红巨星分支尖端的贝叶斯推断：I. 一维分析
Bayesian Inference of the Tip of the Red Giant Branch: I. One-Dimensional Analysis
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中文总结 AI 辅助
提出贝叶斯框架推断红巨星分支尖端，考虑选择效应和恒星不确定性，通过合成数据验证并应用于NGC 4258，确定TRGB绝对星等为-4.073±0.026，与近期分析一致但更亮。
中文摘要 AI 辅助
红巨星分支尖端（TRGB）可作为宇宙距离阶梯中的相对距离度量，用于推断哈勃常数。我们提出一个用于TRGB推断的贝叶斯框架，该框架考虑了选择效应并传播每颗恒星的不确定性，将观测星表建模为非齐次泊松点过程的一个实现，该过程包括RGB以及来自渐近巨星分支（AGB）的污染。我们推导了预测TRGB不确定性的表达式，其与光度噪声、比尖端更暗的恒星密度以及AGB与AGB+RGB数密度之比$r$有关。我们使用简化光度函数的合成数据验证了这些表达式。将完整模型应用于合成星表，我们发现对$r$的依赖性是三者中最强的，并且可靠的推断要求$r \lesssim 0.5$；超过此值，后验分布变为多模态，TRGB无法可靠识别。然后，我们拟合了校准星系NGC 4258的11个哈勃太空望远镜视场的数据。我们发现视场间固有散射超出测量噪声，为$\tau = 0.067^{+0.023}_{-0.017}$星等，以及星系级、消光校正的TRGB星等为$25.324 \pm 0.026$。将此与NGC 4258的脉泽距离相结合，我们确定TRGB的绝对星等为${M}_{\rm{F814W}}^{\rm{TRGB}} = -4.073 \pm 0.026$（尖端）$\pm$ $0.032$（距离），这与同一数据的其他近期分析一致，但更亮。
英文摘要
The tip of the red giant branch (TRGB) can be used as a relative distance measure as part of the cosmic distance ladder to infer the Hubble constant. We present a Bayesian framework for TRGB inference that incorporates selection effects and propagates per-star uncertainties, modelling the observed catalogue as a realisation of an inhomogeneous Poisson point process which includes the RGB and contamination from the asymptotic giant branch (AGB). We derive expressions for the predicted TRGB uncertainty in terms of the photometric noise, stellar density fainter than the tip, and the ratio of the AGB to AGB+RGB number densities, $r$. We validate these using synthetic data from a simplified luminosity function. Applying the full model to synthetic catalogues, we find that the dependence on $r$ is the strongest of the three, and that reliable inference requires $r \lesssim 0.5$; beyond this, the posterior is multimodal, and the TRGB cannot reliably be identified. We then fit data from 11 Hubble Space Telescope fields of the calibrator galaxy NGC 4258. We find intrinsic field-to-field scatter beyond measurement noise of $τ= 0.067^{+0.023}_{-0.017}$ mag, and a galaxy-level, extinction-corrected TRGB magnitude of $25.324 \pm 0.026$. Combining this with the maser distance to NGC 4258, we determine the absolute magnitude of the TRGB to be ${M}_{\rm{F814W}}^{\rm{TRGB}} = -4.073 \pm 0.026$ (tip) $ \pm$ $0.032$ (dist), consistent with, but brighter than, other recent analyses of the same data.
发表机构
- Imperial College London（帝国理工学院）
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