<figure><img src="image_1.png" /></figure>

# Correction to: Characterizing X-ray, UV, and optical variability in NGC 6814 using high-cadence *Swift* observations from a 2022 monitoring campaign

by A. G. Gonzalez<sup>1,1*</sup> L. C. Gallo,<sup>1</sup> J. M. Miller,<sup>2</sup> E. S. Kammoun<sup>1,3,4,5</sup> A. Ghosh<sup>1</sup> and B. A. Pottie<sup>1</sup>

**Key words:** errata, addenda – accretion, accretion discs – galaxies: active – galaxies: individual: NGC 6814 – galaxies: Seyfert.

We recently published the paper ‘Characterizing X-ray, UV, and optical variability in NGC 6814 using high-cadence *Swift* observations from a 2022 monitoring campaign’ in Monthly Notices of the Royal Astronomical Society 527, 5569–5579 (2024). We have since discovered that an outdated Calibration Database (CALDB) version was erroneously used to process the *Swift* UVOT data in that work. We have reprocessed those data using the most recent CALDB version (20240201) and find that the original UV flux densities are significantly larger than those obtained with the new CALDB. Fortunately, the variability products (i.e. fractional variability, structure function, and interpolated cross-correlation function) of sections 3.1–3.3 remain consistent within the uncertainties reported in the original work due to the normalization processes that are performed when computing each product. section 3.4 (i.e. flux-flux analysis), however, changes, as do the related Discussion points and Conclusions that are based on that result. We present the updated results and interpretations using the reprocessed data below.

We performed the flux-flux analysis presented in section 3.4 of Gonzalez et al. (2024) following the exact same procedure, changing only the input light curves to the reprocessed ones. The updated results are shown in Fig. 1 and Table 1, where it can be seen that the UV fit parameters for the average flux [A(λ)] and RMS [R(λ)], and consequently computed intrinsic AGN variability spectrum [D(λ)] and constant (i.e. host galaxy) component [G(λ)], are ~1.6 times smaller on average than those in the original work. Now, the intrinsic AGN variability spectrum does not differ significantly from the expected F<sub>v</sub> ∝ λ<sup>-1/3</sup> of a standard accretion disc, except for in the U band. Fitting of the host galaxy component does not change due to the minimal effect of the updated CALDB version on the optical results, which dominate that fit.

We jointly fit the updated intrinsic AGN variability spectrum and time-averaged X-ray spectrum from the original work using KYNSED (Dovčiak et al. 2022) in XSPEC (Arnaud 1996) following the exact same procedure outlined in the Discussion of Gonzalez et al. (2024). While we fixed the black hole mass to M<sub>BH</sub> = 1.85 × 10<sup>7</sup> M<sub>☉</sub> in the original work, here we left it free to vary when fitting in order to achieve realistic X-ray luminosities that did not exceed the total disc luminosity.

<table><caption>**Table 1.** Flux–flux fit parameters for the average [A(λ)] and RMS [R(λ)] as well as computed values to isolate the AGN [D(λ)] and host galaxy [G(λ)] components, in units of mJy. The fit to all UVOT light curves yields χ<sup>2</sup><sub>v</sub> = 1.22.</caption><thead><tr><th rowspan="2">Waveband</th><th colspan="2">Fit parameters</th><th colspan="2">Computed values</th></tr><tr><th>A(λ)</th><th>R(λ)</th><th>D(λ)</th><th>G(λ)</th></tr></thead><tbody><tr><td>W2</td><td>3.75 ± 0.01</td><td>0.95 ± 0.01</td><td>3.95 ± 0.03</td><td>—</td></tr><tr><td>M2</td><td>4.36 ± 0.01</td><td>0.98 ± 0.01</td><td>4.06 ± 0.05</td><td>0.50 ± 0.07</td></tr><tr><td>W1</td><td>4.57 ± 0.01</td><td>0.84 ± 0.01</td><td>3.49 ± 0.04</td><td>1.25 ± 0.06</td></tr><tr><td>U</td><td>6.16 ± 0.01</td><td>0.98 ± 0.02</td><td>4.04 ± 0.05</td><td>2.33 ± 0.07</td></tr><tr><td>B</td><td>9.65 ± 0.02</td><td>0.79 ± 0.02</td><td>3.29 ± 0.07</td><td>6.53 ± 0.09</td></tr><tr><td>V</td><td>15.15 ± 0.04</td><td>0.70 ± 0.04</td><td>2.88 ± 0.12</td><td>12.42 ± 0.16</td></tr></tbody></table>

We note that we kept the colour-temperature correction factor fixed to f<sub>col</sub> = 1.7 as we found it to provide the best fit to the data, which was determined by following the procedure in appendix B of the original work. Moreover, when using the prescription of colour-temperature correction factor described by Done et al. (2012) the fit became worse at the >99 per cent confidence level. We were able to adequately fit the updated AGN SED (excluding the U band), finding a black hole mass of M<sub>BH</sub> = (9 ± 1) × 10<sup>6</sup> M<sub>☉</sub>, Eddington accretion rate of ṁ<sub>Edd</sub> = ṁ<sub>Edd</sub>/ṁ<sub>Edd</sub> = 0.035<sup>+0.019</sup><sub>-0.006</sub> where ṁ and ṁ<sub>Edd</sub> are the accretion rate and Eddington rate, and outer disc radius of R<sub>out</sub> ≳ 1800 r<sub>g</sub> as well as neutral, partially covering X-ray absorption consistent with what was reported in the original work. For these best-fitting parameters, we find that the dust sublimation radius (Baskin & Laor 2018) is R<sub>dust</sub> ≈ 1350 r<sub>g</sub> and that the self-gravity radius (Laor & Netzer 1989) is R<sub>sg</sub> ≈ 580 r<sub>g</sub>, which may suggest the former as a possible truncation mechanism of the outer accretion disc. The un-fit U band data exceed the predicted model flux by ~20 per cent.

Although the inter-band continuum lags found with the reprocessed data are consistent with those in the original work, we computed the predicted model lags using KYNXILTR (Kammoun et al. 2023) following the exact same procedure outlined in the Discussion of Gonzalez et al. (2024) now using M<sub>BH</sub> = 9 × 10<sup>6</sup> M<sub>☉</sub> as the input black hole mass. We find that with this lower mass ṁ<sub>Edd</sub> = 4<sup>+9</sup><sub>-3</sub> and R<sub>out</sub> = 2800 ± 800 r<sub>g</sub> best fit the lags when excluding the U band, parameters which yield R<sub>dust</sub> ≈ 5370 r<sub>g</sub> and R<sub>sg</sub> ≈

<footnote n="1"><sup>1</sup>Department of Astronomy and Physics, Saint Mary's University, 923 Robie Street, Halifax, NS B3H 3C3, Canada</footnote>

<footnote n="2"><sup>2</sup>Department of Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48109-1107, USA</footnote>

<footnote n="3"><sup>3</sup>IRAP, Université de Toulouse, CNRS, UPS, CNES, 9 Avenue du Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France</footnote>

<footnote n="4"><sup>4</sup>INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy</footnote>

<footnote n="5"><sup>5</sup>Dipartimento di Matematica e Fisica, Università Roma Tre, via della Vasca Navale 84, I-00146 Rome, Italy</footnote>

<footnote>*E-mail: adam.gonzalez@smu.ca</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Left: Flux–flux plots for all de-reddened and filtered UVOT flux density light curves. Colour-coded solid lines represent the best-fitting lines $F_v(\lambda, t) = A(\lambda) + R(\lambda)X(t)$, with fit parameters given in Table 1. The vertical grey dashed line represents the W2 zero crossing point, which is used to estimate the minimum host galaxy contribution in each other band. Right: Measured total [$A(\lambda)$] and RMS [$R(\lambda)$] spectra alongside the computed AGN [$D(\lambda)$] and host galaxy [$G(\lambda)$] spectra based on the best-fitting lines to the flux–flux plots in the left panel (all values given in Table 1). The expected accretion disc spectrum of $F_v \propto \lambda^{-1/3}$ is plotted alongside the RMS and AGN spectra as the dashed dark grey curves and has been scaled by the V-band flux of each. The Sc spiral template is shown as the solid light grey curve.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 2.** The lag–wavelength spectrum (top left) and AGN SED (top right; observed as dotted curves, intrinsic as solid curves) are shown as the black data points. Each panel in the top row displays the results from individually fitting the lag–wavelength spectrum (red) and SED (blue) with KYNXILTR and KYNSED, respectively. The relevant colour-coded fit statistics when fitting filled data points are shown in each panel of the top row, where the values in parentheses include the excluded empty data points in each panel. For the SED fits, the fit statistics for the UV/optical ($\chi^2$) and X-ray (C) data are shown separately, near the corresponding data. The bottom two rows display the colour-coded best-fitting model residuals corresponding to the SED and lag fits, respectively.</figcaption></figure>

4750 $r_g$, both of which are too large to explain the required outer disc truncation. The un-fit U band data exceed the predicted model lag by ~50 per cent.

The results of both fitting procedures are shown in Fig. 2, where we have also plotted the corresponding inter-band continuum lag and AGN SED model predictions as in the Discussion of Gonzalez et al. (2024). The results obtained using the reprocessed data make it clear that no extreme outer disc truncation is required by the data, as was reported in the original work. However, it remains that a standard accretion disc does not provide a self-consistent description of both the AGN SED and inter-band continuum lags. A significant contribution from the diffuse continuum emission in NGC 6814 seems a plausible explanation for the observed discrepancies.

## ACKNOWLEDGEMENTS

The authors would like to thank Hannah Cornfield and Keith Horne for contacting us about the UV flux discrepancy when using the updated CALDB.

## DATA AVAILABILITY

The data presented here are publicly available through the NASA HEASARC Archive (https://heasarc.gsfc.nasa.gov/docs/archive.htm l) and Swift observatory (https://www.swift.ac.uk/index.php) web-sites. The reprocessed light curves are available via the corresponding author (AGG) upon reasonable request.
REFERENCES

Arnaud K. A., 1996, in Jacoby G. H., Barnes J., eds, ASP Conf. Ser. Vol. 101, Astronomical Data Analysis Software and Systems V. Astron. Soc. Pac., San Francisco, p. 17

Baskin A., Laor A., 2018, MNRAS, 474, 1970

Done C., Davis S. W., Jin C., Blaes O., Ward M., 2012, MNRAS, 420, 1848

Dovčiak M., Papadakis I. E., Kammoun E. S., Zhang W., 2022, A&A, 661, A135

Gonzalez A. G., Gallo L. C., Miller J. M., Kammoun E. S., Ghosh A., Pottie B. A., 2024, MNRAS, 527, 5569

Kammoun E. S., Robin L., Papadakis I. E., Dovčiak M., Panagiotou C., 2023, MNRAS, 526, 138

Laor A., Netzer H., 1989, MNRAS, 238, 897

This paper has been typeset from a *TEX/LATEX* file prepared by the author.