Quasiperiodic eruptions (QPEs) are repeated x-ray bursts originating in galactic nuclei. Of the many proposed models, the favored model is the disk-collision model, in which a stellar mass orbiter collides with a disk formed from a tidal disruption event, generating flares twice per orbit. In this model QPEs are tracers of circular extreme mass ratio inspirals (EMRIs) and can be used to infer the EMRI formation rate and estimate their contribution to the stochastic gravitational wave background (SGWB) in the Laser Interferometer Space Antenna (LISA) band. Whether the secondary is a stellar mass black hole or a main-sequence star is still debated and leads to different results for the EMRI rate and SGWB. We obtain fiducial rates—subject to systematic uncertainties—of $R_{\mathrm{SE}}=2.88\times {10}^{-6}$ per galaxy per year for stellar EMRIs and $R_{\mathrm{BHE}}=6.07\times {10}^{-6}$ per galaxy per year for black hole EMRIs, then estimate their contribution to the SGWB. We find that only black hole EMRIs contribute to the 1–10 mHz band resolvable by LISA and, depending on the secondary mass and formation radius, can contribute from just below the LISA sensitivity curve to roughly 2 orders of magnitude above it. Stellar EMRIs, being tidally disrupted before reaching the 1–10 mHz band, only contribute to submillihertz frequencies and remain below the LISA sensitivity curve.

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• Gravitational wave detection
• Gravitational wave sources
• Gravitational waves
• Accretion disk & black-hole plasma
• Astronomical black holes
• Galactic nuclei & quasars
• Numerical simulations in gravitation & astrophysics