Gravitational Wave Signatures of Quasi-Periodic Eruptions: LISA Detection Prospects for RX J1301.9+2747

Quasiperiodic eruptions (QPEs) are intense, recurring outbursts of X-ray radiation originating from the nuclei of distant galaxies. One of the promising models of QPE explains these eruptions using extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass object-such as a star or a stellar-mass black hole-orbits a central massive black hole (MBH) and periodically plows through its accretion disk. In this work, we compute the gravitational wave (GW) signals emitted by such EMRI systems. We find that the physical drag and perturbations due to shock caused by the orbiter-disk collisions leave a distinct imprint on the emitted waveforms. Rather than the smooth, monochromatic evolution observed in vacuum systems, these interactions excite non-discrete modes that manifest as subtle shifts in the orbital frequency and as high-frequency ``tails'' in the signal spectrum. We demonstrate as an example outcome of our model that a specific QPE source RX J1301.9+2747 could be detectable by future space-based GW detectors, provided the orbiter maintains a moderate eccentricity of approximately $0.25$ and a mass exceeding $35\;M_\odot$. Our analysis shows that the signal-to-noise ratio for these events would be high enough to clearly distinguish them from standard vacuum EMRIs. Consequently, GW observations offer a powerful tool to probe the dense environments surrounding MBHs and could give further insight into the elusive origins of QPEs.