Relativistic boost as the cause of periodicity in a massive black-hole binary candidate

Because most large galaxies contain a central black hole, and galaxies often merge, black-hole binaries are expected to be common in galactic nuclei. Although they cannot be imaged, periodicities in the light curves of quasars have been interpreted as evidence for binaries, 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.