标题： 通过脉冲星计时阵列寻找引力波背景的各向异性 显示英文标题

标题： The search for anisotropy in the gravitational-wave background with pulsar-timing arrays

摘要： 脉冲星计时阵列（PTAs）正在寻找来自超大质量黑洞双星的引力波，并且有望通过恒星天体测量测量来补充这些搜索。然而，理论学家仍然存在分歧，即本地引力波背景是否具有统计各向同性，这可能来自于许多SMBH双星的贡献之和，或者是否表现出统计各向异性的类型，这种各向异性可能来自于少数（甚至一个）明亮源的主导。在这里，我们使用双极球谐函数推导出PTA对GW背景中统计各向异性的最优估计器，以及对这种各向异性的可检测性的简单估计。我们提供了关于可检测到的偶极各向异性（以及其他低阶多极矩）最小振幅的结果，以及关于引力波“束”的最小可检测振幅的结果。结果以GW信号的信噪比为函数以及以脉冲星数量为函数（假设在天空上均匀分布且每个脉冲星的灵敏度相等）的形式呈现。我们首先给出了使用单个时域窗口函数的测量结果，然后展示了如何通过包含时域信息来增强结果。此方法旨在概念上简单明了，并补充更详细（但相应地更不直观）的实际测量建模结果。 显示英文摘要

摘要： Pulsar-timing arrays (PTAs) are seeking gravitational waves from supermassive-black-hole binaries, and there are prospects to complement these searches with stellar-astrometry measurements. Theorists still disagree, however, as to whether the local gravitational-wave background will be statistically isotropic, as arises if it is the summed contributions from many SMBH binaries, or whether it exhibits the type of statistical anisotropy that arises if the local background is dominated by a handful (or even one) bright source. Here we derive, using bipolar spherical harmonics, the optimal PTA estimators for statistical anisotropy in the GW background and simple estimates of the detectability of this anisotropy. We provide results on the smallest detectable amplitude of a dipole anisotropy (and several other low-order multipole moments) and also the smallest detectable amplitude of a "beam" of gravitational waves. Results are presented as a function of the signal-to-noise with which the GW signal is detected and as a function of the number of pulsars (assuming uniform distribution on the sky and equal sensitivity per pulsar). We provide results first for measurements with a single time-domain window function and then show how the results are augmented with the inclusion of time-domain information. The approach here is intended to be conceptually straightforward and to complement the results of more detailed (but correspondingly less intuitive) modeling of the actual measurements.