Using Pulsar Parameter Drifts to Detect Subnanohertz Gravitational Waves

Gravitational waves with frequencies below 1 nHz are notoriously difficult to detect. With periods exceeding current experimental lifetimes, they induce slow drifts in observables rather than periodic correlations. Observables with well-known intrinsic contributions provide a means to probe this regime. In this Letter, we demonstrate the viability of using observed pulsar timing parameters to discover such “ultralow” frequency gravitational waves, presenting two complementary observables for which the systematic shift induced by ultralow-frequency gravitational waves can be extracted. Using existing data for these parameters, we search the ultralow-frequency regime for continuous-wave signals, finding a sensitivity near the expected prediction from inspirals of supermassive black holes. We do not see an excess in the data, setting a limit on the strain of $1.3\times {10}^{-12}$ at 450 pHz with a sensitivity dropping approximately quadratically with frequency until 10 pHz. Our search method opens a new frequency range for gravitational wave detection and has profound implications for astrophysics, cosmology, and particle physics.

Figure 1

Sensitivity of pulsar timing arrays to continuous-wave sources from inspirals of supermassive black hole using $\ddot{P}$ and ${\dot{P}}_b$ analyses (red). For the $\ddot{P}$ analysis, we use the width of the line as an estimate of the influence of ultralow-frequency red noise (see text for details). Constraints from traditional PTA searches shown by EPTA (light blue) [73], PPTA (blue) [74], and NANOGrav (dark blue) [75]. We also show results from a previous search using statistical analysis of $\dot{P}$ [35] (green). Finally, we plot the output from a simulation of SMBH mergers (orange) [76].