Ultra-compact X-ray binaries as dual-line gravitational-wave sources

By virtue of their sub-hour orbital periods, ultra-compact X-ray binaries are promising sources for the space-borne gravitational-wave interferometers LISA, Taiji, and TianQin. Some of these systems contain a neutron star primary, whose spin period can be measured directly via pulse timing, or indirectly through rotational modulations of burst phenomena. It is pointed out here that since actively accreting stars, with spin frequencies in the hundreds of Hz, may continuously emit appreciable gravitational waves due to the presence of accretion-built mountains, toroidal magnetic fields, and/or $r$-mode oscillations, such binaries are also candidate sources for ground-based interferometers. Two Galactic systems (4U 1728-34 and 4U 1820-30) are identified as being potentially detectable by both LISA and aLIGO simultaneously: a dual-line detection of this sort could provide percent-level constraints on the mass, radius, and internal magnetic field strength of the neutron star. With the Einstein Telescope, we find that at least four of the known ultra-compact binaries become dual-line visible.