| Description |
1 online resource (xii, 211 pages) : illustrations |
| Contents |
Intro; Contents; Preface; Chapter 1; 1.1 Introduction; 1.2 Jeans' problems; 1.3 Isolating integrals; 1.4 Self-consistent models; 1.5 Stellar statistics; 1.6 Velocity moments; Chapter 2; 2.1 Comoving-frame equations; 2.2 Conservation of pressures; 2.3 Conservation of moments; 2.4 Closure example; 2.5 Absolute reference frame; 2.6 Remarks; Chapter 3; 3.1 Quadratic integral; 3.2 Schwarzschild distribution; 3.3 Closure for Schwarzschild distributions; 3.4 Chandrasekhar's a; 3.5 Generalised Schwarzschild distribution; 3.6 Remarks; Chapter 4; 4.1 The Boltzmann and moment equations |
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4.2 Maximum entropy function4.3 Fundamental system of equations; 4.4 Closure of moment equations; 4.5 Arbitrary polynomial function; 4.6 Remarks; Chapter 5; 5.1 The problem of moments; 5.2 Maximum entropy distribution; 5.3 Moments problem; 5.4 Gramian system; 5.5 Remarks; Chapter 6; 6.1 Stellar samples; 6.2 Large-scale structure; 6.3 Truncated distributions; 6.4 Small-scale structure; 6.5 Orbital eccentricity; 6.6 Radial velocity distribution; 6.7 Remarks; Chapter 7; 7.1 Mixture approach; 7.2 Two-component mixture; 7.3 Moment constraints; 7.4 Local velocity ellipsoids |
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7.5 Second moments of a n-population mixture7.6 Remarks; Chapter 8; 8.1 Model hypotheses; 8.2 Dynamical model; 8.3 Chandrasekhar's axial system; 8.4 Conditions of consistency for mixtures; 8.5 The solar neighbourhood; 8.6 Local values of the pot; 8.7 Remarks; Chapter 9; 9.1 Point-axial symmetry; 9.2 Single point-axial system; 9.3 The potential is axisymmetric; 9.4 The potential is spherical; 9.5 Conditions of consistency; 9.6 Remarks; Appendices; Appendix A; A.1 Equation of order n = 3; A.2 Property; A.3 Equation of order n = 2; A.4 Property; A.5 Equation of order n = 1 |
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A.6 Equation of order n = 0Appendix B; Appendix C; Appendix D; Appendix E; Appendix F; F.1 U-cumulants; F.2 Constraints; Appendix G; G.1 Components of A2 and v; G.2 Second central moments; G.3 Moment gradients; Appendix H; Appendix I; Bibliography; Index |
| Summary |
"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."-- Publisher's web site |
| Bibliography |
Includes bibliographical references (pages 201-207) and index |
| Notes |
Print version record |
| Subject |
Galactic dynamics.
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Stellar dynamics.
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Galaxies.
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Astronomy
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Theoretical & mathematical astronomy.
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Galaxies & stars.
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Astrophysics.
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SCIENCE -- Astronomy.
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Galactic dynamics
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Galaxies
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Stellar dynamics
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| Form |
Electronic book
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| ISBN |
9781527514805 |
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1527514803 |
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