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At least 19 records

Vorticity Transport and Wave Emission In A Protoplanetary Disk

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler 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 disk 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 from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.

Davis, S. S.↗

Annual Research Briefs - 2000: Center for Turbulence Research

This report contains the 2000 annual progress reports of the postdoctoral Fellows and visiting scholars of the Center for Turbulence Research (CTR). It summarizes the research efforts undertaken under the core CTR program. Last year, CTR sponsored sixteen resident Postdoctoral Fellows, nine Research Associates, and two Senior Research Fellows, hosted seven short term visitors, and supported four doctoral students. The Research Associates are supported by the Departments of Defense and Energy. The reports in this volume are divided into five groups. The first group largely consists of the new areas of interest at CTR. It includes efficient algorithms for molecular dynamics, stability in protoplanetary disks, and experimental and numerical applications of evolutionary optimization algorithms for jet flow control. The next group of reports is in experimental, theoretical, and numerical modeling efforts in turbulent combustion. As more challenging computations are attempted, the need for additional theoretical and experimental studies in combustion has emerged. A pacing item for computation of nonpremixed combustion is the prediction of extinction and re-ignition phenomena, which is currently being addressed at CTR. The third group of reports is in the development of accurate and efficient numerical methods, which has always been an important part of CTR's work. This is the tool development part of the program which supports our high fidelity numerical simulations in such areas as turbulence in complex geometries, hypersonics, and acoustics. The final two groups of reports are concerned with LES and RANS prediction methods. There has been significant progress in wall modeling for LES of high Reynolds number turbulence and in validation of the v(exp 2) - f model for industrial applications.

Source record↗

Dust Coagulation in Protoplanetary Accretion Disks

The time evolution of dust particles in circumstellar disk-like structures around protostars and young stellar objects is discussed. In particular, we consider the coagulation of grains due to collisional aggregation. The coagulation of the particles is calculated by solving numerically the non-linear Smoluchowski equation. The different physical processes leading to relative velocities between the grains are investigated. The relative velocities may be induced by Brownian motion, turbulence and drift motion. Starting from different regimes which can be identified during the grain growth we also discuss the evolution of dust opacities. These opacities are important for both the derivation of the circumstellar dust mass from submillimeter/millimeter continuum observations and the dynamical behavior of the disks. We present results of our numerical studies of the coagulation of dust grains in a turbulent protoplanetary accretion disk described by a time-dependent one-dimensional (radial) alpha-model. For several periods and disk radii, mass distributions of coagulated grains have been calculated. From these mass spectra, we determined the corresponding Rosseland mean dust opacities. The influence of grain opacity changes due to dust coagulation on the dynamical evolution of a protostellar disk is considered. Significant changes in the thermal structure of the protoplanetary nebula are observed. A 'gap' in the accretion disk forms at the very frontier of the coagulation, i.e., behind the sublimation boundary in the region between 1 and 5 AU.

Schmitt, W.↗

Numerical Simulation of Protoplanetary Vortices

The fluid dynamics within a protoplanetary disk has been attracting the attention of many researchers for a few decades. Previous works include, to list only a few among many others, the well-known prescription of Shakura & Sunyaev, the convective and instability study of Stone & Balbus and Hawley et al., the Rossby wave approach of Lovelace et al., as well as a recent work by Klahr & Bodenheimer, which attempted to identify turbulent flow within the disk. The disk is commonly understood to be a thin gas disk rotating around a central star with differential rotation (the Keplerian velocity), and the central quest remains as how the flow behavior deviates (albeit by a small amount) from a strong balance established between gravitational and centrifugal forces, transfers mass and momentum inward, and eventually forms planetesimals and planets. In earlier works we have briefly described the possible physical processes involved in the disk; we have proposed the existence of long-lasting, coherent vortices as an efficient agent for mass and momentum transport. In particular, Barranco et al. provided a general mathematical framework that is suitable for the asymptotic regime of the disk; Barranco & Marcus (2000) addressed a proposed vortex-dust interaction mechanism which might lead to planetesimal formation; and Lin et al. (2002), as inspired by general geophysical vortex dynamics, proposed basic mechanisms by which vortices can transport mass and angular momentum. The current work follows up on our previous effort. We shall focus on the detailed numerical implementation of our problem. We have developed a parallel, pseudo-spectral code to simulate the full three-dimensional vortex dynamics in a stably-stratified, differentially rotating frame, which represents the environment of the disk. Our simulation is validated with full diagnostics and comparisons, and we present our results on a family of three-dimensional, coherent equilibrium vortices.

Lin, H.↗

VLA Imaging of Protoplanetary Environments

Our program uses the techniques of millimeter interferometry to make high resolution observations of dust continuum emission to study the structure of protoplanetary disks around nearby stars. We continue to use the Very Large Array (VLA) of the National Radio Astronomy Observatories (NRAO) to make produce high angular resolution images, and we are improving our capabilities to interpret these observations with detailed numerical models. We have also made the first millimeter interferometer observations of protoplanetary disks in the southern hemisphere, using the recently upgraded Australia Telescope Compact Array (ATCA), taking advantage of the techniques we have developed in our work on northern sources.

Wilner, David J.↗

Dynamics of the accumulation process of the Earth group of planets: Formation of the reverse rotation of Venus

A numerical simulation of the process of formation of the terrestrial planets is carried within the framework of a new theory for the accumulation of planetary and satellite systems. The numerical simulation permitted determining the parameters of the protoplanetary disk from which Mercury, Venus and the Earth were formed as result of the evolution. The acquisition of a slow retrograde rotation for Venus was discovered during the course of the investigation, whereas Mercury and the Earth acquired direct rotation about their axes. Deviations of the semimajor axes of these three planets as well as the masses of the Earth and Venus from the true values are small as a rule (l 10%). It is shown that during the accumulation of the terrestrial planets, there existed a profound relationship between the process of formation of the orbits and masses of the planet and the process of formation of their rotation about their axes. Estimates are presented for the radii of the initial effective bodies and the time of evolution for the terrestrial accumulation zone.

Koslov, N. N.↗

Vorticity and Wave Motion in a Compressible Protoplanetary Disk

The impact of an isolated vortex in a compressible Keplerian disk is examined using higher order numerical solutions of the Euler and entropy-conserving Energy equations. The vortex is stretched by the background shear flow with longer lasting anticyclonic vortices persisting for about 10 vortex revolutions. Simultaneously, the vortex emits transient radial waves consisting mainly of axisymmetrical weak shock waves and a slower, nonaxisymmetric Rossby wave. These waves may contribute to certain transient events in protoplanetary disks. The vortex stretching and waves were found to have little long-term feedback on the baseline 'standard solar nebula' disk structure and confirm the extremely stable structure of non self-gravitating disks.

Davis, Sanford S.↗

Generation of dynamo magnetic fields in protoplanetary and other astrophysical accretion disks

A computational method for treating the generation of dynamo magnetic fields in astrophysical disks is presented. The numerical difficulty of handling the boundary condition at infinity in the cylindrical disk geometry is overcome by embedding the disk in a spherical computational space and matching the solutions to analytically tractable spherical functions in the surrounding space. The lowest lying dynamo normal modes for a 'thick' astrophysical disk are calculated. The generated modes found are all oscillatory and spatially localized. Tha potential implications of the results for the properties of dynamo magnetic fields in real astrophysical disks are discussed.

Stepinski, T. F.↗

Simulations of the STIS CCD clear imaging mode PSF

Detailed understanding of the properties of the point-spread function (PSF) of Space Telescope Imaging Spectrograph (STIS) imaging modes is necessary to separate real effects of geometrically complex astronomical sources, such as protoplanetary disks surrounding bright stars, from instrumental effects, such as scattering and diffraction. In order to investigate STIS imaging properties we have numerically simulated broadband stellar PSFs generated by STIS in CCD clear imaging mode, including the effects of the Lyot stop and the coronagraphic wedges. The input spectrum is a stellar model atmosphere of the appropriate spectral type, convolved with the pre-flight STIS CCD response function. The PSF modeler generates broadband PSFs by co-adding weighted monochromatic PSFs across the waveband.

Cornett, R. H.↗

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↗

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.↗

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↗

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.↗

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.↗

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.↗

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.↗

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↗

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↗