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Results for “GRAVITATIONAL INSTABILITY”

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
DOE OSTI2012

Effect of neutral collision and radiative heat-loss function on self-gravitational instability of viscous thermally conducting partially-ionized plasma

The problem of thermal instability and gravitational instability is investigated for a partially ionized self-gravitating plasma which has connection in astrophysical condensations. We use normal mode analysis method in this problem. The general dispersion relation is derived using linearized perturbation equations of the problem. Effects of collisions with neutrals, radiative heat-loss function, viscosity, thermal conductivity and magnetic field strength, on the instability of the system are discussed. The conditions of instability are derived for a temperature-dependent and density-dependent heat-loss function with thermal conductivity. Numerical calculations have been performed to discuss the effect of various physical parameters on the growth rate of the gravitational instability. The temperature-dependent heat-loss function, thermal conductivity, viscosity, magnetic field and neutral collision have stabilizing effect, while density-dependent heat-loss function has a destabilizing effect on the growth rate of the gravitational instability. With the help of Routh-Hurwitz's criterion, the stability of the system is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Jeans self gravitational instability of strongly coupled quantum plasma

The Jeans self-gravitational instability is studied for quantum plasma composed of weakly coupled degenerate electron fluid and non-degenerate strongly coupled ion fluid. The formulation for such system is done on the basis of two fluid theory. The dynamics of weakly coupled degenerate electron fluid is governed by inertialess momentum equation. The quantum forces associated with the quantum diffraction effects and the quantum statistical effects act on the degenerate electron fluid. The strong correlation effects of ion are embedded in generalized viscoelastic momentum equation including the viscoelasticity and shear viscosities of ion fluid. The general dispersion relation is obtained using the normal mode analysis technique for the two regimes of propagation, i.e., hydrodynamic and kinetic regimes. The Jeans condition of self-gravitational instability is also obtained for both regimes, in the hydrodynamic regime it is observed to be affected by the ion plasma oscillations and quantum parameter while in the kinetic regime in addition to ion plasma oscillations and quantum parameter, it is also affected by the ion velocity which is modified by the viscosity generated compressional effects. The Jeans critical wave number and corresponding critical mass are also obtained for strongly coupled quantum plasma for both regimes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

ON THE FORMATION OF PLANETESIMALS VIA SECULAR GRAVITATIONAL INSTABILITIES WITH TURBULENT STIRRING

We study the gravitational instability (GI) of small solids in a gas disk as a mechanism to form planetesimals. Dissipation from gas drag introduces secular GI, which proceeds even when standard GI criteria for a critical density or Toomre's Q predict stability. We include the stabilizing effects of turbulent diffusion, which suppresses small-scale GI. The radially wide rings that do collapse contain up to {approx}0.1 Earth masses of solids. Subsequent fragmentation of the ring (not modeled here) would produce a clan of chemically homogenous planetesimals. Particle radial drift time scales (and, to a lesser extent, disk lifetimes and sizes) restrict the viability of secular GI to disks with weak turbulent diffusion, characterized by {alpha} {approx}< 10{sup -4}. Thus, midplane dead zones are a preferred environment. Large solids with radii {approx}>10 cm collapse most rapidly because they partially decouple from the gas disk. Smaller solids, even below {approx} mm sizes, could collapse if particle-driven turbulence is weakened by either localized pressure maxima or super-solar metallicity. Comparison with simulations that include particle clumping by the streaming instability shows that our linear model underpredicts rapid, small-scale gravitational collapse. Thus, the inclusion of more detailed gas dynamics promotes the formation of planetesimals. We discuss relevant constraints from solar system and accretion disk observations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Eccentric gravitational instabilities in nearly Keplerian disks

The growth of global gravitational instabilities in young stellar objects (YSOs) with associated circumstellar disks is studied. The possibility that the accretion ultimately owes its origin to the growth of spiral gravitational instabilities is explored. The results indicate that YSO disks will be unstable to the growth of eccentric distortions which have growth rates comparable to the orbital frequency at the outer edge of the disk. Thus, the distortions grow on nearly a dynamical time scale. Perturbations with m = 1 force the star to move from the center of mass and thereby transfer angular momentum to the stellar orbit. Depending on whether or not an axisymmetric stability parameter Q barrier exists near the corotation radius of the disturbance, this coupling may lead to mass accretion or to the formation of a binary companion from the disk, or both.

Adams, Fred C.↗
DOE OSTI2011

Gravitational Instability of Dusty Plasma with Radiative Process

The gravitational instability of infinite homogeneous magnetized dusty plasma with radiative process is studied with the help of relevant dusty magnetohydrodynamic (MHD) equations using normal mode analysis. The dispersion relation is obtained with radiative pressure and magnetic field, which is discussed for the transverse and longitudinal mode of propagations. The improvement in the Jeans condition of instability due to dust, magnetic field and radiative pressure is discussed. We find that in transverse mode of propagation the condition of Jeans instability of dusty plasma is modified by magnetic field and radiative pressure. In case of longitudinal mode it is unaffected by magnetic field as this mode provides the Alfven mode separately with the gravitational mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

A generalized Zel'dovich approximation to gravitational instability

The orbits of particles undergoing gravitational instability are parameterized by generalizing the Zel'dovich approximation to a series expansion of arbitrary accuracy in the nonlinear regime. The coefficients of this series are determined from an action principle, or, more generally, from moments of the equation of motion. It is shown that the series is more rapidly convergent than previous nonlinear approximations. The method therefore provides a practical means of determining particle orbits, even for highly nonlinear perturbations. As an alternative, we also outline how the nonlinear dynamics may be computed as a field theory in which the evolution of the density and the velocity is determined in fixed comoving Eulerian coordinates.

Giavalisco, M.↗
DOE OSTI2014

Two-component secular gravitational instability in a protoplanetary disk: A possible mechanism for creating ring-like structures

The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated using linear analysis. In the case where the dust-to-gas ratio is enhanced and turbulence is weak, the instability grows, even in gravitationally stable disks, on a timescale of order 10{sup 4-5} yr at a radius of order 100 AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called ''secular gravitational instability'', which was investigated previously to be an instability of dust in a fixed background gas flow. In this work, we solve the equations of motion for both gas and dust consistently and find that long-wavelength perturbations are stable, in contrast to the secular gravitational instability in the simplified treatment. This may indicate that we should not neglect small terms in the equation of motion if the growth rate is small. The instability is expected to form ring structures in protoplanetary disks. The width of the ring formed at a radius of 100 AU is a few tens of AU. Therefore, the instability is a candidate for the formation mechanism of observed ring-like structures in disks. Another aspect of the instability is the accumulation of dust grains, and hence the instability may play an important role in the formation of planetesimals, rocky protoplanets, and cores of gas giants located at radii ∼100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Testing the gravitational instability hypothesis?

We challenge a widely accepted assumption of observational cosmology: that successful reconstruction of observed galaxy density fields from measured galaxy velocity fields (or vice versa), using the methods of gravitational instability theory, implies that the observed large-scale structures and large-scale flows were produced by the action of gravity. This assumption is false, in that there exist nongravitational theories that pass the reconstruction tests and gravitational theories with certain forms of biased galaxy formation that fail them. Gravitational instability theory predicts specific correlations between large-scale velocity and mass density fields, but the same correlations arise in any model where (a) structures in the galaxy distribution grow from homogeneous initial conditions in a way that satisfies the continuity equation, and (b) the present-day velocity field is irrotational and proportional to the time-averaged velocity field. We demonstrate these assertions using analytical arguments and N-body simulations. If large-scale structure is formed by gravitational instability, then the ratio of the galaxy density contrast to the divergence of the velocity field yields an estimate of the density parameter Omega (or, more generally, an estimate of beta identically equal to Omega(exp 0.6)/b, where b is an assumed constant of proportionality between galaxy and mass density fluctuations. In nongravitational scenarios, the values of Omega or beta estimated in this way may fail to represent the true cosmological values. However, even if nongravitational forces initiate and shape the growth of structure, gravitationally induced accelerations can dominate the velocity field at late times, long after the action of any nongravitational impulses. The estimated beta approaches the true value in such cases, and in our numerical simulations the estimated beta values are reasonably accurate for both gravitational and nongravitational models. Reconstruction tests that show correlations between galaxy density and velocity fields can rule out some physically interesting models of large-scale structure. In particular, successful reconstructions constrain the nature of any bias between the galaxy and mass distributions, since processes that modulate the efficiency of galaxy formation on large scales in a way that violates the continuity equation also produce a mismatch between the observed galaxy density and the density inferred from the peculiar velocity field. We obtain successful reconstructions for a gravitational model with peaks biasing, but we also show examples of gravitational and nongravitational models that fail reconstruction tests because of more complicated modulations of galaxy formation.

Babul, Arif↗
DOE OSTI2012

MINIMUM DUST ABUNDANCES FOR PLANETESIMAL FORMATION VIA SECULAR GRAVITATIONAL INSTABILITIES

We estimate minimum dust abundances required for secular gravitational instability (SGI) to operate at the midplane dust layer of protoplanetary disks. For SGI to be a viable process, the growth time of the instability T{sub grow} must be shorter than the radial drift time of the dust T{sub drift}. The growth time depends on the turbulent diffusion parameter {alpha} because the modes with short wavelengths are stabilized by turbulent diffusion. Assuming that turbulence is excited via the Kelvin-Helmholtz or streaming instabilities in the dust layer, and that its strength is controlled by the energy supply rate from dust accretion, we estimate the diffusion parameter and the growth time of the instability. The condition T{sub grow} < T{sub drift} requires that the dust abundance must be greater than a critical abundance Z{sub min}, which is a function of the Toomre parameter Q{sub g} and the aspect ratio h{sub g} /r of the gas disk. For a wide range of parameter space, the required dust abundance is less than 0.1. A slight increase in dust abundance opens a possible route for the dust to directly collapse to planetesimals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Equilibrium sequences and gravitational instability of rotating isothermal rings

Nuclear rings at the centers of barred galaxies exhibit strong star formation activities. They are thought to undergo gravitational instability when they are sufficiently massive. We approximate them as rigidly rotating isothermal objects and investigate their gravitational instability. Using a self-consistent field method, we first construct their equilibrium sequences specified by two parameters: α corresponding to the thermal energy relative to gravitational potential energy, and R-hat {sub B} measuring the ellipticity or ring thickness. Unlike in the incompressible case, not all values of R-hat {sub B} yield an isothermal equilibrium, and the range of R-hat {sub B} for such equilibria shrinks with decreasing α. The density distributions in the meridional plane are steeper for smaller α, and well approximated by those of infinite cylinders for slender rings. We also calculate the dispersion relations of non-axisymmetric modes in rigidly rotating slender rings with angular frequency Ω{sub 0} and central density ρ{sub c}. Rings with smaller α are found more unstable with a larger unstable range of the azimuthal mode number. The instability is completely suppressed by rotation when Ω{sub 0} exceeds the critical value. The critical angular frequency is found to be almost constant at ∼0.7(Gρ{sub c}){sup 1/2} for α ≳ 0.01 and increases rapidly for smaller α. We apply our results to a sample of observed star-forming rings and confirm that rings without a noticeable azimuthal age gradient of young star clusters are indeed gravitationally unstable.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

GRAVITATIONAL INSTABILITIES IN TWO-COMPONENT GALAXY DISKS WITH GAS DISSIPATION

Growth rates for gravitational instabilities in a thick disk of gas and stars are determined for a turbulent gas that dissipates on the local crossing time. The scale heights are derived from vertical equilibrium. The accuracy of the usual thickness correction, (1 + kH){sup -1}, is better than 6% in the growth rate when compared to exact integrations for the gravitational acceleration in the disk. Gas dissipation extends the instability to small scales, removing the minimum Jeans length. This makes infinitesimally thin disks unstable for all Toomre-Q values and reasonably thick disks stable at high Q primarily because of thickness effects. The conventional gas+star threshold, Q{sub tot}, increases from {approx}1 without dissipation to 2 or 3 when dissipation has a rate equal to the crossing rate over a perturbation scale. Observations of Q{sub tot} {approx} 2-3 and the presence of supersonic turbulence suggest that disks are unstable over a wide range of scales. Such instabilities drive spiral structure if there is shear and clumpy structure if shear is weak; they may dominate the generation of turbulence. Feedback regulation of Q{sub tot} is complex because the stellar component does not cool; the range of spiral strengths from multiple arm to flocculent galaxies suggests that feedback is weak. Gravitational instabilities may have a connection to star formation even when the star formation rate scales directly with the molecular mass because the instabilities return dispersed gas to molecular clouds and complete the cycle of cloud formation and destruction. The mass flow to dense clouds by instabilities can be 10 times larger than the star formation rate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

DIRECT DETECTION OF PRECURSORS OF GAS GIANTS FORMED BY GRAVITATIONAL INSTABILITY WITH THE ATACAMA LARGE MILLIMETER/SUBMILLIMETER ARRAY

Phases of gravitational instability are expected in the early phases of disk evolution, when the disk mass is still a substantial fraction of the mass of the star. Disk fragmentation into sub-stellar objects could occur in the cold exterior part of the disk. Direct detection of massive gaseous clumps on their way to collapse into gas giant planets would offer an unprecedented test of the disk instability model. Here we use state-of-the-art 3D radiation-hydro simulations of disks undergoing fragmentation into massive gas giants, post-processed with RADMC-3D to produce dust continuum emission maps. These are then fed into the Common Astronomy Software Applications (CASA) ALMA simulator. The synthetic maps show that both overdense spiral arms and actual clumps at different stages of collapse can be detected with the Atacama Large Millimeter/submillimeter Array (ALMA) in the full configuration at the distance of the Ophiuchus star forming region (125 pc). The detection of clumps is particularly effective at shorter wavelengths (690 GHz) combining two resolutions with multi-scale clean. Furthermore, we show that a flux-based estimate of the mass of a protoplanetary clump can be comparable to a factor of three higher than the gravitationally bound clump mass. The estimated mass depends on the assumed opacity, and on the gas temperature, which should be set using the input of radiation-hydro simulations. We conclude that ALMA has the capability to detect “smoking gun” systems that are a signpost of the disk instability model for gas giant planet formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk

We consider the dynamics of porous icy dust aggregates in a turbulent gas disk and investigate the stability of the disk. We evaluate the random velocity of porous dust aggregates by considering their self-gravity, collisions, aerodynamic drag, turbulent stirring, and scattering due to gas. We extend our previous work by introducing the anisotropic velocity dispersion and the relaxation time of the random velocity. We find the minimum mass solar nebula model to be gravitationally unstable if the turbulent viscosity parameter α is less than about 4×10{sup −3}. The upper limit of α for the onset of gravitational instability is derived as a function of the disk parameters. We discuss the implications of the gravitational instability for planetesimal formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure p {sub c} to the central energy density ρ{sub c}, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N element of (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number ℓ > 50, while for smaller values of ℓ the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N ≥ 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10{sup −3} of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

The fragmentation of proto-globular clusters. II - Gravitational instabilities

The remarkable homogeneity in the metal abundances within a typical globular cluster may be a consequence of the fragmentation of the proto-globular clouds. In this paper, the late stages of fragmentation are investigated by examining the growth of gravitational instabilities in the shell. It is found that the short dynamical time scale of the shell leads to the rapid growth of gravitational instabilities, so that the entire process of fragmentation to stellar mass scales can be completed on a time scale much less than the dynamical time scale of the parent cloud.

Murray, Stephen D.↗
DOE OSTI2012

GRAVITATIONAL INSTABILITY OF ROTATING, PRESSURE-CONFINED, POLYTROPIC GAS DISKS WITH VERTICAL STRATIFICATION

We investigate the gravitational instability (GI) of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium and bounded by a constant external pressure. We find that the GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. On the other hand, when the disk has free boundaries and is strongly pressure confined, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under their own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c{sub eff} of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart that are appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation, after correcting for c{sub eff} and the reduction factors, closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically stratified, pressure-confined disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

CONVERGENCE STUDIES OF MASS TRANSPORT IN DISKS WITH GRAVITATIONAL INSTABILITIES. II. THE RADIATIVE COOLING CASE

We conduct a convergence study of a protoplanetary disk subject to gravitational instabilities (GIs) at a time of approximate balance between heating produced by the GIs and radiative cooling governed by realistic dust opacities. We examine cooling times, characterize GI-driven spiral waves and their resultant gravitational torques, and evaluate how accurately mass transport can be represented by an {alpha}-disk formulation. Four simulations, identical except for azimuthal resolution, are conducted with a grid-based three-dimensional hydrodynamics code. There are two regions in which behaviors differ as resolution increases. The inner region, which contains 75% of the disk mass and is optically thick, has long cooling times and is well converged in terms of various measures of structure and mass transport for the three highest resolutions. The longest cooling times coincide with radii where the Toomre Q has its minimum value. Torques are dominated in this region by two- and three-armed spirals. The effective {alpha} arising from gravitational stresses is typically a few Multiplication-Sign 10{sup -3} and is only roughly consistent with local balance of heating and cooling when time-averaged over many dynamic times and a wide range of radii. On the other hand, the outer disk region, which is mostly optically thin, has relatively short cooling times and does not show convergence as resolution increases. Treatment of unstable disks with optical depths near unity with realistic radiative transport is a difficult numerical problem requiring further study. We discuss possible implications of our results for numerical convergence of fragmentation criteria in disk simulations.

79 ASTRONOMY AND ASTROPHYSICS↗