# Dynamics of Stellar Systems

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Dynamics of Stellar Systems focuses on the theoretical problems in stellar dynamics. The book first offers information on stellar dynamics, including historical development, fundamentals of synthetic method, and value of stellar dynamics. The text discusses the fundamental concepts of stellar statistics. Properties of univariate distribution functions; multivariate distribution functions; and statistical properties of stars are explained. The text then describes the elementary theory of galactic rotation and irregular forces in stellar systems. The text also tackles statistical stellar dynamics of neglecting encounters. Considerations include Boltzmann equation in curvilinear coordinates; importance of using one-valued integrals of the motion; and fundamental differential equation of stellar dynamics. The book also underscores the regular orbit of stars and dynamics of centroids. The text describes the dynamics of spherical stellar and rotating stellar systems. The theory of polytropic spheres; basic equations for spherical systems; masses and rotation of galaxies; and boundaries of galaxies are discussed. The text is highly recommended for readers interested in stellar dynamics.

## Table of Contents

Contents

Preface to the English Edition

Preface to the Russian Edition

Introduction

1. The Subject of Stellar Dynamics

2. A Brief Outline of the Historical Development of Stellar Dynamics

3. The Fundamentals of the Synthetic Method in Stellar Dynamics

4. The Practical Significance of Stellar Dynamics

I. The Fundamental Concepts of Stellar Statistics

1. Some Properties of Univariate Distribution Functions

2. Multivariate Distribution Functions

3. Statistical Properties of Stars

II. The Kinematics of Stellar Systems

1. The Macroscopic Volume Element and the Star Density Function

2. The Phase Density Function

3. The Velocity Distribution Function

4. Centroids

5. The Local Motion of the Sun in the Galaxy

6. The Velocity Ellipsoid and its Determination from Observations

7. Results of Velocity Ellipsoid Determinations and some Inferences therefrom

8. The Determination of the Actual Form of the Ellipsoidal Velocity Function

9. The Differential Field of Centroid Velocities. Helmholtz' Theorem for Stellar Systems

10. Determination of the Kinematic Parameters of the Differential Field of Centroid

Velocities from the Observed Velocities of Stars

IIT. The Elementary Theory of Galactic Rotation

1. General Formulae of Galactic Rotation

2. The Local Field of Centroid Velocities. Generalization of Oort's Formulae

3. Oort's Formulae for an Arbitrary Plane-parallel Motion

4. The Physical Basis of the Theory of Galactic Rotation. The Nature of the K Term

5. Determination of the Parameters of Galactic Rotation from Observation

6. Determination of the Period of Rotation and Angular Velocity of the Galaxy

7. Determination of the Mass of the Galaxy

8. The Velocity of Escape and the Phenomenon of the High-velocity Stars

9. Kinematics of Centroids in the Metagalaxy

10. The Problem of Setting up a Fundamental Coordinate System

IV. Irregular Forces in Stellar Systems

1. The Fundamental Quantities which Characterize the State of a Stellar System

2. Star Encounters. Regular and Irregular Forces

3. The Effect of Irregular Forces: Individual Encounters

4. The Effect of Irregular Forces: the Cumulative Effect

5. Various Types of Equilibrium of Stellar Systems. The Quasi-steady State

6. The Relaxation Time and the Disintegration Half-life

7. The Fundamental Paradox in the Classical Dynamics of Stellar Systems

8. The Interaction of Stars with Dust Clouds

9. The Invariance of Maxwell's and Schwarzschild's Velocity Distribution Laws in Stellar Encounters

V. Statistical Stellar Dynamics Neglecting Encounters

1. The Fundamental Differential Equation of Stellar Dynamics

2. The Boltzmann Equation in Curvilinear Coordinates

3. Jeans' Theorem and Liouville's Theorem

4. The Integrals of the Motion in Some Typical Cases

5. One-valued and Many-valued Integrals. The Ergodic Hypothesis in Stellar

Dynamics 147

6. Jeans' Problem. The Symmetry of the Distribution in Velocity Space

7. The Inverse Jeans' Problem

8. The Importance of Using One-valued Integrals of the Motion

9. Quasi-integrals of the Motion. Oort's Quasi-integral

10. The Problem of the Third Integral for Systems with Rotational Symmetry

11. The Potential Energy of Stellar Systems

12. The Virial Theorem. Poincare's Theorem on the Limiting Angular Velocity of Rotation

VI. Regular Orbits of Stars

1. Circular and Almost Circular Orbits in a Stellar System with Rotational Symmetry and a Plane of Symmetry

2. Determination of the Potential of the Galaxy

3. Some Properties of Regular Galactic Orbits

4. The Distribution of Mass in the Galaxy and Some Related Problems

5. Some Properties of Star Orbits in Spherical Systems

VTT. The Problem of Local Dynamics

1. Statement of the Problem

2. The Local Cluster and its Motion in the Galaxy

3. Observed Anomalies of Stellar Motions in the Neighbourhood of the Sun

4. The Linearised Equations of Motion in Lindblad's System of Rotating Coordinates

5. Conditions for the Dynamical Stability of Stellar Condensations

6. The Quasi-precession of the Velocity Ellipsoid

7. The Quasi-tidal Effect on the Velocity Ellipsoid

8. The Application of the Theory to the Observational Results

9. The Combined Quasi-precession and Quasi-tidal Effects

10. The K Effect as a Result of the Dissipation of the Local Cluster

11. The Dynamics of the Local Cluster

VIII. Dynamics of Centroids

1. Macroscopic Motions in Stellar Systems

2. Some Properties of the Kinematics of Centroids

3. Equations of Motion of Centroids in Rectangular Coordinates

4. The Dynamical Significance of the Velocity Moment Tensor

5. Equations of Motion of Centroids in Cylindrical and Spherical Coordinates

6. The Hydrodynamical Equations for a Rotationally Symmetrical System in a Steady State

7. The Explanation of the Asymmetry of Stellar Motions in the Galaxy

IX. Dynamics of Spherical Stellar Systems

1. The Basic Equations for Spherical Systems

2. The Use of the Theory of Polytropic Spheres

3. The Most Probable Phase Distribution

4. The Truncation of the Phase Distribution. Determination of the Star Density

5. Discussion of the Expression Obtained for the Phase Density

6. Determination of the Parameter h2 of the Phase Distribution

7. The Distribution of Star Orbits. Lindblad and Bottlinger Diagrams

8. Spherical Systems with an Inhomogeneous Star Population

X. Dynamics of Rotating Stellar Systems

1. The Masses and Rotation of Various Types of Galaxy

2. The Boundaries of the Galaxies

3. The Method of Additive Parameters

4. The Most Probable Phase Distribution for the Simplest Types of Galaxy

5. The Phase Distribution for Dynamically Determinate Galaxies

6. Equilibrium Figures of D Galaxies

7. The Formation of Sharp Edges in Elliptical Galaxies

8. The Formation of Central Nuclei and Ring Structure in Galaxies

9. The Existence of Needle-shaped and Pear-shaped Galaxies

10. Kapteyn-Lindblad Systems

11. The Fourth Additive Parameter for KL Systems

12. The Most Probable Phase Distribution for KL Systems

13. The Galaxy and Similar Spirals as Kapteyn-Lindblad Systems

14. Some Conclusions Regarding the Processes of Evolution of Stellar Systems

References

Indexes

## Product details

- No. of pages: 372
- Language: English
- Copyright: © Pergamon 1965
- Published: January 1, 1965
- Imprint: Pergamon
- eBook ISBN: 9781483137452