Joining forces: 30 years of optical monitoring of the Einstein Cross

¹ Instituto de Física de Cantabria (CSIC-UC), Avda. de Los Castros s/n, E-39005 Santander, Spain
² Departamento de Física Moderna, Universidad de Cantabria, Avda. de Los Castros s/n, E-39005 Santander, Spain
³ O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Acad. Proscury St., UA-61085 Kharkiv, Ukraine
⁴ Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja (UNIR), Avda. Gran Vía Rey Juan Carlos I 41, E-26005 Logroño, Spain
⁵ Instituto de Física y Astronomía, Universidad de Valparaíso, Avda. Gran Bretaña 1111 Valparaíso, Chile
⁶ Department of Physics, United States Naval Academy, 572C Holloway Rd., Annapolis, MD 21402, USA
⁷ Instituto de Astrofísica de Canarias, c/ Vía Láctea s/n, E-38205 La Laguna, Spain
⁸ Departamento de Astrofísica, Universidad de La Laguna, E-38200 La Laguna, Spain
⁹ Department of Astronomy and Atmospheric Science, Faculty of Science, Kyoto Sangyo University, 603-8555 Kyoto, Japan
¹⁰ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, F-06304 Nice, France
¹¹ Institute of Astronomy, V.N. Karazin Kharkiv National University, Sumska 35, UA-61022 Kharkiv, Ukraine
¹² Institute of Radio Astronomy, National Academy of Science of Ukraine, Mystetstv 4, UA-61002 Kharkiv, Ukraine

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Received: 2 December 2025
Accepted: 1 April 2026

Abstract

We present extended optical monitoring of the quadruply-imaged gravitationally lensed quasar QSO 2237+0305, the Einstein Cross, including observations from different observatories in both hemispheres and using a new photometric technique. This technique uses a region far enough from the lens system to accurately determine the sky background level and minimises contamination from the lensing galaxy by combining analytical and numerical modelling of its structure. The resulting light curves of the four quasar images describe variations across practically the entire optical spectrum and span about 9000 days in the VRI bands. We captured the multi-band microlensing variability with an unprecedented level of detail, and a preliminary microlensing analysis reveals an almost linear scaling of the source radius with wavelength, providing direct evidence for the wavelength-dependent structure of the region contributing to optical passband fluxes. Specifically, assuming a mean microlens mass ⟨M⟩ = 0.3 M_⊙ and concentric Gaussian sources that move according to the velocity distribution peaks (speed and direction) reported in a previous microlensing analysis, we find that the half-light radius of the g-band source is 9.6 ± 2.7 lt-day and the size of the sources grows with wavelength, with a power-law index of α = 0.94 ± 0.05. We conclude that these long-term light curves set stringent empirical constraints on models of quasar emission and microlensing physics.