Unveiling the Microhertz Gravitational-Wave Sky with the Square Kilometre Array Observatory

The gravitational-wave sky is expected to contain a rich variety of sources across a very broad range of frequencies. Much like in electromagnetic astronomy, exploring new gravitational-wave frequency bands therefore has the potential to unlock powerful new insights into the Universe. In this chapter, we investigate the prospects for using high-precision timing of binary millisecond pulsars with the Square Kilometre Array Observatory (SKAO) to search for gravitational waves in the microhertz ($\mu$Hz) frequency band by targeting resonant gravitational-wave perturbations to the orbits of these binaries. Using only a handful of known systems, we show that SKAO observations can achieve unprecedented sensitivity to microhertz gravitational waves, with the potential to detect inspiralling massive black hole binaries in this band. These searches are complementary to conventional pulsar timing array analyses, adding a new dimension to the gravitational-wave science achievable with the SKAO.