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M82 X-1, the brightest X-ray source in the galaxy M82, has been thought to bean intermediate-mass black hole (100 to 10,000 solar masses) because of itsextremely high luminosity and variability characteristics, although some modelssuggest that its mass may be only about 20 solar masses. The previous massestimates were based on scaling relations that use low-frequency characteristictimescales which have large intrinsic uncertainties. For stellar-mass blackholes, we know that the high-frequency quasi-periodic oscillations (100-450hertz) in the X-ray emission that occur in a 3:2 frequency ratio are stable andscale in frequency inversely with black hole mass with a reasonably smalldispersion. The discovery of such stable oscillations thus potentially offersan alternative and less ambiguous means of mass determination forintermediate-mass black holes, but has hitherto not been realized. Here wereport stable, twin-peak (3:2 frequency ratio) X-ray quasi-periodicoscillations from M82 X-1 at frequencies of 3.32$\pm$0.06 hertz and5.07$\pm$0.06 hertz. Assuming that we can extrapolate the inverse-mass scalingthat holds for stellar-mass black holes, we estimate the black hole mass of M82X-1 to be 428$\pm$105 solar masses. In addition, we can estimate the mass usingthe relativistic precession model, from which we get a value of 415$\pm$63solar masses.

A 400 solar mass black hole in the Ultraluminous X-ray source M82 X-1 accreting close to its Eddington limit