  X-ray quasi-periodic eruptions (QPEs) are a novel addition to the group of
extragalactic transients. In this work, we report the discovery of two further
galaxies showing QPEs, eRO-QPE3 and eRO-QPE4, with the eROSITA X-ray telescope
on board the Spectrum Roentgen Gamma observatory. Among the properties in
common with those of known QPEs are: the thermal-like spectral shape in
eruption (up to $kT\sim110-120$ eV) and quiescence ($kT\sim50-90$ eV) and its
evolution during the eruptions (with a harder rise than decay); the lack of
strong canonical signatures of active nuclei (from current optical, UV,
infrared and radio data); and the low-mass nature of the host galaxies ($\log
M_*\approx 9-10$) and their massive central black holes ($\log M_{\rm
BH}\approx 5-7$). These discoveries also bring several new insights into the
QPE population: i) eRO-QPE3 shows eruptions on top of a decaying quiescence
flux, providing further evidence for a connection between QPEs and a preceding
tidal disruption event; ii) eRO-QPE3 exhibits the longest recurrence times and
faintest peak luminosity of QPEs, compared to the known QPE population,
excluding a correlation between the two; iii) we find evidence, for the first
time, of a transient component that is harder, albeit much fainter, than the
thermal QPE spectrum in eRO-QPE4; and iv) eRO-QPE4 displays the appearance (or
significant brightening) of the quiescence disk component after the detection
of QPEs, supporting its short-lived nature against a preexisting active
galactic nucleus. Overall, the newly discovered properties (e.g., recent origin
and/or transient nature of the quiescent accretion disk; lack of correlation
between eruption recurrence timescales and luminosity) are qualitatively
consistent with recent models that identify QPEs as extreme mass-ratio
inspirals.
