暗物质是玻色-爱因斯坦凝聚体吗？
Can dark matter be a Bose-Einstein condensate?
摘要：
我们考虑的可能性，暗物质，这是需要解释的动力学的中性氢云在大距离的银河系中心，可能是一个玻色-爱因斯坦凝聚体的形式。为了研究凝聚体，我们使用非相对论性的Gross-Pitaevskii方程。通过引入波函数的马德隆表示，我们根据连续性方程和流体动力学欧拉方程来表达系统的动力学。因此，暗物质可以被描述为一种非相对论性的牛顿玻色-爱因斯坦引力凝析气，其密度和压力由正压状态方程关联。在四次非线性凝聚体的情况下，状态方程是指数为$n=1$的多方方程。为了检验模型的有效性，我们分别用低表面亮度和矮星系的自转曲线样本拟合了模型的牛顿切向速度方程。我们发现低表面亮度星系的理论自转曲线和观测数据之间有很好的一致性。分析了光子穿过暗物质晕时的偏转，计算了光的弯曲角。获得的玻色-爱因斯坦凝聚体的弯曲角大于标准广义相对论和暗物质模型预测的弯曲角。因此，研究星系对光的偏转和引力透镜效应可以区分玻色-爱因斯坦凝聚体暗物质模型和其他暗物质模型。
英文摘要：
We consider the possibility that the dark matter, which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic center, could be in the form of a Bose-Einstein condensate. To study the condensate we use the non-relativistic Gross-Pitaevskii equation. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose-Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analyzed, and the bending angle of light is computed. The bending angle obtained for the Bose-Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose-Einstein condensate dark matter model and other dark matter models.
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