Modeling the TESS Light Curve of Ap Si Star MX TrA

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comments to the Authors

 

The paper, titled 'Modelling the TESS light curve of Ap Si star MX TrA,' authored by Yury Pakhomov et al., presents their work on modelling the TESS light curve of Ap Si star MX TrA. The study uses models that account for the inhomogeneous surface distribution of various chemical elements. The resulting theoretical model, which incorporates the surface distribution of silicon, iron, helium, and chromium, successfully reproduces the observed TESS light curve with good accuracy. This confirms the significant role of these elements in influencing the photometric variations of MX TrA. Additionally, based on the synthetic light curves, the authors calculated the wavelength dependence of the amplitude of MX TrA's light variations and the phase of the maximum. This behavior could serve as a proxy for identifying Ap Si stars using far-UV band photometric observations.

 

Overall, the manuscript is well-structured and well-written, with solid analysis and results. I recommend acceptance for publication once the authors address the following comments or concerns:

 

1. In Section 2, when introducing the TESS data, please provide more details, such as which sector or sectors were used and whether the short or long cadence TESS light curve was analyzed. Given that multiple sectors of TESS data are available for MX TrA, if only one sector was used, please explain why other sectors were not included in the analysis. Additionally, consider discussing whether the inclusion of additional sectors would have impacted the results of the analysis.
2. Line 82, the formula of calculating m_TESS uses “SAP_FLUX”. Please confirm that it is indeed the SAP flux from the SPOC light curve that was used in the analysis. Note that SPOC also provides PDCSAP flux (Pre-search Data Conditioning SAP flux), which has long-term trends removed using Co-trending Basis Vectors (CBVs). PDCSAP flux typically results in cleaner data with fewer systematic trends.
   
   If the authors used PDCSAP flux, please verify that the formula in line 82 is still valid and replace "SAP_FLUX" with "PDCSAP_FLUX." If SAP_FLUX was indeed used, I encourage the authors to provide details on how they pre-processed the light curve to remove any systematic trends or other instrumental effects. Additionally, please include a discussion on whether using PDCSAP flux would have impacted the results of the analysis.
3. Fig. 2 is completely black.
4. Section 4.2, Line 219, when the authors claim that BD+00◦1659 is the slowly rotating twin of MX TrA, it would be beneficial to present the atmospheric parameters and chemical compositions of both stars side by side in a table for clearer comparison. Additionally, it might be useful for the authors to discuss whether the difference in rotation between the two stars could have any impact on the analysis results.

Other small issues:

1. Line 23, “4,5” -> “4, 5”, missing space between the comma and ‘5’. There are other similar cases of missing spaces between multiple reference numbers throughout the document. Please address these as well.
2. Line 32, missing space before and after the number of 1600. There are other similar cases of missing spaces in math mode texts throughout the document.. Please address these as well.
3. Line 34, “Combination” -> “The combination”
4. Line 36, “spectral” -> “the spectral”
5. In lines 57 and 58, the symbols in the parentheses are not yet defined. Please ensure that all symbols are defined before they are used. Additionally, there are missing spaces, such as before and after the "=" and the plus-minus ($\pm$) signs. Please correct these formatting issues.
6. Line 77, the acronym "TESS" has already been defined in the Abbreviations section. There’s no need to redefine it here. There are other similar cases of redefining acronyms throughout the document. Please address these as well.
7. Line 82, italic “log” -> normal “log” when using it as the logarithm operation.
8. Line 84, please change the “E” before “from Potravnov” to italic.
9. Line 92, “10-m.” -> “10-m”, removing the extra period
10. Lines 115 and 116, the chemical symbols should be in normal font. For instance, “A_Si” should be formatted as $A_\mathrm{Si}$ if LaTeX is used.
11. Line 117, “N_X” and “N_tot” are not defined.
12. Eq. 1, the symbol “b” is already used for the coordinate. Please use a different symbol for the limb darkening coefficient to avoid confusion.
13. Figs. 1 and 2, the symbols “l” and “b” should be italicized since they are variables. This will ensure consistency with the main text.
14. Caption of Fig. 2, please consider adding “$I_{l,b}$” after “relative intensity distribution”. However, since $I_{l,b}$ does not exactly represent the “relative intensity distribution,” please rephrase the sentence to express this more precisely.
15. Line 146, remove “of” before “0.1”
16. Eq. 4, “2.06265 \cdot 10^11” -> 2.06265 \times 10^11” to use the correct multiplication symbol for scientific notation.
17. Line 166, remove “The” before “Fig. 3”
18. Line 169, “leg” -> “lag”
19. Line 190, “the MX TrA” -> “MX TrA”
20. Line 191, please define “NLTE”
21. Line 191, please rephrase the first half of the sentence to explicitly define “A_\mathrm{O}” as the mean oxygen abundance.
22. Line 214, remove the redundant use of “lines.”
23. Line 215, remove the space between “stratification” and the following comma
24. Line 234, "F_S" and "F_0" are not defined.
25. Line 236, please add space before "2000"

Comments for author File: Comments.pdf

Author Response

 We thank the referee for his/her detailed comments.

1. In Section 2, when introducing the TESS data, please provide more details, such as which sector or sectors were used and whether the short or long cadence TESS light curve was analyzed. Given that multiple sectors of TESS data are available for MX TrA, if only one sector was used, please explain why other sectors were not included in the analysis. Additionally, consider discussing whether the inclusion of additional sectors would have impacted the results of the analysis.

A: The aim of using TESS photometry in our study was not to examine the photometric variability of MX TrA in details, but to obtain a general shape of the light curve that reproduces well from season to season. Hence we used the 120-s cadence photometric data obtained during Cycle 3 in Sector 39 – at the dates closest to the bulk of the spectroscopic observations used for Doppler Imaging in previous paper (Potravnov et al., 2024). This clarification now is presented in the revised version of the manuscript.

2. Line 82, the formula of calculating m_TESS uses “SAP_FLUX”. Please confirm that it is indeed the SAP flux from the SPOC light curve that was used in the analysis. Note that SPOC also provides PDCSAP flux (Pre-search Data Conditioning SAP flux), which has long-term trends removed using Co-trending Basis Vectors (CBVs). PDCSAP flux typically results in cleaner data with fewer systematic trends. If the authors used PDCSAP flux, please verify that the formula in line 82 is still valid and replace "SAP_FLUX" with "PDCSAP_FLUX." If SAP_FLUX was indeed used, I encourage the authors to provide details on how they pre-processed the light curve to remove any systematic trends or other instrumental effects. Additionally, please include a discussion on whether using PDCSAP flux would have impacted the results of the analysis.

A: We actually used SAP_FLUX to construct the light curve in magnitudes, because in this particular case PDCSAP_FLUX data results in an identical but more noisy phase curve. Therefore, in our case there is no benefit from using PDCSAP_FLUX. This is illustrated by the figure below, with phase curve based on PDCSAP_FLUX (violet points) is superimposed in our Fig. 3. There is an offset of the order ~0.03 mag between the SAP_FLUX and PDCSAP_FLUX. After taking it into account (cyan points), the shape and amplitude of both phase curves coincide perfectly. The scatter in the fluxes between two curves is of about ~0.001 mag which is comparable to the accuracy of our light curve fitting.

3. Fig. 2 is completely black.

A: We repaint Fig.2

4. Section 4.2, Line 219, when the authors claim that BD+00◦1659 is the slowly rotating twin of MX TrA, it would be beneficial to present the atmospheric parameters and chemical compositions of both stars side by side in a table for clearer comparison. Additionally, it might be useful for the authors to discuss whether the difference in rotation between the two stars could have any impact on the analysis results.

A: Careful comparison of the MX TrA spectrum with spectrum of slowly rotating star BD+00 1659 which we called as MX TrA 'twin' is made in a separate paper (Romanovskaya et al.) submitted to MDPI journal Galaxies. BD+00 1659 is a rather rare example of slowly rotating Si-star which allows us to estimate empirically the possible stratification effects. We provide the referee with couple of plots showing a comparison between the observed MX TrA spectrum and the observed BD+00 1659 spectrum broadened with the MX TrA rotational velocity.

Abundance analysis of 17 Si-stars with Vsini in the range 7 - 85 km/s (Bailey & Landstreet, 2013A&A...551A..30) did not reveal any significant difference/trend in Si II/III abundances and Si-anomaly with Vsini, which favors the spread of BD+00 1659 stratification results to faster rotating stars.

Other small issues:

1. Line 23, “4,5” -> “4, 5”, missing space between the comma and ‘5’. There are other similar cases of missing spaces between multiple reference numbers throughout the document. Please address these as well.

A: We redefined natbib command \bibpunct{[}{]}{,}{n}{}{,} to avoid this problem

2. Line 32, missing space before and after the number of 1600. There are other similar cases of missing spaces in math mode texts throughout the document.. Please address these as well.

A: Fixed

3. Line 34, “Combination” -> “The combination”

A: Fixed

4. Line 36, “spectral” -> “the spectral”

A: Fixed

5. In lines 57 and 58, the symbols in the parentheses are not yet defined. Please ensure that all symbols are defined before they are used. Additionally, there are missing spaces, such as before and after the "=" and the plus-minus ($\pm$) signs. Please correct these formatting issues.

A: Fixed

6. Line 77, the acronym "TESS" has already been defined in the Abbreviations section. There’s no need to redefine it here. There are other similar cases of redefining acronyms throughout the document. Please address these as well.

A: Fixed

7. Line 82, italic “log” -> normal “log” when using it as the logarithm operation.

A: Fixed

8. Line 84, please change the “E” before “from Potravnov” to italic.

A: Fixed

9. Line 92, “10-m.” -> “10-m”, removing the extra period

A: Fixed

10. Lines 115 and 116, the chemical symbols should be in normal font. For instance, “A_Si” should be formatted as $A_\mathrm{Si}$ if LaTeX is used.

A: Fixed

11. Line 117, “N_X” and “N_tot” are not defined.

A: Fixed

12. Eq. 1, the symbol “b” is already used for the coordinate. Please use a different symbol for the limb darkening coefficient to avoid confusion.

A: We change the coefficient a,b to c₁,c₂

13. Figs. 1 and 2, the symbols “l” and “b” should be italicized since they are variables. This will ensure consistency with the main text.

A: Fixed

14. Caption of Fig. 2, please consider adding “$I_{l,b}$” after “relative intensity distribution”. However, since $I_{l,b}$ does not exactly represent the “relative intensity distribution,” please rephrase the sentence to express this more precisely.

A: Fixed

15. Line 146, remove “of” before “0.1”

A: Fixed

16. Eq. 4, “2.06265 \cdot 10^11” -> 2.06265 \times 10^11” to use the correct multiplication symbol for scientific notation.

A: Fixed

17. Line 166, remove “The” before “Fig. 3”

A: Fixed

18. Line 169, “leg” -> “lag”

A: Fixed

19. Line 190, “the MX TrA” -> “MX TrA”

A: Fixed

20. Line 191, please define “NLTE”

A: We add NLTE in the Abbreviations section

21. Line 191, please rephrase the first half of the sentence to explicitly define “A_\mathrm{O}” as the mean oxygen abundance.

To do

22. Line 214, remove the redundant use of “lines.”

A: Fixed

23. Line 215, remove the space between “stratification” and the following comma

A: Fixed

24. Line 234, "F_S" and "F_0" are not defined

A: Fixed

25. Line 236, please add space before "2000"

A: Fixed

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper by Y. Pakhomov et al. titled Modelling the TESS Light Curve of Ap Si Star MX TrA focuses on modeling the TESS light curve of the chemically peculiar (Ap) silicon star MX TrA. The objective is to understand the star  photometric variability by using the surface distribution of elements like silicon, iron, helium , and chromium   obtained from Doppler Imaging  data.

The manuscript reads well, is generally clear andconcise, albeit concise. The introduction provides sufficient background on chemically peculiar stars and the significance of light curve modeling.

The main result is the theoretical light curve. The comparison with observational data from TESS agrees very well: the authors successfully fitted the observed TESS light curve with a synthetic one with an accuracy better than 0.001 mag.

The analysis therefore confirms the influence of Si and Fe abundance stratification on the amplitude of photometric variability. These results are of interest. I recommend that acceptance with some minor changes that are needed to improve clarity.

** Description of Figures in the text and their captions could be expanded. For instance, in Fig. 4, replace The dotted line indicates... with The dashed line indicates...

** The figure appears completely black.

** Figure 5: clarify whether it refers to the spots or the full atmosphere,

** It would be interesting to see also how well the integrated spectrum of MX TrA is reproduced as a function of at least a few phases of the star light curve.  

** Consider a more detailed discussion of any limitations or potential sources of error in the modeling approach. For example, what is the role of other more and less abundant elements? Note that the   stratification analysis is   not spatially resolved but is based on integrated radiation.

** Clearly state the relevance of the results presented in Potravnov et al. 2024, MNRAS, 527, 10376, which can be considered as a Paper I by the same group. Explicitly state what this paper adds relative to the previous one.

Author Response

We thank the referee for the reading of the manuscript and his/her comments.

1. Description of Figures in the text and their captions could be expanded. For instance, in Fig. 4, replace The dotted line indicates... with The dashed line indicates… A: The captions to the figures are clarified now. The mistake is fixed. 2. The figure appears completely black.

A: We repainted Fig.2

3. Figure 5: clarify whether it refers to the spots or the full atmosphere,

A: Fig.5 are referred to the disk-integrated flux, this is clarified in the caption and text now.

4. It would be interesting to see also how well the integrated spectrum of MX TrA is reproduced as a function of at least a few phases of the star light curve. A: If we understand the question correctly, examples of the approximation of spectral line profiles by synthetic ones computed with the inhomogeneous surface abundances are given for different rotational phases in previous paper by Potravnov et al., 2024 (Figs. 5-8). 5. Consider a more detailed discussion of any limitations or potential sources of error in the modeling approach. For example, what is the role of other more and less abundant elements? Note that the stratification analysis is not spatially resolved but is based on integrated radiation. A: At the end of Section 4.1, we estimate the role of the background opacity from magnesium and oxygen, which appears to be negligible. Another potential source of opacity in chemically peculiar stars which affects the emergent flux could be the line absorption due to rare-earth elements (REEs). However, they have low ionization potentials and should not be intense at the temperature of MX TrA. A detailed analysis of REEs in MX TrA atmosphere, however, is not possible due to the rapid rotation of the star. Additionally, we considered the effect of an error in silicon abundance, as the element with the greatest contribution to the flux, on the light curve fit. By introducing a systematic error of the order of ~0.2 dex, typical in abundance analysis, we obtain a difference of about 0.005 mag. Indeed, in Sect. 4.2 we point out that we estimate an upper limit of impact of stratification on the emergent flux based on disc-integrated stratification profile, but below we give a simple estimate of effect’s reduction due to surface inhomogeneous stratification. 6. Clearly state the relevance of the results presented in Potravnov et al. 2024, MNRAS, 527, 10376, which can be considered as a Paper I by the same group. Explicitly state what this paper adds relative to the previous one. A: The paper by Potravnov et al. 2024 focuses on Doppler Imaging of MX TrA, while the main objective of the present work is to model the light curve using the previously obtained surface elemental distributions. We add some additional clarifications in the Introduction

 

Author Response File: Author Response.pdf