论文标题
一组任意脉冲星的地狱与唐斯的相关性
Hellings and Downs correlation of an arbitrary set of pulsars
论文作者
论文摘要
Pulsar定时阵列（PTA）通过它们在来自不同脉冲星的脉冲的到来时诱导的相关性检测引力波（GWS）。我们假设GWS是由高斯合奏描述的。平均相关性$ h^2μ_ {\ rm u}（γ）$作为在1983年指示两个脉冲星之间的角度$γ$的函数。 $γ$表明，在平均多对之后，这些方差将减少到固有的宇宙差异$σ^2 _ {\ rm cos}（γ）$。在这里，我们将其扩展到特定的天空位置的$ nutary $ pulsars，并将Pulsar Pairs配对为$γ$。我们得出了脉冲星相关性的线性组合，这是每个垃圾箱的HD相关性的最佳估计量，以从HD曲线远离的预期变异范围的图说明了我们的方法，该图是由三个主动PTA协作监控的脉冲星集。我们计算这些BINNED估计值之间的方差和协方差，并表明这些估计分别减少到宇宙方差和协方差$ s（γ，γ'）$中，以许多速杆极限。可能从HD曲线$μ_ {\ rm u}（γ）$远离的波动在$μ_{\ rm u}（γ）$的三个角区域中密切相关/反相关。我们还构建了平方应变$ H^2 $的最佳估计器。当有很多脉冲星对时，这将确定$ h^2 $以任意精度确定，因为PTA探测了无限的GW模式。为了评估观察到的偏离HD曲线的偏差，我们表征了几个$χ^2 $合适的统计数据。我们还展示了如何包括脉冲星噪声和测量噪声。
Pulsar timing arrays (PTAs) detect gravitational waves (GWs) via the correlations they induce in the arrival times of pulses from different pulsars. We assume that the GWs are described by a Gaussian ensemble. The mean correlation $h^2 μ_{\rm u}(γ)$ as a function of the angle $γ$ between the directions to two pulsars was predicted by Hellings and Downs (HD) in 1983. The variance $σ^2_{\rm tot}(γ)$ in this correlation was recently calculated by Allen[11] for a single noise-free pulsar pair at angle $γ$, which shows that after averaging over many pairs, the variance reduces to an intrinsic cosmic variance $σ^2_{\rm cos}(γ)$. Here, we extend this to an $arbitrary$ set of pulsars at specific sky locations, with pulsar pairs binned by $γ$. We derive the linear combination of pulsar-pair correlations which is the optimal estimator of the HD correlation for each bin, illustrating our methods with plots of the expected range of variation away from the HD curve, for the sets of pulsars monitored by three active PTA collaborations. We compute the variance of and the covariance between these binned estimates, and show that these reduce to the cosmic variance and covariance $s(γ,γ')$ respectively, in the many-pulsar limit. The likely fluctuations away from the HD curve $μ_{\rm u}(γ)$ are strongly correlated/anticorrelated in the three angular regions where $μ_{\rm u}(γ)$ is successively positive, negative, and positive. We also construct the optimal estimator of the squared strain $h^2$. When there are very many pulsar pairs, this determines $h^2$ with arbitrary precision because PTAs probe an infinite set of GW modes. To assess observed deviations away from the HD curve, we characterize several $χ^2$ goodness-of-fit statistics. We also show how pulsar noise and measurement noise can be included.
