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arxiv: 2605.03577 · v1 · submitted 2026-05-05 · 🌌 astro-ph.GA

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Optical Variability Structure Function of Low-Luminosity AGN using ATLAS Lightcurves

Ashley Hai Tung Tan , Christian Wolf , Neelesh Amrutha , Christopher A. Onken , John L. Tonry , Rachel Webster
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Pith reviewed 2026-05-07 15:33 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords AGN variabilitystructure functionlow-luminosity AGNblack hole massoptical lightcurvesSeyfert galaxiesATLAS survey
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The pith

The slope of optical variability in low-luminosity AGN increases with black hole mass.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper measures the ensemble structure function of optical flux changes in 246 nearby low-luminosity AGN using eight years of ATLAS lightcurves. The slope of the structure function rises steadily with black hole mass, from about 0.1 at 10^6.5 solar masses to 0.3 at 10^8 solar masses, while the amplitude anticorrelates with luminosity. Spectra taken 20 years apart show the structure function continues rising on decadal timescales with no breaks, and the overall pattern suggests extinction is not the main factor separating Seyfert subtypes.

Core claim

We characterise the ensemble variability structure function of low-luminosity AGN at z < 0.1 and find that its slope depends on black hole mass, increasing from ∼0.1 at log M_BH/M_⊙ ∼6.5 to ∼0.3 at log M_BH/M_⊙ ∼8. Contrary to some earlier work, we do not find breaks in the SF, and two-epoch spectra taken 20 years apart suggest that the SF keeps rising into decadal timescales. In addition, we measure an anticorrelation of the amplitude with the luminosity and a positive correlation with the black hole mass. The variability behaviour also suggests that extinction is not the main driver of the variety in Seyfert subtypes.

What carries the argument

The ensemble structure function of the optical lightcurves, which tracks how variability amplitude grows with time separation and is compared across bins of black hole mass and luminosity after host-AGN decomposition.

Load-bearing premise

The host-AGN decomposition on recent spectra accurately isolates the variable AGN flux from the constant host galaxy contribution without introducing systematic biases.

What would settle it

A larger sample or longer baseline that shows either a clear break in the structure function at some timescale or no dependence of slope on black hole mass.

Figures

Figures reproduced from arXiv: 2605.03577 by Ashley Hai Tung Tan, Christian Wolf, Christopher A. Onken, John L. Tonry, Neelesh Amrutha, Rachel Webster.

Figure 1
Figure 1. Figure 1: A spectrum decomposition of g0029368-173830 using BADASS3. The top panel shows the spectrum with the fitted components as detailed in the legend. Additional lines indicate the narrow [NII] and [SII] lines. The bottom panel shows the residuals and the noise. 42.0 42.5 43.0 43.5 44.0 44.5 45.0 log L5100,total [erg/s] −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 log ( L5100,host/L5100,AGN) Shen+11 This work view at source ↗
Figure 2
Figure 2. Figure 2: The flux ratio of the host galaxy and AGN at rest-frame 5100Å plotted against the total luminosity. A line indicates the relation by Shen et al. (2011). The spectrum decomposition results fit the relation on average. 3.1 Calibrating AGN parameters using photometry and lightcurves One risk with using a single spectrum to measure AGN parameters such as the luminosity and black hole mass is that weather condi… view at source ↗
Figure 4
Figure 4. Figure 4: The one-day stacked ATLAS difference lightcurves of g0029368-173830 (top panel) and NGC4395 (bottom panel). These lightcurves are relative to the mean brightness of the AGN and the nuclear host component. The vertical line indicates the date of the wallpaper changes at MJD 58882. the 6dFGS spectra for a spectral comparison (Amrutha et al. 2024; Amrutha et al. 2026). We integrate the spectra over the ATLAS … view at source ↗
Figure 5
Figure 5. Figure 5: A summary of the calibration process described in Section 3.1. 3.2 Subtracting the host component from lightcurves The median ATLAS-o and ATLAS-c magnitudes obtained by using SkyMapper magnitudes, ATLAS difference lightcurves, and WiFeS spectra as described in 3.1 are used to shift the difference lightcurves to an absolute scale. We estimate the host galaxy flux by multiplying the host fraction by the medi… view at source ↗
Figure 6
Figure 6. Figure 6: The error distribution with SkyMapper 𝑟 and 𝑔 magnitudes. The error for the ATLAS-o lightcurves are estimated by binning the star-forming galaxies in bins of SkyMapper 𝑟 magnitudes, and likewise for ATLAS-c and SkyMapper 𝑔 magnitudes. The errors before and after MJD 58882 are estimated separately because they appear to differ significantly. SkyMapper magnitude bins and use linear interpolation to obtain th… view at source ↗
Figure 7
Figure 7. Figure 7: The top left and right panels show the SFs binned by only luminosity and only BH mass respectively. The bottom panels show SFs binned by both luminosity and BH mass. In the bottom left panel, all three SFs have similar BH mass and different luminosities, and vice versa for the bottom right panel. In the right panels, the break timescales predicted by B21 are indicated with arrows. timescale of ∼ 2 days. We… view at source ↗
Figure 8
Figure 8. Figure 8: Ensemble SF slopes, using data at 14 days< Δ𝑡< 100 days, vs. luminosity (left) and BH mass (right), compared to results from Tang et al. (2023) (crosses, representing their sample medians). Our slopes are below 0.5 (DRW, dotted line), increase with mass, and appear independent of luminosity. 7 8 9 log MBH/M 102 τbreak [days] Burke+21 (rest frame 2500˚A) Burke+21 (corrected for ATLAS-o) This work 42.6 42.8 … view at source ↗
Figure 9
Figure 9. Figure 9: A comparison of the fitted break timescales in bins of mass and luminosity compared to the scaling relation found byB21. The lower limits are indicated by arrows. Contrary to the predicted relation, we see no correlation of the break timescale with BH mass. and in a number of studies (e.g. Rakshit et al. 2020), it has been observed that Δ𝐿5100 ∼ Δ𝐿H𝛽. The blue points represent our cyan SFs, while the red c… view at source ↗
Figure 11
Figure 11. Figure 11: Variability structure functions in the cyan band binned by mass and luminosity. A power law fit (solid line) is extrapolated to Δ𝑡 ∼20 years (dashed line). Additionally, variability of broad emission lines from two-epoch H𝛽 observations is shown as crosses and their median as filled circles. 5.3 Dependence of variability amplitude on AGN parameters The best fit parameters to Equation 2 at Δ𝑡 = 50d in the … view at source ↗
Figure 12
Figure 12. Figure 12: The median colour of the variable emission component 𝑚𝑐 − 𝑚𝑜 plotted against the median log 𝐿H𝛽/𝐿[OIII] at Δ𝑡 centred at 30, 60, and 90, 120, 150, and 180 days. The arrows indicate the extinction slope derived from the Calzetti et al. (2000) curve with an 𝑅𝑉 of 2, 3, 4, and 5. The vertical dashed lines indicate the divisions between Seyfert subtypes, and the horizontal dotted lines indicate the median 𝑚𝑐 … view at source ↗
read the original abstract

The origin of the optical flux variability in active galactic nuclei (AGN) is largely unknown. Previous studies have correlated features of the variability structure function (SF) with AGN properties, though they mostly involved high-luminosity AGN to avoid biases from host galaxy flux. In this work, we characterise optical variability in a sample of 246 low-luminosity AGN at $z < 0.1$ from the Six-degree Field Galaxy Survey (6dFGS) through the ensemble variability SF. We use lightcurves from the Asteroid Terrestrial-impact Last Alert System (ATLAS) with a cadence of $\sim$2 days over eight years, and perform host-AGN decomposition on recent spectra to obtain the host fraction. We find that the slope of the SF depends on black hole mass, increasing from $\sim 0.1$ at $\log M_{\mathrm{BH}}/M_\odot \sim 6.5$ to $\sim 0.3$ at $\log M_{\mathrm{BH}}/M_\odot \sim 8$. Contrary to some earlier work, We do not find breaks in the SF, and two-epoch spectra taken 20 years apart suggest that the SF keeps rising into decadal timescales. In addition, we measure an anticorrelation of the amplitude with the luminosity and a positive correlation with the black hole mass. The variability behaviour also suggests that extinction is not the main driver of the variety in Seyfert subtypes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript analyzes the ensemble structure function (SF) of optical variability in 246 low-luminosity AGN at z < 0.1 from the 6dFGS survey, utilizing ATLAS light curves with approximately 2-day cadence over 8 years. Host-AGN decomposition is performed on recent spectra to isolate the AGN contribution. Key findings include a black hole mass-dependent SF slope increasing from ~0.1 at log(M_BH/M_⊙) ~6.5 to ~0.3 at ~8, absence of breaks in the SF with evidence for continued rise on decadal timescales from two-epoch spectra, an anticorrelation of SF amplitude with luminosity, and a positive correlation with black hole mass. The variability is also interpreted as indicating that extinction is not the primary cause of differences in Seyfert subtypes.

Significance. If the reported trends are robust, this work fills an important gap by characterizing variability in the dominant low-luminosity AGN population, which has been understudied due to host contamination. The mass-dependent SF slope, lack of breaks, and extension to decadal timescales provide empirical constraints on accretion disk models and the origin of optical variability. The large sample and long baseline from ATLAS are strengths, offering better statistics than many prior studies focused on high-luminosity objects.

major comments (2)
  1. The host-AGN spectral decomposition (described in the methods section following sample selection): All central claims—the M_BH-dependent SF slope rising from ~0.1 to ~0.3, amplitude correlations with luminosity and M_BH, and absence of breaks—depend on accurate isolation of the variable AGN flux after subtracting the constant host contribution. The manuscript reports the decomposition procedure but provides no Monte Carlo validation on simulated spectra with known AGN/host ratios, nor cross-checks against independent photometric host fractions from imaging data. In this z < 0.1, low-luminosity regime where host light typically dominates, unquantified systematics that correlate with luminosity or M_BH would directly bias the ensemble SF measurements and derived trends.
  2. Results section (trends with M_BH and luminosity): The reported SF slopes and correlations lack quoted uncertainties, formal statistical tests (e.g., Spearman coefficients with p-values or bootstrap errors), and details on binning or sample sizes per M_BH bin. Without these, the quantitative claim that the slope increases from ~0.1 at log M_BH/M_⊙ ~6.5 to ~0.3 at ~8 cannot be fully assessed for robustness against sample variance or selection effects.
minor comments (3)
  1. Abstract: The sentence beginning 'Contrary to some earlier work, We do not find breaks' contains an erroneous capital 'W' in 'We'.
  2. Notation consistency: Black hole mass is written variously as log M_BH/M_⊙ and log(M_BH/M_⊙); adopt a single convention throughout, including in figure labels.
  3. Figure captions (variability plots): Captions should explicitly state the number of objects per bin, how errors on the ensemble SF are computed, and whether the plotted points include the host-subtracted AGN flux only.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and positive assessment of the work's significance. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: The host-AGN spectral decomposition (described in the methods section following sample selection): All central claims—the M_BH-dependent SF slope rising from ~0.1 to ~0.3, amplitude correlations with luminosity and M_BH, and absence of breaks—depend on accurate isolation of the variable AGN flux after subtracting the constant host contribution. The manuscript reports the decomposition procedure but provides no Monte Carlo validation on simulated spectra with known AGN/host ratios, nor cross-checks against independent photometric host fractions from imaging data. In this z < 0.1, low-luminosity regime where host light typically dominates, unquantified systematics that correlate with luminosity or M_BH would directly bias the ensemble SF measurements and derived trends.

    Authors: We agree that additional validation of the host-AGN decomposition is important to quantify potential systematics in this low-luminosity regime. In the revised manuscript, we will include Monte Carlo simulations on synthetic spectra with known AGN/host flux ratios to assess uncertainties and check for biases correlated with luminosity or black hole mass. We will also perform cross-checks against photometric host fractions from available imaging data for a subset of objects where such data exist. revision: yes

  2. Referee: Results section (trends with M_BH and luminosity): The reported SF slopes and correlations lack quoted uncertainties, formal statistical tests (e.g., Spearman coefficients with p-values or bootstrap errors), and details on binning or sample sizes per M_BH bin. Without these, the quantitative claim that the slope increases from ~0.1 at log M_BH/M_⊙ ~6.5 to ~0.3 at ~8 cannot be fully assessed for robustness against sample variance or selection effects.

    Authors: We acknowledge that the statistical robustness of the reported trends can be better quantified. In the revised manuscript, we will add bootstrap-derived uncertainties on the SF slopes and amplitudes, include formal Spearman rank correlation coefficients with p-values for the trends with M_BH and luminosity, and provide explicit details on the binning procedure along with the number of objects per M_BH bin to allow assessment against sample variance. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical measurements from data

full rationale

The paper reports direct statistical measurements of the ensemble structure function (SF) slope, amplitude, and lack of breaks from ATLAS lightcurves of 246 low-luminosity AGN, after subtracting host fractions derived from spectra. No equations, ansatzes, or derivations are present that could be self-referential or reduce claims to inputs by construction. Reported trends (SF slope increasing with M_BH, amplitude anticorrelating with luminosity) are observational results, not predictions or fitted quantities renamed as such. Self-citations, if any, are not load-bearing for any uniqueness theorem or central premise. The analysis is self-contained against external benchmarks with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper is purely observational and introduces no new free parameters, axioms, or invented entities; it relies on standard techniques for lightcurve analysis and spectral decomposition already established in the AGN literature.

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