Search for Higher Harmonic Signals from Close White Dwarf Binaries in the mHz Band

Space-based gravitational wave (GW) detectors, such as LISA, are expected to detect thousands of Galactic close white dwarf binaries emitting nearly monochromatic GWs. In this study, we demonstrate that LISA is reasonably likely to detect higher harmonic GW signals, particularly the $(l,\mathrm{\mid }m\mathrm{\mid })=(3,3)$ mode, from a limited sample of nearby close white dwarf binaries, even with small orbital velocities $v\mathrm{/}c$ of order ${10}^{-3}$. The amplitudes of these post-Newtonian modes provide robust probes of mass asymmetry in such systems, making them valuable observational targets, especially in mass-transferring binaries. Long-term, coordinated detector operations will further improve the prospects for detecting these informative signals.