Population synthesis and detection prospects for Galactic long-period transients with LISA
The recently-discovered long-period radio transients represent a puzzling new class of astrophysical sources, some of which are thought to be compact binary systems emitting a pulse once per orbit. If this interpretation is correct, the orbital period--and therefore the gravitational-wave frequency--is directly encoded in the radio signal, which typically lies in the millihertz band. In this work, we explore whether these systems can be detected by the Laser Interferometer Space Antenna (LISA). Assuming that this phase-locking between radio pulses and orbital motion applies broadly across the population, we construct synthetic source catalogues informed by both observations and theoretical models of related systems, such as cataclysmic variables. We estimate that between $\sim 0.05\%$ and $\sim 6\%$ of long-period transients will be detectable within four years of observation with LISA, depending on astrophysical assumptions. For detectable systems, we find injected frequencies are recoverable to one part in $\sim 10^{5}$, amplitudes to within a factor $\sim 2$, and the sky positions to within $\sim$30 square degrees. Our results demonstrate that gravitational-wave observations can provide direct evidence for the binary nature of these sources and, importantly, can guide future radio surveys by predicting pulse periods, sky positions, and orbital properties. The mismatch between extracted frequency derivatives and that imposed by gravitational-wave decay is also computed to show that the likelihood of electromotive losses driving orbital evolution can be assessed for each detectable candidate.