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Constraints on ultra-low-frequency gravitational waves with statistics of pulsar spin-down rates. II. Mann–Whitney U test
Publications of the Astronomical Society of Japan ( IF 2.3 ) Pub Date : 2021-06-03 , DOI: 10.1093/pasj/psab058
Hiroki Kumamoto 1, 2 , Shinnosuke Hisano 1 , Keitaro Takahashi 1, 3, 4
Affiliation  

We investigate gravitational waves with sub-nHz frequencies (10−11 Hz ≲ fGW ≲ 10−9 Hz) from the spatial distribution of the spin-down rates of millisecond pulsars. As we suggested in Yonemaru et al. (2018, MNRAS, 478, 1670), gravitational waves from a single source induce a bias in the observed spin-down rates of pulsars depending on the relative direction between the source and the pulsar. To improve the constraints on the time derivative of gravitational wave amplitude obtained in our previous work (Kumamoto et al. 2019, MNRAS, 489, 3547), we adopt a more sophisticated statistical method called the Mann–Whitney U test. Applying our method to the ATNF pulsar catalogue, we first find that the current data set is consistent with no gravitational wave signal from any direction in the sky. Then, we estimate the effective angular resolution of our method to be 66 deg2 by studying the probability distribution of the test statistic. Finally, we investigate gravitational wave signals from the Galactic Center (GC) and M 87 and, comparing simulated mock data sets with the real pulsar data, we obtain upper bounds on the time derivative as $\dot{h}_{\rm GC} < 8.9 \times 10^{-19}$ s−1 for the GC and $\dot{h}_{\rm M87} < 3.3 \times 10^{-19}$ s−1 for M 87, which are stronger than those obtained in Kumamoto et al. (2019, MNRAS, 489, 3547) by factors of 7 and 25, respectively.

中文翻译:

具有脉冲星自旋率统计的超低频引力波约束。二、曼-惠特尼 U 检验

我们从毫秒脉冲星的自旋下降率的空间分布中研究具有亚 nHz 频率(10-11 Hz ≲ fGW ≲ 10-9 Hz)的引力波。正如我们在 Yonemaru 等人中所建议的那样。(2018, MNRAS, 478, 1670),来自单一来源的引力波会导致观测到的脉冲星自旋下降率出现偏差,具体取决于源和脉冲星之间的相对方向。为了改进我们之前工作(Kumamoto et al. 2019, MNRAS, 489, 3547)中获得的引力波振幅时间导数的约束,我们采用了一种更复杂的统计方法,称为 Mann-Whitney U 检验。将我们的方法应用于 ATNF 脉冲星目录,我们首先发现当前数据集与天空中没有来自任何方向的引力波信号一致。然后,通过研究检验统计量的概率分布,我们估计我们方法的有效角分辨率为 66 度。最后,我们研究了来自银河中心 (GC) 和 M 87 的引力波信号,并将模拟的模拟数据集与真实的脉冲星数据进行比较,我们得到时间导数的上限 $\dot{h}_{\rm GC } < 8.9 \times 10^{-19}$ s−1 对于 GC 和 $\dot{h}_{\rm M87} < M 87 为 3.3 \times 10^{-19}$ s−1,这比 Kumamoto 等人获得的要强。(2019, MNRAS, 489, 3547) 分别乘以 7 和 25 倍。我们得到时间导数的上界 $\dot{h}_{\rm GC} < 8.9 \times 10^{-19}$ s−1 对于 GC 和 $\dot{h}_{\rm M87} < M 87 为 3.3 \times 10^{-19}$ s−1,这比 Kumamoto 等人获得的要强。(2019, MNRAS, 489, 3547) 分别乘以 7 和 25 倍。我们得到时间导数的上界 $\dot{h}_{\rm GC} < 8.9 \times 10^{-19}$ s−1 对于 GC 和 $\dot{h}_{\rm M87} < M 87 为 3.3 \times 10^{-19}$ s−1,这比 Kumamoto 等人获得的要强。(2019, MNRAS, 489, 3547) 分别乘以 7 和 25 倍。
更新日期:2021-06-03
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