Pulsar timing sensitivity to very-low-frequency gravitational waves

We compute the sensitivity, constrained by instrumental, propagation, and other fundamental noises, of pulsar timing to very-low-frequency gravitational waves (GWs). Reaching predicted GW signal strengths will require suppression of time-of-arrival fluctuations caused by interstellar plasma turbulence and a reduction of white rms timing noise to 100 ns. Assuming negligible intrinsic pulsar rotational noise, perfect time transfer from time standard to observatory, and stable pulse profiles, the resulting single-pulsar signal-to-noise ratio=1 sensitivity is limited by terrestrial time standards at ${h}ᵣₘₛ{~}2×{}{10}^{{-}16} [f/{{0ex}{0ex}}(1 cycle/year)]{-}1/2$ for $f<3×{}{10}^{{-}8} Hz$, where f is the Fourier frequency and a bandwidth of 1 cycle/(10 years) is assumed. Since this sensitivity is comparable to predicted GW signal levels, a reliable detection will require substantial signal-to-noise ratio improvement via pulsar timing array.