发表机构
City University of New York Graduate Center; Queens College; American Museum of Natural History; Penn State Wilkes-Barre（纽约市立大学研究生中心; 皇后学院; 美国自然历史博物馆; 宾夕法尼亚州立大学威尔克斯-巴里分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对盖亚时代白矮星星震拟合的简并解问题，提出了插值到精细网格、纳入盖亚绝对星等、拟合一致脉动模式等改进方法，实现了对简并解的稳健表征，可推广至高维情况。
AI 中文摘要
白矮星星震学旨在通过将观测到的脉动周期与恒星模型计算出的周期进行拟合，来约束脉动白矮星的内部结构。然而，采用模型网格拟合方法获得可靠结果仍存在若干障碍。我们针对参数恢复实验模拟了一维（质量）和二维（质量与有效温度）的数据，以展示改进的方法，这些方法用于解决表征简并星震解的挑战。我们表明，将模型周期插值到更精细的网格上，能够充分解决稀疏模型网格会遗漏的星震解。将盖亚（Gaia）天体测量得到的绝对星等纳入统计拟合，可减少解的简并性。我们将星震解定义为模式识别问题的解，并表明对一致的模型脉动模式进行拟合，可在简并解空间中分离每个候选解。采用基于卡方（χ²）的标准来判定何种情况应视为合理拟合，我们识别出所有满足该标准的模型周期组合，而不仅仅是那些最接近测量周期的组合。最后，我们展示了对概率分布拟合高斯函数如何实现对每个候选解（包括不确定性）的稳健表征。我们将自己的解与似然函数的直接边缘化进行比较，验证了我们对简并解空间的准确表征。这些拟合方法可推广到具有两个以上自由参数的更高维度情况。
英文摘要
White dwarf asteroseismology aims to constrain the interior structures of pulsating white dwarf stars by fitting observed pulsation periods to those computed for stellar models. However, there remain several obstacles for achieving reliable results with the model grid-fitting approach. We simulate data for a parameter recovery experiment in one and two dimensions (mass and effective temperature) to demonstrate improved methodologies that address challenges for characterizing degenerate asteroseismic solutions. We show that interpolating model periods onto a finer grid can adequately resolve asteroseismic solutions that would be missed with sparse model grids. Incorporating absolute magnitude from Gaia astrometry into the statistical fitting is shown to reduce solution degeneracy. We define a seismic solution as a solution to the mode identification problem, and we show that fitting to consistent model pulsation modes can isolate each candidate solution in degenerate solution space. A criterion based on $χ^2$ for what should be considered a reasonable fit is adopted, and we identify all combinations of model periods that meet this criterion, not only those nearest to the measured periods. Finally, we demonstrate how fitting Gaussians to probability distributions allows for the robust characterization of each candidate solution, including uncertainties. Our accurate characterization of the degenerate solution landscape is supported by the comparison of our solutions to a direct marginalization of the likelihood function. These fitting approaches can be generalized to higher dimensions, where there are more than two free parameters.
CommentsAccepted for publication in The Astrophysical Journal. 20 pages, 13 figures
