A study of gravitational-wave signatures from quasi-periodic eruptions

Abstract

This thesis develops a comprehensive methodology for modeling gravitational waves (GWs) emitted by quasi-periodic eruptions (QPEs), based on the most studied QPE model in which a stellar-mass object (SMO) orbits around a massive black hole (MBH) and collides with its accretion disk repeatedly. In other words, this model can be taken as an extreme mass-ratio inspiral (EMRI) perturbed by orbiter-disk interactions (ODIs). Therefore, gravitational waves with distinct features are expected to be produced from such systems.

Leveraging black hole perturbation theory, we numerically solve the Teukolsky equation to compute GW signals. Our framework tracks orbital evolution by incorporating both gravitational radiation and impulsive energy and momentum losses from ODIs. Numerical solutions are accelerated using the FastEMRIWaveforms package. We demonstrate that ODIs excite non-discrete GW modes, producing high-frequency tails that enhance detectability. Detection criteria for space-based observatories are established via signal-to-noise ratio calculations and waveform mismatch metrics.

Interestingly, based on the methodology established in this thesis, we find that observed QPE RX J1301.9+2747 can produce GWs detectable by LISA for a reasonable range of parameters. Moreover, across detectable regimes, the GW waveforms from this source should exhibit sufficient mismatch to be differentiated from vacuum EMRIs.

This work establishes QPEs as multi-messenger probes of MBHs, with implications for LISA science and studies of galactic nuclei dynamics. Future work include developing full GW templates for QPE systems to enable targeted searches and extending this framework to model other exotic EMRI environments, which will greatly expand the multi-messenger landscape for next-generation GW observatories.