Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Binary parameters producing the optical flux variations of PG 1302-102 by relativistic boost.
Figure 2: The optical and ultraviolet light curves of PG 1302-102.
Figure 3: Archival UV spectra of PG 1302-102 from 1992–2011.

Similar content being viewed by others

References

  1. Kormendy, J. & Ho, L. C. Coevolution (or not) of supermassive black holes and host galaxies. Annu. Rev. Astron. Astrophys. 51, 511–653 (2013)

    Article  CAS  ADS  Google Scholar 

  2. Begelman, M. C., Blandford, R. D. & Rees, M. J. Massive black hole binaries in active galactic nuclei. Nature 287, 307–309 (1980)

    Article  ADS  Google Scholar 

  3. Komossa, S. Observational evidence for binary black holes and active double nuclei. Mem. Soc. Astron. Ital. 77, 733–741 (2006)

    CAS  ADS  Google Scholar 

  4. Valtonen, M. J. et al. A massive binary black-hole system in OJ 287 and a test of general relativity. Nature 452, 851–853 (2008)

    Article  CAS  ADS  PubMed  Google Scholar 

  5. Liu, T. et al. A periodically varying luminous quasar at z = 2 from the Pan-STARRS1 Medium Deep Survey: a candidate supermassive black hole binary in the gravitational wave-driven regime. Astrophys. J. 803, L16 (2015)

    Article  ADS  Google Scholar 

  6. Graham, M. J. et al. A possible close supermassive black-hole binary in a quasar with optical periodicity. Nature 518, 74–76 (2015)

    Article  CAS  ADS  PubMed  Google Scholar 

  7. Milosavljević, M. & Merritt, D. in The Astrophysics of Gravitational Wave Sources, AIP Conf. Proc. (eds Centrella, J. M. & Barnes, S. ) 686, 201–210 (AIP, 2003)

    Google Scholar 

  8. Hayasaki, K., Mineshige, S. & Ho, L. C. A supermassive binary black hole with triple disks. Astrophys. J. 682, 1134–1140 (2008)

    Article  ADS  Google Scholar 

  9. Shi, J.-M., Krolik, J. H., Lubow, S. H. & Hawley, J. F. Three-dimensional magnetohydrodynamic simulations of circumbinary accretion disks: disk structures and angular momentum transport. Astrophys. J. 749, 118 (2012)

    Article  ADS  Google Scholar 

  10. Roedig, C. et al. Evolution of binary black holes in self gravitating discs. Dissecting the torques. Astron. Astrophys. 545, A127 (2012)

    Article  Google Scholar 

  11. D'Orazio, D. J., Haiman, Z. & MacFadyen, A. Accretion into the central cavity of a circumbinary disc. Mon. Not. R. Astron. Soc. 436, 2997–3020 (2013)

    Article  ADS  Google Scholar 

  12. Nixon, C., King, A. & Price, D. Tearing up the disc: misaligned accretion on to a binary. Mon. Not. R. Astron. Soc. 434, 1946–1954 (2013)

    Article  ADS  Google Scholar 

  13. Farris, B. D., Duffell, P., MacFadyen, A. I. & Haiman, Z. Binary black hole accretion from a circumbinary disk: gas dynamics inside the central cavity. Astrophys. J. 783, 134 (2014)

    Article  ADS  Google Scholar 

  14. Dunhill, A. C., Cuadra, J. & Dougados, C. Precession and accretion in circumbinary discs: the case of HD 104237. Mon. Not. R. Astron. Soc. 448, 3545–3554 (2015)

    Article  CAS  ADS  Google Scholar 

  15. Shi, J.-M. & Krolik, J. H. Three-dimensional MHD simulation of circumbinary accretion disks. II. Net accretion rate. Astrophys. J. 807, 131 (2015)

    Article  ADS  CAS  Google Scholar 

  16. Loeb, A. & Gaudi, B. S. Periodic flux variability of stars due to the reflex Doppler effect induced by planetary companions. Astrophys. J. 588, L117–L120 (2003)

    Article  ADS  Google Scholar 

  17. van Kerkwijk, M. H. et al. Observations of Doppler boosting in Kepler light curves. Astrophys. J. 715, 51–58 (2010)

    Article  ADS  Google Scholar 

  18. Mazeh, T. & Faigler, S. Detection of the ellipsoidal and the relativistic beaming effects in the CoRoT-3 lightcurve. Astron. Astrophys. 521, L59 (2010)

    Article  ADS  Google Scholar 

  19. Shporer, A. et al. A ground-based measurement of the relativistic beaming effect in a detached double white dwarf binary. Astrophys. J. 725, L200–L204 (2010)

    Article  ADS  Google Scholar 

  20. Djorgovski, S. G. et al. Exploring the variable sky with the Catalina Real-time Transient Survey. In The First Year of MAXI: Monitoring Variable X-ray Sources (eds Mihara, T. & Serino, M. ) 32 (MAXI, 2010)

    Google Scholar 

  21. Volonteri, M., Haardt, F. & Madau, P. The assembly and merging history of supermassive black holes in hierarchical models of galaxy formation. Astrophys. J. 582, 559–573 (2003)

    Article  ADS  Google Scholar 

  22. D’Orazio, D. J., Haiman, Z., Duffell, P., Farris, B. D. & MacFadyen, A. I. A reduced orbital period for the supermassive black hole binary candidate in the quasar PG 1302–102? Mon. Not. R. Astron. Soc. 452, 2540–2545 (2015)

    Article  ADS  CAS  Google Scholar 

  23. Wright, J. T. & Gaudi, B. S. in Planets, Stars and Stellar Systems Vol. 3 (eds Oswalt, T. D. et al.) 489–540 (Springer, 2013)

    Book  Google Scholar 

  24. Kelly, B. C., Bechtold, J. & Siemiginowska, A. Are the variations in quasar optical flux driven by thermal fluctuations? Astrophys. J. 698, 895–910 (2009)

    Article  ADS  Google Scholar 

  25. MacFadyen, A. I. & Milosavljević, M. An eccentric circumbinary accretion disk and the detection of binary massive black holes. Astrophys. J. 672, 83–93 (2008)

    Article  ADS  Google Scholar 

  26. Charisi, M., Bartos, I., Haiman, Z., Price-Whelan, A. & Márka, S. Multiple periods in the variability of the supermassive black hole binary candidate quasar PG1302-102? Mon. Not. R. Astron. Soc. Lett. (in the press)

  27. Richards, G. T. et al. Spectral energy distributions and multiwavelength selection of type 1 quasars. Astrophys. J. 166 (Suppl.), 470–497 (2006)

    Article  CAS  Google Scholar 

  28. Yu, Q. & Tremaine, S. Observational constraints on growth of massive black holes. Mon. Not. Astron. R. Soc. 335, 965–976 (2002)

    Article  ADS  Google Scholar 

  29. Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973)

    ADS  Google Scholar 

  30. Jiang, Y.-F., Stone, J. M. & Davis, S. W. A global three-dimensional radiation magneto-hydrodynamic simulation of super-Eddington accretion disks. Astrophys. J. 796, 106 (2014)

    Article  ADS  Google Scholar 

  31. Narayan, R. & McClintock, J. E. Advection-dominated accretion and the black hole event horizon. New Astron. Rev. 51, 733–751 (2008)

    Article  ADS  Google Scholar 

  32. Mahadevan, R. Scaling laws for advection-dominated flows: applications to low-luminosity galactic nuclei. Astrophys. J. 477, 585–601 (1997)

    Article  ADS  Google Scholar 

  33. Narayan, R., Mahadevan, R. & Quataert, E. in Theory of Black Hole Accretion Disks (eds Abramowicz, M. A. et al.) 148–182 (Cambridge Univ. Press, 1998)

    Google Scholar 

  34. Hutchings, J. B., Morris, S. C., Gower, A. C. & Lister, M. L. Correlated optical and radio structure in the QSO 1302-102. Publ. Astron. Soc. Pac. 106, 642–645 (1994)

    Article  ADS  Google Scholar 

  35. Wang, J.-M., Ho, L. C. & Staubert, R. The central engines of radio-loud quasars. Astron. Astrophys. 409, 887–898 (2003)

    Article  ADS  Google Scholar 

  36. Tanaka, T. & Menou, K. Time-dependent models for the afterglows of massive black hole mergers. Astrophys. J. 714, 404–422 (2010)

    Article  ADS  Google Scholar 

  37. Artymowicz, P. & Lubow, S. H. Dynamics of binary-disk interaction. 1. Resonances and disk gap sizes. Astrophys. J. 421, 651–667 (1994)

    Article  ADS  Google Scholar 

  38. Kozłowski, S. et al. Quantifying quasar variability as part of a general approach to classifying continuously varying sources. Astrophys. J. 708, 927–945 (2010)

    Article  ADS  Google Scholar 

  39. Andrae, R., Kim, D.-W. & Bailer-Jones, C. A. L. Assessment of stochastic and deterministic models of 6304 quasar lightcurves from SDSS Stripe 82. Astron. Astrophys. 554, A137 (2013)

    Article  Google Scholar 

  40. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013)

    Article  ADS  Google Scholar 

  41. Kass, R. E. & Raftery, A. E. Bayes factors. J. Am. Stat. Assoc. 90, 773–795 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  42. Lai, D. Star-disc-binary interactions in protoplanetary disc systems and primordial spin-orbit misalignments. Mon. Not. R. Astron. Soc. 440, 3532–3544 (2014)

    Article  ADS  Google Scholar 

  43. Roedig, C., Krolik, J. H. & Miller, M. C. Observational signatures of binary supermassive black holes. Astrophys. J. 785, 115 (2014)

    Article  ADS  Google Scholar 

  44. Evans, I. N. & Koratkar, A. P. A complete atlas of recalibrated Hubble Space Telescope Faint Object Spectrograph spectra of active galactic nuclei and auasars. I. Pre-COSTAR spectra. Astrophys. J. 150 (Suppl.), 73–164 (2004)

    Article  CAS  ADS  Google Scholar 

  45. Cooksey, K. L., Prochaska, J. X., Chen, H.-W., Mulchaey, J. S. & Weiner, B. J. Characterizing the low-redshift intergalactic medium toward PKS 1302–102. Astrophys. J. 676, 262–285 (2008)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

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.).

Author information

Authors and Affiliations

Authors

Contributions

Z.H. conceived and supervised the project, performed the orbital velocity calculations, and wrote the first draft of the paper. D.J.D. computed the emission models and performed the fits to the observed light curve. D.S. analysed the archival UV data. All authors contributed to the text.

Corresponding author

Correspondence to Zoltán Haiman.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Model spectrum of PG 1302-102.

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).

Extended Data Figure 3 Model fits to the optical light curve of PG 1302-102.

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).

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature15262

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing