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Orbital complexity in a time‐dependent potential
Author(s) -
Boily C.M.,
Detemple L.,
Faber N.T.
Publication year - 2008
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.200811100
Subject(s) - physics , gravitation , orbit (dynamics) , stars , entropy (arrow of time) , orbital motion , wavelet , astrophysics , classical mechanics , statistical physics , quantum mechanics , computer science , angular momentum , artificial intelligence , engineering , aerospace engineering
We introduce a method to detect irregular or chaotic orbits in gravitational potentials based on a wavelet transform of stellar orbits. The method is based on a treatment of normalised frequency power‐spectrum coefficients, which we interpret as occupation probabilities (or, weights) of individual frequency modes. Each probability is fed to a Shannon informationentropy formula, before summing over the whole spectrum to compute the total entropy S . This entropy is then monitored in time as the wavelet coefficients change: each orbit is classi.ed as regular or not according to S and its dispersion. We find that diagrams of entropy versus entropy dispersion allow to identify orbits in a simple and efficient way, similarly to surface‐of‐section analysis but requiring less integration time. We apply the method to the case of a gravitational potential modulated by the periodic motion of a massive black hole and find that some 19% of stars are now shifted to highly irregular motion as a result of black hole orbital motion. This is the same fraction of stars that orbit within the black hole radius of influence. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)