With periods much longer than the duration of current pulsar timing surveys, gravitational waves in the picohertz (pHz) regime are not detectable in the typical analysis framework for pulsar timing data. However, signatures of these low-frequency signals persist in the slow variation of pulsar timing parameters. In this work, we present the results of the first Bayesian search for continuous pHz gravitational waves using the drift of two sensitive pulsar timing parameters—the time derivative of pulsar binary orbital period ${\dot{P}}_b$ and the second-order time derivative of pulsar spin period $\ddot{P}$. We apply our new technique to a dataset with more than double the number of pulsars as previous searches in this frequency band, achieving an order-of-magnitude sensitivity improvement. No continuous wave signal is detected in current data; however, we show that future observations by the Square Kilometre Array will provide significantly improved sensitivity and the opportunity to observe continuous pHz signals, including the early stages of supermassive black hole mergers. We explore the detection prospects for this signal by extending existing population models into the pHz regime, finding that future observations will probe phenomenologically interesting parameter space. Our new Bayesian technique and leading sensitivity in this frequency domain pave the way for new discoveries in both black hole astrophysics and the search for new physics in the early Universe.

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• General relativity
• Gravitational waves