  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.
