  M82 X-1, the brightest X-ray source in the galaxy M82, has been thought to be
an intermediate-mass black hole (100 to 10,000 solar masses) because of its
extremely high luminosity and variability characteristics, although some models
suggest that its mass may be only about 20 solar masses. The previous mass
estimates were based on scaling relations that use low-frequency characteristic
timescales which have large intrinsic uncertainties. For stellar-mass black
holes, we know that the high-frequency quasi-periodic oscillations (100-450
hertz) in the X-ray emission that occur in a 3:2 frequency ratio are stable and
scale in frequency inversely with black hole mass with a reasonably small
dispersion. The discovery of such stable oscillations thus potentially offers
an alternative and less ambiguous means of 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 frequencies of 3.32$\pm$0.06 hertz and
5.07$\pm$0.06 hertz. Assuming that we can extrapolate the inverse-mass scaling
that holds for stellar-mass black holes, we estimate the black hole mass of M82
X-1 to be 428$\pm$105 solar masses. In addition, we can estimate the mass using
the relativistic precession model, from which we get a value of 415$\pm$63
solar masses.
