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

One prominent model for quasi-periodic eruptions (QPEs) is that they originate from extreme mass-ratio inspirals (EMRIs) involving stellar-mass objects orbiting around massive black holes and colliding with their accretion disks. We compute the gravitational wave signals from such a model, demonstrating that orbiter-disk interactions result in small frequency shifts and high-frequency tails due to the excitation of non-discrete modes. Interestingly, we show that QPE RX J1301.9+2747 could be detectable by future space-based gravitational wave detectors, provided a moderate eccentricity around $0.25$ and a mass exceeding $35\,M_\odot$ for the orbiter. Moreover, based on this QPE model, we show that the signal-to-noise ratio of the gravitational wave signals from QPEs, if detectable, will be sufficiently high to distinguish such systems from vacuum EMRIs and shed light on the origin of QPEs and environments around massive black holes.