Contopoulos / Patsis Chaos in Astronomy

Conference 2007
1. Auflage 2009
ISBN: 978-3-540-75826-6
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 497 Seiten

Reihe: Astrophysics and Space Science Proceedings

The conference ““Chaos in Astronomy”” was held in Athens on 17-20 Sept. 2007. International leaders in the field addressed the topics - Chaos in large N-body systems and in galactic dynamics, - Chaos in solar system dynamics, - Statistical mechanics of systems with regular and chaotic orbits, - Chaos in the formation of large-scale structure in the Universe, - Fundamental concepts, methods and tools. The book contains carefully edited refereed contributions. It serves as a reference to researchers and will give an overview to students and newcomers entering any field of dynamical astronomy.

Autoren/Hrsg.

Contopoulos, G.

Patsis, P.A.

Patsis, P. A.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;List of Contributors;13
4;Nikolaos Voglis (1948–2007);19
5;Part I Galactic Dynamics;23
5.1;Ordered and Chaotic Orbits in Spiral Galaxies;24
5.1.1;1 Introduction;24
5.1.2;2 Normal Spirals;25
5.1.3;3 Barred Spirals;26
5.1.4;4 Velocity Fields;37
5.1.5;5 Conclusions;39
5.1.6;Appendix: The Families of Short Period Orbits;39
5.1.7;References;42
5.2;Order and Chaos in Spiral Galaxies Seen through their Morphology;44
5.2.1;1 Introduction;44
5.2.2;2 Observations vs. Models;45
5.2.3;3 Special Regions and Features;46
5.2.4;4 Interpretation of Morphology;47
5.2.5;5 Pitfalls and Other Issues;48
5.2.6;6 Case Studies: Bars and Spirals;49
5.2.7;7 Conclusions;52
5.2.8;References;53
5.3;The Flow through the Arms of Normal and Barred-Spiral Galaxies;54
5.3.1;1 Spiral Flows and Orbital Theory;54
5.3.2;3 Barred Galaxies with Spirals;62
5.3.3;4 Conclusions;64
5.3.4;References;65
5.4;Ansae in Barred Galaxies, Observations and Simulations;66
5.4.1;1 Introduction;66
5.4.2;2 Observations;68
5.4.3;3 Simulations of Barred Galaxies and Ansae;70
5.4.4;4 Summary and Future Work;71
5.4.5;Acknowledgements;72
5.4.6;References;72
5.5;Orbital Structure in Barred Galaxies and the Role of Chaos;74
5.5.1;1 Initial Conditions and Characteristics of the Bar;74
5.5.2;2 Classification in Ordered and Chaotic Orbits;76
5.5.3;3 Orbital Structure of the Barred Galaxy;77
5.5.4;4 Conclusions;81
5.5.5;References;81
5.6;Chaos in Galaxies;83
5.6.1;1 Introduction;83
5.6.2;2 Chaos in Galaxies;86
5.6.3;3 Cases of Sensitive Dependence in Galaxy Models;90
5.6.4;4 Conclusions;95
5.6.5;References;96
5.7;Boxy/Peanut Bulges: Formation, Evolution and Properties;97
5.7.1;1 Introduction;97
5.7.2;2 Orbital Structure;98
5.7.3;3 Formation and Evolution of Boxes and Peanuts;98
5.7.4;Acknowledgements;103
5.7.5;References;103
5.8;Invariant Manifolds as Building Blocks for the Formation of Spiral Arms and Rings in Barred Galaxies;104
5.8.1;1 Introduction;104
5.8.2;2 Description of the Model and Equations of Motion;106
5.8.3;3 Dynamics Around L1 and L2;107
5.8.4;4 Results;109
5.8.5;Acknowledgement;111
5.8.6;References;111
5.9;Secular Instabilities of Stellar Systems: Slow Mode Approach;112
5.9.1;1 Introduction;112
5.9.2;2 Spherical Stellar Clusters Around MBH;114
5.9.3;3 Galactic Disks;119
5.9.4;4 General Conclusions;122
5.9.5;References;123
5.10;Stellar Velocity Distribution in Galactic Disks;124
5.10.1;1 Introduction;124
5.10.2;2 The Boltzmann Moment Equations: BEADS-2D;126
5.10.3;3 Test Particle Simulations;126
5.10.4;4 Results;128
5.10.5;5 Summary and Future Plans;130
5.10.6;References;131
5.11;Dynamical Study of 2D and 3D Barred Galaxy Models;133
5.11.1;1 Introduction;133
5.11.2;2 Definition of the Smaller Aligment Index (SALI);134
5.11.3;3 The Model;134
5.11.4;4 Results in the 2D and 3D Ferrers Model;136
5.11.5;5 Conclusions;139
5.11.6;Acknowledgments;139
5.11.7;References;140
5.12;Chaos in the Mergers of Galaxies;141
5.12.1;1 Introduction;141
5.12.2;2 A Model of Chaos in the Mergers of Galaxies;142
5.12.3;3 Chaotic Decay of Stationary Oscillations in Galaxies Formed by Mergers: A Conjecture;149
5.12.4;4 Epilogue: Transient Chaos in the Mergers of Galaxies;152
5.12.5;Acknowledgments;152
5.12.6;References;152
5.13;Hamiltonian Normal Forms and Galactic Potentials;154
5.13.1;1 Introduction;154
5.13.2;2 The Hamiltonian Normal Form;155
5.13.3;3 Applications;159
5.13.4;4 Comments and Outlook;164
5.13.5;Acknowledgments;165
5.13.6;References;165
5.14;Local Phase Space: Shaped by Chaos?;167
5.14.1;1 Introduction;167
5.14.2;2 Local Phase Space;168
5.14.3;3 Simulations;169
5.14.4;4 Results;170
5.14.5;6 The Role of Chaos;173
5.14.6;7 Summary and Future Work;173
5.14.7;References;174
5.15;Barred Galaxies: An Observer’s Perspective;175
5.15.1;1 Some Basic Facts;175
5.15.2;2 Observed Properties of Barred Galaxies;176
5.15.3;3 Estimating the Dynamical Ages of Bars;179
5.15.4;4 The Structural Properties of Bars;180
5.15.5;5 Future Work;184
5.15.6;References;185
5.16;Invariant Manifolds and the Spiral Arms of Barred Galaxies;189
5.16.1;1 Introduction;189
5.16.2;2 Model;190
5.16.3;3 Results;192
5.16.4;4 Conclusions;197
5.16.5;References;198
5.17;Collisional N-Body Simulations and Time-Dependent Orbital Complexity;199
5.17.1;1 Introduction;199
5.17.2;2 Method;199
5.17.3;3 Application to the N = 3 Pythagorean Problem;203
5.17.4;4 Conclusion;206
5.17.5;References;206
5.18;Resonances in Galactic and Circumstellar Disks;207
5.18.1;1 Introduction;207
5.18.2;2 Lindblad and Mean Motion Resonances;208
5.18.3;3 Chaos Due to Resonance Overlap in Galaxies;216
5.18.4;References;218
5.19;Regular and Chaotic Motion in Elliptical Galaxies;219
5.19.1;1 Introduction;219
5.19.2;2 Highly Chaotic Triaxial Stellar Systems;220
5.19.3;3 Partially and Fully Chaotic Orbits;222
5.19.4;4 Figure Rotation in Triaxial Systems;224
5.19.5;5 Musings on Orbital Classi.cation Through Frequency Analysis;224
5.19.6;6 Discussion;228
5.19.7;7 Acknowledgements;229
5.19.8;References;229
5.20;Orbital Distributions and Self-Consistency in Elliptical Galaxies;231
5.20.1;1 Introduction;231
5.20.2;2 SCF Code;232
5.20.3;3 Models;233
5.20.4;4 Results;234
5.20.5;5 Conclusions;238
5.20.6;References;239
5.21;The Connection Between Orbits and Isophotal Shape in Elliptical Galaxies;241
5.21.1;1 Introduction;241
5.21.2;2 Superposition of Orbit Classes and Isophotal Shape;242
5.21.3;3 Discussion and Conclusion;244
5.21.4;References;244
5.22;Gas Orbits in a Spiral Potential;246
5.22.1;1 Introduction;246
5.22.2;2 The Simulations;246
5.22.3;3 The Gaseous Orbits;247
5.22.4;References;249
5.23;The Structure of the Phase Space in Galactic Potentials of Three Degrees of Freedom;250
5.23.1;1 Introduction;250
5.23.2;2 4D Surfaces of Section;251
5.23.3;References;253
5.24;Regular and Chaotic Orbits in Narrow 2D Bar Models;255
5.24.1;1 Model Description;255
5.24.2;2 Variation of the Bar Axial Ratio a/c;256
5.24.3;3 Surfaces of Section;256
5.24.4;4 A Closer Look at the Propeller Orbit Family;257
5.24.5;5 Conclusions;259
5.24.6;References;259
5.25;The Coalescence of Invariant Manifolds in Barred-Spiral Galaxies;260
5.25.1;1 Unstable Periodic Orbits and their Invariant Manifolds;260
5.25.2;2 Conclusions;263
5.25.3;References;263
6;Part II Celestial Mechanics;265
6.1;Chaotic Dynamics in Planetary Systems;266
6.1.1;1 Introduction;266
6.1.2;2 Detection Methods;267
6.1.3;3 The Structure of EPS;269
6.1.4;4 Our Planetary System as Dynamical Model;271
6.1.5;5 Multiplanetary Systems;274
6.1.6;6 Conclusions;277
6.1.7;References;279
6.2;Routes to Chaos in Resonant Extrasolar Planetary Systems;280
6.2.1;1 Introduction;280
6.2.2;2 Resonant Extrasolar Planetary Systems;281
6.2.3;3 A Stable System at the 2:1 Resonance. (.2 . .1) = 00;284
6.2.4;4 A Stable System at the 2:1 Resonance. .2 . .1 = 1800;286
6.2.5;5 An Unstable System at the 3:1 Resonance. (.2 . .1) = 00;288
6.2.6;6 A Stable System at the 3:1 Resonance. (.2 . .1) = 00;290
6.2.7;7 Discussion;292
6.2.8;References;293
6.3;Prometheus and Pandora, the Champions of Dynamical Chaos;295
6.3.1;Acknowledgments;301
6.3.2;References;301
6.4;Planets in Multiple Star Systems: A Symplectic Approach;303
6.4.1;1 Introduction;303
6.4.2;2 Method;305
6.4.3;3 Application and Results;307
6.4.4;4 Conclusions;310
6.4.5;References;310
6.5;Stabilized Chaos in the Sitnikov Problem;311
6.5.1;1 Formulation of the Problem;311
6.5.2;2 Stabilization of Chaotic Behavior in the Extended Sitnikov Problem;312
6.5.3;References;314
7;Part III Fundamental Concepts and Methods;316
7.1;Nonextensive Statistical Mechanics – An Approach to Complexity;317
7.1.1;1 Introduction;317
7.1.2;2 Nonextensivity of the Nonadditive Entropy Sq;318
7.1.3;3 Entropy Production per Unit Time;319
7.1.4;4 q-Generalization of the Standard and the L´evy-Gnedenko Central Limit Theorems;320
7.1.5;5 Current Applications of Nonextensive Statistical Mechanics to Astrophysical Systems;322
7.1.6;Acknowledgments;322
7.1.7;References;322
7.1.8;Absolute Versus Relative Motion in Mechanics;327
7.1.9;References;331
7.2;Far Fields, from Electrodynamics to Gravitation, and the Dark Matter Problem;333
7.2.1;1 Introduction;333
7.2.2;2 Far Fields in Electrodynamics, and the Wheeler Feynman Identity;334
7.2.3;3 The Virial Theorem in the Theory of Gases and in Astrophysics, and the Role of the External Forces;336
7.2.4;4 Relevance of the Far Matter if Hubble’s Law is Taken into Account;337
7.2.5;5 Estimate of the Gravitational Forces. Role of the Discreteness of the Sources, and of the Fractal Nature of the Universe;339
7.2.6;6 Application to the Virial for a Cluster of Galaxies;341
7.2.7;7 Conclusion;342
7.2.8;Acknowledgement;342
7.2.9;References;342
7.3;Distribution Functions for Galaxies using Quadratic Programming;344
7.3.1;1 Introduction;344
7.3.2;2 The Quadratic Programming Modeling Method;344
7.3.3;3 Self-consistent Instabilities;346
7.3.4;4 Conclusions and Future Prospects;353
7.3.5;References;353
7.4;Chaos Analysis Using the Patterns Method;354
7.4.1;1 Introduction;354
7.4.2;2 The Patterns Method;356
7.4.3;3 Conclusions;360
7.4.4;References;361
7.5;On the Topology of Regions of 3-D Particle Motions in Annular Configurations of n Bodies with a Central Post-Newtonian Potential;363
7.5.1;1 Introduction;363
7.5.2;2 The Three-Dimensional Ring Problem of (n + 1) Bodies and the Normalized Equations of Motion;363
7.5.3;3 Equilibrium Zones and Evolution of the Zero-Velocity Surfaces in 3-D Motion;364
7.5.4;4 Applications;365
7.5.5;References;367
7.6;The Average Power-Law Growth of Deviation Vector and Tsallis Entropy;368
7.6.1;1 Introduction;368
7.6.2;2 Q-Entropy and the Growth of Deviation Vectors;368
7.6.3;3 Numerical Examples;370
7.6.4;Acknowledgments;371
7.6.5;References;371
7.7;Global Dynamics of Coupled Standard Maps;372
7.7.1;1 Definition and Behavior of GALI;372
7.7.2;2 Dynamical Study of a 4D Standard Map;373
7.7.3;Acknowledgments;376
7.7.4;References;376
8;Part IV Other Astronomical Systems;377
8.1;The Chaotic Light Curves of Accreting Black Holes;378
8.1.1;1 Introduction;378
8.1.2;2 From Light Curves to Dynamics;380
8.1.3;3 The Power Density Spectra;380
8.1.4;4 The Lags;382
8.1.5;5 Modeling the X-ray Light Curves;384
8.1.6;6 Conclusions, Discussion;386
8.1.7;Acknowledgments;388
8.1.8;References;388
8.2;3D Accretion Discs Dynamics: Numerical Simulations;389
8.2.1;1 Introduction;389
8.2.2;2 Model;390
8.2.3;3 Shock Waves in Accretion Discs;391
8.2.4;4 The “Precessional” Spiral Density Wave in the Cold Accretion Disc;395
8.2.5;5 The Spiral-Vortex Structure in the Hot Accretion Disc;398
8.2.6;6 Conclusions;399
8.2.7;Acknowledgments;399
8.2.8;References;399
8.2.9;Growth of Density Fluctuations at the Time of Leptogenesis;401
8.2.10;References;403
8.3;Fully Developed Turbulence in Accretion Discs of Binary Stars: Turbulent Viscosity Coe.cient and Power Spectrum;405
8.3.1;1 Introduction;405
8.3.2;2 Statement of the Problem, Basic Equations, and Numerical Approach;407
8.3.3;3 Collective Mode m=1;408
8.3.4;4 Over-Re.ection Instability;411
8.3.5;5 Estimation of the Turbulent Viscosity Coe.cient;416
8.3.6;6 Spectrum of Turbulence in the Accretion Disc of IP Peg;417
8.3.7;7 Conclusions;420
8.3.8;Acknowledgments;421
8.3.9;References;422
8.4;Solar and Stellar Active Regions A Cosmic Laboratory for the study of Complexity;424
8.4.1;1 Solar Active Regions as Driven Non Linear Systems;424
8.4.2;2 Active Region Formation: A Percolating Driver?;425
8.4.3;3 How Active Regions Evolve by Dissipating Energy: Are AR in a Self Organized Critical State?;426
8.4.4;4 Active Regions as Multi-Scale Physics Laboratories;431
8.4.5;5 Summary;433
8.4.6;Acknowledgement;433
8.4.7;References;433
8.5;Chaos and Self-Organization in Solar Flares: A Critical Analysis of the Present Approach;435
8.5.1;1 Introduction;435
8.5.2;2 Solar Flares as Manifestation of Chaos III: “Disruption of the Turbulent Current Sheet of the Flare into Random Resistors Network”‘;440
8.5.3;Acknowledgement;447
8.5.4;References;447
8.6;Charged Particles’ Acceleration through Reconnecting Current Sheets in Solar Flares;449
8.6.1;1 Introduction;449
8.6.2;2 Analytical Formulation of the Problem;450
8.6.3;3 Numerical Results;450
8.6.4;4 Conclusions;452
8.6.5;References;452
8.7;The Perturbed Photometric-Magnetic Dynamical Model for the Sunspot Evolution;454
8.7.1;1 Introduction;454
8.7.2;2 The Conservative Perturbed PhMD Model;455
8.7.3;3 The Dissipative Perturbed PhMD Model;457
8.7.4;References;458
8.8;The Dynamics of Non-Symmetrically Collapsing Stars;459
8.8.1;1 Introduction;459
8.8.2;2 Equations of Motion and Numerical Results;459
8.8.3;3 The Poincar´e Section;461
8.8.4;4 Conclusions;461
8.8.5;Acknowledgments;463
8.8.6;References;463
8.9;Cosmic Order out of Primordial Chaos: A Tribute to Nikos Voglis;464
8.9.1;1 Some Early History;464
8.9.2;2 Angular Momentum Generation: The Tidal Mechanism;465
8.9.3;3 Gravitational Instability;469
8.9.4;4 Tidal Shear;471
8.9.5;5 The Cosmic Web;472
8.9.6;7 Tidal Fields and Void Alignment;474
8.9.7;8 Final Remarks;477
8.9.8;Acknowledgments;478
8.9.9;References;478
8.10;Cosmological Inflation: A Personal Perspective;481
8.10.1;1 Introduction;481
8.10.2;2 The Cosmological Problems;482
8.10.3;3 Phase Transitions, Baryogenesis;484
8.10.4;4 Resolving the Horizon Problem;485
8.10.5;5 “Nothing Succeeds like Success”;488
8.10.6;6 Conclusions and Speculations;489
8.10.7;Acknowledgments;492
8.10.8;References;492