Cluster and IC 348, transitional disks are more numerous for very low-mass M3--M6 stars than for more massive K5-M2 stars, while Taurus lacks a strong spectral type-dependent frequency. Assuming standard values for the gas-to-dust ratio and other disk properties, the lower limit for the masses of optically-thick primordial disks is Mdisk approx. 0.001-0.003 M*. We find that single color-color diagrams do not by themselves uniquely identify transitional disks or primordial disks. Full SED modeling is required to accurately assess disk evolution for individual sources and inform statistical estimates of the transitional disk population in large samples using mid-IR colors.

Currie, Thayne↗

NASA NTRS1999

Computer Modeling of Electrostatic Aggregation of Granular Materials in Planetary and Astrophysical Settings

Electrostatic forces strongly influence the behavior of granular materials in both dispersed (cloud) systems and semi-packed systems. These forces can cause aggregation or dispersion of particles and are important in a variety of astrophysical and planetary settings. There are also many industrial and commercial settings where granular matter and electrostatics become partners for both good and bad. This partnership is important for human exploration on Mars where dust adheres to suits, machines, and habitats. Long-range Coulombic (electrostatic) forces, as opposed to contact-induced dipoles and van der Waals attractions, are generally regarded as resulting from net charge. We have proposed that in addition to net charge interactions, randomly distributed charge carriers on grains will result in a dipole moment regardless of any net charge. If grains are unconfined, or fluidized, they will rotate so that the dipole always induces attraction between grains. Aggregates are readily formed, and Coulombic polarity resulting from the dipole produces end-to-end stacking of grains to form filamentary aggregates. This has been demonstrated in USML experiments on Space Shuttle where microgravity facilitated the unmasking of static forces. It has also been demonstrated in a computer model using grains with charge carriers of both sign. Model results very closely resembled micro-g results with actual sand grains. Further computer modeling of the aggregation process has been conducted to improve our understanding of the aggregation process, and to provide a predictive tool for microgravity experiments slated for Space Station. These experiments will attempt to prove the dipole concept as outlined above. We have considerably enhanced the original computer model: refinements to the algorithm have improved the fidelity of grain behavior during grain contact, special attention has been paid to simulation time steps to enable establishment of a meaningful, quantitative time axis, and calibration of rounding accuracies have been conducted to test cumulative numerical influences in the model. The model has been run for larger grain populations, variable initial cloud densities, and we have introduced random net charging to individual grains, as well as a net charge to the cloud as a whole. The model uses 3 positive and 3 negative charges randomly distributed on each grain, with up to 160 grains contained within various size "boxes" that define the initial number densities in the clouds. Each charge represents localized charged region on a grain, but does not necessarily imply single quantized charge carriers. The Coulomb equations are then allowed to interact for each monopole: dipoles and any higher order charge coupling is a natural product of these "free" interactions over which the modeler exerts no influence. The charges are placed on surfaces of grains at random locations. A series of runs was conducted for neutral grains that had a perfect balance of negative and positive char carriers. Runs were also conducted with grains having additional fractional charges ranging between 0 and 1. By adding fractional charges of one sign, the model created grain populations in which all grains had excess charges the same sign, giving the cloud an overall net charge. This simulates clouds subjected to ionizing radiation (e. protoplanetary debris disk around a protosun), or any other process of charge biasing in a grain population (e.g., volcanic plumes). In another run series, random fractional charges of either sign were added to the grains so th some grains had a slight net positive charge while others had a slight net negative charge. This simulates triboelectrically-charged grain populations in which acquisition of an electron by one surface is at the expense creating a hole elsewhere. This dual sign charging was applied in two ways: in one case the cloud remained neutral by ensuring that all grain excess charges added to zero; in the other case, the cloud was permitted slight net char by not imposing a charge-balance condition. Additional information is contained in the original.

Marshall, J.↗