发表机构
Chirchik State Pedagogical University（奇尔奇克国立师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究评估星系团面密度各向异性诊断量$A_{\rm ani}$与幂律轮廓斜率$\rm \u03b1$的关联，通过模拟验证发现无噪声下可恢复，但实际测光无法可靠识别，幂律相关性非轨道各向异性的独立证据。
AI 中文摘要
我们评估了一种面密度各向异性诊断量 $A_{\rm ani}$，及其与幂律星系轮廓斜率 $\alpha$ 的关联。我们在规范网格 $0 \leq A_{\rm ani} \leq 1.92$ 和延伸至1.99的扩展网格上，重新处理了85个光学富星系团的20环带轮廓。24个规范拟合和12个扩展拟合达到各自的上边界；85个上$\rm \u0394\rm \u03c7^2=1$界限中有69个保持开放，仅4个星系团具有双侧区间。在40个预选的幂律拟合中，观测到的$\rm \u03b1$-$A_{\rm ani}$斯皮尔曼系数为0.616。在一个模型原生的前向恢复实验中，注入11个值，所有935个无噪声轮廓在0.02内恢复输入。在匹配观测计数和背景条件的46,750个泊松星表中，恢复的均方根误差（RMSE）为0.992，斯皮尔曼$\rm \u03c1=0.093$；40.0%的拟合达到规范上边界，81.4%具有开放的上区间。在9,350个星表的敏感性测试中，固定背景和径向尺度将RMSE改善至0.564。作为单独的结构控制，由拟合幂律生成的4,250个泊松星表再现了观测到的斜率关联：40个星系团子集的模拟中位系数为0.608（95%范围0.453-0.731）。因此，该诊断量在其定义模型下无噪声时数值上可恢复，但现有测光数据无法可靠地识别单个星系团的该诊断量。幂律相关性可能源于共享的投影轮廓形状，并非轨道各向异性的独立证据。
英文摘要
We assess a surface-density anisotropy diagnostic, $A_{\rm ani}$, and its association with the slope $α$ of a power-law galaxy profile. We reprocess 20-annulus profiles of 85 optically rich clusters on a canonical grid, $0 \leq A_{\rm ani} \leq 1.92$, and an extended grid reaching 1.99. Twenty-four canonical fits and 12 extended fits reach their respective upper boundaries; 69 of 85 upper $Δχ^2=1$ bounds remain open, and only four clusters have two-sided intervals. Among 40 preselected power-law fits, the observed $α$-$A_{\rm ani}$ Spearman coefficient is 0.616. In a model-native forward-recovery experiment with 11 injected values, all 935 noiseless profiles recover the input within 0.02. Across 46,750 Poisson catalogs matched to observed count and background conditions, recovery instead has root-mean-square error (RMSE) 0.992 and Spearman $ρ=0.093$; 40.0% of fits reach the canonical upper boundary and 81.4% have an open upper interval. Fixing both background and radial scale improves RMSE to 0.564 in a 9,350-catalog sensitivity test. As a separate structural control, 4,250 Poisson catalogs generated from fitted power laws reproduce the observed slope association: the median mock coefficient for the 40-cluster subset is 0.608 (95% range 0.453-0.731). Thus the diagnostic is numerically recoverable under its defining model without noise, but the available photometry does not reliably identify it for individual clusters. The power-law correlation can arise from shared projected profile shape and is not independent evidence for orbital anisotropy.
Comments9 pages, 4 figures, 4 tables
