参数化具有量子核和等温大气的BEC暗物质晕的启发式波动方程
A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
摘要：
Gross-Pitaevskii-Poisson方程控制着自引力玻色-爱因斯坦凝聚体的演化，可能代表着暗物质晕，经历了一个引力冷却和剧烈弛豫的过程。我们提出了一个启发式的参数化这个复杂的过程中的精神林登-贝尔的理论的暴力松弛无碰撞恒星系统。我们导出了一个广义波动方程（在[P. H.沙瓦尼斯Phys. J. Plus { \bf 132}，248（2017）]），涉及与有效温度$T_{\rm eff}$相关的对数非线性和与摩擦$ξ$相关的阻尼项。这些项可以从最大熵产生原理中得到，并通过表达涨落耗散定理的爱因斯坦关系的形式联系起来。波动方程满足林登-贝尔熵的$H$ -定理，并向稳定的平衡态弛豫，该平衡态是在固定质量和能量下的熵的最大值。这种平衡态代表了玻色-爱因斯坦凝聚体暗物质晕的最可能状态。它一般具有核-晕结构。量子核可以防止引力坍缩，并可能解决核尖问题。等温晕导致与观测一致的平坦的旋转曲线。这些结果与暗物质晕现象相一致。此外，如前一篇论文[P. H. Chavanis，Phys. Rev. D { \bf 100}，123506（2019）]，在固定的总质量和总能量下相对于核心质量的熵的最大化确定了核心质量-晕质量关系，该关系与直接数值模拟中获得的关系一致。我们强调的重要性，而不是一个典型的使用微规范的描述。我们还解释了如何我们的形式主义可以适用于费米暗物质晕的情况下。
英文摘要：
The Gross-Pitaevskii-Poisson equations that govern the evolution of self-gravitating Bose-Einstein condensates, possibly representing dark matter halos, experience a process of gravitational cooling and violent relaxation. We propose a heuristic parametrization of this complicated process in the spirit of Lynden-Bell's theory of violent relaxation for collisionless stellar systems. We derive a generalized wave equation (that was introduced phenomenologically in [P.H. Chavanis, Eur. Phys. J. Plus {\bf 132}, 248 (2017)]) involving a logarithmic nonlinearity associated with an effective temperature $T_{\rm eff}$ and a damping term associated with a friction $ξ$. These terms can be obtained from a maximum entropy production principle and are linked by a form of Einstein relation expressing the fluctuation-dissipation theorem. The wave equation satisfies an $H$-theorem for the Lynden-Bell entropy and relaxes towards a stable equilibrium state which is a maximum of entropy at fixed mass and energy. This equilibrium state represents the most probable state of a Bose-Einstein condensate dark matter halo. It generically has a core-halo structure. The quantum core prevents gravitational collapse and may solve the core-cusp problem. The isothermal halo leads to flat rotation curves in agreement with the observations. These results are consistent with the phenomenology of dark matter halos. Furthermore, as shown in a previous paper [P.H. Chavanis, Phys. Rev. D {\bf 100}, 123506 (2019)], the maximization of entropy with respect to the core mass at fixed total mass and total energy determines a core mass--halo mass relation which agrees with the relation obtained in direct numerical simulations. We stress the importance of using a microcanonical description instead of a canonical one. We also explain how our formalism can be applied to the case of fermionic dark matter halos.
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