用脉冲星探测随机引力波背景的最低要求
Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars
摘要：
我们评估的检测能力的纳赫兹引力波（GW）背景相对于加性的红，白噪声的毫秒脉冲的定时。我们发展了基于脉冲星定时阵列中脉冲星对的交叉关联函数的检测准则。相关幅度的分布被发现是非高斯和高度偏斜，这显着影响检测和虚警概率。当只有白噪声和GWs贡献时，我们的检测结果与其他人发现的结果一致。然而，红噪声极大地改变了结果。我们讨论的方法，以满足GW检测（“登山意义”）的挑战，通过区分GW为主的红色或白噪声限制制度。我们通过评估必须在高节奏、5年定时计划中监测的毫秒级射电望远镜的数量来表征探测机制，该计划用于GW背景光谱$h_c(f) = A f^{-2/3}$和$A = 10^{-15}$年$^{-2/3}$。除非能找到20个超稳定毫秒级脉冲的样本-那些具有来自红噪声贡献$σ_r \lesssim 20$ ns的定时残差的脉冲-否则将需要一个更大的关于$\gtrsim 50 - 100$ MSP的定时程序。对于$A$的其他值，约束为$σ_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$。识别合适的MSP本身需要一个积极的调查活动，其次是每个对象的定时残差的自旋噪声水平的特性。搜索和计时计划可能需要南半球新阵列望远镜以及现有望远镜的大量时间。
英文摘要：
We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $σ_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $σ_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.
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