Physics of Gravitating Systems II : Nonlinear Collective Processes: Nonlinear Waves, Solitons, Collisionless Shocks, Turbulence. Astrophysical Applications

Book by Fridman AM Polyachenko VL

(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- § 1. Beam Instability of a Gravitating Medium.- 1.1. Theorem of a Number of Instabilities of the Heterogeneous System with Homogeneous Flows.- 1.2. Expression for the Growth Rate of the Kinetic Beam Instability in the Case of a Beam of Small Density (for an Arbitrary Distribution Function).- 1.3. Beam with a Step Function Distribution.- 1.4. Hydrodynamical Beam Instability. Excitation of the Rotational Branch.- 1.5. Stabilizing Effect of the Interaction of Gravitating Cylinders and Disks.- 1.6. Instability of Rotating Inhomogeneous Cylinders with Oppositely Directed Beams of Equal Density.- § 2. Gradient Instabilities of a Gravitating Medium.- 2.1. Cylinder of Constant Density with Radius-Dependent Temperature. Hydrodynamical Instability.- 2.2. Cylinder of Constant Density with a Temperature Jump. Kinetic Instability.- 2.3. Cylinder with Inhomogeneous Density and Temperature.- § 3. Hydrodynamical Instabilities of a Gravitating Medium with a Growth Rate Much Greater than that of Jeans.- 3.1. Hydrodynamical Instabilities in the Model of a Flat Parallel Flow.- 3.2. Hydrodynamical Instabilities of a Gravitating Cylinder.- §4. General Treatment of Kinetic Instabilities.- 4.1. Beam Effects in the Heterogeneous Model of a Galaxy.- 4.2. Influence of a “Black Hole” at the Center of a Spherical System on the Resonance Interactions Between Stars and Waves.- 4.3. Beam Instability in the Models of a Cylinder and a Flat Layer.- VII Problems of Nonlinear Theory.- § 1. Nonlinear Stability Theory of a Rotating, Gravitating Disk.- 1.1. Nonlinear Waves and Solitons in a Hydrodynamical Model of an Infinitely Thin Disk with Plane Pressure.- 1.2. Nonlinear Waves in a Gaseous Disk.- 1.3. Nonlinear Waves and Solitons in a Stellar Disk.- 1.4. Explosive Instability.- 1.5. Remarks on the Decay Processes.- 1.6. Nonlinear Waves in a Viscous Medium.- § 2. Nonlinear Interaction of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- § 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- § 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- §5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- § 1. Oort’s Antievolutionary Hypothesis.- § 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- § 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- § 4. Lynden-Bell’s Collisionless Relaxation.- § 5. Estimates of “Collisionlessness” of Particles in Different Real Systems.- IX Spherical Systems.- § 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- § 2. Classification of Unstable Modes in Scales.- § 3. Universal Criterion of the Instability.- § 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the System’s Evolution.- § 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- § 6. Example of Strongly Unstable Model.- § 7. Can Lynden-Bell’s Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- § 8. Is the “Unstable” Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a “Black Hole”?.- X Ellipsoidal Systems.- § 1. Objects Under Study.- § 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the Observed Oblatenesses of S- and SO-Galaxies with the Oblateness of E-Galaxies.- 2.3. Two Possible Solutions of the Problem.- 2.4. The Boundary of the Anisotropic (Fire-Hose) Instability Determines the Critical Value of Oblateness.- 2.5. Universal Criterion of Instability.- §3. SB-Galaxies.- 3.1. The Main Problem.- 3.2. Detection in NGC 4027 of Counterflows as Predicted by Freeman.- 3.3. Stability of Freeman Models of SB-Galaxies with Observed Oblateness.- XI Disk-like Systems. Spiral Structure.- § 1. Different Points of View on the Nature of Spiral Structure.- § 2. Resonant Interaction of the Spiral Wave with Stars of the Galaxy.- 2.1. Derivation of Expressions for the Angular Momentum and Energy of the Spiral Wave.- 2.2. Physical Mechanisms of Energy and Angular Momentum Exchange Between the Spiral Waves and the Resonant Stars.- § 3. The Linear Theory of Stationary Density Waves.- 3.1. The Primary Idea of Lin and Shu of the Stationary Density Waves.- 3.2. The Spiral Galaxy as an Infinite System of Harmonic Oscillators.- 3.3. On “Two-Armness” of the Spiral Structure.- 3.4. The Main Difficulties of the Stationary Wave Theory of Lin and Shu.- §4. Linear Theory of Growing Density Waves.- 4.1. Spiral Structure as the Most Unstable Mode.- 4.2. Gravitational Instability at the Periphery of Galaxies.- 4.3. Waves of Negative Energy Generated Near the Corotation Circle and Absorbed at the Inner Lindblad Resonance―Lynden-BellKalnaj’s Picture of Spiral Pattern Maintenance.- 4.4. Kelvin–Helmholz Instability and Flute-like Instability in the Near-Nucleus Region of the Galaxy as Possible Generators of Spiral Structure.- 4.5. The “Trailing” Character of Spiral Arms.- § 5. Comparison of the Lin–Shu Theory with Observations.- 5. 1 The Galaxy.- 5.2. M33, M51, M81.- § 6. Experimental Simulation of Spiral Structure Generation.- 6. 1 In a Rotating Laboratory Plasma.- 6.2. In Numerical Experiment.- § 7. The Hypothesis of the Origin of Spirals in the SB-Galaxies.- XII Other Applications.- § 1 On the Structure of Saturn’s Rings.- l.1. Introduction.- 1.2. Model. Basic Equations.- 1.3. Jeans Instability.- 1.4. Dissipative Instabilities.- 1.5. Modulational Instability.- Appendix. Derivation of the Expression for the Perturbation Energy of Maclaurin’s Ellipsoid.- § 2. On the Law of Planetary Distances.- §3. Galactic Plane Bending.- 3.1. Quasistationary Tidal Deformation.- 3.2. Free Modes of Oscillations.- 3.3. Close Passage.- § 4. Instabilities in Collisions of Elementary Particles.- § 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- § 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- § 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- § 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- § 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. “Lagrange” Derivation of the Matrix Equation.- § 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- § 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- § 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- § 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- § 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- §11. Derivation of the Kinetic Equation for Waves.- § 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.