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.

  • Article
  • Published:

Universality in the random walk structure function of luminous quasi-stellar objects

Nature Astronomy volume 7, pages 473–480 (2023)Cite this article

Subjects

Abstract

Rapidly growing black holes are surrounded by accretion disks that make them the brightest objects in the Universe. Their brightness is known to be variable, but the causes of this are not implied by simple disk models and still debated. Due to the small size of accretion disks and their great distance, there are no resolved images addressing the puzzle. In this work, we study the dependence of their variability on luminosity, wavelength and orbital/thermal timescale. We use over 5,000 of the most luminous such objects with light curves of almost nightly cadence from >5 years of observations by the NASA/ATLAS project, which provides 2 billion magnitude pairs for a structure function analysis. When time is expressed in units of orbital or thermal timescale in thin-disk models, we find a universal structure function, independent of luminosity and wavelength, supporting the model of magneto-rotational instabilities as a main cause. Over a >1 dex range in time, the fractional variability amplitude follows \(\log (A/{A}_{0})\simeq 1/2\times \log (\Delta t/{t}_{{{{\rm{th}}}}})\). Deviations from the universality may hold clues as to the structure and orientation of disks.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Coefficients of the structure function from equation (10) in narrow time intervals, comparing bootstrap results and simple bin averages.
Fig. 2: Global coefficient estimates from equation (11) (bootstrap case).
Fig. 3: Variability amplitudes logA versus logΔt and log(Δt/tth).
Fig. 4: One example time separation bin, Δtrest = [125, 141] days.

Similar content being viewed by others

Data availability

The QSO samples are selected from the publicly available MILLIQUAS database (http://quasars.org/milliquas.htm) complemented with publicly available Gaia data (https://gea.esac.esa.int/archive/). Data from NASA/ATLAS are publicly available at https://fallingstar-data.com/forcedphot/. The QSO light curves used in this study are available from J.-J.T. on request.

Code availability

The main analysis routines were written by J.-J.T. in IDL and are available on request.

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  ADS  Google Scholar 

  2. Richards, G. T. et al. The Sloan Digital Sky Survey quasar survey: quasar luminosity function from Data Release 3. Astron. J. 131, 2766–2787 (2006).

    Article  ADS  Google Scholar 

  3. Wolf, C. et al. Discovery of the most ultra-luminous QSO using Gaia, SkyMapper, and WISE. Publ. Astron. Soc. Aust. 35, e024 (2018).

    Article  ADS  Google Scholar 

  4. Pringle, J. E. & Rees, M. J. Accretion disc models for compact X-ray sources. Astron. Astrophys. 21, 1–9 (1972).

    ADS  Google Scholar 

  5. Balbus, S. A. & Hawley, J. F. A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376, 214–222 (1991).

    Article  ADS  Google Scholar 

  6. Balbus, S. A. Enhanced angular momentum transport in accretion disks. Annu. Rev. Astron. Astrophys. 41, 555–597 (2003).

    Article  ADS  Google Scholar 

  7. Shakura, N. I. & Sunyaev, R. A. Reprint of 1973A&A….24…337S. Black holes in binary systems. Observational appearance. Astron. Astrophys. 500, 33–51 (1973).

    ADS  Google Scholar 

  8. Clavel, J. et al. Correlated hard X-ray and ultraviolet variability in NGC 5548. Astrophys. J. 393, 113–125 (1992).

    Article  ADS  Google Scholar 

  9. Peterson, B. M. Reverberation mapping of active galactic nuclei. Publ. Astron. Soc. Pac. 105, 247–268 (1993).

    Article  ADS  Google Scholar 

  10. Cackett, E. M., Horne, K. & Winkler, H. Testing thermal reprocessing in active galactic nuclei accretion discs. Mon. Not. R. Astron. Soc. 380, 669–682 (2007).

    Article  ADS  Google Scholar 

  11. Shappee, B. J. et al. The man behind the curtain: X-rays drive the UV through NIR variability in the 2013 active galactic nucleus outburst in NGC 2617. Astrophys. J. 788, 48 (2014).

    Article  ADS  Google Scholar 

  12. Fausnaugh, M. M. et al. Space telescope and optical reverberation mapping project. III. Optical continuum emission and broadband time delays in NGC 5548. Astrophys. J. 821, 56 (2016).

    Article  ADS  Google Scholar 

  13. Jiang, Y.-F. et al. Detection of time lags between quasar continuum emission bands based on Pan-STARRS light curves. Astrophys. J. 836, 186 (2017).

    Article  ADS  Google Scholar 

  14. Fausnaugh, M. M. et al. Continuum reverberation mapping of the accretion disks in two Seyfert 1 galaxies. Astrophys. J. 854, 107 (2018).

    Article  ADS  Google Scholar 

  15. Yu, Z. et al. Quasar accretion disk sizes from continuum reverberation mapping in the DES standard-star fields. Astrophys. J. Suppl. Ser. 246, 16 (2020).

    Article  ADS  Google Scholar 

  16. 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 

  17. MacLeod, C. L. et al. Modeling the time variability of SDSS Stripe 82 quasars as a damped random walk. Astrophys. J. 721, 1014–1033 (2010).

    Article  ADS  Google Scholar 

  18. Wang, H. & Shi, Y. The deviation of optical variability of radio-quiet quasars from damped random walk. Astrophys. Space Sci. 364, 27 (2019).

    Article  ADS  Google Scholar 

  19. Hughes, P. A., Aller, H. D. & Aller, M. F. The University of Michigan Radio Astronomy Data Base. I. Structure function analysis and the relation between BL Lacertae objects and quasi-stellar objects. Astrophys. J. 396, 469-486 (1992).

  20. Kozłowski, S. Revisiting stochastic variability of AGNs with structure functions. Astrophys. J. 826, 118 (2016).

    Article  ADS  Google Scholar 

  21. Palanque-Delabrouille, N. et al. Variability selected high-redshift quasars on SDSS Stripe 82. Astron. Astrophys. 530, A122 (2011).

    Article  Google Scholar 

  22. Vanden Berk, D. E. et al. The ensemble photometric variability of ~25,000 quasars in the Sloan Digital Sky Survey. Astrophys. J. 601, 692–714 (2004).

    Article  ADS  Google Scholar 

  23. Morganson, E. et al. Measuring quasar variability with Pan-STARRS1 and SDSS. Astrophys. J. 784, 92 (2014).

    Article  ADS  Google Scholar 

  24. Caplar, N., Lilly, S. J. & Trakhtenbrot, B. Optical variability of AGNs in the PTF/iPTF survey. Astrophys. J. 834, 111 (2017).

    Article  ADS  Google Scholar 

  25. Li, Z., McGreer, I. D., Wu, X.-B., Fan, X. & Yang, Q. The ensemble photometric variability of over 105 quasars in the Dark Energy Camera Legacy Survey and the Sloan Digital Sky Survey. Astrophys. J. 861, 6 (2018).

    Article  ADS  Google Scholar 

  26. Suberlak, K. L., Ivezić, Ž. & MacLeod, C. Improving damped random walk parameters for SDSS Stripe 82 quasars with Pan-STARRS1. Astrophys. J. 907, 96 (2021).

    Article  ADS  Google Scholar 

  27. Mushotzky, R. F., Edelson, R., Baumgartner, W. & Gandhi, P. Kepler observations of rapid optical variability in active galactic nuclei. Astrophys. J. Lett. 743, L12 (2011).

    Article  ADS  Google Scholar 

  28. Kasliwal, V. P., Vogeley, M. S. & Richards, G. T. Are the variability properties of the Kepler AGN light curves consistent with a damped random walk? Mon. Not. R. Astron. Soc. 451, 4328–4345 (2015).

    Article  ADS  Google Scholar 

  29. Smith, K. L. et al. The Kepler light curves of AGN: a detailed analysis. Astrophys. J. 857, 141 (2018).

    Article  ADS  Google Scholar 

  30. Tachibana, Y. et al. Deep modeling of quasar variability. Astrophys. J. 903, 54 (2020).

    Article  ADS  Google Scholar 

  31. Stone, Z. et al. Optical variability of quasars with 20-yr photometric light curves. MNRAS 514, 164–184 (2022).

  32. Burke, C. J. et al. A characteristic optical variability time scale in astrophysical accretion disks. Science 373, 789–792 (2021).

    Article  ADS  Google Scholar 

  33. Rakshit, S., Stalin, C. S. & Kotilainen, J. Spectral properties of quasars from Sloan Digital Sky Survey Data Release 14: the catalog. Astrophys. J. Suppl. Ser. 249, 17 (2020).

    Article  ADS  Google Scholar 

  34. Tonry, J. L. et al. ATLAS: a high-cadence all-sky survey system. Publ. Astron. Soc. Pac. 130, 064505 (2018).

    Article  ADS  Google Scholar 

  35. Heckman, T. M. Long-time-scale optical variability in quasars. Publ. Astron. Soc. Pac. 88, 844–848 (1976).

    Article  ADS  Google Scholar 

  36. Collaboration, G. et al. Gaia Early Data Release 3. Summary of the contents and survey properties. Astron. Astrophys. 649, A1 (2021).

    Article  Google Scholar 

  37. Kozłowski, S. Limitations on the recovery of the true AGN variability parameters using damped random walk modeling. Astron. Astrophys. 597, A128 (2017).

    Article  ADS  Google Scholar 

  38. Kelly, B. C., Treu, T., Malkan, M., Pancoast, A. & Woo, J.-H. Active galactic nucleus black hole mass estimates in the era of time domain astronomy. Astrophys. J. 779, 187 (2013).

    Article  ADS  Google Scholar 

  39. Frank, J., King, A. & Raine, D. J. Accretion Power in Astrophysics 3rd edn. (Cambridge Univ. Press, 2002).

  40. Sun, M. et al. Corona-heated accretion-disk reprocessing: a physical model to decipher the melody of AGN UV/optical twinkling. Astrophys. J. 891, 178 (2020).

    Article  ADS  Google Scholar 

  41. Campitiello, S., Ghisellini, G., Sbarrato, T. & Calderone, G. How to constrain mass and spin of supermassive black holes through their disk emission. Astron. Astrophys. 612, A59 (2018).

    Article  ADS  Google Scholar 

  42. Abramowicz, M. A., Czerny, B., Lasota, J. P. & Szuszkiewicz, E. Slim accretion disks. Astrophys. J. 332, 646-658 (1988).

  43. Sadowski, A. et al. Relativistic slim disks with vertical structure. Astron. Astrophys. 527, A17 (2011).

    Article  MATH  Google Scholar 

  44. Yu, W., Richards, G. T., Vogeley, M. S., Moreno, J. & Graham, M. J. Examining agn uv/optical variability beyond the simple damped random walk. ApJ 936, 132 (2022).

  45. Kasliwal, V. P., Vogeley, M. S., Richards, G. T., Williams, J. & Carini, M. T. Do the Kepler AGN light curves need reprocessing? Mon. Not. R. Astron. Soc. 453, 2075–2081 (2015).

    Article  ADS  Google Scholar 

  46. Brandt, W. N. et al. Active galaxy science in the LSST deep-drilling fields: footprints, cadence requirements, and total-depth requirements. Preprint at arXiv https://doi.org/10.48550/arXiv.1811.06542 (2018).

  47. Ivezić, Ž. et al. LSST: from science drivers to reference design and anticipated data products. Astrophys. J. 873, 111 (2019).

    Article  ADS  Google Scholar 

  48. Chan, J. H. H., Millon, M., Bonvin, V. & Courbin, F. Twisted quasar light curves: implications for continuum reverberation mapping of accretion disks. Astron. Astrophys. 636, A52 (2020).

    Article  Google Scholar 

  49. Kawaguchi, T., Mineshige, S., Umemura, M. & Turner, E. L. Optical variability in active galactic nuclei: starbursts or disk instabilities? Astrophys. J. 504, 671–679 (1998).

    Article  ADS  Google Scholar 

  50. Flesch, E. W. The half million quasars (HMQ) catalogue. Publ. Astron. Soc. Aust. 32, e010 (2015).

    Article  ADS  Google Scholar 

  51. Schlegel, D. J., Finkbeiner, D. P. & Davis, M. Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds. Astrophys. J. 500, 525–553 (1998).

    Article  ADS  Google Scholar 

  52. Lemon, C. et al. Gravitationally lensed quasars in Gaia—IV. 150 new lenses, quasar pairs, and projected quasars. Preprint at arXiv https://doi.org/10.48550/arXiv.2206.07714 (2022).

  53. Tonry, J. L. et al. The ATLAS all-sky stellar reference catalog. Astrophys. J. 867, 105 (2018).

    Article  ADS  Google Scholar 

  54. Riello, M. et al. Gaia Early Data Release 3. Photometric content and validation. Astron. Astrophys. 649, A3 (2021).

    Article  Google Scholar 

  55. Shen, Y. & Burke, C. J. A sample bias in quasar variability studies. Astrophys. J. Lett. 918, L19 (2021).

    Article  ADS  Google Scholar 

  56. Becker, R. H., White, R. L. & Helfand, D. J. The first survey: faint images of the radio sky at twenty centimeters. Astrophys. J. 450, 559–577 (1995).

    Article  ADS  Google Scholar 

  57. Condon, J. J. et al. The NRAO VLA Sky Survey. Astron. J. 115, 1693–1716 (1998).

    Article  ADS  Google Scholar 

  58. Mauch, T. et al. SUMSS: a wide-field radio imaging survey of the southern sky—II. The source catalogue. Mon. Not. R. Astron. Soc. 342, 1117–1130 (2003).

    Article  ADS  Google Scholar 

  59. Casagrande, L. & VandenBerg, D. A. On the use of Gaia magnitudes and new tables of bolometric corrections. Mon. Not. R. Astron. Soc. 479, L102–L107 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  61. Morgan, C. W., Kochanek, C. S., Morgan, N. D. & Falco, E. E. The quasar accretion disk size–black hole mass relation. Astrophys. J. 712, 1129–1136 (2010).

    Article  ADS  Google Scholar 

  62. King, A. R., Pringle, J. E. & Livio, M. Accretion disc viscosity: how big is alpha? Mon. Not. R. Astron. Soc. 376, 1740–1746 (2007).

    Article  ADS  Google Scholar 

  63. di Clemente, A., Giallongo, E., Natali, G., Trevese, D. & Vagnetti, F. The variability of quasars. II. Frequency dependence. Astrophys. J. 463, 466–472 (1996).

    Article  ADS  Google Scholar 

  64. Markwardt, C. B. Non-linear least-squares fitting in IDL with MPFIT. In Astronomical Society of the Pacific Conference Series Vol. 411 (eds Bohlender, D. A. et al.) 251-254 (2009).

Download references

Acknowledgements

J.-J.T. was supported by the Taiwan Australian National University PhD scholarship and the Australian Research Council through Discovery Project DP190100252 and also acknowledges support by the Institute of Astronomy and Astrophysics, Academia Sinica (ASIAA). J.T. has been funded in part by the Stromlo Distinguished Visitor Program at RSAA. We thank M. Krumholz for comments on the manuscript and S. Wagner for helpful discussions. This work uses data from the University of Hawaii’s ATLAS project, funded through NASA grants NN12AR55G, 80NSSC18K0284 and 80NSSC18K1575, with contributions from the Queen’s University Belfast, STScI, the South African Astronomical Observatory and the Millennium Institute of Astrophysics, Chile. This work has made use of SDSS spectroscopic data. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the US Department of Energy Office of Science and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS website is http://www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics ∣ Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University and Yale University. This research has made use of data obtained from LAMOST quasar survey. LAMOST is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. This work has made use of data from the European Space Agency mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

Author information

Authors and Affiliations

  1. Research School of Astronomy and Astrophysics, Australian National University, Weston Creek, Australian Capital Territory, Australia

    Ji-Jia Tang & Christian Wolf

  2. Centre for Gravitational Astrophysics, Australian National University, Acton, Australian Capital Territory, Australia

    Christian Wolf

  3. Institute for Astronomy, University of Hawaii, Honolulu, HI, USA

    John Tonry

Authors
  1. Ji-Jia Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Wolf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Tonry
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.-J.T. contributed the data analysis, and drafted and edited the article. C.W. contributed the conception and design of the work, supervision of J.-J.T., and drafted and edited the article. J.T. contributed the observation and data collection.

Corresponding authors

Correspondence to Ji-Jia Tang or Christian Wolf.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Fig. 1.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, JJ., Wolf, C. & Tonry, J. Universality in the random walk structure function of luminous quasi-stellar objects. Nat Astron 7, 473–480 (2023). https://doi.org/10.1038/s41550-022-01885-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-022-01885-8

Search

Advanced 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