Reverberation mapping of high-mass and high-redshift quasars using gravitational time delays

Mass estimates of black holes (BHs) in the centers of Active Galactic Nuclei (AGN) often rely on the radius-luminosity relation. However, this relation, usually probed by reverberation mapping (RM), is poorly constrained in the high-luminosity and high-redshift ends due to the very long expected RM lag times. Multiply imaged AGN may offer a unique opportunity to explore the radius-luminosity relation at these ends. In addition to comprising several magnified images enabling a more efficient light-curve sampling, the time delay between multiple images of strongly lensed quasars can also aid in making such RM measurements feasible on reasonable timescales: If the strong-lensing time delay is, for example, of the order of the expected RM time lag, changes in the emission lines in the leading image can be observed around the same time as the changes in the continuum in the trailing image. In this work we probe the typical time-delay distribution in galaxy-cluster lenses and estimate the number of both high-mass ($\sim10^9-10^{10}$ M$_{\odot}$), and high-redshift ($z\gtrsim4-12$) quasars that are expected to be strongly lensed by clusters. We find that up to several dozen thousand M$_{BH}\sim10^{6}$-$10^{8}$ M$_{\odot}$ broad-line AGN at $z>4$ should be multiply imaged by galaxy clusters and detectable with JWST, hundreds with Euclid and several thousands with the Roman Space Telescope, across the whole sky. These could supply an important calibration for the BH mass scaling in the early Universe.