Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation
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 ob...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2016-08-01
|
| Series: | Galaxies |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2075-4434/4/3/9 |
| _version_ | 1818695972133273600 |
|---|---|
| author | Viktor T. Toth |
| author_facet | Viktor T. Toth |
| author_sort | Viktor T. Toth |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T13:53:57Z |
| format | Article |
| id | doaj.art-2e0cff58d3d945a892bd0cf7db375ef6 |
| institution | Directory Open Access Journal |
| issn | 2075-4434 |
| language | English |
| last_indexed | 2024-12-17T13:53:57Z |
| publishDate | 2016-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Galaxies |
| spelling | doaj.art-2e0cff58d3d945a892bd0cf7db375ef62022-12-21T21:45:59ZengMDPI AGGalaxies2075-44342016-08-0143910.3390/galaxies4030009galaxies4030009Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi ApproximationViktor T. Toth0Ottawa, ON K1N 9H5, CanadaSelf-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.http://www.mdpi.com/2075-4434/4/3/9Bose-Einstein condensatesdark matter halos |
| spellingShingle | Viktor T. Toth Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation Galaxies Bose-Einstein condensates dark matter halos |
| title | Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation |
| title_full | Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation |
| title_fullStr | Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation |
| title_full_unstemmed | Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation |
| title_short | Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation |
| title_sort | self gravitating bose einstein condensates and the thomas fermi approximation |
| topic | Bose-Einstein condensates dark matter halos |
| url | http://www.mdpi.com/2075-4434/4/3/9 |
| work_keys_str_mv | AT viktorttoth selfgravitatingboseeinsteincondensatesandthethomasfermiapproximation |