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

## Abstract

**:**

## 1. Introduction

## 2. Discussion

## 3. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

- Kaup, D.J. Klein-Gordon Geon. Phys. Rev.
**1968**, 172, 1331–1342. [Google Scholar] [CrossRef] - Ruffini, R.; Bonazzola, S. Systems of self-gravitating particles in general relativity and the concept of an equation of state. Phys. Rev.
**1969**, 187, 1767–1783. [Google Scholar] [CrossRef] - Colpi, M.; Shapiro, S.L.; Wasserman, I. Boson stars—Gravitational equilibria of self-interacting scalar fields. Phys. Rev. Lett.
**1986**, 57, 2485–2488. [Google Scholar] [CrossRef] [PubMed] - Chavanis, P.H.; Harko, T. Bose-Einstein condensate general relativistic stars. Phys. Rev. D
**2012**, 86, 064011. [Google Scholar] [CrossRef] - Lee, J.W.; Koh, I.G. Galactic halos as boson stars. Phys. Rev. D
**1996**, 53, 2236–2239. [Google Scholar] [CrossRef] - Böhmer, C.G.; Harko, T. Can dark matter be a Bose Einstein condensate? J. Cosmol. Astropart. Phys.
**2007**, 2007, 025. [Google Scholar] [CrossRef] - Chavanis, P.H. Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions. I. Analytical results. Phys. Rev. D
**2011**, 84, 043531. [Google Scholar] [CrossRef] - Chavanis, P.H.; Delfini, L. Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions. II. Numerical results. Phys. Rev. D
**2011**, 84, 043532. [Google Scholar] [CrossRef] - Goodman, J. Repulsive dark matter. New Astron.
**2000**, 5, 103–107. [Google Scholar] [CrossRef] - Arbey, A.; Lesgourgues, J.; Salati, P. Galactic halos of fluid dark matter. Phys. Rev. D
**2003**, 68, 023511. [Google Scholar] [CrossRef] - Suárez, A.; Robles, V.; Matos, T. A Review on the Scalar Field/Bose-Einstein Condensate Dark Matter Model. In Accelerated Cosmic Expansion; Springer: Berlin, Germany, 2013; pp. 107–142. [Google Scholar]
- Schroven, K.; List, M.; Lämmerzahl, C. Stability of self-gravitating Bose-Einstein condensates. Phys. Rev. D
**2015**, 92, 124008. [Google Scholar] [CrossRef] - Kühnel, F.; Rampf, C. Astrophysical Bose-Einstein condensates and superradiance. Phys. Rev. D
**2014**, 90, 103526. [Google Scholar] [CrossRef] - Bahrami, M.; Großardt, A.; Donadi, S.; Bassi, A. The Schrödinger-Newton equation and its foundations. New J. Phys.
**2014**, 16, 115007. [Google Scholar] [CrossRef] - Giulini, D.; Großardt, A. Centre-of-mass motion in multi-particle Schrödinger-Newton dynamics. New J. Phys.
**2014**, 16, 075005. [Google Scholar] [CrossRef] - Guzmán, F.S.; Lora-Clavijo, F.D.; González-Avilés, J.J.; Rivera-Paleo, F.J. Stability of BEC galactic dark matter halos. J. Cosmol. Astropart. Phys.
**2013**, 2013, 034. [Google Scholar] [CrossRef] - Dalfovo, F.; Pitaevskii, L.P.; Stringari, S. The condensate wave function of a trapped atomic gas. J. Res. Natl. Inst. Stand. Tech.
**1996**, 101, 537–544. [Google Scholar] [CrossRef] - Pethick, C.J.; Smith, H. Bose-Einstein Condensation in Dilute Gases, 2nd ed.; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
- Wang, X.Z. Cold Bose stars: Self-gravitating Bose-Einstein condensates. Phys. Rev. D
**2001**, 64, 124009. [Google Scholar] [CrossRef] - Madarassy, E.J.M.; Toth, V.T. Numerical simulation code for self-gravitating Bose–Einstein condensates. Comput. Phys. Commun.
**2013**, 184, 1339–1343. [Google Scholar] [CrossRef] - Madarassy, E.J.M.; Toth, V.T. Evolution and dynamical properties of Bose-Einstein condensate dark matter stars. Phys. Rev. D
**2015**, 91, 044041. [Google Scholar] [CrossRef]

**Figure 2.**Density cross-section of a stable simulated $1\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$, $r\simeq 50$ km Bose-star (or stellar core) after approximately 300,000 numerical iterations that corresponds to 3 s [21]. (For comparison, the period of a circular orbit at $r=50$ km is approximately 0.006 s.) Axes are in km, density is in units of ${10}^{30}\phantom{\rule{3.33333pt}{0ex}}\mathrm{kg}/{\mathrm{km}}^{3}\simeq 0.5\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}/{\mathrm{km}}^{3}$. NB: The spatial grid used in this simulation is low resolution ($60\times 60\times 60$) and image smoothing was used to improve the presentation quality.

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Toth, V.T.
Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation. *Galaxies* **2016**, *4*, 9.
https://doi.org/10.3390/galaxies4030009

**AMA Style**

Toth VT.
Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation. *Galaxies*. 2016; 4(3):9.
https://doi.org/10.3390/galaxies4030009

**Chicago/Turabian Style**

Toth, Viktor T.
2016. "Self-Gravitating Bose-Einstein Condensates and the Thomas-Fermi Approximation" *Galaxies* 4, no. 3: 9.
https://doi.org/10.3390/galaxies4030009