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Aims.The goal of this project is to construct an estimator for the masses of supermassive black holes in active galactic nuclei (AGNs) based on the broad Hαemission line. Methods.We made use of published reverberation mapping data. We remeasured all Hαtime lags from the original data as we find that reverberation measurements are often improved by detrending the light curves. Results.We produced mass estimators that require only the Hαluminosity and the width of the Hαemission line as characterized by either the full width at half maximum or the line dispersion. Conclusions.It is possible, on the basis of a single spectrum covering the Hαemission line, to estimate the mass of the central supermassive black hole in AGNs with all three parameters believed to affect mass measurement – luminosity, line width, and Eddington ratio – taken into account. The typical formal accuracy in such estimates is of order 0.2–0.3 dex relative to the reverberation-based masses. 

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.