Introduction To Stellar Dynamics

A thorough presentation of the fundamental concepts of stellar dynamics that bridges the gap between standard texts and advanced treatises.

The study of stellar dynamics is experiencing an exciting new wave of interest thanks to observational campaigns and the ready availability of powerful computers. Whilst its relevance includes many areas of astrophysics, from the structure of the Milky Way to dark matter halos, few texts are suited to advanced students. This volume provides a broad overview of the key concepts beyond the elementary level, bridging the gap between the standard texts and specialist literature. The author reviews Newtonian gravity in depth before examining the dynamical properties of collisional and collisionless stellar-dynamical systems that result from gravitational interactions. Guided examples and exercises ensure a thorough grounding in the mathematics, while discussions of important practical applications give a complete picture of the subject. Readers are given a sound working knowledge of the fundamental ideas and techniques employed in the field and the conceptual background needed to progress to more advanced graduate-level treatises.

In this classic text, a Nobel Prize-winning astrophysicist presents the theory of stellar dynamics as a branch of classical dynamics--a discipline in the same general category as celestial mechanics. His method offers the advantages of clarifying the theory's fundamental issues and defining its underlying motivations. S. Chandrasekhar investigates two areas. The first concerns problems in which the time of relaxation of a stellar system is central. His method consists of analyzing the effects of stellar encounters in terms of the two-body problem of classical dynamics and applying this theory to the dynamics of star clusters. The second area investigates problems centering around Liouville's theorem and the solutions of the equation of continuity; here, the author discusses the dynamic implications of the existence of a field of differential motions, which appears to be the most striking kinematic feature of the galaxy and the extragalactic systems. This edition includes two papers by the author that were published after Principles of Stellar Dynamics and that have been studied and quoted extensively: "New Methods in Stellar Dynamics" (originally published in the Annals of the New York Academy of Sciences) and "Dynamical Friction" (originally published in The Astrophysical Journal).

Galaxies, along with their underlying dark matter halos, constitute the building blocks of structure in the Universe. Of all fundamental forces, gravity is the dominant one that drives the evolution of structures from small density seeds at early times to the galaxies we see today. The interactions among myriads of stars, or dark matter particles, in a gravitating structure produce a system with fascinating connotations to thermodynamics, with some analogies and some fundamental differences. Ignacio Ferreras presents a concise introduction to extragalactic astrophysics, with emphasis on stellar dynamics, and the growth of density fluctuations in an expanding Universe. Additional chapters are devoted to smaller systems (stellar clusters) and larger ones (galaxy clusters). Fundamentals of Galaxy Dynamics, Formation and Evolution is written for advanced undergraduates and beginning postgraduate students, providing a useful tool to get up to speed in a starting research career. Some of the derivations for the most important results are presented in detail to enable students appreciate the beauty of maths as a tool to understand the workings of galaxies. Each chapter includes a set of problems to help the student advance with the material.

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.

Stellar dynamics is an interdisciplinary field where mathematics, statistics, physics, and astronomy overlap. The approaches to studying a stellar system include dealing with the collisionless Boltzmann equation, the Chandrasekhar equations, and stellar hydrodynamic equations, which are comparable to the equations of motion of a compressible viscous fluid. Their equivalence gives rise to the closure problem, connected with the higher-order moments of the stellar velocity distribution, which is explained and solved for maximum entropy distributions and for any velocity distribution function, depending on a polynomial function in the velocity variables. On the other hand, the Milky Way kinematics in the solar neighbourhood needs to be described as a mixture distribution accounting for the stellar populations composing the Galactic components. As such, the book offers a statistical study, according to the moments and cumulants of a population mixture, and a dynamical approach, according to a superposition of Chandrasekhar stellar systems, connected with the potential function and the symmetries of the model.

Since it was first published in 1987, Galactic Dynamics has become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, making Galactic Dynamics the most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers. Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject. This new edition of the classic text is the definitive introduction to the field. ? A complete revision and update of one of the most cited references in astrophysics Provides a comprehensive description of the dynamical structure and evolution of galaxies and other stellar systems Serves as both a graduate textbook and a resource for researchers Includes 20 color illustrations, 205 figures, and more than 200 problems Covers the gravitational N-body problem, hierarchical galaxy formation, galaxy mergers, dark matter, spiral structure, numerical simulations, orbits and chaos, equilibrium and stability of stellar systems, evolution of binary stars and star clusters, and much more Companion volume to Galactic Astronomy, the definitive book on the phenomenology of galaxies and star clusters