The impact of a stochastic gravitational-wave background on pulsar timing parameters

TL;DR

This study investigates how a stochastic gravitational-wave background affects pulsar timing measurements, revealing underestimation of uncertainties and setting upper limits on gravitational wave amplitude using simulations and observational data.

Contribution

It quantifies the impact of gravitational-wave backgrounds on pulsar timing parameters and establishes new upper limits on gravitational wave amplitude from observational data.

Findings

Timing uncertainties are underestimated by up to a factor of 10 at certain amplitudes.

Detected low-frequency spectral leakage in simulated data with gravitational waves.

Set a 2-sigma upper limit of A ≤ 9.1×10^{-14} on gravitational wave amplitude.

Abstract

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.