The brightest X-ray source in M82 has been thought to be an intermediatemass black hole (10 2−4 solar masses, M ⊙ ) because of its extremely high luminosity and variability characteristics 1−6 , although some models suggest that its mass may be only ∼ 20 M ⊙ 3,7 . The previous mass estimates are based on scaling relations which use low-frequency characteristic timescales which have large intrinsic uncertainties 8,9 . In stellar-mass black holes we know that the high frequency quasi-periodic oscillations that occur in a 3:2 ratio (100-450 Hz) are stable and scale inversely with black hole mass with a reasonably small dispersion 10−15 . The discovery of such stable oscillations thus potentially offers an alternative and less ambiguous mass determination for intermediate-mass black holes, but has hitherto not been realized. Here, we report stable, twin-peak (3:2 frequency ratio) X-ray quasi-periodic oscillations from M82 X-1 at the frequencies of 3.32±0.06Hz and 5.07±0.06 Hz. Assuming that we can scale the stellar-mass relationship, we estimate its black hole mass to be 428±105 M ⊙ . In addition, we can estimate the mass using the relativistic precession model, from which we get a value ofOscillations arising from general relativistic effects should scale inversely with the black hole mass if they arise from orbital motion near the innermost stable circular orbit in the We detected two power spectral peaks at 3.32±0.06 Hz (coherence, Q = centroid frequency (ν)/width(∆ν) > 27) and 5.07±0.06 Hz (Q > 40) consistent with a 3:2 frequency ratio ( Fig. 1a, b). The combined statistical significance of the detection is greater than 4.7σ (see Methods for details).The proportional counter array's field of view (1 • ×1 • ) of M82 includes a number of accreting X-ray sources in addition to M82 X-1 18 . The remarkable stability of the two quasiperiodic oscillations on timescales of a few years (Movies 1 & 2), their 3:2 frequency ratio and their high oscillation luminosities strongly suggest they are not low-frequency quasi-periodic oscillations from a contaminating stellar-mass black hole (see Methods for details). Also a pulsar origin is very unlikely for several reasons. First, a pulsar signal would be much more coherent than that of the observed quasi-periodic oscillations, which clearly have a finite width. Second, based on the observed high quasi-periodic oscillation luminosities it is extremely implausible that they originate from a pulsar (see Methods for details). Finally, it would be highly coincidental to have two pulsars in the same field of view with spins in the 3:2 ratio. Also, based on the average power spectra of the background sky and a sample of accreting super-massive black holes monitored by the proportional counter array in the same epoch as M82, we rule out an instrumental origin for these oscillations 3 & 4). This leaves M82 X-1, persistently the brightest source in the field of view, as the most likely source associated with the 3:2 ratio quasi-periodic oscillation pair.We estimated M82 X-1's black hole ...

Quasi-periodic eruptions (QPEs) are very-high-amplitude bursts of X-ray radiation recurring every few hours and originating near the central supermassive black holes of galactic nuclei1,2. 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 data1,2, with emission lines in their optical spectra classifying their nuclei as hosting an actively accreting supermassive black hole3,4. Here we report observations of QPEs in two further galaxies, obtained with a blind and systematic search of 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 that is typical of active galactic nuclei is not required to trigger these events. Indeed, the periods, amplitudes and profiles of the QPEs reported here are inconsistent with current models that invoke radiation-pressure-driven instabilities in the accretion disk5–9. 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 that of the main body10, and future X-ray observations may constrain possible changes in their period owing to orbital evolution. This model could make QPEs a viable candidate for the electromagnetic counterparts of so-called extreme-mass-ratio inspirals11–13, with considerable implications for multi-messenger astrophysics and cosmology14,15.