Quasi-Periodic Eruptions (QPEs) are extreme high-amplitude bursts of X-ray radiation recurring every few hours and originating near the central supermassive black holes in galactic nuclei. It is currently unknown what triggers these events, how long they last and how they are connected to the physical properties of the inner accretion flows. Previously, only two such sources were known, found either serendipitously or in archival data, with emission lines in their optical spectra classifying their nuclei as hosting an actively accreting supermassive black hole. Here we present the detection of QPEs in two further galaxies, obtained with a blind and systematic search over half of the X-ray sky. The optical spectra of these galaxies show no signature of black hole activity, indicating that a pre-existing accretion flow typical of active nuclei is not required to trigger these events. Indeed, the periods, amplitudes and profiles of the newly discovered QPEs are inconsistent with current models that invoke radiation-pressure driven accretion disk instabilities. Instead, QPEs might be driven by an orbiting compact object. Furthermore, their observed properties require the mass of the secondary object to be much smaller than the main body and future X-ray observations may constrain possible changes in the period due to orbital evolution. This scenario could make QPEs a viable candidate for the electromagnetic counterparts of the so-called extreme mass ratio inspirals, with considerable implications for multi-messenger astrophysics and cosmology.
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