Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters.
Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters.
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来自聚结双星的引力波：检测策略和参数的蒙特卡罗估计。
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
S. Dhurandhar
中科院分区：
文献类型：
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作者：
R. Balasubramanian;B. Sathyaprakash;S. Dhurandhar
从天体物理源探测到引力波可能是天体物理学史上最令人期待的事件之一。与电磁领域的引力波相比，引力波源的缺乏和探测引力波的相对困难，使得有必要开发最佳数据分析技术来探测信号，并从探测到的信号中提取尽可能多的信息。合并双星系统是最有希望的引力波源之一。这是因为这样的源更容易建模，因此可以设计特别针对这样的信号的检测策略。大量的注意力一直致力于在文献中研究这样的技术，大部分的工作都围绕着维纳滤波和二进制系统的参数的最大似然估计。我们调查这样的技术与微分几何的帮助下，提供几何洞察力的问题。这种形式使我们能够独立于选择来表示波形的参数来探索检测方案的优点和缺点。形式主义还概括了选择一组最佳模板来检测隐藏在噪声数据中的已知波形的问题。我们强调需要找到一组方便的参数的波形，并表明，即使在列入二阶后牛顿修正，波形基本上可以通过采用一维晶格的模板检测。
这对于进行模拟以及实际检测过程都非常有用。建立这样一个形式主义后，我们进行了Monte Carlo模拟的检测过程中的第一个后牛顿校正合并二进制波形的初始LIGO-VIRGO配置。我们比较我们的模拟结果与目前可用的估计的准确性，在确定的参数和概率分布的最大似然估计。我们的研究结果表明，协方差矩阵低估，超过2倍，在参数估计的实际误差，即使当信噪比高达10。由于预期仅检测到极少数事件的信噪比高于该值，因此协方差矩阵严重不足以描述波形参数测量中的误差。从我们的Monte Carlo模拟中发现，与协方差矩阵的偏差是更多的情况下的第一后牛顿波形比在牛顿的情况下。包含高阶后牛顿修正引入了与较低后牛顿波形相关的新参数。预计这种相关性将进一步增加协方差矩阵结果与蒙特卡罗模拟推断的结果之间的差异。因此，需要考虑后牛顿修正超过第一后牛顿阶的数值模拟，以便更清楚地了解参数确定的准确性。我们发现，借助于合并的瞬间，可以比利用到达时间更准确地确定源的方向。
The detection of gravitational waves from astrophysical sources is probably one of the most keenly awaited events in the history of astrophysics. The paucity of gravitational wave sources and the relative difficulty in detecting such waves, as compared to those in the electromagnetic domain, necessitate the development of optimal data analysis techniques to detect the signal, as well as to extract the maximum possible information from the detected signals. Coalescing binary systems are one of the most promising sources of gravitational waves. This is due to the fact that such sources are easier to model and thus one can design detection strategies particularly tuned to such signals. A lot of attention has been devoted in the literature to studying such techniques and most of the work has revolved around the Weiner filtering and the maximum likelihood estimators of the parameters of the binary system. We investigate such techniques with the aid of differential geometry which provides geometric insight into the problem. Such a formalism allows us to explore the merits and faults of a detection scheme independent of the parameters chosen to represent the waveform. The formalism also generalizes the problem of choosing an optimal set of templates to detect a known waveform buried in noisy data. We stress the need for finding a set of convenient parameters for the waveform and show that even after the inclusion of the second-order post-Newtonian corrections, the waveform can essentially be detected by employing a one-dimensional lattice of templates.
This would be very useful both for the purpose of carrying out the simulations as well as for the actual detection process. After setting up such a formalism we carry out a Monte Carlo simulation of the detection process for the initial LIGO-VIRGO configuration for the first post-Newtonian corrected coalescing binary waveform. We compare the results of our simulations with the currently available estimates of the accuracies in the determination of the parameters and the probability distribution of the maximum likelihood estimators. Our results suggest that the covariance matrix underestimates, by over a factor of 2, the actual errors in the estimation of parameters even when the signal-to-noise ratio is as high as 10. As only a tiny fraction of the events is expected to be detected with a signal-to-noise higher than this value, the covariance matrix is grossly inadequate to describe the errors in the measurement of the parameters of the waveform. It is found from our Monte Carlo simulations that the deviations from the covariance matrix are more in the case of the first post-Newtonian waveform than in the case of the Newtonian one. Inclusion of higher-order post-Newtonian corrections introduces new parameters that are correlated with those at the lower post-Newtonian waveform. Such correlations are expected to further increase the discrepancy of the covariance matrix results with those inferred from Monte Carlo simulations. Consequently, numerical simulations that take into account post-Newtonian corrections beyond the first post-Newtonian order are needed in order to get a clearer picture about the accuracy in the determination of parameters. We find that with the aid of the instant of coalescence the direction to the source can be determined more accurately than with the time of arrival.