Hawkin, John Alexander (2006) Stochastic dynamics of globular clusters. Masters thesis, Memorial University of Newfoundland.
- Accepted Version
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The most common approach to studying the dynamics of globular clusters is to calculate and analyze the position and velocity for each star. The rapid variation of these variables is a limitation of this approach. It is perhaps easier to study star cluster dynamics by analyzing more slowly changing variables, such as the period of a star. In this thesis, I study two particular slow-changing variables of stars in N -body simulations, these being the aforementioned theoretical period, and the angle between the star's closest approach to and its farthest retreat from the center of the cluster. Our work involves fitting these variables to ARMA models, both through careful individual analysis and through an automated procedure. While the ARMA models which we considered could not be successfully fit to these variables, it is possible that an analysis using higher order ARMA models, or possibly GARCHMA models, would be more successful. -- The second portion of this thesis deals with the distribution of forces in a star cluster. A simple approximation of this distribution was given by Holtsmark in 1917. This approximation assumes that the cluster has an infinite radius and a constant density, and thus it assumes the force distribution is not spatially dependent. We showed from studies of simulations that these assumptions are not valid for a real cluster, because stars on the edge of the cluster do not experience the same force, on average, as stars in the middle. A new force distribution which takes this fact into account must be used instead. -- It would seem that research such as the statistical time series models mentioned above, as well as the new force distribution, could eventually lead to the derivation a new set of dynamical equations for star clusters. This work is not covered in this thesis, but is an obvious and quite likely very fruitful continuation which we hope to explore in the future.
|Item Type:||Thesis (Masters)|
|Additional Information:||Includes bibliographical references (leaves 143-147).|
|Department(s):||?? ComptSci ??|
|Library of Congress Subject Heading:||Stars--Globular clusters; Stochastic processes.|
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