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Galaxies 2016, 4(3), 9; doi:10.3390/galaxies4030009

Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation

Ottawa, ON K1N 9H5, Canada
Academic Editor: Emilio Elizalde
Received: 27 April 2016 / Revised: 19 July 2016 / Accepted: 8 August 2016 / Published: 15 August 2016
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Abstract

Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson equations (the GPP system). In the analysis of these hypothetical objects, the Thomas-Fermi (TF) approximation is widely used. This approximation is based on the assumption that in the presence of a large number of particles, the kinetic term in the Gross-Pitaevskii energy functional can be neglected, yet it is well known that this assumption is violated near the condensate surface. We also show that the total energy of the self-gravitating condensate in the TF-approximation is positive. The stability of a self-gravitating system is dependent on the total energy being negative. Therefore, the TF-approximation is ill suited to formulate initial conditions in numerical simulations. As an alternative, we offer an approximate solution of the full GPP system. View Full-Text
Keywords: Bose-Einstein condensates; dark matter halos Bose-Einstein condensates; dark matter halos
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Toth, V.T. Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation. Galaxies 2016, 4, 9.

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