玻色-爱因斯坦凝聚体暗物质晕的Jeans不稳定性和湍流引力坍缩
Jeans instability and turbulent gravitational collapse of Bose-Einstein Condensate dark matter halos
摘要：
我们考虑的Jeans不稳定性和引力坍缩的旋转玻色-爱因斯坦凝聚体暗物质晕，零温非相对论Gross-Pitaevskii方程，与排斥粒子间的相互作用。在波函数的Madelung表象中，星系晕的动力学演化由连续性方程和流体力学欧拉方程描述，凝聚态暗物质满足指数为$n=1$的多方状态方程.通过考虑小扰动的量子流体动力学方程，我们得到的色散关系和Jeans波数，其中包括涡（湍流）的影响，量子压力和量子势，分别。详细讨论了凝聚态暗物质坍缩的临界尺度（金斯半径和质量）。我们还研究了旋转凝聚暗物质晕的坍缩/膨胀，我们发现了一个家庭的精确的半解析解的流体动力学演化方程，通过使用分离变量的方法。流体流动方程的近似一阶解也得到了。用数值方法计算了坍缩/膨胀凝聚暗物质晕的质量、密度和速度分布。
英文摘要：
We consider the Jeans instability and the gravitational collapse of the rotating Bose-Einstein Condensate dark matter halos, described by the zero temperature non-relativistic Gross-Pitaevskii equation, with repulsive inter-particle interactions. In the Madelung representation of the wave function, the dynamical evolution of the galactic halos is described by the continuity and the hydrodynamic Euler equations, with the condensed dark matter satisfying a polytropic equation of state with index $n=1$. By considering small perturbations of the quantum hydrodynamical equations we obtain the dispersion relation and the Jeans wave number, which includes the effects of the vortices (turbulence), of the quantum pressure and of the quantum potential, respectively. The critical scales above which condensate dark matter collapses (the Jeans radius and mass) are discussed in detail. We also investigate the collapse/expansion of rotating condensed dark matter halos, and we find a family of exact semi-analytical solutions of the hydrodynamic evolution equations, derived by using the method of separation of variables. An approximate first order solution of the fluid flow equations is also obtained. The radial coordinate dependent mass, density and velocity profiles of the collapsing/expanding condensate dark matter halos are obtained by using numerical methods.
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