Stacked Reverberation Mapping of High Redshift Quasars in DESI. I. Feasibility Analysis

Rahma Alfarsy, R. E. A. Canning, Eva-Maria Mueller, Jessica Aguilar, Steven Ahlen, David Alexander, Davide Bianchi, David Brooks, Peter Clark, Todd Claybaugh, Andrei Cuceu, Tamara Davis, Axel de la Macorra, Saisrinivas Dhavala, Victoria A. Fawcett, Benjamin Floyd, Andreu Font-Ribera, Jaime Forero-Romero, Enrique Gaztañaga, Wei-Jian Guo, Gaston Gutierrez, Klaus Honscheid, Richard Joyce, Stephanie Juneau, David Kirkby, Theodore Kisner, Anthony Kremin, Claire Lamman, Martin Landriau, Laurent Le Guillou, Paul Martini, Hugh McDougall, Aaron Meisner, Ramon Miquel, John Moustakas, Seshadri Nadathur, Nathalie Palanque-Delabrouille, Zhiwei Pan, Swayamtrupta Panda, Ignasi Pérez-Ràfols, Francisco Prada, Ragadeepika Pucha, Graziano Rossi, Eusebio Sanchez, David Schlegel, Michael Schubnell, Tom Shanks, Małgorzata Siudek, David Sprayberry, Gregory Tarlé, Benjamin Alan Weaver, Hu Zou

First listed 2026-07-27 | Last updated 2026-07-23

Abstract

The broad line region of quasars has long been probed by reverberation mapping techniques that measure time lags between continuum and broad emission line variations. Stacked reverberation mapping has been proposed as a less observationally expensive alternative to traditional methods. This ensemble approach also reduces biases from small-number statistics. The Dark Energy Spectroscopic Instrument (DESI) is conducting the most extensive spectroscopic survey of quasars to date. We create mock light curves emulating expected DESI quasar observations at redshifts $1.48<z<5.2$ and luminosities $ 44.68 \leq \log L_{1350} λ/ \mathrm{erg\,s^{-1}} \leq 45.99 $ to test stacked reverberation mapping feasibility using sparse spectroscopic data paired with well-sampled photometric data. The pipeline, using the lag estimation code JAVELIN, successfully recovers the simulated C IV lags within one sigma of the true values using spectroscopic light curves composed of only a few spectral epochs (2-10) with irregular cadences. We investigate how observational factors, including C IV flux error magnitude, number of stacked quasars, and spectral epoch count, affect performance. This work motivates a pathway for future stacked reverberation mapping projects with large scale spectroscopic surveys of quasars having $\geq 2$ spectroscopic observations. Our results suggest an economical alternative for constraining and extending the radius-luminosity relation to higher redshifts and luminosities. Subsequently, this relation can be employed more reliably in single-epoch black hole mass measurements and quasar cosmology in these distant regimes.

Short digest

This feasibility study asks whether DESI’s sparse repeat spectroscopy can support stacked reverberation mapping of high-redshift quasars when paired with well-sampled ZTF continuum light curves. Mock C IV light curves spanning 1.48 < z < 5.2 show that a JAVELIN-based pipeline can recover ensemble lags within 1σ of their input values even when individual quasars have only 2–10 irregular spectroscopic epochs, because stacking turns noisy, multimodal single-object posteriors into a clear population signal. The recovered C IV radius–luminosity relation closely follows the input relation, offering a practical route to extend its calibration into the luminous, distant-quasar regime relevant for single-epoch black-hole masses and quasar cosmology. The key operational constraint is temporal leverage: a spectroscopic baseline of at least a few hundred days, comparable to the observed lag, matters more for recovery than simply adding epochs, while gains from larger stacks level off beyond roughly 450 quasars.

Key figures to inspect

• Figure 4. This defines the simulated DESI C IV reverberation-mapping sample in luminosity and redshift, including the ZTF r-band limit and the population-balanced luminosity-redshift bins that underpin every stacked measurement.
• Figure 13. This is the central end-to-end result: the radius–luminosity relation recovered from the DESI-like mock stacks agrees with the Hoormann et al. input C IV relation, directly supporting the paper’s proposed application.
• Figure 17. This figure shows why stacking works despite unreliable individual lag posteriors: the ensemble peak strengthens as more quasars are combined, while the lag-recovery improvement plateaus beyond about 450 objects.
• Figure 19. This diagnostic isolates the dominant observing requirement. Accurate stacked lags require spectroscopic observations spread over a baseline of at least several hundred days, whereas adding more spectral epochs has a weaker effect if that baseline is too short.