Investigating the AGN variability timescale -- black hole mass relationship with Gaia, SDSS and ZTF

Active galactic nuclei (AGNs) exhibit variability in their luminosities with timescales that correlate with the mass of the black hole at the centre of the AGN. Presently, the empirical correlation lacks sufficient precision to confidently convert these timescales into black hole masses, especially at the low-mass end. To find more AGNs with timescale measurements, we study a very large catalog of AGNs from the Gaia Data Release 3 called GLEAN (Gaia variabLE AgN; 872228 objects). We identify GLEAN objects with optical spectra from the Sloan Digital Sky Survey DR17 and light curves from the Zwicky Transient Facility (ZTF) DR21. After fitting the light curves with a damped random walk model, we find that the GLEAN light curves have insufficient sampling to extract reliable amplitude and timescale measurements outside the range of 50-100 days. On the other hand, well-sampled ZTF light curves allow more accurate estimations of these parameters. The fractional variability amplitude is an effective, model-independent metric for measuring variability amplitude, but only when derived from high-quality light curves. We provide a catalog of 127 GLEAN AGNs with spectroscopic virial black hole masses, and variability amplitudes and timescales. Though we do not find any low-mass black holes in this AGN sample, we confirm a relationship between the damped random walk timescale and the black hole mass that is consistent with previous studies.

💡 Research Summary

This paper investigates the empirical relationship between active galactic nucleus (AGN) variability timescales and the masses of their central super‑massive black holes, with the goal of improving the precision of black‑hole mass estimates derived from variability. The authors start from the Gaia Data Release 3 (DR3) catalog of variability‑selected AGN, GLEAN, which contains 872 228 objects identified solely on the basis of Gaia photometric variability. They cross‑match GLEAN with the Sloan Digital Sky Survey Data Release 17 (SDSS DR17) to obtain optical spectra and with the Zwicky Transient Facility Data Release 21 (ZTF DR21) to acquire well‑sampled optical light curves.

The SDSS cross‑match yields 203 915 objects, of which 98.9 % are classified as QSOs, confirming the high purity of GLEAN. The remaining small fractions are galaxies, stars, or ambiguous classifications, but these are negligible for the present analysis. Black‑hole masses are derived from the SDSS spectra using standard virial estimators based on the widths of H β, Mg II, and C IV emission lines, adopting the calibrations of Wu & Shen (2022).

Variability analysis is performed with a damped random walk (DRW) model, equivalent to a CARMA(1,0) process. The authors employ the Python package taufit, which uses Markov Chain Monte Carlo sampling to infer three parameters: the DRW amplitude (β_DRW), the characteristic relaxation timescale (τ_DRW = 1/α₁), and an excess white‑noise term (σ_n). Following Burke et al. (2021, hereafter B21), they impose four reliability criteria on τ_DRW and β_DRW: (1) the light‑curve baseline must exceed ten times τ_DRW, (2) the average cadence must be shorter than τ_DRW, (3) the signal‑to‑noise ratio must be sufficient, and (4) the reduced χ² of the fit must be acceptable.

When applied to the Gaia light curves, these criteria reveal a severe limitation: the irregular sampling and relatively long cadence of Gaia (spanning roughly three years with ≈20–30 points per source) allow reliable DRW fits only for timescales in the narrow range of 50–100 days. Outside this window, τ_DRW and β_DRW become poorly constrained or biased. In contrast, ZTF provides densely sampled light curves (daily to a few‑day cadence) over comparable baselines, satisfying all four criteria for the vast majority of sources. Consequently, ZTF‑based DRW parameters are deemed trustworthy, while Gaia‑only results are used only as a sanity check.

From the combined dataset, the authors isolate a high‑quality subsample of 127 AGN that possess (i) a reliable ZTF light curve, (ii) a spectroscopic virial black‑hole mass, and (iii) DRW parameters meeting the B21 reliability thresholds. All objects in this final sample have black‑hole masses above 10⁶·⁷ M⊙, with a distribution peaking near 10⁹ M⊙; no low‑mass (10⁴–10⁶ M⊙) AGN are present. This reflects the intrinsic bias of GLEAN toward luminous, high‑mass quasars, as well as the detection limits of both Gaia and ZTF for low‑amplitude variability.

Plotting log τ_DRW against log M_BH for the 127 AGN reproduces the previously reported positive correlation. The best‑fit slope (≈0.5) and intercept are consistent with B21 and with the extension by Wang et al. (2023), which added dwarf‑galaxy AGN in the 10⁶–10⁷ M⊙ regime. The authors therefore confirm that, at least for the super‑massive regime, the DRW timescale is a robust proxy for black‑hole mass.

The paper concludes with several key points: (1) Gaia‑only light curves lack the cadence and baseline required for precise DRW timescale measurements, limiting their utility for mass estimation; (2) high‑cadence surveys such as ZTF are essential for reliable DRW modeling; (3) the τ–M_BH relation is well‑established for massive AGN but remains poorly constrained at low masses due to selection effects and the limited sensitivity of current variability surveys; and (4) future time‑domain facilities (e.g., LSST/Rubin Observatory) with deeper magnitude limits and nightly cadence will be crucial to extend variability‑based mass estimates into the low‑mass regime, potentially providing an independent method for identifying intermediate‑mass black holes in dwarf galaxies.