Pulsar Timing Sensitivity to Very-Low-Frequency Gravitational Waves

At nanohertz frequencies gravitational waves (GWs) cause variations in time-of-arrival of pulsar signals potentially measurable via precision timing observations. Here we compute very-low-frequency GW sensitivity constrained by instrumental, propagation, and other noises fundamentally limiting pulsar timing observations. Reaching expected GW signal strengths will require estimation and removal of $\simeq$99% of time-of-arrival fluctuations caused by typical interstellar plasma turbulence and a reduction of white rms timing noise to $\sim$100 nsec or less. If these were achieved, single-pulsar signal-to-noise ratio (SNR) = 1 sensitivity is then limited by the best current terrestrial time standards at $h_{rms} \sim$2 $\times 10^{-16}$ [f/(1 cycle/year)]$^{-1/2}$ for $f < 3 \times 10^{-8}$ Hz, where f is Fourier frequency and a bandwidth of 1 cycle/(10 years) is assumed. This sensitivity envelope may be optimistic in that it assumes negligible intrinsic pulsar rotational noise, perfect time transfer from time standard to observatory, and stable pulse profiles. Nonetheless it can be compared to predicted signal levels for a broadband astrophysical GW background from supermassive black hole binaries. Such a background is comparable to timekeeping-noise only for frequencies lower than about 1 cycle/(10 years), indicating that reliable detections will require substantial improvements in signal-to-noise ratio through pulsar array signal processing.