We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus 2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.

中文翻译：

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具有排斥性或吸引力的自相互作用的耗散自重玻色-爱因斯坦凝聚物的牛仔裤不稳定性：在暗物质上的应用

我们研究了由广义Gross-Pitaevskii-Poisson方程描述的无限均质耗散自重玻色-爱因斯坦凝聚体的Jeans不稳定性[Chavanis，PH Eur。物理 J.加上2017年，132，248]。这个问题与宇宙学中暗物质晕的形成有关。我们考虑静态和扩展宇宙的情况。我们考虑了玻色子之间排斥或吸引的自相互作用的任意形式（吸引的自相互作用对轴的作用特别重要）。我们同时考虑了重力和流体动力学（速动）不稳定性，并确定了该不稳定性的最大增长率以及相应的波数。我们研究了它们如何取决于玻色子的散射长度（或更普遍地取决于声速的平方）以及摩擦系数。先前获得的结果（特别是在无耗散情况下）在我们研究的特定范围内得以恢复。