VAR-PZ: Constraining the photometric redshifts of quasars using variability

¹ Instituto de Astrofísica, Facultad de Ciencias Exactas, Universidad Andres Bello, Fernández Concha 700, 7591538 Las Condes, Santiago, Chile
² Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército Libertador 441 Santiago, Chile
³ Millennium Institute of Astrophysics, Nuncio Monseñor Sótero Sanz 100 Providencia, Santiago, Chile
⁴ European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany
⁵ Max-Planck-Institut für extraterrestrische Physik, Giessenbachstr. 1, 85748 Garching, Germany
⁶ Department of Physics and Astronomy, Wayne State University, 666 W. Hancock St, Detroit, MI 48201, USA
⁷ Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
⁸ School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
⁹ ARC Centre of Excellence for Gravitational Wave Discovery – OzGrav, Clayton, VIC 3800, Australia
¹⁰ Instituto de Astronomía Teórica y Experimental, (IATE, CONICET-UNC), Córdoba, Argentina
¹¹ Universidad Nacional de Córdoba, Observatorio Astronómico de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina
¹² Institute for Theoretical Physics, Heidelberg University, Philosophenweg 12, D–69120 Heidelberg, Germany
¹³ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
¹⁴ Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA
¹⁵ The Institute for Gravitation for and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
¹⁶ Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA
¹⁷ Department of Physics, University of Napoli “Federico II”, Via Cinthia 9, 80126 Napoli, Italy
¹⁸ INAF – Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
¹⁹ Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
²⁰ Dipartimento di Fisica “Ettore Pancini”, Università di Napoli Federico II, Via Cintia 80126, Naples, Italy
²¹ Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
²² Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8578, Japan
²³ Global Center for Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku, Tokyo 169-8555, Japan
²⁴ Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia
²⁵ Hamburger Sternwarte, Universitat Hamburg, Gojenbergsweg 112, D-21029 Hamburg, Germany
²⁶ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People’s Republic of China
²⁷ Departamento de Física, Universidad Técnica Federico Santa María, Vicuña Mackenna 3939 San Joaquín, Santiago, Chile
²⁸ Universidade Federal de Santa Maria (UFSM), Centro de Ciências Naturais e Exatas (CCNE), Santa Maria, 97105-900, RS, Brazil
²⁹ International Gemini Observatory/NSF NOIRLab, Casilla 603 La Serena, Chile
³⁰ Eureka Scientific, 2452 Delmer Street, Suite 100 Oakland, CA 94602-3017, USA
³¹ Department of Physics, Yale University, P.O. Box 208120 New Haven, CT 06520, USA
³² NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
³³ Center for Space Science and Technology, University of Maryland Baltimore County, Baltimore, MD 21250, USA
³⁴ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
³⁵ Department of Physics, Drexel University, 32 S. 32nd Street, Philadelphia, PA 19104, USA
³⁶ Exzellenzcluster ORIGINS, Boltzmannstr. 2, D-85748 Garching, Germany
³⁷ Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom
³⁸ Physics Department, Tor Vergata University of Rome, Via della Ricerca Scientifica 1, 00133 Rome, Italy
³⁹ INAF – Astronomical Observatory of Rome, Via Frascati 33, 00040 Monte Porzio Catone, Italy
⁴⁰ INFN – Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
⁴¹ Department of Physics & Astronomy, Bishop’s University, 2600 rue College, Sherbrooke, QC J1M 1Z7, Canada
⁴² National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22904, USA
⁴³ Department of Astronomy, University of Virginia, 530 McCormick Rd, Charlottesville, VA 22904, USA
⁴⁴ Department of Astronomy, University of Michigan, 1085 S University, Ann Arbor, MI 48109, USA

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Received: 12 September 2025
Accepted: 13 February 2026

Abstract

The Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) is expected to obtain observations of over ten million quasars. The survey’s exceptional cadence and sensitivity will enable a significant fraction of these objects to be monitored in the ugrizy bands, spanning observed wavelengths of approximately 0.3 − 1.0 μm. The unprecedented number of sources makes spectroscopic follow-up for the vast majority of them unfeasible in the near future, so most studies will have to rely on photometric redshift estimates which are traditionally much less reliable for Active Galactic Nuclei (AGNs) than for inactive galaxies. This work presents a novel methodology to constrain the photometric redshift of AGNs that leverages the effects of cosmological time dilation, and of the luminosity and wavelength dependence of AGN variability. Specifically, we assume that the variability can be modeled as a damped random walk (DRW) process, and we adopted a parametric model to characterize the DRW timescale (τ) and asymptotic amplitude of the variability (SF_∞) based on the redshift, the rest-frame wavelength, and the AGN luminosity. We constructed variability-based photometric redshift (photo-z) priors by modeling the observed variability using the expected DRW parameters at a given redshift. These variability-based photo-z (VAR-PZ) priors were then combined with traditional spectral energy distribution (SED) fitting to improve the redshift estimates from SED fitting. Validation was performed using observational data from the Sloan Digital Sky Survey (SDSS), demonstrating significant reduction in catastrophic outliers by more than 10% in comparison with SED fitting techniques and improvements in redshift precision. The simulated light curves with both SDSS and LSST-like cadences and baselines confirm that VAR-PZ will be able to constrain the photometric redshifts of SDSS-like AGNs by bringing the outlier fractions down to below 15% from 32% (SED alone) at the end of the survey.