Erratum: “Confronting a Thin Disk-wind Launching Mechanism of Broad-line Emission in Active Galactic Nuclei with GRAVITY Observations of Quasar 3C 273” (2023, ApJ, 953, 184)

in Active Galactic Nuclei with GRAVITY Observations of Quasar 3C 273” (2023, ApJ, 953, 184) Kirk Long , Jason Dexter , Yixian Cao, Ric Davies , Frank Eisenhauer, Dieter Lutz , Daryl Santos, Jinyi Shangguan , Taro Shimizu, and Eckhard Sturm 1 Department of Astrophysical & Planetary Sciences, JILA, Duane Physics Bldg., 2000 Colorado Ave., University of Colorado, Boulder, CO 80309, USA; kirk.long@colorado.edu 2 Max Planck Institute for Extraterrestrial Physics, Giessenbachstraße 1, 85748 Garching, Germany Received 2023 August 30; published 2023 September 20


Correcting Our Previously Published Values for r
At the end of Section 2 (Methods) of the published article we incorrectly derived the mean size (as weighted by the intensity of line emission) of the broad-line region (BLR) disk, r, by integrating only over the radial coordinate instead of the area of the disk.The correct integral thus introduces an extra factor of r we omitted previously: .Comparing this to the r previously published, we can obtain a correction factor (by keeping r min and r max fixed) for what r was actually fit, without needing to redo the fitting itself.
We present our fit results for r in units of r s ; however, in fitting to the phase data we must ascribe an angular size of the model on the sky, which can be obtained by multiplying our code coordinates by the model r s and dividing by the assumed distance to 3C 273 of ∼550 Mpc.We have also noticed a typo where this happens in the published model code (line 172 of functions.jl in Long & Dexter 2023) where this angular size was accidentally calculated using r g instead of r s , which means the fit produced models that were twice as large as they needed to be to correctly fit the data (since the size we report is in r s , not r g ).Accounting for both of these errors gives a correction factor of Our fit converged to a value of r fac = 47, which means that on average our published values for r are underestimated by a factor of 1.3 from these errors.
Here we provide a corrected version of Table 1, where we show the corrected values for our fit to the average BLR size.No other parameters from the fit are impacted by this update, and the quality of the fit remains identical; the values for r were simply calculated and reported incorrectly.The labels on Figure 9 in the published article (MCMC distributions) for r are thus also slightly off, but we do not include an update here as the shape of the distribution is the same.No other figures are impacted by this change, as the line profiles are normalized (the radial scaling between r s and r g is the same) and the centroid map had this error applied consistently (used r g in both the fit and in producing the figure).

Implications
In Section 4 (Discussion) of the published article we compared our inferred BLR size to that of the size inferred from previous cloud modeling work, noting that the best-fit solution for the disk-wind model was a factor of ∼2 smaller than the cloud model size.With the update correcting the errors in calculating the BLR size described above, our sizes are now slightly larger than previously published, but this statement about the size difference between the disk-wind and cloud models in the discussion remains true.If we convert our fit values for M BH and r to angular sizes we obtain = - + r 23 14 3.0 μas.This is larger than the previous value in our discussion (∼17 μas) but still ∼2 times smaller than the characteristic size of the BLR inferred from the clouds (∼50 μas).Thus, this error in the calculation of r does not substantially change the results or discussion in the published article.
r) ∝ r −5/2 as shown in the published article.Keeping the definition of =