发表机构
Lanzhou University; Hangzhou Institute for Advanced Study, UCAS（兰州大学; 中国科学院大学杭州高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出层次贝叶斯流水线Galena，利用LISA数据挑战中2151个双白矮星源，通过Fisher矩阵误差传播恢复银河系盘标长、标高和核球参数，精度显著提升。
AI 中文摘要
毫赫兹引力波天空将由银河系中约$10^{4}$-$10^{7}$个可分辨的双白矮星双星主导，其三维空间分布追踪着银河系的结构参数。我们提出\textsc{Galena}，一个通过非齐次泊松过程似然从双白矮星星表中恢复这些参数的层次贝叶斯流水线。每个源的$3\times3$银河系位置协方差由波形Fisher信息矩阵计算，并通过$3\times5$雅可比矩阵解析传播；由此产生的测量误差卷积被分解为预计算的稀疏权重矩阵，使嵌套采样推断变得可行。应用于GBSIEVER报告的LISA数据挑战源（质量筛选后$N=2151$），\textsc{Galena}恢复了盘标长$R_d=2175^{+51}_{-52}$~pc和标高$z_d=282^{+7}_{-7}$~pc，与典型薄盘一致，同时得到核球占比$A=0.187^{+0.011}_{-0.012}$和核球标长半径$R_b=773^{+26}_{-25}$~pc；核球占比现在恢复得比我们早期精确位置拟合更接近文献值$0.25$，统计精度约为$\sim6\\%$。对同一似然的独立粒子群优化将这些值复现到百分之零点几以内，支持将改进归因于Fisher矩阵误差传播而非采样器。搜索阶段的天体物理先验改善了每个源的距离估计，但使层次推断基本不变。
英文摘要
The millihertz gravitational-wave sky will be dominated by $\sim10^{8}$ double white dwarfs while $\sim10^{4}$ be resolvable in the Milky Way, whose three-dimensional spatial distribution traces the Galaxy's structural parameters. We present \textsc{Galena}, a hierarchical Bayesian pipeline that recovers these parameters from a double white dwarf catalogue through an inhomogeneous Poisson-process likelihood. Each source's $3\times3$ Galactic position covariance is computed from the waveform Fisher information matrix and propagated analytically through a $3\times5$ Jacobian; the resulting measurement-error convolution is factored into a pre-computed sparse weight matrix, rendering the nested-sampling inference tractable. Applied to GBSIEVER-reported LISA Data Challenge sources ($N=2151$ after quality cuts), \textsc{Galena} recovers the disk scale length $R_d=2175^{+51}_{-52}$~pc and scale height $z_d=282^{+7}_{-7}$~pc, consistent with a canonical thin disk, together with the bulge fraction $A=0.187^{+0.011}_{-0.012}$ and bulge scale radius $R_b=773^{+26}_{-25}$~pc; the bulge fraction, now recovered much closer to the literature value of $0.25$ than in our earlier exact-position fit, is measured at $\sim6\%$ statistical precision. An independent particle-swarm optimisation of the same likelihood reproduces these values to within a fraction of a percent, supporting the attribution of the improvement to the Fisher-matrix error propagation rather than to the sampler. The search-stage astrophysical prior improves per-source distance estimates but leaves the hierarchical inference essentially unchanged.
Comments14 pages,6 figures
