标题： 完全退化的自引力费米子暗物质：对星系团A1689的密度分布以及黑洞的质量层次的影响 显示英文标题

标题： Fully Degenerate Self-Gravitating Fermionic Dark Matter: Implications to the Density Profile of the Cluster of Galaxies A1689, and the Mass Hierarchy of Black Holes

摘要： 考虑了宇宙中不同尺度下弱相互作用的完全退化的费米子暗物质的平衡构型。 我们处理从牛顿引力到广义相对论以及从非相对论到相对论退化的一般情况。 一个无量纲的平衡构型由单个参数指定，与粒子属性、中心费米速度无关，质量和长度的标度由暗物质粒子的静止质量和统计权重决定。 我们集中关注最近由布罗德赫斯特等人使用引力透镜报道的星系团A1689的质量柱密度分布轮廓的平顶特性。 我们将柱密度分布转换为体积密度分布，并假设球对称性，得到A1689的三维包围质量分布轮廓，与退化费米子结构的模型分布进行比较。 平顶分布被再现。 对应的费米子质量范围从2 eV到30 eV，具体取决于退化结构的实际尺度。 如果大质量中微子是主要的暗物质，对于马约拉纳中微子和狄拉克中微子，静止质量分别为约4.7 eV或2.3 eV。 马约拉纳中微子的退化结构质量和尺寸为$10^{14}M_\odot$和100 kpc，而狄拉克中微子则为5$\times10^{14}M_\odot$和300 kpc。 如果我们把费米子识别为更重的惰性中微子，它们会产生黑洞的质量层次结构；星系中心的超大质量黑洞和中间质量黑洞。 因此，我们提出了费米子的质量层次可能决定了宇宙中黑洞的质量层次的可能性。 显示英文摘要

摘要： Equilibrium configurations of weakly interacting fully degenerate fermionic dark matter are considered at various scales in the Universe. We treat the general situations for the gravity from Newtonian to general relativity and the degeneracy from nonrelativistic to relativistic. A dimensionless equilibrium configuration is specified by a single parameter regardless of particle properties, the Fermi velocity at the center, and the scalings of mass and length are specified by the rest mass and statistical weight of the dark matter particle. We focus our attention to the flat-top nature of the mass column density profile of the cluster of galaxies, A1689, recently reported by Broadhurst et al. using gravitational lensing. We convert the column density profile to a volume density profile assuming spherical symmetry and derive a 3D encircled mass profile of A1689, which is compared with the model profiles of degenerate fermion structures. The flat-top profile is reproduced. The corresponding fermion mass ranges from 2 eV to 30 eV depending on the actual scale of the degenerate structure. If massive neutrinos are the dominant dark matter, the rest mass will be about 4.7 or 2.3 eV respectively for Majorana or Dirac neutrinos. The mass and size of the degenerate structure are $10^{14}M_\odot$ and 100 kpc for Majorana neutrinos, and 5$\times10^{14}M_\odot$ and 300 kpc for Dirac neutrinos. If we identify the fermions as heavier sterile neutrinos, they yield the characteristic mass hierarchy of black holes; giant black hole at the center of a galaxy and the intermediate mass black holes. Thus we propose the possibility that the mass hierarchy of fermions determines that of black holes in the Universe.