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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

On the tidal interaction between protoplanets and the protoplanetary disk. III - Orbital migration of protoplanets

The tidal interaction between a protoplanet and a gaseous protoplanetary disk is investigated, and the dynamical evolution of the disk and the orbital migration of the protoplanet in a self-consistent manner is considered. It is shown that the orbital migration of a protoplanet does not suppress the tendency for tidal truncation in the vicinity of its orbit. If the necessary condition for tidal truncation is satisfied, the protoplanet induces a tidal feedback mechanism that regulates the rate of angular momentum transfer between the protoplanet and the disk. Significant orbital migration can only occur on the viscous evolution time scale of the disk.

Lin, D. N. C.↗
NASA NTRS1991

Accretion rates of protoplanets

The rate at which planetesimals in a uniform surface density disk collide with, and are (assumed to be) accreted by, a massive protoplanet is calculated. The collision cross-section of a protoplanet is enhanced relative to its geometric cross-section due to its gravitational focusing of planetesimal trajectories. The gravitation enhancement (eccentricities and inclinations) decrease. For large random velocity planetesimals, encounters are sufficiently rapid (less than or approximately = 5 percent of and orbital period) that F(sub g) is well approximated by the two-body particle in a box formula, which neglects the gravitational effect of the Sun. As planetesimal velocities decrease, F(sub g) increases to approximately twice the two-body value, and then rises less rapidly than the two-body value, eventually dropping below it and asymptotically approaching a constant for sufficiently small random velocities. A scaling argument is presented that generalizes the results to protoplanets of arbitrary mass, radius, and orbital semimajor axis. Gravitational scatterings by a protoplanet prevent random velocities of the planetesimals within its accretion zone from becoming to small. When gravitational stirring is included, the maximum plausible value of the gravitation enhancement factor for rock protoplanets 1 Au from the Sun is F(sub g) of approximately 1000. If one protoplanet dominates gravitational scatterings in a given region of a protoplanetary disk, then it was found that the planetesimal inclinations are excited much less rapidly than eccentricities, in contrast to the two-body approximation, in which energy is roughly equipartitioned between eccentric and inclined random motions. The resulting skewed velocity dispersion allows for a more rapid rate of protoplanet growth.

Greenzweig, Yuval↗
NASA NTRS1979

The interaction between giant gaseous protoplanets and the primitive solar nebula

The manner in which a giant gaseous protoplanet becomes embedded in the primitive solar nebula determines surface boundary conditions which must be used in studying the evolution of such objects. On the one hand, if the system resembles a contact binary system, then the envelope of the protoplanet should approach the entropy of the surrounding nebula. On the other hand angular momentum transfer by resonance and tidal effects between the nebula and the protoplanet may cause the nebula to exhibit a zone of avoidance near the protoplanet, thus inhibiting exchange of material. This problem has been studied with a computer program developed by D. N. C. Lin which simulates disk hydrodynamics by particle motions with dissipation. These studies suggest that for expected values of the protoplanet/protosun mass ratios, significant inhibition of mass exchange is likely, so that it is a reasonable next step to undertake protoplanet evolution studies with the imposition of minimum protoplanet surface temperatures.

Cameron, A. G. W.↗
NASA NTRS1982

Evolution of giant gaseous protoplanets embedded in the primitive solar nebula

In contrast to earlier evolutionary calculations, which assumed that protoplanets are isolated, the present spherically symmetric approximation for a protoplanet of one Jovian mass during the early phase of quasi-static contraction invokes a time-dependent surface boundary condition that simulates physical conditions in an evolving primitive solar nebula. Assuming in a first set of calculations that the protoplanet is surrounded by a thermal bath whose temperature varies with time, and whose pressure is small and constant, results show evaporation and complete dispersal of the object. A second set of calculations varies both temperature and pressure at the surface with time, according to solar nebula models, and yields an acceleration or retardation of evolution, relative to that of an isolated protoplanet, depending on the relative entropy of the nebula and the protoplanet's outer layers. Processes by which terrestrial planets can form in the cores of giant gaseous protoplanets are discussed.

Cameron, A. G. W.↗
NASA NTRS1990

Accretion rates of protoplanets

Projections are made of the collision/accretion rates of planetesimals in a uniform surface-density disk with a massive protoplanet, whose collision cross-section is enhanced, relative to its geometric cross-section, by a gravitational focusing of the planetesimals' trajectories. A scaling method is presented which generalizes the results obtained to protoplanets of arbitrary mass, radius, and orbital semimajor axis. It is established that, in the case where one protoplanet dominates gravitational scattering in a given protoplanetary disk region, planetesimal inclinations are substantially less rapidly excited than eccentrocities; the skewed velocity dispersion thus generated allows for a more rapid rate of protoplanet growth.

Greenzweig, Yuval↗
NASA NTRS1991

Long-term evolution of a planetesimal swarm in the vicinity of a protoplanet

Many models of planet formation involve scenarios in which one or a few large protoplanets interact with a swarm of much smaller planetesimals. In such scenarios, three-body perturbations by the protoplanet as well as mutual collisions and gravitational interactions between the swarm bodies are important in determining the velocity distribution of the swarm. We are developing a model to examine the effects of these processes on the evolution of a planetesimal swarm. The model consists of a combination of numerical integrations of the gravitational influence of one (or a few) massive protoplanets on swarm bodies together with a statistical treatment of the interactions between the planetesimals. Integrating the planetesimal orbits allows us to take into account effects that are difficult to model analytically or statistically, such as three-body collision cross-sections and resonant perturbations by the protoplanet, while using a statistical treatment for the particle-particle interactions allows us to use a large enough sample to obtain meaningful results.

Kary, David M.↗
NASA NTRS1993

On the delivery of planetesimals to a protoplanet in the solar nebula

A planetesimal moving in the solar nebula experiences an aerodynamic drag which causes its orbit to circularize and shrink. However resonant perturbations from a protoplanet interior to the planetesimal's orbit can counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to an equilibrium value. The resonance trapping phenomenon is sensitive to several factors and we elaborate on these below. Orbital resonances form (partial) barriers to the transport of planetesimals into the feeding zone of the protoplanet. Here we report on a systematic study of the idealized system of a single protoplanet of mass much larger than the masses of the planetesimals, comparing relevant analytic estimates with numerical simulations. Our principal conclusion is that in a gas-rich environment, the bulk of the solid material delivered to the feeding zone of the protoplanet is in the form of bodies of small radius.

Malhotra, Renu↗
NASA NTRS2019

No Clear, Direct Evidence for Multiple Protoplanets Orbiting LkCa 15: LkCa 15 bcd are Likely Inner Disk Signals

Two studies utilizing sparse aperture-masking (SAM) interferometry and Hα differential imaging have reported multiple Jovian companions around the young solar-mass star, LkCa 15 (LkCa 15 bcd): thefirst claimed direct detection of infant, newly formed planets (“protoplanets”). We present new near-infrared direct imaging/spectroscopy from the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system coupled with Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) integral field spectrograph and multi-epoch thermal infrared imaging from Keck/ NIRC2 of LkCa 15 at high Strehl ratios. These data provide the first direct imaging look at the same wavelengths and in the same locations where previous studies identified the LkCa 15 protoplanets,and thus offer the first decisive test of their existence.The data do not reveal these planets. Instead,we resolve extended emission tracing adust disk with a brightness and location comparable to that claimed for LkCa 15 bcd. Forward-models attributing this signal to orbiting planets are inconsistent with the combined SCExAO/CHARIS and Keck/NIRC2 data. An inner disk provides a more compelling explanation for the SAM detections and perhaps also the claimed Hα detection of LkCa 15 b. We conclude that there is currently no clear, direct evidence for multiple protoplanets orbiting LkCa 15, although the system likely contains at least one unseen Jovian companion. To identify Jovian companions around LkCa 15 from future observations, the inner disk should be detected and its effect modeled, removed, and shown to be distinguishable from planets. Protoplanet candidates identified from similar systems should likewise be clearly distinguished from disk emission through modeling.

Thayne Currie↗
NASA NTRS1979

Structure and evolution of isolated giant gaseous protoplanets

A model is developed describing the structure and evolution of isolated giant gaseous protoplanets in the mass range 0.3-4.5 Jovian masses. The central region of protoplanets of mass less than about 1 Jovian mass is, at some evolutionary epoch, thermodynamically favorable to the liquefaction of major interstellar grain components. All protoplanets studied are convective throughout most of their interior. In addition, it was found that the thermal contraction time depends sensitively on the surface opacity (at T less than 200 K).

Decampli, W. M.↗
NASA NTRS1978

Physics of the primitive solar nebula and of giant gaseous protoplanets

It has been proposed that the supernova responsible for injecting Al-26 into the early solar system was in fact responsible for triggering the collapse of an interstellar cloud in order to produce a system of stars, one of which would be the solar system. Details concerning the mechanism involved in such a process are discussed. Attention is given to the evolution of the primitive solar nebula, the instabilities in the primitive solar nebula, and the giant gaseous protoplanets. The principal conclusion to be drawn from the material presented is that the primitive solar nebula was a rather chaotic place, highly turbulent, with the multiple formation of giant gaseous protoplanets.

Cameron, A. G. W.↗
NASA NTRS1989

Orbital migration of protoplanets - The inertial limit

The dynamical evolution of a disk and the orbital migration of an embedded protoplanet are examined. It is shown how the migration of a protoplanet due to density wave torques can suppress the tendency for tidal truncation of the disk. A critical mass is determined as a function of the disk properties that represents the limiting mass that can sustain drift without stalling. This inertial limit is derived analytically, using a quasi-steady state theory, and confirmed by numerical experiment. This result contradicts the claim of Lin and Papaloizou (1986) that such a limit does not exist. Orbital mobility of objects due to density wave torques may have played an important role in the early evolution of the solar system.

Ward, William R.↗
NASA NTRS1991

Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities

The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.

Greenzweig, Yuval↗
NASA NTRS1992

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Greenzweig, Yuval↗
NASA NTRS1993

Numerical calculations of the linear response of a gaseous disk to a protoplanet

Numerical calculations of the linear response of a 2D gaseous disk to the perturbations induced by a protoplanet and the corresponding torque are presented. When the pressure gradient is taken into account, torques are increased in disks with gradients in either surface density and sound speed, the effect of the latter being much greater for the same-sized gradient as measured by the power law index. The torques in turn may be used to calculate timescales for orbital migration of protoplanets.

Korycansky, D. G.↗
NASA NTRS1984

Mechanical models of close approaches and collisions of large protoplanets

In models of lunar origin by great impact, attention is usually paid to the hydrodynamic expansion resulting from the great amount of thermal energy. However, the source of this disruption is inevitably significant in a close approach between large bodies, it is to be expected that significant departures from simple hyperbolic orbits would occur even before impact. These departures could arise from mechanical effects, and hence purely mechanical models are worth pursuing. The most interesting results obtained for approach offsets are small multiples of the planet radius and approach velocities of a few kilometers/second. In an interaction between Mars and Earth sized protoplanets, most of the material ends in collision, but a few percent end in elliptic orbits and a few percent escape. Another model considered is an offset collision, arising from a wide range of approach velocities and offsets.

Kaula, W. M.↗
NASA NTRS1986

On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction

A method to analyze the full nonlinear response and physical processes associated with the tidal interaction between a binary system and a thin disk in the steady state is presented. Using this approach, density wave propagation, induced by tidal interaction, may be studied for a wide range of sound speeds and viscosities. The effect of self-gravity may also be incorporated. The results of several calculations relevant to the tidal interaction between a protoplanet and the primordial solar nebula are also presented.

Lin, D. N. C.↗
NASA NTRS1987

A vaporization model for iron/silicate fractionation in the Mercury protoplanet

A study has been carried out on the vaporization of a totally molten silicate magma of chondritic composition heated into the range 2500-3500 K. The motivation for this was to determine the changes in the composition of the mantle that would occur in the Mercury protoplanet should that body have been subjected to the high-temperature phase in the evolution of the primitive solar nebula, but the results are of more general interest. An empirical model based on ideal mixing of complex components was used to describe the nonideal magma. It is found that vaporization of about 70-80 percent of the original amount of silicate from a chondritic planet is required to produce an iron-rich body with a mean uncompressed density equal to that deduced for Mercury. At this point the silicate is depleted in the alkalis, FeO, and SiO2, and enriched in CaO, MgO, Al2O3, and TiO2 relative to chondritic material.

Fegley, Bruce, Jr.↗
NASA NTRS1991

Tidal disruption of inviscid protoplanets

Roche showed that equilibrium is impossible for a small fluid body synchronously orbiting a primary within a critical radius now termed the Roche limit. Tidal disruption of orbitally unbound bodies is a potentially important process for planetary formation through collisional accumulation, because the area of the Roche limit is considerably larger then the physical cross section of a protoplanet. Several previous studies were made of dynamical tidal disruption and different models of disruption were proposed. Because of the limitation of these analytical models, we have used a smoothed particle hydrodynamics (SPH) code to model the tidal disruption process. The code is basically the same as the one used to model giant impacts; we simply choose impact parameters large enough to avoid collisions. The primary and secondary both have iron cores and silicate mantles, and are initially isothermal at a molten temperature. The conclusions based on the analytical and numerical models are summarized.

Boss, Alan P.↗