# Correction to: Optical variability of quasars with 20-year photometric light curves

Zachary Stone, Yue Shen, Colin J. Burke, Yu-Ching Chen, Qian Yang, Xin Liu, R. A. Gruendl, M. Adamów, F. Andrade-Oliveira, J. Annis, et al.

► To cite this version:

Zachary Stone, Yue Shen, Colin J. Burke, Yu-Ching Chen, Qian Yang, et al. Correction to: Optical variability of quasars with 20-year photometric light curves. Monthly Notices of the Royal Astronomical Society, 2023, 521, pp.836-839. 10.1093/mnras/stad592. insu-04863664

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<figure><img src="image_1.png" /></figure>

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# Correction to: Optical variability of quasars with 20-year photometric light curves

by Zachary Stone<sup>1,1*</sup> Yue Shen,<sup>1,2*</sup> Colin J. Burke<sup>1,3</sup> Yu-Ching Chen<sup>1,3</sup> Qian Yang<sup>1,4</sup> Xin Liu,<sup>1,2</sup>
R. A. Gruendl,<sup>1,3</sup> M. Adamów,<sup>3</sup> F. Andrade-Oliveira,<sup>5,6</sup> J. Annis,<sup>7</sup> D. Bacon<sup>8</sup>, E. Bertin<sup>9,10</sup>
S. Bocquet,<sup>11</sup> D. Brooks,<sup>12</sup> D. L. Burke,<sup>13,14</sup> A. Carnero Rosell<sup>6</sup>, M. Carrasco Kind<sup>1,3</sup>
J. Carretero<sup>15,16</sup> L. N. da Costa,<sup>6,17</sup> M. E. S. Pereira,<sup>19</sup> J. De Vicente<sup>20</sup> S. Desai,<sup>21</sup> H. T. Diehl,<sup>7</sup>
P. Doel,<sup>12</sup> I. Ferrero<sup>22</sup> D. N. Friedel,<sup>3</sup> J. Frieman,<sup>7,13</sup> J. García-Bellido,<sup>23</sup> E. Gaztanaga<sup>24,25</sup>
D. Gruen<sup>26</sup> G. Gutierrez,<sup>7</sup> S. R. Hinton<sup>27</sup> D. L. Hollowood<sup>28</sup> K. Honscheid,<sup>29,30</sup> D. J. James,<sup>4</sup>
K. Kuehn,<sup>31,32</sup> N. Kuropatkin,<sup>7</sup> C. Lidman<sup>33,34</sup> M. A. G. Maia,<sup>6,17</sup> F. Menanteau,<sup>1,3</sup> R. Miquel,<sup>35,36</sup>
R. Morgan,<sup>37</sup> F. Paz-Chinchón,<sup>3,38</sup> A. Pieres,<sup>6,17</sup> A. A. Plazas Malagón,<sup>39</sup> M. Rodriguez-Monroy,<sup>20</sup>
E. Sanchez,<sup>20</sup> V. Scarpine,<sup>7</sup> S. Serrano,<sup>24,25</sup> I. Sevilla-Noarbe,<sup>20</sup> M. Smith<sup>40</sup>, E. Suchyta<sup>41</sup>,
M. E. C. Swanson,<sup>42</sup> G. Tarlé,<sup>18</sup> and C. To<sup>29</sup> (DES Collaboration)

*Affiliations are listed at the end of the paper*

**Key words:** errata, addenda – surveys – quasars: general – quasars: supermassive black holes.

This is a correction to: Zachary Stone, Yue Shen, Colin J. Burke, Yu-Ching Chen, Qian Yang, Xin Liu, R. A. Gruendl, M. Adamów, F. Andrade-Oliveira, J. Annis, D. Bacon, E. Bertin, S. Bocquet, D. Brooks, D. L. Burke, A. Carnero Rosell, M. Carrasco Kind, J. Carretero, L. N. da Costa, M. E. S. Pereira, J. De Vicente, S. Desai, H. T. Diehl, P. Doel, I. Ferrero, D. N. Friedel, J. Frieman, J. García-Bellido, E. Gaztanaga, D. Gruen, G. Gutierrez, S. R. Hinton, D. L. Hollowood, K. Honscheid, D. J. James, K. Kuehn, N. Kuropatkin, C. Lidman, M. A. G. Maia, F. Menanteau, R. Miquel, R. Morgan, F. Paz-Chinchón, A. Pieres, A. A. Plazas Malagón, M. Rodriguez-Monroy, E. Sanchez, V. Scarpine, S. Serrano, I. Sevilla-Noarbe, M. Smith, E. Suchyta, M. E. C. Swanson, G. Tarlé, C. To (DES Collaboration), Optical Variability of Quasars with 20-Year Photometric Light Curves, Monthly Notices of the Royal Astronomical Society, Volume 514, Issue 1, July 2022, Pages 164–184, https://doi.org/10.1093/mnras/stac1259.

In the originally published version of this manuscript, an indexing issue in our analysis code caused certain properties to be misassigned to incorrect objects in our sample. This occurred during three separate parts in our analysis: calculating the rest-frame wavelengths in which each object was observed $\lambda_{\text{rest}}$, calculating the individual and ensemble structure functions (SFs), and calculating the intrinsic variability of individual objects $\sigma_0$. This error caused the incorrect redshift $z$ to be used for certain objects when computing $\lambda_{\text{rest}}$ and the incorrect light curves to be used when calculating SFs and $\sigma_0$. All other analyses are consistent with the correctly assigned redshifts and light curves, including the power spectrum density (PSD) analysis. It should be noted that the reported redshifts and light curves for the sample are correct, but were used incorrectly due to this bug in code.

This error affected certain columns in the output data products, located at https://zenodo.org/record/7624056. In particular,

<figure><img src="image_2.png" /><figcaption>Figure 2. Updated Fig. 2.</figcaption></figure>

the SIG0_x, SIG0_x_ERR, LAMBDA_REST_x, DT_REST_x, SF_x, SF_x_ERR_L, and SF_x_ERR_U columns were incorrect in the data table described in Table 1 in the original manuscript, where ‘x’ signifies the band, and can be either g, r, or i. Similarly, the columns DT_REST_x, SF_x, and SF_x_ERR for the different ensembles in the data table described in Table 2 in the original manuscript were also incorrect. These values have been corrected using the correct analysis and reuploaded to the same location.

This error affected a number of figures in the original manuscript, namely Figs 2, 8, 9, and 10. All updated figures are shown here, with the following changes to our results:

(i) The values for $\sigma_0$ are now accurate, and follow all prior relations discussed in the original manuscript.

<footnote>* E-mail: stone28@illinois.edu (ZS); shenyue@illinois.edu (YS)</footnote>
<figure><img src="image_3.png" /><figcaption>Figure 8. Updated Fig. 8.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 9. Updated Fig. 9.</figcaption></figure>

(ii) The dependence of $\tau_{\text{DRW, rest}}$ on $\lambda_{\text{rest}}$ is weaker, which better matches the results of MacLeod et al. (2010), with an updated relation of $\tau_{\text{DRW, rest}} \propto \lambda^{0.35 \pm 0.14}$ for the subsample of 27 objects with $\tau_{\text{DRW, rest}}$ shorter than 20 per cent of the baseline.

(iii) The subsample still displays a weak dependence between $SF_{\infty}$ and $\lambda_{\text{rest}}$, though deviating further from the results in MacLeod et al. (2010).

(iv) The total sample produces a stronger dependence than in the original manuscript, with $\tau_{\text{DRW, rest}} \propto \lambda^{0.43 \pm 0.10}$. The strengthened dependence of $\tau_{\text{DRW, rest}}$ on $\lambda_{\text{rest}}$ for the entire sample is still consistent with the results found in MacLeod et al. (2010).

(v) The total sample produces a weaker dependence with respect to $SF_{\infty}$, with $SF_{\infty} \propto \lambda^{0.00 \pm 0.07}$.

(vi) After reconstructing the SFs for individual objects, the correct ensemble SFs are displayed in Figs 9 and 10. In Fig. 9, the subsample SFs more closely match the total ensemble SF. Fig. 10 shows similar results to the original figure, with slightly differing values for each of the subsamples shown.

In summary, this erratum fixed an indexing error that affected a few figures and tabulated data in Table 1. However, none of the main conclusions are changed.
<figure><img src="image_5.png" /><figcaption>Figure 10. Updated Fig. 10.</figcaption></figure>

DATA AVAILABILITY

We provide all updated data in two online FITS tables located at
https://zenodo.org/record/7624056. The format of these FITS tables
is described in Tables 1, 2 in the original manuscript.

REFERENCE

MacLeod C. L. et al., 2010, ApJ, 721, 1014

<footnote n="1">¹Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA</footnote>

<footnote n="2">²National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA</footnote>

<footnote n="3">³Center for AstroPhysical Surveys, National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA</footnote>

<footnote n="4">⁴Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cam-
bridge, MA 02138, USA</footnote>

<footnote n="5">⁵Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil</footnote>

<footnote n="6">⁶Laboratório Interinstitucional de e-Astronomia - LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil</footnote>

<footnote n="7">⁷Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA</footnote>

<footnote n="8">⁸Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, UK</footnote>

<footnote n="9">⁹Canada-France-Hawaii Telescope Corporation, 65-1238 Mamaloahoa Hwy, Kamuela, HI 96743, USA</footnote>
<footnote n="10">¹⁰Sorbonne Université, CNRS, UMR 7095, Institut d'Astrophysique de Paris,
98 bis boulevard Arago, F-75014 Paris, France</footnote>

<footnote n="11">¹¹Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679
Munich, Germany</footnote>

<footnote n="12">¹²Department of Physics & Astronomy, University College London, Gower
Street, London, WC1E 6BT, UK</footnote>

<footnote n="13">¹³Kavli Institute for Particle Astrophysics & Cosmology, P. O. Box 2450,
Stanford University, Stanford, CA 94305, USA</footnote>

<footnote n="14">¹⁴SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA</footnote>

<footnote n="15">¹⁵Institut de Física d'Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona) Spain</footnote>

<footnote n="16">¹⁶Port d'Informació Científica (PIC), Campus UAB, C. Albareda s/n, 08193 Bellaterra (Cerdanyola del Vallès), Spain</footnote>

<footnote n="17">¹⁷Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ -
20921-400, Brazil</footnote>

<footnote n="18">¹⁸Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA</footnote>

<footnote n="19">¹⁹Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany</footnote>

<footnote n="20">²⁰Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain</footnote>

<footnote n="21">²¹Department of Physics, IIT Hyderabad, Kandi, Telangana 502285, India</footnote>

<footnote n="22">²²Institute of Theoretical Astrophysics, University of Oslo. P.O. Box 1029
Blindern, NO-0315 Oslo, Norway</footnote>

<footnote n="23">²³Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid,
28049 Madrid, Spain</footnote>

<footnote n="24">²⁴Institut d'Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain</footnote>

<footnote n="25">²⁵Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain</footnote>

<footnote n="26">²⁶Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany</footnote>

<footnote n="27">²⁷School of Mathematics and Physics, University of Queensland, Brisbane,
QLD 4072, Australia</footnote>

<footnote n="28">²⁸Santa Cruz Institute for Particle Physics, Santa Cruz, CA 95064, USA</footnote>

<footnote n="29">²⁹Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, OH 43210, USA</footnote>

<footnote n="30">³⁰Department of Physics, The Ohio State University, Columbus, OH 43210,
USA</footnote>

<footnote n="31">³¹Australian Astronomical Optics, Macquarie University, North Ryde, NSW
2113, Australia</footnote>

<footnote n="32">³²Lowell Observatory, 1400 Mars Hill Rd, Flagstaff, AZ 86001, USA</footnote>

<footnote n="33">³³Centre for Gravitational Astrophysics, College of Science, The Australian National University, ACT 2601, Australia</footnote>

<footnote n="34">³⁴The Research School of Astronomy and Astrophysics, Australian National University, ACT 2601, Australia</footnote>

<footnote n="35">³⁵Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona,
Spain</footnote>

<footnote n="36">³⁶Institut de Física d'Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona) Spain</footnote>

<footnote n="37">³⁷Physics Department, University of Wisconsin-Madison, Madison, WI, USA</footnote>

<footnote n="38">³⁸Institute of Astronomy, University of Cambridge, Madingley Road, Cam-
bridge CB3 0HA, UK</footnote>

<footnote n="39">³⁹Department of Astrophysical Sciences, Princeton University, Peyton Hall,
Princeton, NJ 08544, USA</footnote>

<footnote n="40">⁴⁰School of Physics and Astronomy, University of Southampton, Southampton,
SO17 1BJ, UK</footnote>

<footnote n="41">⁴¹Computer Science and Mathematics Division, Oak Ridge National Labora-
tory, Oak Ridge, TN 37831, USA</footnote>

<footnote n="42">⁴²Waldorf High School of Massachusetts Bay, Belmont, MA 02478, USA</footnote>

<footnote>This paper has been typeset from a TeX/LA TeX file prepared by the author.</footnote>