Because most large galaxies contain a central black hole, and galaxies often merge1, black-hole binaries are expected to be common in galactic nuclei2. Although they cannot be imaged, periodicities in the light curves of quasars have been interpreted as evidence for binaries3,4,5, most recently in PG 1302-102, which has a short rest-frame optical period of four years (ref. 6). If the orbital period of the black-hole binary matches this value, then for the range of estimated black-hole masses, the components would be separated by 0.007–0.017 parsecs, implying relativistic orbital speeds. There has been much debate over whether black-hole orbits could be smaller than one parsec (ref. 7). Here we report that the amplitude and the sinusoid-like shape of the variability of the light curve of PG 1302-102 can be fitted by relativistic Doppler boosting of emission from a compact, steadily accreting, unequal-mass binary. We predict that brightness variations in the ultraviolet light curve track those in the optical, but with a two to three times larger amplitude. This prediction is relatively insensitive to the details of the emission process, and is consistent with archival ultraviolet data. Follow-up ultraviolet and optical observations in the next few years can further test this prediction and confirm the existence of a binary black hole in the relativistic regime.
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The authors thank M. Graham, J. Halpern, A. Price-Whelan, J. Andrews, M. Charisi, E. Quataert, and B. Kocsis for discussions. We also thank M. Graham for providing the optical data in electronic form. This work was supported by the National Science Foundation Graduate Research Fellowship under grant no. DGE1144155 (D.J.D.) and by the NASA grant NNX11AE05G (Z.H.).
The authors declare no competing financial interests.
Extended data figures and tables
Circumbinary (dashed blue) and circumsecondary (solid black) disk spectra for a total binary mass of 109.4, binary mass ratio of q = 0.05, and ratio of accretion rates . A vertical dashed line marks the centre of the V band and the approximate flux from an advection-dominated accretion flow (ADAF) is shown as a red dot for the V-band contribution of the primary. The spectrum for a radiatively efficient, thin disk around the primary is shown by the thin red dashed curve for reference.
Extended Data Figure 2 Parameter combinations for which the combined V-band luminosity of the three-component system varies by the required 0.14 mag.
M is the binary mass, q is the mass ratio, and i is the orbital inclination angle. This figure is analogous to Fig. 1, except instead of adopting an ad-hoc fractional luminosity contribution f2 by the secondary, the luminosities of each of the three components are computed from a model: the luminosity of the primary is assumed to arise from an ADAF, whereas the luminosity of the secondary is generated by a modestly super-Eddington thin disk. Emission from the circumbinary disk is also from a thin disk, and is negligible except for binaries with the lowest mass ratio (see text).
Best-fit curves assuming relativistic boost from a circular binary (solid black curves), a pure sinusoid (red dotted curves), and accretion rate variability adopted from hydrodynamic simulations11 (blue dashed curves) for a q = 0.075 (left) and a q = 0.1 (right) binary. The grey points with 1σ error bars are the data for PG 1302-102 (ref. 6).
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D'Orazio, D., Haiman, Z. & Schiminovich, D. Relativistic boost as the cause of periodicity in a massive black-hole binary candidate. Nature 525, 351–353 (2015). https://doi.org/10.1038/nature15262
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