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Abstract In the past 5 yr, six X-ray quasi-periodic eruption (QPE) sources have been discovered in the nuclei of nearby galaxies. Their origin remains an open question. We present Multi Unit Spectroscopic Explorer integral field spectroscopy of five QPE host galaxies to characterize their properties. We find that 3/5 galaxies host extended emission-line regions (EELRs) up to 10 kpc in size. The EELRs are photoionized by a nonstellar continuum, but the current nuclear luminosity is insufficient to power the observed emission lines. The EELRs are decoupled from the stars both kinematically and in projected sky position, and the low velocities and velocity dispersions (<100 km s⁻¹and ≲75 km s⁻¹, respectively) are inconsistent with being driven by active galactic nuclei (AGNs) or shocks. The origin of the EELRs is likely a previous phase of nuclear activity. QPE host galaxies share several similarities with tidal disruption event (TDE) hosts, including an overrepresentation of galaxies with strong Balmer absorption and little ongoing star formation, as well as a preference for a short-lived (the typical EELR lifetime is ∼15,000 yr), gas-rich phase where the nucleus has recently faded significantly. This suggests that QPEs and TDEs may share a common formation channel, disfavoring AGN accretion disk instabilities as the origin of QPEs. If QPEs are related to extreme mass ratio inspiral systems (EMRIs), e.g., stellar-mass objects on bound orbits about massive black holes, the high incidence of EELRs and recently faded nuclei could be used to localize the hosts of EMRIs discovered by low-frequency gravitational-wave observatories. 

Context.Accretion disk winds launched close to supermassive black holes (SMBHs) are a viable mechanism providing feedback between the SMBH and the host galaxy. Aims.We aim to characterize the X-ray properties of the inner accretion disk wind of the nearby active galactic nucleus PG 1126-041 and to study its connection with the UV-absorbing wind. Methods.We performed a spectroscopic analysis of eightXMM-Newtonobservations of PG 1126-041 taken between 2004 and 2015, using both phenomenological models and the most advanced accretion disk wind models available. For half of the data set, we were able to compare the X-ray analysis results with the results of quasi-simultaneous, high-resolution, spectroscopic UV observations taken with the Cosmic Origins Spectrograph on board theHubbleSpace Telescope. Results.The X-ray spectra of PG 1126-041 are complex and absorbed by ionized material, which is highly variable on multiple timescales, sometimes as short as 11 days. Accretion disk wind models can account for most of the X-ray spectral complexity of PG 1126-041, with the addition of massive clumps, represented by a partially covering absorber. Variations in column density (N_H ∼ 5 − 20 × 10²²cm⁻²) of the partially covering absorber drive the observed X-ray spectral variability of PG 1126-041. The absorption from the X-ray partially covering gas and from the blueshifted C IVtroughs appear to vary in a coordinated way. Conclusions.The line of sight toward PG 1126-041 offers a privileged view through a highly dynamic nuclear wind originating on inner accretion disk scales, making the source a very promising candidate for future detailed studies of the physics of accretion disk winds around SMBHs.