Microlensing timescales and flux magnification probabilities of a sample of 204 lensed quasars

¹ Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111 Valparaíso, Chile
² Instituto de Astrofísica de Canarias, Vía Láctea S/N, La Laguna, 38200, Tenerife, Spain
³ Departamento de Astrofísica, Universidad de la Laguna, La Laguna, 38200, Tenerife, Spain

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 29 September 2025
Accepted: 4 May 2026

Abstract

Context. Quasar microlensing is a very useful tool in cosmology and astrophysics, as well as a source of uncertainty in certain investigations, such as the determination of the Hubble constant from lensed quasars. Microlensing probability and timescales have been studied statistically using the Einstein ring crossing time of an isolated mass as a reference scale.

Aims. Our goal is to extend the statistical analysis of microlensing to all currently known lensed quasars with the data currently available, while considering realistic optical depths and the gravitational effect of the lens galaxy. We take into account new observational results on quasar sizes and the peculiar velocities of lens galaxies.

Methods. We applied automatic lens modeling to the 204 systems available. For each image, we computed microlensing magnification maps and histograms.

Results. Using thin disk source sizes scaled to take into account recent measurements of accretion disk sizes, we find a mean source crossing time of 2.59 ± 0.07 years. The mean Einstein radius crossing time is 11.29 ± 0.05 years. When a fraction of mass in microlenses α = 0.2 is adopted, we find a good matching between the modeled histogram of mean microlensing magnifications for the images in our sample and the experimental histogram of microlensing magnifications.

Conclusions. From the modeling of microlensing magnification histograms, we estimated the average half-light radius of the quasar source, R_1/2 = 5.4 ± 2.7 light-days, and a lower limit to the mass fraction in microlenses, α ≥ 0.15. From the microlensing magnification maps, we find that a lensed quasar image has a mean probability of approximately 9% of being involved in a high-magnification event (Δm ≤ −0.32). We selected a group of images with the highest probabilities and the smallest crossing times.