AI 中文总结
该研究针对FIRE-2模拟校准的艾因斯坦托轮廓，推导了保留密度的黑洞解，结合事件视界望远镜数据给出暗物质晕的严格限制，发现旋转曲线补全方案的阴影偏移量远大于保留密度解，当前观测无法约束光滑核心-艾因斯坦托晕。
AI 中文摘要
牛顿晕密度无法唯一确定相对论时空，由此产生的不确定性会主导视界尺度信号的预测。我们针对基于FIRE-2模拟校准的反馈核心型艾因斯坦托（Einasto）轮廓，明确了这种依赖关系。在史瓦西（Schwarzschild）规范下，爱因斯坦方程给出了由有效各向异性流体支撑的渐近平坦、保留密度的几何结构，未假设无碰撞暗物质的微观描述。相比之下，常用的旋转曲线补全方案会将有限的种子核心替换为反平方源尖点。对于保留密度的解，我们推导出了封闭形式的 enclosed mass（ enclosed mass），得到了明确的单视界判据和三视界相的极值边界，并建立了固定晕的第一定律。更一般地，球形黑洞阴影的领先分数偏移量为真空光子球内包含的环境质量除以中心黑洞质量。将该结果应用于已发表的事件视界望远镜（Event Horizon Telescope）阴影偏差汇总，得到了射手座A*（Sgr A*）的单侧95%可信限为4.8×10²³ M☉ pc⁻³，M77的为4.1×10¹⁷ M☉ pc⁻³，远高于现实中的光滑晕密度。银河系校准预测的分数阴影偏移量为1.7×10⁻²⁵，而对于相同的星系输入，旋转曲线补全方案给出的偏移量大19个数量级。协变极化薄盘计算显示出相同的弱核心抑制效应。因此，当前的视界尺度图像并未限制千秒差距尺度的光滑核心-艾因斯坦托晕；可观测的环境信号反而需要致密的内成分或物理上不同的相对论源。
英文摘要
A Newtonian halo density does not uniquely determine a relativistic spacetime, and the resulting completion ambiguity can dominate predicted horizon-scale signals. We make this dependence explicit for the feedback-cored Einasto profile calibrated on FIRE-2 simulations. In Schwarzschild gauge, the Einstein equations give an asymptotically flat, density-preserving geometry supported by an effective anisotropic fluid; no microscopic description of collisionless dark matter is assumed. By contrast, a commonly used rotation-curve completion replaces the finite seed core by an inverse-square source cusp. For the density-preserving solution we derive the enclosed mass in closed form, obtain a sharp one-horizon criterion and the extremal boundaries of a three-horizon phase, and establish the fixed-halo first law. More generally, the leading fractional shift of a spherical black-hole shadow is the environmental mass enclosed within the vacuum photon sphere divided by the central black-hole mass. Applying this result to published Event Horizon Telescope shadow-deviation summaries gives illustrative one-sided 95\% credible limits of $4.8\times10^{23}\,\Msun\,{\rm pc}^{-3}$ for $\sgr$ and $4.1\times10^{17}\,\Msun\,{\rm pc}^{-3}$ for $\mseven$, far above realistic smooth-halo densities. A Milky-Way calibration predicts a fractional shadow shift of $1.7\times10^{-25}$, whereas the rotation-curve completion gives a shift 19 orders of magnitude larger for the same galactic inputs. A covariant polarized thin-disk calculation shows the same weak-core suppression. Thus current horizon-scale images do not constrain a smooth kiloparsec-scale core-Einasto halo; an observable environmental signal would instead require a compact inner component or a physically different relativistic source.
Comments14 pages. twocolumn, 8 figures
