来自具有游荡自旋的中子星的连续引力波的隐马尔可夫模型跟踪。III。旋转相位跟踪
Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin. III. Rotational phase tracking
摘要：
一个隐马尔可夫模型（HMM）解决递归的维特比算法可以被配置为搜索持久的，准单色的引力辐射从一个孤立的或吸积中子星，其旋转频率是未知的，随机漫游。在这里，现有的HMM分析流水线被推广到同时跟踪旋转相位和频率，通过根据相位包裹的Ornstein-Uhlenbeck过程对步骤内旋转演化进行建模，并且通过使用被称为$\mathcal{B}$ -统计的贝叶斯匹配滤波器的相位敏感版本来计算发射概率。广义算法跟踪信号从孤立和二进制源的特征波应变$h_0 \geq 1.3\times 10^{-26}$在高斯噪声与振幅谱密度$4\times 10^{-24}\,{\rm Hz^{-1/2}}$，模拟观测组成的$N_T=37$数据段，每个$T_{\rm drift}=10\,{\rm days}$长，典型的持续时间搜索的低质量X射线二进制（LMXB）的Sco X $-$ 1与激光干涉引力波天文台（LIGO）。它对隔离源和二进制源同样敏感，$\approx 1.5$比以前的管道敏感一倍。接收机工作特性曲线和恢复参数的误差范围内的实际$h_0$和$N_T$值。广义算法在LIGO科学合作组织召集的Sco X $-$ 1模拟数据挑战赛的第一阶段中成功地检测了每个可用的合成信号，恢复频率和轨道半长轴的精度分别优于$9.5\times 10^{-7}\,{\rm Hz}$和$1.6\times 10^{-3}\,{\rm lt\,s}$。在典型的宽带（$0.5$ - ${\rm kHz}$）搜索中，Viterbi求解器在隔离源的$\approx 2\times 10^3$ CPU-hr和LMXB源的$\sim 10^5$ CPU-hr中运行。
英文摘要：
A hidden Markov model (HMM) solved recursively by the Viterbi algorithm can be configured to search for persistent, quasimonochromatic gravitational radiation from an isolated or accreting neutron star, whose rotational frequency is unknown and wanders stochastically. Here an existing HMM analysis pipeline is generalized to track rotational phase and frequency simultaneously, by modeling the intra-step rotational evolution according to a phase-wrapped Ornstein-Uhlenbeck process, and by calculating the emission probability using a phase-sensitive version of the Bayesian matched filter known as the $\mathcal{B}$-statistic. The generalized algorithm tracks signals from isolated and binary sources with characteristic wave strain $h_0 \geq 1.3\times 10^{-26}$ in Gaussian noise with amplitude spectral density $4\times 10^{-24}\,{\rm Hz^{-1/2}}$, for a simulated observation composed of $N_T=37$ data segments, each $T_{\rm drift}=10\,{\rm days}$ long, the typical duration of a search for the low-mass X-ray binary (LMXB) Sco X$-$1 with the Laser Interferometer Gravitational Wave Observatory (LIGO). It is equally sensitive to isolated and binary sources and $\approx 1.5$ times more sensitive than the previous pipeline. Receiver operating characteristic curves and errors in the recovered parameters are presented for a range of practical $h_0$ and $N_T$ values. The generalized algorithm successfully detects every available synthetic signal in Stage I of the Sco X$-$1 Mock Data Challenge convened by the LIGO Scientific Collaboration, recovering the frequency and orbital semimajor axis with accuracies of better than $9.5\times 10^{-7}\,{\rm Hz}$ and $1.6\times 10^{-3}\,{\rm lt\,s}$ respectively. The Viterbi solver runs in $\approx 2\times 10^3$ CPU-hr for an isolated source and $\sim 10^5$ CPU-hr for a LMXB source in a typical, broadband ($0.5$-${\rm kHz}$) search.
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