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 characteristics1,2,3,4,5,6, although some models suggest that its mass may be only about 20 solar masses3,7. The previous mass estimates were based on scaling relations that use low-frequency characteristic timescales which have large intrinsic uncertainties8,9. 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 dispersion10,11,12,13,14,15. 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 ± 0.06 hertz and 5.07 ± 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 ± 105 solar masses. In addition, we can estimate the mass using the relativistic precession model, from which we get a value of 415 ± 63 solar masses.
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This work is based on observations made with the Rossi X-ray Timing Explorer, a mission that was managed and controlled by NASA’s Goddard Space Flight Center in Greenbelt, Maryland, USA. All the data used in the present article is publicly available through NASA’s HEASARC archive. D.R.P. would like to thank M. Trippe, C. Miller and C. Reynolds for discussions.
The authors declare no competing financial interests.
Extended data figures and tables
The 128 s X-ray (3–13 keV) light curves (a, c) and the corresponding power spectra (b, d) of M82. The corresponding observation IDs are shown in the top right of each panel. The light curves have a bin size of 1 s, and the power spectra have a frequency resolution of 0.125 Hz. The error bars in a and c represent the standard error of the mean.
Extended Data Figure 2 Long-term X-ray (3–13 keV) light curves of three accreting supermassive black holes.
These were extracted from the same time window as the M82 observations (2004 September 2 to 2005 April 30 and 2006 March 3 to 2009 December 30). Data from 3C 111, MKN 110 and 3C 273 are shown in a, b and c, respectively. The count rates are not corrected for background.
Extended Data Figure 3 Average X-ray (3–13 keV) power spectra of three accreting supermassive black holes.
Similar to the M82 analysis, these spectra were extracted by combining all the data (128 s data segments) shown in Extended Data Fig. 2. The Poisson noise level is equal to 2, and the 99.73% and 99.99% confidence contours are indicated by horizontal dotted lines. The two dashed vertical lines are drawn at 3.32 and 5.07 Hz. In all three cases, 3C 111 (a), MKN 110 (b) and 3C 273 (c), there are no significant power spectral features. The total PCA exposures used for these spectra were 630 ks (a), 738 ks (b) and 711 ks (c).
Extended Data Figure 4 Long-term X-ray light curve and the average power density spectrum of a background sky field of RXTE/PCA.
Similar to Extended Data Fig. 3, the 99.73% and 99.99% contours and the vertical lines at 3.32 and 5.07 Hz are indicated in the power density spectrum (b). Again, only observations coincident with M82 monitoring were used (2004 September 2 to 2005 April 30 and 2006 March 3 to 2009 December 30), and the total exposure time was 1,450 ks. The light curve (3–13 keV) is shown in (a). The background has coordinates of RA = 5.0°, dec. = −67.0°.
Dynamic power density spectrum of M82 X1 using 128-second light curves. As the video frames progress more data is being added which decreases the overall noise level. The two horizontal lines show the 99.73% and 99.99% confidence levels. The two statistically significant features are at 3.32 Hz and 5.07 Hz consistent with a 3:2 frequency ratio. (MP4 4165 kb)
Same as Supplementary Video 1 but instead we used 1024-second light curves (see Methods for details). (MP4 3299 kb)
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Pasham, D., Strohmayer, T. & Mushotzky, R. A 400-solar-mass black hole in the galaxy M82. Nature 513, 74–76 (2014). https://doi.org/10.1038/nature13710
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