Secular Orbital Dynamics of the Possibly Habitable Planet K2-18 b with and without the Proposed Inner Companion
Round 1
Reviewer 1 Report
The paper titled "Secular orbital dynamics of the possibly habitable planet K2-18 4 b with and without the proposed inner companion" by Valeri V. Makarov, and Alexey Goldin is a theoretical and numerical analysis of the secular evolution of the system K2-18 either considering the presence of two planets or the presence of the only outer planet. The paper is timely due to the recent observations of the K2-18 b atmosphere by JWST, and gives insights into the real habitability of that planet, and it worth publishing.
Nevertheless, the authors shall address the following points:
Major:
- Row 46: This sentence is too sharp. Perhaps I'm wrong, but the hypothetical planet c is inside the orbit of planet b that is in the HZ of the M star K2-18. So, if planet c exists, as it seems, its orbital motion should be synchronized with its rotation and synchronization should also work for the central star. It depend by the age of the star, but could the rotation period of the star (that has a Mass of 0.4 M Sun) be close to the orbital period of the planet? Could the author expand, and argue a little bit more about the sentence " This is suspiciously etc." ?
- Row 383 up to Row 384. Also in this case the sentence is too sharp. Could the authors argue the sentence better? the example of the planets of the Solar system from row 364 to row 366 does not seem to be so suitable due to the difference in distances involved (the semi-major axis of K2-18 b is about a tenth of that of Mercury).
and the following minor points and misprint
- Row 40:it is Earth Mass. Please check the subcript.
- Table 1: Why do not extend the table considering also the other major parameters of the star and the planets? I think that's useful.
- Most of the figures are nearly unreadable. Please enlarge the fonts or enhance the weight of the characters.
- along the text, there are several acronyms not explained. Please define them at their first appearance.
- In section 4 no reference to Figure 4 is set. Please, provide it.
- Row 313: are functions are functions. Fix the repetition.
- References: in most of the reference entries, the name of the journal is not reported. Perhaps "bibtem" is using commands (e.g. \apj) that are not defined in the class file.
- row 276: "It is widely assumed that the tidal dissipation mechanisms are responsible", please put some reference here to sustain the point.
- Row 320 "Planet K1-18 b is presumed". Correct to "Planet K2-18 b is presumed "
- Row 320 "Planet K1-18 b is presumed to have an Earth-like core covered by a massive water ocean" Please sustain this with a reference.
Author Response
We thank the anonymous referee for the substantial and helpful review. Our answers and a list of updates and changes are listed below.
Major:
- Row 46: This sentence is too sharp. Perhaps I'm wrong, but the hypothetical planet c is inside the orbit of planet b that is in the HZ of the M star K2-18. So, if planet c exists, as it seems, its orbital motion should be synchronized with its rotation and synchronization should also work for the central star. It depend by the age of the star, but could the rotation period of the star (that has a Mass of 0.4 M Sun) be close to the orbital period of the planet? Could the author expand, and argue a little bit more about the sentence " This is suspiciously etc." ?
****** These are actually the points we were trying to present. There are two options: 1) the inner planet is real and it managed to synchronize the star; 2) there is no inner planet c, and the detected periodic signal is a transient perturbation caused by photometric features on the rotating surface. The 1st option does not seem to be very credible though, in our opinion. The tidal quality factor is expected to be pretty low for M dwarfs, and the mass of this tentative planet is modest too. Anyway, we have split this long paragraph into two, modified and extended the second part, and suggested the best way to resolve the uncertainty by extended RV observations.
- Row 383 up to Row 384. Also in this case the sentence is too sharp. Could the authors argue the sentence better? the example of the planets of the Solar system from row 364 to row 366 does not seem to be so suitable due to the difference in distances involved (the semi-major axis of K2-18 b is about a tenth of that of Mercury).
****** Our line numbers do not match these row numbers, but we think this concerns the paragraph beginning with "Finally, the third option..." We shortened this paragraph removing a couple of sentences, which were somewhat off the main topic, admittedly.
and the following minor points and misprint
****** These are excellent points, we have used all of them except for those listed below, where we are not sure.
- Row 40:it is Earth Mass. Please check the subcript.
****** We have used $M_{\earth}$ in the source tex file, and it does show up as a crossed circle in the pdf output. Is not it the right symbol for Earth? May be, we should switch to $M_{\rm Earth}$ to avoid confusion.
- Most of the figures are nearly unreadable. Please enlarge the fonts or enhance the weight of the characters.
****** Perhaps, the pdf file available to the referee differs from ours. The figures in our version occupy half of the page, and the tick labels and axes captions are rendered with a font size that is dowble the size of the text. They seems to be very legible. We will leave this issue for technical editor's consideration.
- References: in most of the reference entries, the name of the journal is not reported. Perhaps "bibtem" is using commands (e.g. \apj) that are not defined in the class file.
****** This is puzzling, because the submitted PDF file (which used MNRAS class and bibtex style) does include the journal names correctly in the abbreviated form (e.g., MNRAS). Perhaps, the referee used a processed text in a different style?
- Row 320 "Planet K1-18 b is presumed to have an Earth-like core covered by a massive water ocean" Please sustain this with a reference.
****** This model is already mentioned in the 1st paragraph of Introduction, with a reference to Cloutier et al. 2017.
Reviewer 2 Report
This is good research work, with a sufficiently novel approach in the field under investigation; I have not found any essential flaws, errors or methodological issues.
In this manuscript (“Secular orbital dynamics of the possibly habitable planet K2-18 b with and without the proposed inner companion”, authorships of Valeri Makarov *, Alexey Goldin), which was submitted to journal "Universe" (MDPI), authors present qualified and professional investigation of the long-term orbital evolution of planet K2-18 b using both theoretical and purely numerical techniques for two possible configurations: a single planet and a two-planet system (including the proposed inner planet close to the 4:1 resonance in mean motion). They made emphasis on the secular changes of eccentricity and orbital inclination, which are turned to be the periodic on the time scale of stellar age and important for the climate stability of the planet.
General ansatz seems to be professionally presented, all the simple logic and mathematical derivation are under responsibility of the authors.
My only recommendation is to mention recent research regarding influencing of Milankovitch cycles on orbital dynamics of planet:
Ershkov S., Leshchenko D., Prosviryakov E.Yu. (2023). A novel type of ER3BP introducing Milankovitch cycles or seasonal irradiation processes influencing onto orbit of planet. Archive of Applied Mechanics, 93, pp. 813-822.
Nevertheless, I should especially note that the presented manuscript is the self-consistent development in such area of researches. My recommendation: accept as is (with taking into account my remark above).
Author Response
We thank the anonymous referee for the positive review of our paper and the suggested relevant paper recently published on the topic of Milancovitch-like cycles in 3-body systems. This reference has been added in Section 7, second paragraph.
