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

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

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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.

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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.

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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.

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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.

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  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

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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.

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Correspondence to Ji-Jia Tang or Christian Wolf.

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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

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