Using Molecular Lines to Determine Carbon and Nitrogen Abundances in the Atmospheres of Cool Stars

Round 1

Reviewer 1 Report

The paper “Using molecular lines...” by Tatiana Ryabchikova and others suggests new method to determine abundances of carbon and nitrogen in the atmospheres of the solar-like stars. They argue that atomic spectral lines, which were used for this purpose, are often blended, in particular, for nitrogen, while the analysis based on the molecular spectra of C₂ and CN molecules is less sensitive to possible overlaps with other lines. Analysis of the molecular spectra in question is based on the resent improvement of the data on the spectra of C₂ and CN molecules in the VALD database. The authors demonstrate performance of their method on several examples and compare their results with the previous analyses, where atomic lines were used. In all considered cases new results agree with the previous ones, so the authors conclude that the method is working both for carbon and nitrogen.

 The paper may be interesting for astrophysicists and reports new results. However, in the present form it is not fully convincing and needs some further editing. Two points, which need additional clarification are listed below.

 1.      In the abstract the authors write that their main goal is to improve the accuracy for the abundances of nitrogen, which is very important for stellar astrophysics. They argue that for nitrogen the method based on atomic lines is not very accurate, because there are not many lines suitable for the analysis and they are often blinded, as demonstrated by Fig. 1. However, the results presented in Table 2 show that the accuracy of the new molecular method for nitrogen abundances is lower than that of the previous atomic method. At the same time, the accuracy of the new method for the carbon abundances is higher. This seems to disagree with the discussion in the paper. Thus, I am not convinced that suggested method can indeed be used to improve the data for nitrogen, as claimed by the authors.

2.      In the left panel of Fig. 2 there is significant deviation between the synthetic and observed spectra around 5162.7 Angstroms. The authors do not discuss this discrepancy and how it may affect the accuracy of their method. Are there still some missing C₂ lines in the VALD database, or this difference is caused by the lines of other species?

 When the authors clarify these points, I think the paper will be suitable for the special issue of Atoms devoted to atomic and molecular databases.

Author Response

Review 1: Q1. In the abstract the authors write that their main goal is to improve the accuracy for the abundances of nitrogen, which is very important for stellar astrophysics. They argue that for nitrogen the method based on atomic lines is not very accurate, because there are not many lines suitable for the analysis and they are often blinded, as demonstrated by Fig. 1. However, the results presented in Table 2 show that the accuracy of the new molecular method for nitrogen abundances is lower than that of the previous atomic method. At the same time, the accuracy of the new method for the carbon abundances is higher. This seems to disagree with the discussion in the paper. Thus, I am not convinced that suggested method can indeed be used to improve the data for nitrogen, as claimed by the authors. Reply: Indeed, SME error estimates (including that for N abundance in Table 2) are known to be overestimated because the cumulative distribution for a single free parameter is derived from residuals of spectral fitting in all spectral points. This methods works best for parameters that indeed affect all points (e.g. Teff) and less well for parameters that affect only a small parts of the spectrum often leading to exaggerated estimate of uncertainty. Therefore, even intercomparison of uncertainties between carbon and nitrogen is not simple. This SME method assumes that the model errors rather than the measurement errors dominate the resulting uncertainties of free parameters. Model errors include data reduction glitches, errors in line data, neglected NLTE effects, imperfections of 1D model atmospheres etc. The alternative method in SME is a conventional assessment of the Least Squares fits uncertainties based the main diagonal of the covariance matrix. This method assumes that the model is perfect and on convergence the reduced chi^2 always reaches the value of 1. In reality when fitting many spectral lines simultaneously chi^2 never approaches this level and thus this estimate typically underestimates the uncertainties. The corresponding explanation is added in \section{Carbon and nitrogen abundance determination}. Note, that for stars cooler than the Sun it is much more difficult to use N 1 atomic lines because they become weaker while the overlapping CN bands become stronger, which makes deblending more problematic. Q2. In the left panel of Fig. 2 there is significant deviation between the synthetic and observed spectra around 5162.7 Angstroms. The authors do not discuss this discrepancy and how it may affect the accuracy of their method. Are there still some missing C2 lines in the VALD database, or this difference is caused by the lines of other species? Reply: There are many unidentified weak and even strong features in the solar and stellar spectra, therefore SME performs fitting to the carefully chosen spectral intervals called 'mask'. Our mask consists of 21 intervals with C_2 lines and 12 intervals with CN lines. The corresponding explanation is added to the text. An example of the full 5100-5177 region calculations with the marked mask intervals (yellow colour) is included as additional Figure. The same mask was used for all other spectra. Regions around 5162.7 Angstroms as well as few others with unidentified features are synthesised but not included in the fitting procedure and so they do not influence the final abundance results. Interval included in the fitting are now marked in Fig.2.

Author Response File: Author Response.docx

Reviewer 2 Report

Referee report on the paper entitled:
Using molecular lines to determine carbon and nitrogen abundances in the atmospheres
of cool stars
by: T. Ryabchikova, N. Piskunov, Y. Pakhomov
The SME code performs differently form most spectrum synthesis codes, in the sense
that it operates trying to fit full regions, and this is the basis of this paper. The paper is
well-presented. I have a few comments and corrections before acceptation.
Major comments:
1) The use of C 2 Swan bands in the region 5100-5200 Å is not that clean, given that
wavelength region 5162-5167 Å (as shown in Fig. 2) where C 2 lines are most prominent,
contains as well the well-known Mg 2 or Mgb indices. This region contains not only the
MgI triplet 5167.32, 5172.68, 5183.60 Å lines, but also MgH lines. In galaxies the important
behaviour of the the Mg 2 or Mgb indices is exactly the lowering of the continuum. The authors
should cite this and explain why and how they avoid the MgH and MgI lines correctly.
2) Please compare your results and methods with those by Asplund et al. 2021, A&A,
653, A141
Minor corrections:
1) Introduction, 1st line: Abundance of CNO elements −→ The abundance of CNO
elements, or Abundances of CNO elements
2) Introduction, 6th line: in circumstellar disk −→ in circumstellar disks or in a circum-
stellar disk
3) Introduction, 8th line: The differences −→ differences about what, please be explicit
4) Introduction, 12th line: abundance derived −→ abundances derived
5) Please write C 2 and not C −2 as given in the Conclusions.

Author Response

Review 2: Major comments: Q1) The use of C 2 Swan bands in the region 5100-5200 A is not that clean, given that wavelength region 5162-5167 A (as shown in Fig. 2) where C 2 lines are most prominent, contains as well the well-known Mg 2 or Mgb indices. This region contains not only the MgI triplet 5167.32, 5172.68, 5183.60 A lines, but also MgH lines. In galaxies the important behaviour of the the Mg 2 or Mgb indices is exactly the lowering of the continuum. The authors should cite this and explain why and how they avoid the MgH and MgI lines correctly. Reply: For clarity Fig.2 presents a small part of 5100-5200 A region to show places with the crowded and more intense lines of C_2. We do not avoid the MgIb lines as well as numerous (very weak in solar-like stars) MgH lines; they are included in spectrum synthesis. To illustrate that we have included an additional figure (new figure 2) showing 5100-5175 A spectral region from Solar Flux Atlas where small spectral intervals with relatively clean C_2 lines are marked. These intervals define the line mask used in the SME fitting procedure. Please, note that in this figure only 10% of the strongest transition are labelled. C_2 transitions are indicated as C2 1. MgH lines are present but not labelled because they are too weak. Observations and synthetic calculations are shown by black and red lines, respectively. Q2) Please compare your results and methods with those by Asplund et al. 2021, A&A,653, A141 Reply: The results and methods by Asplund et al. 2021, A&A, 653, A141 are the same as described in more details in the papers by Amarsi et al. (2019. 2020, 2021) cited in our paper. We add a corresponding sentence in Section "Discussion". In both works, Asplund et al. (2021) and Amarsi et al. (2021) a difference of 0.14 dex for N abundance obtained from atomic and molecular lines is reported. Their analysis is based on the measured equivalent widths of the blended N I features, while our analysis is based on detailed spectrum synthesis and it seems to resolve this inconsistency. We shortly discuss it in Section "Discussion". Minor corrections: Q1) Introduction, 1st line: Abundance of CNO elements -- The abundance of CNO elements, or Abundances of CNO elements Done. Q2) Introduction, 6th line: in circumstellar disk -- in circumstellar disks or in a circumstellar disk Done. Q3) Introduction, 8th line: The differences -- differences about what, please be explicit We added an explanation for the differences Q4) Introduction, 12th line: abundance derived -- abundances derived Done. Q5) Please write C 2 and not C -2 as given in the Conclusions. Corrected.

Author Response File: Author Response.docx