AI 中文总结
研究静态爱因斯坦-标量-高斯-博内特黑洞中的中性粒子圆周运动和高频准周期振荡，通过确定相关物理量并应用相对论进动模型于多组数据，发现观测频率对可重现，但因参数拟合约束不足，推断区间为模型相关兼容区而非独立测量，为未来测试提供基线。
AI 中文摘要
爱因斯坦-标量-高斯-博内特（EsGB）引力提供了一个物理框架，用于通过标量毛发测试与史瓦西几何的强场偏差。我们研究了在史瓦西连接二次耦合分支上具有单个无量纲变形参数\(p\)的连续分数度量描述的静态EsGB黑洞中的中性粒子圆周运动和高频准周期振荡（HF-QPOs）。我们确定了有效势、圆轨道能量和角动量、特征半径以及轨道和径向周转频率，并将相对论进动模型应用于来自XTE J1550--564、GRO J1655--40、GRS 1915+105和M82 X-1的双峰QPO数据。逐个源的马尔可夫链蒙特卡罗分析表明，观测到的频率对可以在其不确定性范围内重现，并且径向周转频率对\(p\)具有主要的模型级敏感性。然而，使用均匀和截断高斯先验的受控先验敏感性分析发现，对于所有四个源，\(p\)的边际后验紧密遵循采用的先验。这反映了将三个相关参数\((M,p,r)\)拟合到两个测量频率的内在约束不足。推断的区间因此代表了与模型相关的兼容区域，而不是EsGB变形的独立测量或优选值。静态结果为未来的旋转和多观测测试提供了基线。
英文摘要
Einstein--scalar--Gauss--Bonnet (EsGB) gravity provides a physically motivated framework for testing strong-field deviations from the Schwarzschild geometry through scalar hair. We study neutral-particle circular motion and high-frequency quasi-periodic oscillations (HF-QPOs) in static EsGB black holes described by a continued-fraction metric with a single dimensionless deformation parameter \(p\) on the Schwarzschild-connected quadratic-coupling branch. We determine the effective potential, circular-orbit energy and angular momentum, characteristic radii, and orbital and radial epicyclic frequencies, and apply the relativistic precession model to twin-peak QPO data from XTE J1550--564, GRO J1655--40, GRS 1915+105, and M82 X-1. A source-by-source Markov chain Monte Carlo analysis shows that the observed frequency pairs can be reproduced within their uncertainties and that the radial epicyclic frequency carries the main model-level sensitivity to \(p\). However, a controlled prior-sensitivity analysis using uniform and truncated Gaussian priors finds that the marginal posterior of \(p\) closely follows the adopted prior for all four sources. This reflects the intrinsic underconstraint of fitting three correlated parameters \((M,p,r)\) to two measured frequencies. The inferred intervals therefore represent model-dependent compatibility regions rather than an independent measurement or preferred value of the EsGB deformation. The static results provide a baseline for future rotating and multi-observable tests.
