Revealing the nature of ultra-long period objects with space-based gravitational-wave interferometers

Abstract: A few members of the recently-discovered class of ultra-long period objects have been identified as binaries with white-dwarf primaries. In most cases however, electromagnetic data are inconclusive and isolated magnetars or compact binaries remain viable. If the pulsation period matches that of the orbit though -- as is the case for ILT J1101+5521 and GLEAM-X J0704-37 -- some of these elusive radio transients could be gravitational-wave bright in the mHz band. Space-based interferometers could thus be used to provide independent constraints on their nature. We quantify the signal-to-noise ratio for the known systems, under a variety of scenarios, and show that a few could be detectable for sufficiently large chirp masses. Astrophysical implications for (non-)detections are discussed.