Self-gravitational Forces Research Articles

Numerical Simulations of Tidal Deformation and Resulting Light Curves of Small Bodies: Material Constraints of 99942 Apophis and 1I/‘Oumuamua

In this paper, we present an open-source software (Simulator of Asteroid Malformation Under Stress, SAMUS) that simulates constant-density, constant-viscosity liquid bodies subject to tidal forces for a range of assumed viscosities and sizes. This software solves the Navier–Stokes equations on a finite-element mesh, incorporating the centrifugal, Coriolis, self-gravitational, and tidal forces. The primary functionality is to simulate the deformation of minor bodies under the influence of tidal forces. It may therefore be used to constrain the composition and physical structure of bodies experiencing significant tidal forces, such as 99942 Apophis and 1I/‘Oumuamua. We demonstrate that SAMUS will be useful to constrain the material properties of Apophis during its near-Earth flyby in 2029. Depending on the material properties, Apophis may experience an area change of up to 0.5%, with similar effects on the photometric brightness. We also apply SAMUS to constrain the material dynamic viscosity of 1I/‘Oumuamua, the first interstellar object discovered traversing the inner solar system. ‘Oumuamua experienced a close approach to the Sun at perihelion (q ≃ 0.25 au) during which there were significant tidal forces that may have caused deformation of the body. This deformation could have lead to observable changes in the photometric light curve based on the material properties. The application of SAMUS to produce synthetic observations which incorporate tidal deformation effects demonstrates that no deformation—an infinite dynamic viscosity—best reproduces the photometric data. While these results indicate that ‘Oumuamua did not experience significant tidal deformation, a sophisticated model incorporating nonprincipal axis rotation is necessary to conclusively analyze both ‘Oumuamua and Apophis.

Influence of quantum particles on self-gravitational magnetic dust acoustic double layers

The impact of Fermi–Dirac distributed electrons and ions on the features of dust acoustic double layers in a four-component magnetized dusty plasma was investigated. In this model, the plasma consists of Fermi–Dirac distributed electrons and ions and negative and positive dust particles. The plasma species experience electrical, magnetical, and self-gravitational forces as well as the degeneracy pressure force that is caused by the Pauli exclusion law and the quantum tunneling force due to Bohm force. Employing a reductive perturbation method, the quantum extended Korteweg-de Vries equation was extracted from the set of fluid equations. The results show that the energy of generated dust acoustic double layers is extremely smaller than that in similar classical plasmas. The ratio of the Fermi temperature of ions to electrons is an effective parameter in the structure of double layers. With the variation of this parameter, the structure of double layers changes from compressive to rarefactive, and its polarity switches from negative to positive.

Self-gravitational Force Calculation of High-order Accuracy for Infinitesimally Thin Gaseous Disks

Abstract Self-gravitational force calculation for infinitesimally thin disks is important for studies on the evolution of galactic and protoplanetary disks. Although high-order methods have been developed for hydrodynamic and magnetohydrodynamic equations, high-order improvement is desirable for solving self-gravitational forces for thin disks. In this work, we present a new numerical algorithm that is of linear complexity and of high-order accuracy. This approach is fast since the force calculation is associated with a convolution form, and the fast calculation can be achieved using Fast Fourier Transform. The nice properties, such as the finite supports and smoothness, of basis spline functions are exploited to stably interpolate a surface density and to achieve a high-order accuracy in forces. Moreover, if the mass distribution of interest is exclusively confined within a calculation domain, the method does not require artificial boundary values to be specified before the force calculation. To validate the proposed algorithm, a series of numerical tests, ranging from first- to third-order implementations, are performed, and the results are compared with analytic expressions derived for third- and fourth-order generalized Maclaurin disks. We conclude that the improvement on the numerical accuracy is significant with the order of the method, with only little increase of the complexity of the method.

Note on Electrogravitational Stability of a Double Fluids Interface

This study deals with the axisymmetric stability of the interface between two incompressible Selfgravitating non-conducting fluids in the presence of an electric field. The pressure in the unperturbed state is not constant because the Selfgravitating force is a long-range force. The dispersion relation is derived and discussed. Some previous reported works may be obtained as limiting cases from the presented work with appropriate choices. The study under consideration has strong correlation with instabilities of sun spots and other physical phenomena.

The Effect of Modified Gravity on the Odds of the Bound Violations of the Turn-around Radii

Abstract The turn-around radii of the galaxy groups show the imprint of a long battle between their self-gravitational forces and the accelerating space. The standard ΛCDM cosmology based on the general relativity (GR) predicts the existence of an upper bound on the expectation value of the turn-around radius that is rarely violated by individual galaxy groups. We speculate that a deviation of the gravitational law from GR on the cosmological scale could cause an appreciable shift of the mean turn-around radius to higher values and make the occurrence of the bound violation more probable. Analyzing the data from high-resolution N-body simulations for two specific models with modified gravity (MG) and the standard GR+ΛCDM cosmology, we determine the turn-around radii of the massive Rockstar groups from the peculiar motions of the galactic halos located in the bound zone where the fifth force generated by MG is expected to be, at most, partially shielded. We detect a signal of difference in the odds of the bound violations between a fiducial MG and the GR models, which proves that the odds of the bound violations increase with the strength of the fifth force produced by the presence of MG. The advantage of using the odds of the bound violations as a complementary diagnostics to probe the nature of gravity is discussed.

Self-gravitating stability of a rotating fluid layer

The self-gravitating instability of the present model is discussed by using a simple linear theory. The problem is formulated for a rotating fluid layer, and a dispersion relation valid for all kinds of perturbations is derived and discussed. The self-gravitating force is found to be a destabilizing factor for a small range of wavenumbers, while it is stabilizing in other ranges, depending on the density ratio of the fluids. For high values of the angular velocity, the rotational force produces a stabilizing effect and can suppress the self-gravitating instability. In the absence of the self-gravitating force, the model of a rotating fluid layer is marginally stable.

SELF-GRAVITATIONAL FORCE CALCULATION OF SECOND-ORDER ACCURACY FOR INFINITESIMALLY THIN GASEOUS DISKS IN POLAR COORDINATES

Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two- dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calcu- lations of the hydrodynamics and self-gravitational forces are relatively straight- forward for attaining second order accuracy. However, in polar coordinates, a second order calculation of self-gravitational forces is required for matching the second order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second order accuracy without artifi- cial boundary conditions. The Poisson integral in polar coordinates is expressed in a convolution form and the corresponding numerical complexity is nearly lin- ear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

AbstractWe introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh–Bénard convection that have been performed for both temperature-independent (‘GeoFlow I’) and temperature-dependent fluid viscosity properties (‘GeoFlow II’) with a measured viscosity contrast up to 1.5. To set up a self-gravitating force field, we use a high-voltage potential between the inner and outer boundaries and a dielectric insulating liquid; the experiments were performed under microgravity conditions on the International Space Station. We further run numerical simulations in three-dimensional spherical geometry to reproduce the results obtained in the ‘GeoFlow’ experiments. We use Wollaston prism shearing interferometry for flow visualization – an optical method producing fringe pattern images. The flow patterns differ between our two experiments. In ‘GeoFlow I’, we see a sheet-like thermal flow. In this case convection patterns have been successfully reproduced by three-dimensional numerical simulations using two different and independently developed codes. In contrast, in ‘GeoFlow II’, we obtain plume-like structures. Interestingly, numerical simulations do not yield this type of solution for the low viscosity contrast realized in the experiment. However, using a viscosity contrast of two orders of magnitude or higher, we can reproduce the patterns obtained in the ‘GeoFlow II’ experiment, from which we conclude that nonlinear effects shift the effective viscosity ratio.

Magnetogravitodynamic stability of streaming fluid cylinder under the effect of capillary force

The magnetohydrodynamic stability criterion of self-gravitating streaming fluid cylinder under the combined effect of self-gravitating, magnetic, and capillary forces has been derived. The results are discussed analytically and some data are verified numerically for different parameters of the problem. The magnetic and capillary forces are stabilizing, but the streaming is destabilizing while the self-gravitating is stabilizing or destabilizing according to restrictions. The stable and unstable domains are identified and, moreover, the influences of the magnetic and capillary forces on the self-gravitating instability of the model have been examined. Including the magnetic force together with self-gravitating force improves the instability of the model. However, the self-gravitating instability will never be suppressed whatever the effects of the MHD force stabilizing effects are.

Traveling waves in low and intermediate rotating spherical shell convection

The spherical shell convection in the lower rotational regime is discussed with numerical simulation by the use of a pseudo-spectral code and experimental observation by the use of a microgravity experiment in self-gravitating force field. While a low Coriolis force produces traveling waves of cubic, five-fold and frozen tetrahedral symmetry with a prograde drift, in the transition zone to chaos an axisymmetric flow is visible. The chaotic fluid flow does neither show a specific drift nor a dominating pattern of convection. Numerical and experimental data are in a good agreement.

Electrogravitational stability of oscillating streaming fluid cylinder ambient with a transverse varying electric field

The electrogravitational instability of a dielectric oscillating streaming fluid cylinder surrounded by tenuous medium of negligible motion pervaded by transverse varying electric field has been investigated for all the perturbation modes. The model is governed by Mathieu second-order integro-differential equation. Some limiting cases are recovering from the present general one. The self-gravitating force is destabilizing only in the axisymmetric perturbation for long wavelengths, while, the axial electric field interior, the fluid has strong destabilizing effect for all short and long wavelengths. The transverse field is strongly stabilizing. In the case of non-axisymmetric perturbation, the self-gravitating force is stabilizing for short and long waves, while the electric field has stabilizing effect on short waves.

Magneto hydrodynamic stability of self-gravitational fluid cylinder

The self-gravitating instability of a fluid cylinder pervaded by magnetic field and endowed with surface tension has been discussed. The dispersion relation is derived and some reported works are recovered as limiting cases from it. The capillary force is destabilizing only in the small axisymmetric domain and stabilizing otherwise. The magnetic field has a strong stabilizing effect in all modes of perturbation for all wavelengths. The self-gravitating force is destabilizing in the axisymmetric perturbation. However the magnetic field effect modified a lot the destabilizing character of the model and could overcome the capillary and self-gravitating instability of the model for all short and long wavelengths.

Note on magneto-hydrodynamic gravitational stability of a double fluids interface

The magneto–gravitational stability of double-fluid interface is discussed. The pressure in the unperturbed state is not constant because the self-gravitating force is a long-range force. The dispersion relation is derived and discussed. The self-gravitating model is unstable in the symmetric mode m = 0 (m is the transverse wave number), while it is stable in all other states. The effects of the densities, the liquid-fluid radii ratios, and the electromagnetic force on the stability of the present model are identified for all wavelengths.PACS Nos.: 47.35.Tv, 47.65.–d, 04.40.–b

Capillary instability of a streaming fluid-core liquid jet underself-gravitating forces

The stability criterion of a fluid cylinder (density ρ(1)) embedded in a different fluid (density ρ(2)) is derived and discussed. The model is capillary unstable in the domain 0 < x < 1 as m = 0 where x and m are the axial and transverse wave numbers, while it is stable in all other domains. The densities ratio ρ(2) / ρ(1) decreases the unstable domains but never suppress them. The streaming increases the unstable domains. Gravitationally, in m = 0 mode the model is unstable in the domain 0 < x < 1.0668 as ρ(2) < ρ(1), while as ρ(2) = ρ(1) it is marginally stable but when ρ(2) > ρ(1) the model is purely unstable for all short and long wavelengths. In m ≠ 0 modes, the self-gravitating model is neutrally stable as ρ(1) = ρ(2), ordinarily stable as ρ(2) < ρ(1), but is purely unstable as ρ(2) > ρ(1). The streaming destabilizing effect makes the self-gravitating instability worse and shrinks the stable domains. The stability analysis of the model under the combined effect of the capillary and self-gravitating forces is performed analytically and verified numerically. When ρ(2) < ρ(1) the capillary force and the axial flow have destabilizing influences but the ratio of the densities ρ(2) / ρ(1) has a stabilizing effect on the gravitating instability. If ρ(1) = ρ(2), the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When ρ(2) > ρ(1) the capillary force improves the gravitational instability and creates domains of much stability and moreover the instability of the self-gravitating force disappears in several cases of axisymmetric disturbances. PACS No.: 47.17+e

Modeling the NIR-silhouette massive disk candidate in M 17

Aims. The physical properties of the massive disk candidate in the star-forming region M 17 are analyzed. Methods. Making use of the rare configuration in which the gas and dust structure is seen in silhouette against the background radiation at λ = 2.2 µm, we determine the column density distribution from a high-resolution NAOS/CONICA image. The influence of scattered light on the mass determination is analyzed using 3D radiative transfer calculations. Further upper flux limits derived from observations with the Spitzer telescope at MIR wavelengths are used together with the NACO image to estimate the flux from the central object. For a range of stellar radii, stellar surface temperatures, and dust grain sizes, we apply three different models to account for the observed fluxes. The stability of the disk against self-gravitational forces is analyzed calculating the ratio of the gravitational acceleration by the central object and the disk, and the deviations from a Keplerian profile. Results. We find that the column density is consistent with a central source surrounded by a rotationally symmetric distribution of gas and dust. The extent of the symmetric disk part is about 3000 AU, with a warped point-symmetrical extension beyond that radius, and therefore larger than any circumstellar disk yet detected. The modeling yields a radial density powerlaw exponent of −1.1 indicating a flat radial density distribution, and a large e-folding scale height ratio H/R of about 0.5. The mass of the entire disk estimated from the column density is discussed depending on the assumed distance and the dust model and ranges between 0.02 and 5 M� . We conclude that unless a star is located close to the disk in the foreground, scattered light will have little influence on the mass determination. We present a Spitzer image taken at λ = 7.8 µm with the disk seen in emission and identify polycyclic aromatic hydrocarbon (PAH) emission on the disk surface excited by the nearby massive stars as a possible source. Our 3D radiative transfer calculations for the scattered light image of the central source through an edge-on disk indicate that the elliptical shape seen in the NACO image does not require the assumption of a binary system and that it is consistent with a single object. We derive stellar main sequence masses of several M� ,5 0M� ,o r 10M� , depending on our assumptions that the extinction of the stellar flux is dominated (i) by the outer disk, (ii) by an inner disk comparable to the disks around intermediate-mass stars, or (iii) by an inner disk with dominating hot dust emission. We find that even for a star-disk mass ratio of 1, only the outer parts of the circumstellar disk may be influenced by self-gravity effects due to the large e-folding scale height ratio.

GEOFLOW: simulation of convection in a spherical shell under central force field

Abstract. Time-dependent dynamical simulations related to convective motion in a spherical gap under a central force field due to the dielectrophoretic effect are discussed. This work is part of the preparation of the GEOFLOW-experiment which is planned to run in a microgravity environment. The goal of this experiment is the simulation of large-scale convective motion in a geophysical or astrophysical framework. This problem is new because of, on the one hand, the nature of the force field (dielectrophoretic effect) and, on another hand, the high degree of symmetries of the system, e.g. the top-bottom reflection. Thus, the validation of this simulation with well-known results is not possible. The questions concerning the influence of the dielectrophoretic force and the possibility to reproduce the theoretically expected motions in the astrophysical framework, are open. In the first part, we study the system in terrestrial conditions: the unidirectional Earth's force is superimposed on the central dielectrophoretic force field to compare with the laboratory experiments during the development of the equipment. In the second part, the GEOFLOW-experiment simulations in weightless conditions are compared with theoretical studies in the astrophysical framework's, in the first instance a fluid under a self-gravitating force field. We present complex time-dependent dynamics, where the dielectrophoretic force field causes significant differences in the flow compared to the case that does not involve this force field.

Magnetogravitational stability of a bounded gas-core fluid jet

The self-gravitating stability of a gas volume embedded in a bounded liquid, under the influence of an electromagnetic force, has been assessed. The pressure in the unperturbed state is not constant due to the self-gravitating force being a long-range force. The stability criterion has been established in its general form and discussed. The liquid–gas radii ratio influences the stabilization. The electromagnetic force, due to the magnetic field pervading throughout the gas and liquid regions, has a strong stabilizing effect for all short and long wavelengths in all modes of perturbation.

Hydromagnetic stability of gravitational streaming coaxial cylinders with double perturbed interfaces

The magnetohydrodynamic stability of streaming self-gravitational coaxial fluid cylinders with doubly perturbed interfaces has been developed. The problem is formulated and solved. A crucial feature of this work is that we have considered all mathematical solutions of the differential equations because singular solutions are not present at all in this case. Using appropriate boundary conditions, the stability criterion is derived and discussed analytically and numerically for determining the stable and unstable domains and their characteristics. The magnetic fields interior and exterior to the fluid cylinders have stabilizing effects while the streaming is strongly destabilizing. The fluid densities ratio factor is stabilizing while that of the cylinders' radii ratio plays an important role in stabilizing the annular coaxial cylinders. The self-gravitational forces is destabilizing only for axisymmetric modes while it is stabilizing for the rest. Some reported and previously published works are obtained as limiting cases of the present general work.

Three‐dimensional Dynamics of Narrow Planetary Rings

Narrow planetary rings are eccentric and inclined. Particles within a given ring must therefore share the same pericenter and node. We solve for the three-dimensional geometries and mass distributions that enable the Uranian α- and β-rings and the Saturnian Maxwell and Colombo (Titan) rings to maintain simultaneous apsidal and nodal lock. Ring self-gravity, interparticle collisions, and the quadrupole field of the host planet balance each other to achieve this equilibrium. We prove that such an equilibrium is linearly stable. Predictions for the Saturnian ringlets to be tested by the Cassini spacecraft include (1) ringlet masses are of order a few × 1019 g, (2) surface mass densities should increase from ring midline to ring edges, and (3) rings are vertically warped such that the fractional variation of inclination across the ring is of order 10%. Analogous predictions are made for the Uranian rings. Simultaneous apsidal and nodal locking forces the narrowest portion of the ring—its "pinch," where self-gravitational and collisional forces are strongest—to circulate relative to the node and introduces previously unrecognized time-varying forces perpendicular to the planet's equator plane. We speculate that such periodic stressing might drive kilometer-scale bending waves at a frequency twice that of apsidal precession; such flexing might be observed over a few weeks by Cassini.

Blowup phenomena of solutions to Euler–Poisson equations

In this paper, we consider the Euler–Poisson equations governing the evolution of the gaseous stars with the Poisson equation describing the energy potential for the self-gravitating force. By assuming that the initial density is of compact support in R N , we first give a family of blowup solutions for non-isentropic polytropic gas when γ=(2 N−2)/ N which generalizes the known result for the isentropic case. Then we extend the previous result on non-blowup phenomena to the case when (2 N−2)/ N⩽ γ<2 in N-dimensional space. Here γ is the adiabatic gas constant.