Erratum: “Robust Absolute Solar Flux Density Calibration for the Murchison Widefield Array” (2022, ApJ, 927, 17)

In the published article, we presented a robust solar ﬂ ux density calibration method for solar observations with the Murchison Wide ﬁ eld Array ( MWA; Tingay et al. 2013; Wayth et al. 2018 ) . At the MWA, two orthogonal dipoles measure voltages, V = ( V X , V Y ) , of the orthogonal electromagnetic signal from the sky, e = ( e θ , e f ) , incident on it. e is mapped to V through a 2 × 2 primary beam Jones matrix, E , as ( Sokolowski et al. 2017 )

In the published article, we presented a robust solar flux density calibration method for solar observations with the Murchison Widefield Array (MWA; Tingay et al. 2013;Wayth et al. 2018).At the MWA, two orthogonal dipoles measure voltages, V = (V X , V Y ), of the orthogonal electromagnetic signal from the sky, e = (e θ , e f ), incident on it.e is mapped to V through a 2 × 2 primary beam Jones matrix, E, as (Sokolowski et al. 2017) where E xθ and E xf are the primary beam response of the X polarization toward θ and f directions on the sky, and E yθ and E yf are the primary beam response of the Y polarization toward θ and f directions on the sky.Stokes I primary beam is then given as In the published article, the off-diagonal components of the primary beam Jones matrix, E xf and E yθ , were not included, and the Stokes I primary beam was incorrectly defined as The missing terms in the definition of Stokes I led to an error in the estimates of the flux scaling parameters, referred to as F ref and amp(B ref ) in the published work.This erratum corrects this error and provides updated values of these parameters.Table 2 in the published article presents the coefficients of the best-fit polynomial to F ref and amp(B ref ).As the numerical values of these parameters have changed, the updated polynomial coefficients are provided in the revised Table 2 here. Figures 4, 5, 6, and 7  1."Using all sources at 80 MHz, the inverse variance weighted mean of F ref (ν) is found to be 62.4 ± 0.9" in Section 3.1 of the published article should become "Using all sources at 80 MHz, the inverse variance weighted mean of F ref (ν) is found to be 124.2± 2.7." 2. "This approach yields an F ref (ν) of 62 ± 2 at 80 MHz" in Section 3.1 of the published article should be replaced by "This approach yields an F ref (ν) of 125.6 ± 4.9 at 80 MHz." 3. "As is evident from this figure, it does not show a systematic trend with frequency, and it has a mean and rms of 44 and 4, respectively, for 10 dB attenuation" in Section 3.4 of the published article should be replaced by "As is evident from this figure (Figure 7 in the erratum), it does not show a systematic trend with frequency, and it has a mean and rms of −10.25 dB and 0.2 dB, respectively, for 10 dB attenuation." In addition, the published article does not specifically mention the need to correct for the so-called digital gains used during the observations.It is important to correct these digital gains and the easiest way to ensure this is to switch on the relevant flag when downloading the data from the MWA All Sky Virtual Observatory (ASVO). 6hese corrections do not change the main conclusion or the method of flux calibration described in the published article in any manner.
The Astrophysical Journal, 955:83 (3pp), 2023 September 20 https://doi.org/10.3847/1538-4357/acf30d Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
in the published article either show or depend on the values of F ref and amp(B ref ) and hence need to be revised as well.Figures 4-7 in this erratum present the corresponding updated figures.The change in the numerical values of F ref and amp(B ref ) also leads to changes in numerical values of various other parameters mentioned in the following sentences.

Figure 4 .
Figure 4.The locations of the subset of detected sources from the observation on 2014 May 4 used for determining F ref (ν) are shown by colored dots.The colors of the dots denote their flux-scaling factor determined for each of the sources, and the primary beam gain at those locations is shown by the background gray scale.The arrows mark the shift of these sources from their GLEAM catalog positions, multiplied by a factor of 15 to make them visible.The location of the Sun is shown by a blue cross mark.

Figure 5 .
Figure 5. Left panel: estimated F ref (ν) against the logarithm of GLEAM flux density, ( ) F log 10 cat , for individual sources at 80 MHz.Middle panel: histogram of reference flux-scaling factors, F ref (ν).Right panel: histogram of F ref (ν) obtained from random sampling.The black solid line shows the median scaling factor, and the red dashed lines show the 1σ uncertainty.

Figure 6 .
Figure 6.Left panel: the reference flux-scaling factor, F ref (ν), obtained for different observations.The black line shows the fitted polynomial.Right panel: mean reference bandpass amplitude, amp(B ref ), for 2014 July 12.

Figure 7 .
Figure 7. Variation of A ref , which is the inverse of the product of F ref (ν) and n ( ( )) B amp ref 2 with frequency.