Gravitational waves are predicted by Einstein's theory of general relativity as well as other theories of gravity. The rotational stability of the fastest pulsars means that timing of an array of these objects can be used to detect and investigate gravitational waves. Simultaneously, however, pulsar timing is used to estimate spin period, period derivative, astrometric, and binary parameters. Here we calculate the effects that a stochastic background of gravitational waves has on pulsar timing parameters through the use of simulations and data from the millisecond pulsars PSR J0437--4715 and PSR J1713+0747. We show that the reported timing uncertainties become underestimated with increasing background amplitude by up to a factor of $\sim10$ for a stochastic gravitational-wave background amplitude of $A=5\times 10^{-15}$, where $A$ is the amplitude of the characteristic strain spectrum at one-year gravitational wave periods. We find evidence for prominent low-frequency spectral leakage in simulated data sets including a stochastic gravitational-wave background. We use these simulations along with independent Very Long Baseline Interferometry (VLBI) measurements of parallax to set a 2--sigma upper limit of $A\le9.1\times 10^{-14}$. We find that different supermassive black hole assembly scenarios do not have a significant effect on the calculated upper limits. We also test the effects that ultralow--frequency (10$^{-12}$--10$^{-9}$ Hz) gravitational waves have on binary pulsar parameter measurements and find that the corruption of these parameters is less than those due to $10^{-9}$--$10^{-7}$ Hz gravitational waves.
Why Gravitational Wave Science Needs Pulsar Timing Arrays And Why Pulsar Timing Arrays Need Both Arecibo and the GBT: A Response to the NSF-AST Portfolio Review from the NANOGrav Collaboration
Timing of young radio pulsars I: Timing noise, periodic modulation and proper motion
年轻恒星的平稳降旋受到两种非确定性现象的扰动：毛刺和定时噪声。虽然定时噪声提供了对极端密度下的核物理和等离子体物理的见解，但它是高精度脉冲星定时实验的障碍。本文提出了一种改进的基于贝叶斯推理的方法，用于同时模拟用64 m Parkes射电望远镜观测了$\sim$ 10年的85个高$\dot{E}$射电望远镜样本的随机和确定性参数。定时噪声是一个红色的过程，我们开发了一个参数化的基础上的红色噪声幅度（$A_{\rm red}$）和频谱指数（$β$）。我们测量的中位数$A_{\rm red}$为$-10.4^{+1.8}_{-1.7}$ yr $^{3/2}$和$β$为$-5.2^{+3.0}_{-3.8}$，并表明定时噪声的强度与$ν^{1}|\dotν|^{-0.6\pm0.1}$成正比，其中$ν$是脉冲星的自旋频率，$\dotν$是其自旋下降率。最后，我们测量了19颗恒星的重要制动指数，两颗恒星的自行，并讨论了五颗恒星到达时间的周期性调制。
