X-ray quasi-periodic eruptions (QPEs) are intense soft X-ray bursts from the nuclei of nearby low-mass galaxies typically lasting about one hour and repeating every few hours. Their physical origin remains a matter of debate, although so-called impact models appear promising. These models posit a secondary orbiting body piercing through the accretion disc around the primary supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI) system. In this work, we study the QPE timing properties of GSN 069, the first galactic nucleus in which QPEs have been identified. We primarily focus on observed minus calculated (O-C) diagrams. The O-C data in GSN 069 are consistent with a super-orbital modulation of several tens of days, whose properties do not comply with the impact model. We suggest that rigid precession of a misaligned accretion disc or, alternatively, the presence of a second SMBH forming a sub-milliparsec binary with the inner EMRI is needed to reconcile the model with the data. In both cases, the quiescent accretion disc emission should also be modulated on similar timescales. Current X-ray monitoring indicates that this might be the case, although a longer baseline of higher cadence observations is needed to confirm the tentative X-ray flux periodicity on firm statistical grounds. Future dedicated monitoring campaigns will be crucial for testing the overall impact-plus-modulation model in GSN 069 and to distinguish between the two proposed modulating scenarios. If our interpretation is correct, QPEs in GSN 069 represent the first electromagnetic detection of a short-period EMRI system in an external galaxy, paving the way to future multi-messenger astronomical observations. Moreover, QPEs encode unique information on SMBHs inner environments, which can be used to gain insights on the structure and dynamics of recently formed accretion flows and to possibly infer the presence of tight SMBH binaries in galactic nuclei.
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