AI 中文总结
该研究探究暗物质环境对旋转黑洞光子环回波的形变影响，通过数值模拟得到相关延迟、可见度等参数，发现发现光子回波与将形变归因于暗物质是不同任务，稳健归因需源控制与延迟覆盖。
AI 中文摘要
旋转黑洞周围的强透镜效应即使在克尔（Kerr）时空中也会产生延迟且旋转的高阶图像。我们探究在主导环尺度与克尔匹配后，暗物质（DM）环境如何改变这些光子环回波。我们追踪从旋转暗物质几何结构到有限阶光子传输、慢光发射、干涉测量可见度以及源种群测试的信号。对于具有 $a/M=0.8$、$i=70^\circ$ 的强中心尖峰基准情况，环匹配后仍保留 $1.49\\%$ 的临界参数特征。1阶和2阶延迟中位数分别为 $13.33M$ 和 $33.06M$，230GHz 静态与动态可见度对比度分别为 $0.070F_0$ 和 $0.112F_0$。在共享源预言机测试中，差分信号也保持显著。当源未知时，归因是更困难的步骤：类EHT原始闭合曲线给出 AUC 为 $0.658$，而采用总流量和紧凑空间源驱动的新验证分别给出 $0.507$ 和 $0.500$。因此，我们利用新源上的分离度损失推导观测要求，而非做出探测声明。在预定义的克尔阈值下，75%功率要求 $d=2.319$，而原始独立源测试的 $d=0.553$。在固定均值诊断下，剩余源散布需约为当前值的 $0.238$，尽管自举范围 $0.022$–$0.444$ 较宽。每日时间间隔也可能错过较小的尖峰-克尔延迟差。因此，发现光子回波与将小形变归因于暗物质是不同的任务，稳健归因需要源控制和合适的延迟覆盖范围，而非仅灵敏度。
英文摘要
Strong lensing around a rotating black hole produces delayed and rotated higher-order images even in Kerr. We ask how a dark matter (DM) environment changes these photon-ring echoes after the leading ring scale is matched to Kerr. We follow the signal from rotating DM geometry to finite-order photon transfer, slow-light emission, interferometric visibilities, and source-population tests. For a strong central-spike benchmark with $a/M=0.8$ and $i=70^\circ$, a $1.49\%$ critical-parameter fingerprint remains after ring matching. The order-1 and order-2 delay medians are $13.33M$ and $33.06M$, and the 230-GHz static and dynamic visibility contrasts are $0.070F_0$ and $0.112F_0$. The differential signal also remains distinct in a shared-source oracle test. The harder step is attribution when the source is unknown. Raw EHT-like closures give AUC $0.658$, while fresh validation with total-flux and compact spatial source drivers gives $0.507$ and $0.500$. We therefore use the loss of separation on new sources to derive observing requirements rather than a detection claim. At the pre-defined Kerr threshold, 75\% power requires $d=2.319$, compared with $d=0.553$ for the raw independent-source test. Under a fixed-mean diagnostic, the residual source scatter would need to be about $0.238$ of its present value, although the bootstrap range $0.022$--$0.444$ is broad. Daily gaps can also miss the smaller spike--Kerr delay difference. Finding a photon echo and attributing a small deformation to DM are therefore different tasks. Robust attribution needs source control and suitable delay coverage, not sensitivity alone.
Comments16 pages, 10 figures, 3 tables
