非最小耦合暗物质晕的自引力平衡
Self-gravitating Equilibria of Non-minimally Coupled Dark Matter Halos
摘要：
本文研究了由非最小引力耦合的暗物质（DM）构成的晕的自引力平衡。特别是，我们认为一个理论上动机的非最小耦合时，可能会出现的平均/相干长度$L$相关联的DM集体行为的流体描述是可比的局部曲率尺度。在牛顿极限中，这种非最小耦合相当于通过与DM密度$ρ$本身的拉普拉斯算子成比例的项$L^2\,\nabla^2ρ$对泊松方程的修改。我们进一步采用了一般的幂律状态方程$p\propto ρ^Γ\, r^α$的DM动态压力$p$的密度$ρ$和半径$r$，如预期的相空间密度分层的引力在宇宙学的背景下组装晕。我们证实了以前的研究结果，即在没有非最小耦合，所得到的密度$ρ(r)$具有陡峭的中央尖点和整体形状，反映了$N-$身体模拟的结果，在标准的$Λ$ CDM宇宙学，所描述的经典NFW或Einasto配置文件。最重要的是，我们发现，非最小的耦合导致密度分布发展的内核和形状密切关注，出几个核心规模半径，Burkert配置文件。事实上，我们强调，由此产生的质量分布可以适合，与Burkert的一个，共同添加的矮，DM为主的星系的旋转曲线的准确性。最后，我们表明，非最小耦合DM晕是一致的核心半径$r_0$和核心密度$ρ_0$之间观察到的标度关系，在一个通用的核心表面密度$ρ_0\times r_0$在不同的星系。
英文摘要：
We investigate self-gravitating equilibria of halos constituted by dark matter (DM) non-minimally coupled to gravity. In particular, we consider a theoretically motivated non-minimal coupling which may arise when the averaging/coherence length $L$ associated to the fluid description of the DM collective behavior is comparable to the local curvature scale. In the Newtonian limit, such a non-minimal coupling amounts to a modification of the Poisson equation by a term $L^2\,\nabla^2ρ$ proportional to the Laplacian of the DM density $ρ$ itself. We further adopt a general power-law equation of state $p\propto ρ^Γ\, r^α$ relating the DM dynamical pressure $p$ to density $ρ$ and radius $r$, as expected by phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in absence of the non-minimal coupling, the resulting density $ρ(r)$ features a steep central cusp and an overall shape mirroring the outcomes of $N-$body simulations in the standard $Λ$CDM cosmology, as described by the classic NFW or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape closely following, out to several core scale radii, the Burkert profile. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to the Burkert's one, the co-added rotation curves of dwarf, DM-dominated galaxies. Finally, we show that non-minimally coupled DM halos are consistent with the observed scaling relation between the core radius $r_0$ and core density $ρ_0$, in terms of an universal core surface density $ρ_0\times r_0$ among different galaxies.
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