Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

I commend you on a comprehensive and detailed study of period variations in eclipsing binaries within the Northern Continuous Viewing Zone of TESS. The extended time coverage significantly strengthens the statistical reliability of your findings.

This manuscript provides a valuable, statistically robust reanalysis of eclipsing binaries in the NCVZ using extended TESS data. The methodology is sound, the comparisons to previous studies are appropriate, and the results support continued investigation of compact triple systems.

Best regards,

Author Response

Thank you for the Reviewer's brief notes. As no additional comments and suggestions can be found in Reviewer #1's note, we do not have any additional answers to this report.

Reviewer 2 Report

Comments and Suggestions for Authors

This work is yet another proof of the usefulness of space monitoring of the sky. There is always something new to discover and analyze. The authors have built on their previous work, correctly noting the differences in the estimates of some of the objects. A lot of work has been done on data processing and analysis. I have a few notes and questions for the authors.

1. It is not immediately clear to the reader what fitting procedure was used to determine the periods of the third component. Is it automatic or do the authors choose the polynomial depending on the error? (To clarify the procedure, one must refer to the first article on the topic).
2. The figures do not show the residuals between the data and the fit. We assume that this is the best fit of the data. Has the fact that these may be harmonics of another period been assessed? It is especially uncertain for the larger periods in the groups after L1.
3. It would be interesting to see whether some of the triple systems appear in the catalog of (Kreiner, 2004) and, if so, to what extent do the periods coincide? (Bibcode: 2005yCatp005005402K)

Author Response

We thank the reviewer for his/her kind remarks. Here we summarize those modifications which we made to the text in accord with the question of the reviewer.
All the new modifications can be seen with blue, boldfaced characters.

This work is yet another proof of the usefulness of space monitoring of the sky. There is always something new to discover and analyze. The authors have built on their previous work, correctly noting the differences in the estimates of some of the objects. A lot of work has been done on data processing and analysis. I have a few notes and questions for the authors.

  1.  It is not immediately clear to the reader what fitting procedure was used to determine the periods of the third component. Is it automatic or do the authors choose the polynomial depending on the error? (To clarify the procedure, one must refer to the first article on the topic).
   
     Now we have included a short new subsection '2.2 Numerical representation of the fitting process' where we address these questions.
  
  2.  The figures do not show the residuals between the data and the fit. We assume that this is the best fit of the data. Has the fact that these may be harmonics of another period been assessed? It is especially uncertain for the larger periods in the groups after L1.
  
     We feel that the robustness and/or uncertain nature of the outer periods are also discussed adequately at the end of the previously mentioned new subsection.
  
  3.  It would be interesting to see whether some of the triple systems appear in the catalog of (Kreiner, 2004) and, if so, to what extent do the periods coincide? (Bibcode: 2005yCatp005005402K)

     We make this comparison in the new subsection 4.7.

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents a re-analysis of eclipse timing variations (ETVs) of eclipsing binaries (EBs) in the Northern Continuous Viewing Zone (NCVZ) observed by TESS. The study extends the earlier work of Mitnyan et al. (2024) by including approximately two additional years of TESS observations, increasing the total time baseline to nearly 2000 days. The authors identify 168 candidate hierarchical triple systems and refine orbital solutions for many previously reported systems.

The paper is clearly written and logically structured. Whenever details are not fully explained, the authors provide appropriate references to previous publications or review material. In particular, Section 2 provides an excellent and thorough (although somewhat long) summary of the theoretical background of eclipse timing variations, especially the treatment of the light-travel time effect (LTTE) and dynamical effects (DE).

The study represents a natural and scientifically justified continuation of Mitnyan et al. (2024), since the significantly extended TESS time baseline allows a much more reliable identification of long-period triple systems. The work is therefore well motivated.

The main strengths of the manuscript include a large underlying database (3553 eclipsing binaries identified in previous work; cf. Mitnyan et al. 2024), from which 351 systems with suspected non-linear ETVs were selected. The authors (essentially the same team) maintain a consistent methodology (LTTE and dynamical solutions) relative to the previous study, allowing direct comparison with their earlier results. The main new aspect is the significantly longer time baseline, which has led to an increase in the number of identified triple candidates (168 instead of 135), including several systems requiring more complex (four-body) models.

The extension of the previous study is scientifically meaningful and clearly demonstrates how longer time coverage improves the reliability of LTTE solutions.

The authors appear to have followed essentially the same analysis pipeline as in Mitnyan et al. (2024), with LIGHTKURVE serving as the primary tool for processing the TESS data. However, the manuscript does not clearly summarize the data-processing workflow. Instead, the reader is referred almost entirely to the previous paper. Even a short paragraph describing the photometric extraction, eclipse-timing determination, fitting procedure, and optimization method (e.g., MCMC) would make the paper more self-contained and easier to follow.

The manuscript could benefit from a discussion of observational selection effects. For example:

- What is the approximate minimum detectable LTTE amplitude for the present TESS dataset?

- Does the detection limit depend on the outer period?

- Can the authors comment on the approximate completeness of their original sample?

The manuscript primarily presents a catalog of solutions, but a global statistical interpretation is largely missing. For example, distributions of outer orbital periods, eccentricities, tertiary masses, and the period ratio P2​/P1​ would be useful (as was done in previous work). Therefor, the question remains, if the conclusions are still valid. Figures analogous to those shown in previous work (e.g. Mitnyan et al. 2024, A&A 685, A43, and Borkovits et al. 2015, MNRAS 455, 4136), such as: P1 vs P2 detection limits, P2 distributions, e2 distributions; could further strengthen the paper.

Some small comments on figures and individual systems: some systems may show additional effects or systematic trends not discussed in the text.

Figure 1:

- TIC 229412530 may show deviations from a simple LTTE model.

- TIC 232610209 possibly shows flare-like events near BJD ~ 60300.

Figure 4:

- For TIC 230007820 the ground-based points appear significantly offset from the TESS data. Was it necessary to include them as constraints? Do they influence the fitted solution?

Figure 7:

- TIC 229507536 shows systematic trends near BJD ~ 59000 and 59900.

- TIC 219900027 (AU Dra) also appears to show additional variability.

Figure 9:

- For TIC 288734990 the ground-based data between BJD ~ 54000–56000 appear unusual and should be explained.

Figure 10:

- For TIC 377307592 (KK Dra), it is unclear whether the earliest data points before BJD ~ 55000 are consistent with the model.

Figure 11:

- TIC 219885468 appears to show evidence for an additional long-period signal that is not discussed further.

Figure 13:

- TIC 2300002837 shows features that might deserve a brief comment.

The color scheme follows Mitnyan et al. (2024) and earlier works, which is acceptable. However, red data points are sometimes fitted with red curves and blue data points with blue (or similar-colored) curves, which occasionally reduces readability (at least for me) .

This manuscript presents a carefully executed extension of earlier work on TESS triple-star candidates. The authors have re-analysed the same 351 systems previously selected by Mitnyan et al. (2024) from a parent sample of ~3500 eclipsing binaries, increasing the number of vetted triple-star candidates from 135 to 168 while reclassifying some of the previous results.

The analysis is technically sound and the results are significant for the study of hierarchical stellar systems.

I recommend publication after minor revisions addressing the points above.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf