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Time-domain implementation of the optimal cross-correlation statistic for stochastic gravitational-wave background searches in pulsar timing data

机译:脉冲星计时数据中随机重力波背景搜索的最佳互相关统计量的时域实现

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摘要

Supermassive black hole binaries, cosmic strings, relic gravitational waves from inflation, and first-order phase transitions in the early Universe are expected to contribute to a stochastic background of gravitational waves in the 10^(−9) –10^(−7)  Hz frequency band. Pulsar timing arrays (PTAs) exploit the high-precision timing of radio pulsars to detect signals at such frequencies. Here we present a time-domain implementation of the optimal cross-correlation statistic for stochastic background searches in PTA data. Due to the irregular sampling typical of PTA data as well as the use of a timing model to predict the times of arrival of radio pulses, time-domain methods are better-suited for gravitational-wave data analysis of such data. We present a derivation of the optimal cross-correlation statistic starting from the likelihood function, a method to produce simulated stochastic background signals, and a rigorous derivation of the scaling laws for the signal-to-noise ratio of the cross-correlation statistic in the two relevant PTA regimes: the weak-signal limit where instrumental noise dominates over the gravitational-wave signal at all frequencies, and a second regime where the gravitational-wave signal dominates at the lowest frequencies.
机译:预计宇宙早期的超大质量黑洞双星,宇宙弦,遗留的引力波和一阶相变将对10 ^(− 9)–10 ^(− 7)中的引力波产生随机背景Hz频段。脉冲星定时阵列(PTA)利用无线电脉冲星的高精度定时来检测此类频率的信号。在这里,我们为PTA数据中的随机背景搜索提供了最佳互相关统计量的时域实现。由于PTA数据典型的不规则采样以及使用时序模型预测无线电脉冲的到达时间,因此时域方法更适合此类数据的重力波数据分析。我们提出了从似然函数开始的最佳互相关统计量的推导,产生模拟随机背景信号的方法,以及严格推导了互相关统计量信噪比的定标定律。两种相关的PTA体制:在所有频率下仪器噪声在重力波信号上占主导地位的弱信号极限,以及在最低频率下重力波信号占主导地位的第二种体制。

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