论文标题
部分可观测时空混沌系统的无模型预测
On Detecting Nearby Nano-Hertz Gravitational Wave Sources via Pulsar Timing Arrays
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Massive binary black holes (MBBHs) in nearby galactic centers, if any, may be nano-Hertz gravitational wave (GW) sources for pulsar timing arrays (PTAs) to detect. Normally the objective GWs for PTA experiments are approximated as plane waves because its sources are presumably located faraway. For nearby GW sources, however, this approximation may be inaccurate due to the curved GW wave front and the GW strength changes along the paths of PTA pulsar pulses. In this paper, we analyze the near-field effect in the PTA detection of nearby sources and find it is important if the source distance is less than a few tens Mpc, and ignoring this effect may lead to a significant signal-to-noise underestimation especially when the source distance is comparable to the pulsar distances. As examples, we assume a nano-Hertz MBBH source located at either the Galactic Center (GC) or the Large Magellanic Cloud (LMC) according to the observational constraints/hints on the MBBH parameter space, and estimate its detectability by current/future PTAs. We find that the GC MBBH may be detectable by the Square Kilometer Array (SKA) PTA. It is challenging for detecting the LMC MBBH; however, if a number ($N\gtrsim10$) of stable millisecond pulsars can be found in the LMC center, the MBBH may be detectable via a PTA formed by these pulsars. We further illustrate the near-field effects on the PTA detection of an isotropic GW background contributed mainly by nearby GW sources, and the resulting angular correlation is similar to the Hellings-Downs curve.
