Evgeny Griv

Quasi-linear theory of the Jeans instability in disk-shaped galaxies

We analyse the reaction between almost aperiodically growing Jeans-unstable gravity perturbations and stars of a rotating and spatially inhomogeneous disk of flat galaxies. A mathematical formalism in the approx- imation of weak turbulence (a quasi-linearization of the Boltzmann collisionless kinetic equation) is developed. A diusion equation in conguration space is derived which describes the change in the main body of equilibrium distribution of stars. The distortion in phase space resulting from such a wave{star interaction is studied. The theory, applied to the Solar neighborhood, accounts for the observed Schwarzschild shape of the velocity ellipsoid, the increase in the random stellar velocities with age, and the essential radial migration of the Sun from its birth-place in the inner part of the Galaxy outwards during its lifetime.

Role of overshoots in the formation of the downstream distribution of adiabatic electrons

We analyze the influence of the magnetic overshoot on the downstream electron distributions formed as a result of the collisionless adiabatic motion of the electrons in the quasi-stationary electric field in shock front. We show that a substantial overshoot can result in a significant distortion of the downstream distribution due to cutting out the electrons with high perpendicular velocities. We calculate numerically the electron distribution in the v∥ - v⊥ plane, as well as expected cuts through the distribution depending on the angle with respect to the magnetic field direction, also taking into account the averaging procedure of the ISEE type apparatus. These distorted distributions and cuts should be clearly observed in the downstream region just behind the shock transition layer. Absence of such observations would indicate that the above picture of adiabatic electron dynamics in the static field is significantly incomplete, and estimates based on these assumptions should be considered with caution.

On the Schwarzschild Velocity Distribution of the Local Stellar Disk

The reaction between aperiodically growing Jeans-type gravity perturbations and stars in a rapidly rotating disk is analyzed with quasi-linear theory. The theory, applied to the solar neighborhood in the Galaxy, accounts for the observed Schwarzschild (anisotropic Maxwellian) shape for the stellar velocity ellipsoid and the increase in the random stellar velocities with age.

Local stability criterion for the Saturnian ring system

Abstract The self-gravitating particulate disk of the Saturnian ring system is studied using linear theory to determine its evolution and stability against gravitational Jeans-type perturbations. The analysis is carried out in approximation of the basically homogeneous and two-dimensional system. In addition, the case is considered with rare collisions between particles when the squared epicyclic frequency κ2 as well as the squared orbital angular frequency Ω 2 greatly exceeds the squared frequency of interparticle physical collisions νc2; that is, the analysis presented here is valid only in the regime of low optical depth in Saturns rings, τ⋍ ν c Ω . According to observations, such low optical depth regions can be found in the C ring, the inner portions of the B ring at distances r 123 000 km from the planetary center. The analogy with magnetized plasma problems is utilized by applying the so-called single particle dynamics method (the Lagrangian description): The motion of an “average” particle is considered. In the framework of this analytical method the local dispersion relation for small-amplitude oscillations is derived. Using the dispersion relation, an analysis is given of the dispersion law both for axisymmetric (radial) and nonaxisymmetric (spiral) Jeans perturbations. The main result, which follows from the dispersion relation, is the local stability criterion. The criterion generalizes the well-known Toomres one (Astrophys. J. 139, 1217–1238, 1964) for spiral gravity perturbations. The dynamical behavior of the different models of Saturns ring disk is studied by N-body computer simulations in order to confirm the validity of the generalized stability criterion. The numerical method of local simulations (or N-body simulations in a Hills approximation) is applied. It is shown that the stability criterion obtained from the computer models is in general agreement with the theoretical prediction. It is proposed that as a direct result of the Jeans instability of nonaxisymmetric perturbations the Saturnian ring disk is subdivided into numerous irregular ringlets. with size and spacing of the order 50–100 m. Forth-coming Cassini spacecraft high-resolution images of Saturns rings may reveal this kind of structure.

The weakly nonlinear theory of density waves in a stellar disk

Quasilinear theory is applied to the adiabatic wave-star interaction of a differentially-rotating stellar disk of a galaxy. Under the influence of growing spiral waves the velocity dispersion of stars increases and the surface mass density becomes more peaked. The resulting distortion in phase space leads to a decrease in the growth rate of the waves, and as the result the Jeans instability should end after a few rotations of the system. The theory is confirmed by N-body computer simulations.

ANGULAR MOMENTUM TRANSPORT IN ASTROPHYSICAL DISKS

The evolution of astrophysical disks is dominated by instabilities of gravity perturbations (e.g., those produced by a spontaneous disturbance). We develop a hydrodynamic theory of nonresonant Jeans instability in a dynamically cold subsystem (identified as the gaseous component) of a disk. We show analytically that gravitationally unstable systems, such as disks of rotationally supported galaxies, protoplanetary disks, and, finally, the solar nebula are efficient at transporting mass and angular momentum: already on a timescale of on the order of 2-3 rotational periods an unstable disk sees a large portion of its angular momentum transferred outward, and mass transferred both inward and outward.

Resonant excitation of density waves in Saturn's rings

Abstract The dynamics of regions in the Saturnian ring system with rare collisions between particles, that is, Ω 2 ⪢ν c 2 , where Ω is the orbital angular frequency and νc the collision frequency, is considered. According to observations, such low optical depth regions can be found in the C ring, the inner portions of the B ring and the A ring. Kinetic theory with the Vlasov and Poisson equations is used to obtain the eigen-frequencies of oscillations propagating in the plane of the system. In the considered case of rare collisions the resulting kinetic equation for the perturbed distribution function can be solved by successive approximations, neglecting the effect of binary particle collisions in the zeroth-order approximation. An oscillating instability of the kinetic type is discussed. This instability of a particulate disk is similar to the magneto-drift instability first discovered by Krall and Rosenbluth (Physics Fluids6, 254–265, 1963) in a nonuniform magnetic plasma, and belongs to the class of microinstabilities of an inhomogeneous plasma. The cause of the oscillating instability in Saturns rings is a resonant interaction of drifting particles with nonaxisymmetric Jeans-stable waves at the corotation. The waves that may be produced by the corotation-resonance interaction represent non-radial normal modes of the gravitationally stable disk modified by a particle drift. It is shown that density waves are effectively excited at this resonance: the growth rate of the mode of maximum instability is large, Im ω∗∼Ω. The resonant excitation of density waves investigated in the present paper may be proposed as the cause of the irregular, small-scale ∼ 100 m structure in regions of low optical depth in Saturns rings. It is suggested that Cassini spacecraft high-resolution images of low optical depth regions will show this kind of structure.

THE POSSIBLE ORBITAL DECAY AND TRANSIT TIMING VARIATIONS OF THE PLANET WASP-43b

Motivated by the previously reported high orbital decay rate of the planet WASP-43b, eight newly transit light curves are obtained and presented. Together with other data in literature, we perform a self-consistent timing analysis with data covering a timescale of 1849 epochs. The results give an orbital decay rate dP/dt = -0.02890795\pm 0.00772547 sec/year, which is one order smaller than previous values. This slow decay rate corresponds to a normally assumed theoretical value of stellar tidal dissipation factor. In addition, through the frequency analysis, the transit timing variations presented here are unlikely to be periodic, but could be signals of a slow orbital decay.

The First Detection of Warping of Outer Stellar Disks in N-Body Simulations of Isolated and Rapidly Rotating Disk-shaped Galaxies

The evolution of the isolated, axially Jeans-stable (an initial velocity dispersion of particles is equal to Toomres stabilizing one), and rapidly rotating stellar disk of flat galaxies is investigated by N-body simulations. An algorithm of the direct summation for a simulation code is used. As the model evolves during the first rotation, the density wave spiral structure develops in the plane. At somewhat later times, in the normal to the plane direction, a characteristic warping of the outer disk begins to grow. The origin of this new phenomenon, which has not been illustrated previously via simulations, is studied. It seems likely that the outer vertical resonance produces the warp.

Resonant excitation of density waves in Saturn's rings: the effect of interparticle collisions

Abstract Kinetic theory with the phenomenological Bhatnagar-Gross-Krook binary collision integral is used to study the small amplitude oscillations and their stability of a collisional planetary ring system of identical particles. A differentially rotating, spatially homogeneous disk is considered, with the property that both the epicyclic frequency and the angular velocity of differential rotation exceeds the frequency of inelastic (physical) collisions between particles, that is, a disk with rare collisions is considered. The stabilizing influence of collisions on the growth rate of the oscillating resonant type instability, studied in the first paper of the series, is shown. Also it is shown that in low optical depth regions of Saturns rings rare collisions cannot suppress the resonant excitation of spiral density waves investigated by Griv (Planet. Space Sci. 44, 579–587, 1996) in the first paper of the present series.