论文标题
通过PULSAR定时阵列的重叠波搜索重叠函数的分析系列扩展
Analytic series expansion of the overlap reduction function for gravitational wave search with pulsar timing arrays
论文作者
论文摘要
在我们以前的论文\ cite {pta1}中，我们得出了脉冲红移的通用表达，可观察到脉冲星时阵列（PTA）实验的主要表达式，用于检测引力波的重力波，用于通过一般相对论的修改引起的所有可能的极化（GR）。在这项工作中，我们提供了PTA重叠函数的通用表达，而无需使用短波长近似进行张力偏振。我们坚信，短波长近似不适用于PTA的重叠降低功能，因为在集成媒体中删除指数项将导致POLES以$ x，y $ $ $ $ $ $ $ $ y $ polartivations和$+$ $ $和$ \ times $ $ $ $ $ $ $。在这项工作中，我们提供了一个系列扩展，以精确计算积分，并通过分析系列的数值评估来研究短波长值的串联行为。我们发现与Hellings \＆Downs曲线的共同定位的脉冲星的极限分歧。
In our previous paper \cite{PTA1} we derived a generic expression for the pulse redshift the main observable for the Pulsar Timing Array (PTA) experiment for detection of gravitational waves for all possible polarizations induced by modifications of general relativity (GR). In this work we provide a generic expression of the overlap reduction function for PTA without using the short wavelength approximation for tensorial polarization. We are convinced, that the short wavelength approximation is not applicable to the overlap reduction function for PTA's, since the removal of the exponential terms in the integrand would lead to poles for $x, y$ and $l$ polarizations and discontinuities for $+$ and $\times$. In this work we provide a series expansion to calculate the integral exactly and investigate the behaviour of the series for short wavelength values via numerical evaluation of the analytical series. We find a disagreement for the limit of co-located pulsars with the Hellings \& Downs curve.
