Probing the structure of the lensed quasar SDSS J1004+4112 through microlensing analysis of spectroscopic data

¹ Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100 Burjassot, Valencia, Spain
e-mail: carina.fian@uv.es
² Observatorio Astronómico, Universidad de Valencia, 46980 Paterna, Valencia, Spain
³ Instituto de Astrofísica de Canarias, Vía Láctea s/n, La Laguna, 38200 Tenerife, Spain
⁴ Departamento de Astrofísica, Universidad de la Laguna, La Laguna, 38200 Tenerife, Spain
⁵ Departamento de Física Teórica y del Cosmos, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain
⁶ Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
⁷ Department of Physics, Faculty of Natural Sciences, University of Haifa, Haifa 3498838, Israel
⁸ Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
⁹ School of Physics and Astronomy and Wise Observatory, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 6997801, Israel
¹⁰ Department of Physics, Drexel University, 32 S. 32nd Street, Philadelphia, PA 19104, USA

Received: 6 July 2023
Accepted: 8 October 2023

Abstract

Aims. We aim to reveal the sizes of the continuum and broad emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1004+4112 by analyzing the unique signatures of microlensing in this system. Through a comprehensive analysis of 20 spectroscopic observations acquired between 2003 and 2018, we studied the striking deformations of various BEL profiles and determined the sizes of their respective emitting regions.

Methods. Our approach involves a detailed analysis of the magnitude differences in the BEL wings and their adjacent continua, and the implementation of a statistical model to quantify the distribution and impact of microlensing magnifications. To ensure a reliable baseline for no microlensing, we used the emission line cores as a reference. We then applied a Bayesian estimate to derive the size lower limits of the Lyα, Si IV, C IV, C III], and Mg II emitting regions, as well as the sizes of the underlying continuum-emitting sources.

Results. We analyzed the outstanding microlensing-induced distortions in the line profiles of various BELs in the quasar image A, characterized by a prominent magnification of the blue part and a strong demagnification of the red part. From the statistics of microlensing magnifications and using Bayesian methods, we estimate the lower limit to the overall size of the regions emitting the BELs to be a few light-days across, which is significantly smaller than in typically lensed quasars. The asymmetric deformations in the BELs indicate that the broad-line region is generally not spherically symmetric, and is likely confined to a plane and following the motions of the accretion disk. Additionally, the inferred continuum-emitting region sizes are larger than predictions based on standard thin-disk theory by a factor of ∼3.6 on average. The size-wavelength relation is consistent with that of a geometrically thin and optically thick accretion disk.