VAR-PZ: Constraining the Photometric Redshifts of Quasars using Variability

TL;DR

This work addresses the challenge of obtaining reliable photometric redshifts for large AGN samples by introducing VAR-PZ, a framework that leverages AGN variability modeled as a damped random walk with parameters $\tau$ and $SF_\infty$, including the effects of cosmological time dilation. By linking DRW parameters to rest-frame wavelength and luminosity, the authors generate variability-based redshift priors and combine them with traditional SED-based PDFs to form a joint redshift posterior. Validation on SDSS Stripe 82 data shows substantial reductions in outlier fractions (e.g., from ~32% to ~22% overall) and improved precision, while simulations indicate that Rubin LSST’s longer baselines and higher cadence could push outlier rates down to around 7% by survey end. The method offers a practical, modular enhancement to photo-$z$ pipelines for upcoming large-scale AGN surveys, with potential as a complementary tool alongside ML-based approaches and LF priors.

Abstract

The Vera C. Rubin Observatory LSST is expected to discover tens of millions of new Active Galactic Nuclei (AGNs). The survey's exceptional cadence and sensitivity will enable UV/optical/NIR monitoring of a significant fraction of these objects. The unprecedented number of sources makes spectroscopic follow-up for the vast majority of them unfeasible in the near future, so most studies will have to rely on photometric redshifts estimates which are traditionally much less reliable for AGN than for inactive galaxies. This work presents a novel methodology to constrain the photometric redshift of AGNs that leverages the effects of cosmological time dilation, and of the luminosity and wavelength dependence of AGN variability. Specifically, we assume that the variability can be modeled as a damped random walk (DRW) process, and adopt a parametric model to characterize the DRW timescale ($τ$) and asymptotic amplitude of the variability (SF$_\infty$) based on the redshift, the rest-frame wavelength, and the AGN luminosity. We construct variability-based photo-$z$ priors by modeling the observed variability using the expected DRW parameters at a given redshift. These variability-based photometric redshift (VAR-PZ) priors are then combined with traditional SED fitting to improve the redshift estimates from SED fitting. Validation is performed using observational data from the SDSS, demonstrating significant reduction in catastrophic outliers by more than 10% in comparison with SED fitting techniques and improvements in redshift precision. The simulated light curves with both SDSS and LSST-like cadences and baselines confirm that, VAR-PZ will be able to constrain the photometric redshifts of SDSS-like AGNs by bringing the outlier fractions down to below 7% from 32% (SED-alone) at the end of the survey.

Figures (10)

• Figure 1: Distribution of the parent-sample quasars in the luminosity (bolometric) and redshift space. The bolometric luminosities ($L_{\mathrm{bol}}$) of the quasars in this sample were estimated by Shen2011.
• Figure 2: The distribution of the variability parameters, SF$_\infty$ and $\tau$, in the observed frame, measured from the $ugriz$ bands as a function of rest frame wavelength. The coefficients of the Eq. \ref{['equation']} are calculated by fitting these values, corresponding to both the amplitude and timescale of variability. The dotted line represents the linear fit with slopes -0.456 and 0.19 for SF$_\infty$ and $\tau$, respectively.
• Figure 3: The heatmap illustrates the influence of observational cadence and baseline length (in SDSS seasons) on photometric redshift estimation metrics: the NMAD (top) as a measure of precision, and the outlier fraction (bottom). The color bar, presented on a logarithmic scale, maps these metrics such that regions depicting lower values correspond to the most promising observing conditions, yielding higher precision and a reduced fraction of outliers in photometric redshift predictions.
• Figure 4: Violin plot showing the median AGN variability timescale ($\tau$) estimated from M10 over the SDSS bands as a function of redshift. The dashed black line represents one-third of the SDSS baseline duration, showing the redshift-dependent threshold beyond which the condition $3\tau<\mathrm{baseline}$ is no longer satisfied. This requirement defines the redshift range over which VAR-PZ can constrain redshifts with the current data. The red and purple line represent one-third of the 5 and 10 year LSST baseline, respectively. LSST's enhanced sensitivity will enable the detection of fainter objects, resulting in lower overall timescale values ($\tau$) and consequently providing greater constraining power.
• Figure 5: Binned scatter diagrams comparing photometric redshifts derived from SED fitting using LRT, independently (top) and combined with our variability model (bottom), against spectroscopic redshifts. The dashed line represents the one-to-one correspondence between the axes.