Jeans' criterion of gravitational instability
Investigation into Jeans criterion of gravitational instability
GRAVITATIONAL FIELD↗
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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.↗
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.↗
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↗
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↗
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↗
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↗
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↗
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.↗
The Effect of Protoplanetary Disk Cooling Times on the Formation of Gas Giant Planets by Gravitational Instability
Observational evidence exists for the formation of gas giant planets on wide orbits around young stars by disk gravitational instability, but the roles of disk instability and core accretion for forming gas giants on shorter period orbits are less clear. The controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process. The latter refers largely to the handling of radiative transfer in three-dimensional (3D) hydrodynamical models, which controls heating and cooling processes in gravitationally unstable disks, and hence dense clump formation. A suite of models using the β cooling approximation is presented here. The initial disks have masses of 0.091 M {sub ⊙} and extend from 4 to 20 au around a 1 M {sub ⊙} protostar. The initial minimum Toomre Qi values range from 1.3 to 2.7, while β ranges from 1 to 100. We show that the choice of Q {sub i} is equal in importance to the β value assumed: high Q{sub i} disks can be stable for small β , when the initial disk temperature is taken as a lower bound, while low Q{sub i} disks can fragment for high β . These results imply that the evolution of disks toward low Q{sub i} must be taken into account in assessing disk fragmentation possibilities, at least in the inner disk, i.e., inside about 20 au. The models suggest that if low Q{sub i} disks can form, there should be an as yet largely undetected population of gas giants orbiting G dwarfs between about 6 au and 16 au.
79 ASTRONOMY AND ASTROPHYSICS↗
Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. II. Locality of Gravitoturbulence, Clumpy Spirals, and Implications for Observable Substructure
Spiral perturbations in a gravitationally unstable accretion disk regulate disk evolution through angular momentum transport and heating and provide an observational signature of gravitational instability (GI). We use global 3D simulations to systematically characterize and understand these spiral perturbations. The spiral perturbations and the resulting transport are overall insensitive to the cooling type, with the exception that radiative cooling, especially in the optically thick regime, reduces the amplitude of temperature perturbations. Spiral perturbations are localized around corotation, allowing transport to be approximated by a local α viscosity to zeroth order in aspect ratio (H/R), but only after averaging over multiple orbits in time and/or multiple scale heights in space. Meanwhile, large-amplitude perturbations from strong gravitoturbulence can cause $\mathcal{O}$(α 1/2 ) deviation in the cooling rate of the disk. We develop empirical prescriptions for the angular momentum transport, heating, and cooling in a gravitoturbulent disk that capture the deviation from a viscous, unperturbed disk to first order in H/R and α 1/2 . The spiral perturbations in saturated gravitoturbulence are clumpy, with dense clumps forming through the nonlinear coupling between multiple modes at different m. Observationally, the clumpy gravitoturbulence produced by saturated GI can be mistaken with observational noise or embedded companions, especially under finite resolution. Meanwhile, grand-design spirals with m-fold symmetry may be uncommon among disks in saturated gravitoturbulence, and we speculate that they may instead be a signature of recently triggered or decaying GI.
Gravitational instability↗
Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. I. Stochastic Fragmentation with Optical-depth-dependent Rate and Universal Fragment Mass
Fragmentation in a gravitationally unstable accretion disk can be an important pathway for forming stellar/planetary companions. To characterize quantitatively the condition for and outcome of fragmentation under realistic thermodynamics, we perform global 3D simulations of gravitationally unstable disks at various cooling rates and cooling types, including the first global simulations of gravitational instability that employ full radiation transport. We find that fragmentation is a stochastic process, with the fragment generation rate per disk area p frag showing an exponential dependence on the parameter β ≡ Ω K t cool , where Ω K is the Keplerian rotation frequency, and t cool is the average cooling timescale. Compared to a prescribed constant β, radiative cooling in the optically thin/thick regime makes p frag decrease slower/faster in β; the critical β corresponding to ∼1 fragment per orbit is ≈3, 5, and 2 for constant β, optically thin, and optically thick cooling, respectively. The distribution function of the initial fragment mass is remarkably insensitive to disk thermodynamics. Regardless of cooling rate and optical depth, the typical initial fragment mass is m frag ≈ 40M tot h 3 , with M tot being the total (star+disk) mass and h = H/R being the disk aspect ratio. Applying this result to typical Class 0/I protostellar disks, we find m frag ∼ 20M J , suggesting that fragmentation more likely forms brown dwarfs. Given the finite width of the m frag distribution, forming massive planets is also possible.
gravitational instability↗
Gravitational instability of a rotating partially-ionized plasma carrying a uniform magnetic field with Hall effect
The problem of gravitational instability of an infinite homogeneous self-gravitating medium carrying a uniform magnetic field in the presence of Hall effect has been investigated to include the effect due to rotation. The dispersion relation has been obtained. It has been found that the Jeans's criterion for the instability remains unaffected even when the effect due to rotation is considered in the presence of Hall effect carrying a uniform magnetic.
Kumar, Vinod↗
AN ORIGIN OF MULTIPLE RING STRUCTURE AND HIDDEN PLANETS IN HL TAU: A UNIFIED PICTURE BY SECULAR GRAVITATIONAL INSTABILITY
Recent ALMA observation has revealed multiple ring structures formed in a protoplanetary disk around HL Tau. Prior to the ALMA observation of HL Tau, theoretical analysis of secular gravitational instability (GI) described a possible formation of multiple ring structures with separations of 13 au around a radius of 100 au in protoplanetary disks under certain conditions. In this article, we reanalyze the viability of secular GI by adopting the physical values inferred from the observations. We derive the radial distributions of the most unstable wavelength and the growth timescale of secular GI and verify that secular GI can form the ring structures observed in HL Tau. When a turbulent viscosity coefficient α remains small in the inner region of the disk, secular GI grows in the whole disk. Thus, the formation of planetary mass objects should occur first in the inner region as a result of gravitational fragmentation after the nonlinear growth of secular GI. In this case, the resulting objects are expected to create gaps at r ∼ 10 au and ∼30 au. As a result, all ring structures in HL Tau can be created by secular GI. If this scenario is realized in HL Tau, the outer region corresponds to the earlier growth phase of the most unstable mode of secular GI, and the inner region corresponds to the outcome of the nonlinear growth of secular GI. Therefore, this interpretation suggests that we are possibly witnessing both the beginning and the end of planet formation in HL Tau.
79 ASTRONOMY AND ASTROPHYSICS↗
SIGNATURES OF GRAVITATIONAL INSTABILITY IN RESOLVED IMAGES OF PROTOSTELLAR DISKS
Protostellar (class 0/I) disks, which have masses comparable to those of their nascent host stars and are fed continuously from their natal infalling envelopes, are prone to gravitational instability (GI). Motivated by advances in near-infrared (NIR) adaptive optics imaging and millimeter-wave interferometry, we explore the observational signatures of GI in disks using hydrodynamical and Monte Carlo radiative transfer simulations to synthesize NIR scattered light images and millimeter dust continuum maps. Spiral arms induced by GI, located at disk radii of hundreds of astronomical units, are local overdensities and have their photospheres displaced to higher altitudes above the disk midplane; therefore, arms scatter more NIR light from their central stars than inter-arm regions, and are detectable at distances up to 1 kpc by Gemini/GPI, VLT/SPHERE, and Subaru/HiCIAO/SCExAO. In contrast, collapsed clumps formed by disk fragmentation have such strong local gravitational fields that their scattering photospheres are at lower altitudes; such fragments appear fainter than their surroundings in NIR scattered light. Spiral arms and streamers recently imaged in four FU Ori systems at NIR wavelengths resemble GI-induced structures and support the interpretation that FUors are gravitationally unstable protostellar disks. At millimeter wavelengths, both spirals and clumps appear brighter in thermal emission than the ambient disk and can be detected by ALMA at distances up to 0.4 kpc with one hour integration times at ∼0.″1 resolution. Collapsed fragments having masses ≳1 M {sub J} can be detected by ALMA within ∼10 minutes.
79 ASTRONOMY AND ASTROPHYSICS↗
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↗
The effect of suspended particles on Jean's criterion for gravitational instability
The effect that the proper inclusion of suspended particles has on Jeans' criterion for the self-gravitational instability of an unbounded nonrotating adiabatic gas cloud is examined by formulating the appropriate model system, introducing particular physically plausible equations of state and constitutive relations, performing a linear stability analysis of a uniformly expanding exact solution to these governing equations, and exploiting the fact that there exists a natural small material parameter for this problem given by N sub 1/n sub 1, the ratio of the initial number density for the particles to that for the gas. The main result of this investigation is the derivation of an altered criterion which can substantially reduce Jeans' original critical wavelength for instability. It is then shown that the existing discrepancy between Jeans' theoretical prediction using and actual observational data relevant to the Andromeda nebula M31 can be accounted for by this new criterion of assuming suspended particles of a reasonable grain size and distribution to be present.
Wollkind, David J.↗
Sling amplification and eccentric gravitational instabilities in gaseous disks
An analytical description is presented of the modal mechanisms relevant to a recently discovered type of eccentric gravitational instability in nearly Keplerian disks. A quantum condition is derived which accurately predicts the pattern speeds for these modes. The growth rates for the modes are determined, and it is shown that the mode can grow when the disk is safely stable to axisymmetric disturbances. The case of marginal stability for the outside edge is discussed, and the implications of the results for the formation of binary companions and/or giant planets within disks associated with young stellar objects are considered.
Shu, Frank H.↗