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.
Highlights
Self-gravitating Bose-Einstein condensates (BECs) have been proposed in various astrophysical contexts, including Bose-stars [1,2,3,4] and BEC dark matter halos [5,6,7,8,9,10,11].Nonrelativistic, dilute BECs are well-described by the Gross-Pitaevskii equation (GPE)
We have demonstrated that when the Thomas-Fermi approximation is used to describe self-gravitating Bose-Einstein condensates in astrophysical contexts, the resulting systems have divergent total energy and are unstable
This behavior is a specific consequence that arises from the use of the TF-approximation; GPE-Poisson systems are not inherently unstable
Summary
Self-gravitating Bose-Einstein condensates (BECs) have been proposed in various astrophysical contexts, including Bose-stars [1,2,3,4] and BEC dark matter halos [5,6,7,8,9,10,11]. The long-range gravitational interaction is represented by the external potential Such systems, referred to in the literature as GPE-Poisson or GPN (Gross-Pitaevskii-Newton) systems, are extensively studied (a few recent examples of interest include [12,13,14,15]). It is shown that this instability is the consequence of the TF-approximation, the well-known issue of the divergence of its kinetic energy [7,8,17,18] To overcome this issue, we examine the time-independent GPE and attempt to solve it numerically without truncations. We develop a new approximation that has the desirable property that the system has negative total energy and it is stable This approximation has since been incorporated into our simulation code for self-gravitating GPE-Poisson systems
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