Erratum: ``An Extensive Collection of Stellar Wind X-Ray Source Region Emission Line Parameters, Temperatures, Velocities, and Their Radial Distributions as Obtained from Chandra Observations of 17 OB Stars'' (ApJ, 668, 456 [2007])

Type Journal Article
Names W. L. Waldron, J. P. Cassinelli
Publication The Astrophysical Journal
Volume 680
Issue 2
Pages 1595-1602
Date June 1, 2008
Short Title Erratum
Library Catalog NASA ADS
Abstract The major objective of the paper was to provide a detailed tabulation of the observed HETGS X-ray emission-line flux ratios. We presented the MEG and HEG He-like f/i line ratios, the H-like to He-like (H/He) line ratios, and the He-like G-ratios. The stellar wind spatial locations of the X-ray sources were derived from the f/i ratios, and their associated X-ray temperatures were obtained from the H/He ratios (THHe). This information was used to verify the correlations between Rfir and Rτ=1 (Fig. 6) and THHe and Rfir (Fig. 8). However, we have realized that some of our tabulated uncertainties for these line ratios were underestimated, primarily for those lines with low-S/N data. Hence, the primary purpose of this erratum is to provide a tabulation of the corrected line ratios and their uncertainties. The details of our line fitting procedure are discussed in § 3.3. All uncertainties were determined using standard χ2 statistics (e.g., P. R. Bevington, 1969, Data Reduction and Error Analysis for the Physical Sciences [New York: McGraw-Hill]). First, we would like to clarify a statement in § 3.3 (second paragraph), which states that all parameter uncertainties were determined from 90% confidence regions, but in actuality all uncertainties were established using 68% confidence regions. With regards to the main point of this erratum, we found that our algorithm for determining the χ2 covariance matrix which is used to determine the uncertainties of the fitting parameters had an indexing error in the coding logic which produced errors in some of the off-diagonal terms. From our detailed examination of the code, we found that certain cases were especially vulnerable to this coding error, in particular, those cases where the χ2 normalization ranges were large (i.e., low-S/N data). This code correction has also produced changes in some of the line ratios and their derived quantities (e.g., Rfir and THHe). The algorithm has been corrected and the affected Tables (Tables 3, 4, 5, 6, and 7) have been updated and are given in corrected form in this erratum. We also corrected a few entries that were originally tabulated incorrectly, and some data were removed, as they did not satisfy our S/N criterion, i.e., the HEG S XV f/i data for ζ Ori, the MEG S XV f/i data for ζ Oph, and the HEG Mg XI and Si XIII f/i data for Cyg OB2 No. 9. As discussed in § 3.1, we stated that if a reasonable flux had been established, these results would be used only for estimating line ratios that provide interesting limits. However, the meaning of a ``reasonable`` flux limit was unclear; the criterion used is that the observed total net counts from all three He-like fir lines must have a S/N>=3. We also need to clarify the significance of blank entries in our tables. The blanks just indicate that the given line ratio has either an unphysical result that produces an anomalously large uncertainty, or did not satisfy our He-like S/N>=3 criterion. An example of an unphysical result is when the fitting procedure predicts an He-like i-line flux that is too small. This occurs primarily in low-S/N high-energy He-like fir lines, where the effects of line overlap can lead to a poor determination of the i-line. In addition, we would like to clarify why the relative uncertainties in Rfir are typically smaller than the corresponding f/i relative uncertainties. As shown in equation (2) of the paper, for φ/φC>1 and ne∞), and these Rfir values are tabulated as lower limits; and (5) for those cases where the H/He uncertainty is greater than the H/He ratio, upper limits on THHe are presented. The two key figures of the paper (Figs. 6 and 8) have also been corrected here. In these corrected figures only data with finite limits on Rfir and THHe are plotted, i.e., data with just lower limits on Rfir and upper limits on THHe are not shown. For clarity, we also chose not to display any Rfir data where the uncertainty is >10R*. The impact of these changes in the other figures that depend on the new derived Rfir and uncertainties (Figs. 7 and 9) are found to show minimal differences from the original results. However, we did find an erroneous high-temperature data point in Figure 9 at VO(Rfir)/v∞~0 and Urel(THHe)/v∞~0.82, which should be ignored. This same data point at low Rfir was also in the original Figure 8 for the giants in both the MEG and HEG plots, and it has been removed from the corrected Figure 8 given here. The source of this data point was traced to the star γ Vel, originally considered in our analysis, but was dropped from our study due to its highly unusual X-ray spectra, which were deemed inappropriate for this study of ``normal'' OB stars. We have confirmed that no other data points from γ Vel were present in any of the original plots. We would also like to add a comment concerning the importance of obtaining high-S/N HEG data as illustrated by comparing the S XV MEG and HEG determined f/i ratios for θ1 Ori C. This is a clear example of how line overlap, caused by either the physical line width or the energy resolution capabilities of the instrument, can lead to larger uncertainties. Although for this case both the MEG and HEG do have comparable S/N data, the MEG data had significant line overlap produced by the best-fit line width and lower energy resolution of the MEG, whereas in the HEG data the S XV fir were resolved, leading to a significant reduction in the uncertainty. In general, comparisons of these new derived quantities with the original tabulated data show that the largest differences are seen in the uncertainties, primarily the uncertainty results for O VII and S XV and any other low-S/N lines. In addition, there are minor changes evident in some of the f/i ratios, the H/He ratios, and the G-ratios. In addition, the newly tabulated data and the reproduced Figures 6 and 8 indicate that the fundamental results discussed in the paper have not changed, and these corrections have not altered any of the conclusions discussed in the paper. We wish to thank Maurice Leutenegger for his communication concerning the specific details of our line-fitting approach. This inquiry motivated us to reexamine all aspects of our line fitting algorithms, whereupon we found the above-mentioned coding mistake in the line flux uncertainties.
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