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arXiv 2003.13673gr-qc
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快速频域有效飞越波形

Fast Frequency-Domain Effective Fly-By Waveforms

Nicholas Loutrel

摘要:

最近,我们开发了有效的飞掠(EFB)波形设计的模型从高偏心双星的引力辐射的爆发。我们在这里提出了一个快速评估频域EFB波形。波形是通过使用超几何函数的渐近展开构造的。由于波形是完全解析的,我们研究了使用Fisher分析可以测量的二进制参数的精度。我们发现参数之间存在简并性,使得波形根据啁啾质量${\cal{M}}$和轨道曲率半径${\cal{P}}$进行参数化,而不是二元体的总质量、对称质量比和半横径。通过计算2000个双星系统中单个爆发的费歇尔矩阵,我们发现大多数系统在啁啾质量、光度距离和倾角方面的不确定性大于100%,而大约一半的系统在轨道曲率半径、轨道偏心率和偏振角方面的不确定性小于100%。此外,我们重复此分析后,包括额外的突发内的inspiral序列,并发现,波形的参数的不确定性可以改善的数量级与足够的定时模型的突发。

英文摘要:

Recently, we developed effective fly-by (EFB) waveforms designed to model the burst of gravitational radiation from highly eccentric binaries. We here present a faster to evaluate frequency domain EFB waveform. The waveform is constructed through the use of asymptotic expansions of hypergeometric functions. Since the waveform is fully analytic, we study the accuracy to which the binary's parameters can be measured using a Fisher analysis. We find that degeneracies exist among the parameters, such that the waveform is parameterized in terms of the chirp mass ${\cal{M}}$ and orbital radius of curvature ${\cal{P}}$, instead of the total mass, symmetric mass ratio, and semi-latus rectum of the binary. By computing the Fisher matrix for single bursts from two thousand binary systems, we find that most of the systems will have greater than one hundred percent uncertainty in the chirp mass, luminosity distance, and inclination angle, while roughly half will have less than one hundred percent uncertainty in the orbital radius of curvature, orbital eccentricity, and polarization angle. Further, we repeat this analysis after including additional bursts within the inspiral sequence and find that the uncertainties in the waveform's parameters can improve by orders of magnitude with a sufficient timing model for the bursts.

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