Classification of Planetary Motion around Super-Jupiters and Brown Dwarfs

Round 1

Reviewer 1 Report

The article by Moneer and collaborators titled "Classification of planetary motion around super-Jupiters and brown dwarfs" analyzes one possible architecture of an exoplanet system to understand the fate of an Earth-like planet in such a system with a giant companion.

The work could be published after addressing the following major and minor points:

MAJORS

- why such a system? A solar mass star with an earth-like planet and a transiting super Jupiter or a BDs? Typically Super Jupiters and BD companions have wide orbits and the probability of observing one of them transit their star is very low. How many systems of this kind have been detected? Can the author please explain this choice?

Line 88 to 98: The authors put a sharp threshold at 15 Mj between Planets and BDs ... why? the deuterium limit is 13 MJ, furthermore, due to the direct imaging results, there is a big debate about the difference between what body is really a planet or a brown dwarf. 15 Mj seems an odd choice. Could please the authors justify this choice? Furthermore, it seems that all planets with masses between 5 and 15 Mj should be transiting planets which is not true. A planet could transit or not independently by the value of its mass. So please adjust also this sentence.

Line 92 to line 98: the reason for the choice of the radius of the object seems too loose. The authors should discuss a little bit more introducing the relation between the mass and the radius of these objects. There are several papers (e.g.  Figure 2 of Hatzes and Rauer 2015 ApJ, 810:L25) about this relation and the presence of a local maximum around 1 Mj and the corresponding radius for giant planets.  For larger masses, in the BDs regime, the relation is slightly diminishing maintaining a little bit less than 1 Mj.

MINOR

Line 103: please add the dimension of k.

Line 110: Please specify the acronym ODE

Line 317-318 The authors introduce the D0 as a fractal or uncertainty dimension and put a reference to explain it. Because there will be interested readers not necessarily experts in the field, it could be better to put an equation to define it or, better, to spend a few words on its calculation.

Author Response

Responses to Reviewer #1

Q1.  why such a system? A solar mass star with an earth-like planet and a transiting super Jupiter or a BDs? Typically Super Jupiters and BD companions have wide orbits and the probability of observing one of them transit their star is very low. How many systems of this kind have been detected? Can the author please explain this choice?

R1. Concerning the reviewer's inquiry regarding the choice of our system comprising a solar-mass star, an Earth-like exoplanet, and a transiting super Jupiter or brown dwarf (BD), the selection was made to explore a scenario that represents a plausible configuration in extrasolar planetary systems and to investigate the dynamical interactions within such systems.

While it is true that super Jupiters and brown dwarf companions typically have wide orbits and the probability of observing them transit their host star is low, there have been notable exceptions observed in exoplanetary systems. Though rare, instances of transiting super Jupiters and brown dwarfs have been reported in the literature. For example, recent observational surveys such as the Kepler mission and its successor, K2, have identified several transiting brown dwarf candidates, albeit with relatively low occurrence rates compared to planets (e.g., Bayliss et al. 2016 AJ.). Additionally, advances in observational techniques and instruments, including high-precision photometry and radial velocity measurements, have facilitated the detection of such transiting companions.

While the number of systems with transiting super Jupiters or brown dwarfs is limited compared to those with transiting planets, their inclusion in our study allows for a broader exploration of planetary dynamics and system architectures.

Q2. Line 88 to 98: The authors put a sharp threshold at 15 Mj between Planets and BDs ... why? the deuterium limit is 13 MJ, furthermore, due to the direct imaging results, there is a big debate about the difference between what body is really a planet or a brown dwarf. 15 Mj seems an odd choice. Could please the authors justify this choice? Furthermore, it seems that all planets with masses between 5 and 15 Mj should be transiting planets which is not true. A planet could transit or not independently by the value of its mass. So please adjust also this sentence.

R2. We agree with the reviewer’s comment concerning the debate about the difference between planets and brown dwarfs. To prevent such odd choices the text has been rewritten. Additionally, we have adjusted the text to avoid any implication that all planets within the 5 to 15 Mj range should necessarily be transiting planets, as this was not our intention. We apologize for any confusion caused by the previous version of the manuscript and are grateful for the opportunity to improve the clarity and accuracy of our presentation  

Q3. Line 92 to line 98: the reason for the choice of the radius of the object seems too loose. The authors should discuss a little bit more introducing the relation between the mass and the radius of these objects. There are several papers (e.g.  Figure 2 of Hatzes and Rauer 2015 ApJ, 810:L25) about this relation and the presence of a local maximum around 1 Mj and the corresponding radius for giant planets.  For larger masses, in the BDs regime, the relation is slightly diminishing maintaining a little bit less than 1 Mj.

R3. In response to the reviewer's inquiry, we acknowledge the crucial role of the mass-radius relationship in characterizing both giant planets and brown dwarfs. Notably, studies such as Hatzes and Rauer (2015) have underscored a notable feature in this relationship—a local maximum around 1 Mj for giant planets, followed by a diminishing trend for larger masses within the brown dwarf regime. To provide a more thorough contextualization for our choice of radius for the objects under examination, we enrich our paper with a more detailed analysis of the mass-radius relationship. By incorporating additional references, including Hatzes and Rauer (2015), we aim to offer a comprehensive overview of the observed trends in the mass-radius relationship for these celestial objects.

Q4. Line 103: please add the dimension of k.

R4. Thanks for bringing this to our attention. We will ensure that the dimension of k is clearly stated. In the context of our work, k represents the square root of the Gaussian gravitational constant, typically expressed in units of (rad / day). We will explicitly state this dimension in the manuscript at Line 103 to enhance clarity for readers.

Q5. Line 110: Please specify the acronym ODE

R5. We have clarified that ODE stands for ordinary differential equations (ODEs) in Line 110 of the manuscript.

Q6. Line 317-318 The authors introduce the D0 as a fractal or uncertainty dimension and put a reference to explain it. Because there will be interested readers not necessarily experts in the field, it could be better to put an equation to define it or, better, to spend a few words on its calculation.

R6. In response to the reviewer’s suggestion, we have included a brief explanation of the fractal or uncertainty dimension, denoted as D0, along with an equation defining it in the revised version of the manuscript.

Reviewer 2 Report

Reviewer Report 

I have carefully read the manuscript entitled "Classification of planetary motion around super-Jupiters and brown dwarfs" by Eman M. Moneer et al.

This manuscript investigates the orbital dynamics of an exosystem consisting of a solar-mass host star, a transiting body, and an Earth-size exoplanet within the framework of the generalized three-body problem. This topic is fascinating and significant in the planetary motion field. As such, the topic is appropriate and worthy of consideration for publication in Universe. 

The manuscript is almost ready for publication, I only have some comments/suggestions for the author before recommending the manuscript.

**Major comments:

1.What are the physical origins of some calculated results? Please present some brief discussions on these issues. For example, lines 177-179: "a multitude of islands consisting of secondary resonant crossing orbits emerges for relatively low values of m_2 (m_2 < 15 Jupiter masses). However, as the value of m_2 increases, the number of these secondary resonant orbits significantly decreases." Why?

2.The authors assume a radius of 1 Jupiter radius for the body with mass m_2, which seems plausible. However, at least some discussions about the effect of the radisu of the body with mass m_2 on the final results are needed.

**Minor comments:

1.Line 110, what is the meaning of the abbreviation "ODEs"?

2.I suggest that the authors define M_J as a Jupiter mass.

3.Lines 193-194, the authors mentioned "For relatively low values of m_2 (m_2 < 20 Jupiter masses) the regions between the several stability islands seem to have a "chaotic" structure". In my understanding, you can only make the same conclusion for 5<=m_2<=15 Jupiter mass.

4. Line 250, the authors mentioned "For extremely high initial eccentricity values (e_3 > 0.9)". It seems to be e_3>0.95?

***end***

No.

Author Response

Responses to reviewer #2

Q1. What are the physical origins of some calculated results? Please present some brief discussions on these issues. For example, lines 177-179: "a multitude of islands consisting of secondary resonant crossing orbits emerges for relatively low values of m_2 (m_2 < 15 Jupiter masses). However, as the value of m_2 increases, the number of these secondary resonant orbits significantly decreases." Why?

R1. We apologize for a confusing formulation in the submitted text. The multitude of islands corresponds to location in (a,e) space where the two bodies are in a mean-motion resonant configuration. The largest island correspond to the 1:1 mean-motion resonance. In the revised version of the paper, we have revised the corresponding text for better understanding.

Q2. The authors assume a radius of 1 Jupiter radius for the body with mass m_2, which seems plausible. However, at least some discussions about the effect of the radius of the body with mass m_2 on the final results are needed.

R2. We appreciate the reviewer's attention to the potential influence of the radius of the body with mass m2 on our findings. In response to this concern, we have reorganized the text to provide further clarification on why we adopted a radius of 1 Jupiter radius for m2.

On the other hand, while our equations of motion do not explicitly include the radius of the primaries, we acknowledge that the integration process should indeed consider the effect of radius on the final results. According to previous findings, we recognize the importance of investigating the impact of the radius, mainly, on the extent of regions associated with collision with the exoplanet.

Regrettably, due to space constraints and to maintain consistency with the astrophysical parameters employed in our study, we did not conduct an explicit analysis of the influence of m2's radius on the outcomes presented in this paper. However, we agree that such an investigation could provide valuable insights into the dynamics of the system.

Q3. Line 110, what is the meaning of the abbreviation "ODEs"?

R3. We have clarified that ODE stands for ordinary differential equations (ODEs) in Line 110 of the manuscript.

Q4. I suggest that the authors define M_J as a Jupiter mass.

R4. Following the reviewer’s suggestion throughout the manuscript, we have replaced the phrase "Jupiter mass" with the symbol M_J, to denote a Jupiter mass.

Q5. Lines 193-194, the authors mentioned "For relatively low values of m_2 (m_2 < 20 Jupiter masses) the regions between the several stability islands seem to have a "chaotic" structure". In my understanding, you can only make the same conclusion for 5<=m_2<=15 Jupiter mass.

R5. Upon reevaluation, we agree with the reviewer's suggestion. While our observations did extend up to 20 Jupiter masses for m_2, the figures presented in the manuscript primarily support conclusions for the interval 5 <= m_2 <= 15 Jupiter masses.

Q6. Line 250, the authors mentioned "For extremely high initial eccentricity values (e_3 > 0.9)". It seems to be e_3>0.95?

R6. We acknowledge and appreciate the reviewer's observation. Following their suggestion, we have revised the statement on line 250 to reflect the correct threshold for extremely high initial eccentricity values, which is indeed e_3 > 0.95.

Reviewer 3 Report

Comments to the Authors

The paper, titled "Classification of planetary motion around super-Jupiters and brown dwarfs" authored by Eman M. Moneer et al., investigated the orbital dynamics of an exoplanet system consisting of a solar-mass host star, a super-Jupiter to brown-dwarf size transiting body, and an Earth-size exoplanet using numerical methods and the theory of the generalized three-body problem. The work explored the initial conditions of different space trajectories to theoretically determine the final states of the Earth-size exoplanet. The results of the analysis provide insights into the initial conditions where the motion of the Earth-size exoplanet can be dynamically stable, including a particular case that the Earth-size exoplanet acts as an exomoon of the transiting body.

In general, the manuscript is well structured and written. I recommend acceptance for publication at the present form, with the following minor issues addressed:

1) I noticed that the authors have incorporated substantial portions of text and a few figures from their previous paper. For instance, the majority of Section 2 and Figs. 1 & 2 are from Moneer, E. M., Dubeibe+2023. I recommend that the authors explicitly state their intentions for reusing these texts and figures, ensuring that readers are aware of the context and acknowledging the source appropriately. Additionally, they should consider rephrasing or reorganizing these texts to minimize redundancy and enhance the clarity of the current manuscript.

2) Line 103, the unit (rad / day) of the Gaussian gravitational constant K is missing.

3) In Figures 3 - 10, a more detailed description of each final state of the Earth-size exoplanet would be beneficial. For instance, the term 'exomoon' is not explicitly associated with any orbit type introduced in Section 3, although it should refer to the ‘Circumplanetary orbit’. I recommend that the authors consider including a table for a clearer presentation of the final states.

4) Line 223, Fig.4 -> Fig. 4; Fig.5(a-f) -> Fig. 5(a-f), missing space

5) Line 257, all most of these regions -> most of these regions

6) Line 293, Figs.9(a-f) -> Figs. 9(a-f), missing space. Please check similar typos throughout the manuscript.

Author Response

Responses to Reviewer #3

Q1. I noticed that the authors have incorporated substantial portions of text and a few figures from their previous paper. For instance, the majority of Section 2 and Figs. 1 & 2 are from Moneer, E. M., Dubeibe+2023. I recommend that the authors explicitly state their intentions for reusing these texts and figures, ensuring that readers are aware of the context and acknowledging the source appropriately. Additionally, they should consider rephrasing or reorganizing these texts to minimize redundancy and enhance the clarity of the current manuscript.

R1. We appreciate the referee's observation and recommendation. Regarding the reuse of text and figures from our previous work (ApJ. 2023 Moneer et al.), we aim to ensure that readers are fully informed about the context. Moreover, it is important to clarify the following: In our current paper, Figure 1 illustrates the distribution of masses for Jovian-like exoplanets, plotting exoplanet mass vs. exoplanet radius. While this figure bears resemblance to Figure 1 in our previous publication in ApJ. 2023 Moneer et al., it serves a distinct purpose since it focuses on the relationship between exoplanet mass and host star mass. Similarly, Figure 2 in our current manuscript closely resembles a figure from ApJ. 2023 Moneer et al., with the primary difference being the designation of the massive object as a transiting body rather than a Hot Jupiter. This distinction is essential for the specific context of our study.

We have added a new paragraph to ensure readers are aware of the context and appropriately acknowledge the original source. Additionally, we have rephrased and reorganized the text to minimize redundancy.

Q2. Line 103, the unit (rad / day) of the Gaussian gravitational constant K is missing.

R2. We have revised Line 103 to include the unit (rad/day) alongside the Gaussian gravitational constant k for clarity. 

Q3. In Figures 3 - 10, a more detailed description of each final state of the Earth-size exoplanet would be beneficial. For instance, the term 'exomoon' is not explicitly associated with any orbit type introduced in Section 3, although it should refer to the ‘Circumplanetary orbit’. I recommend that the authors consider including a table for a clearer presentation of the final states.

R3. In the revised version of the paper, we added a new paragraph in Section 3, where we explicitly describe the connections between the terms used in Fig. 2 and in the following figures. Thus, all the orbital types discussed in the color-coded basin diagrams of Section 4 are clear.

Q4. Line 223, Fig.4 -> Fig. 4; Fig.5(a-f) -> Fig. 5(a-f), missing space

R4. We have rectified the formatting error by adding the necessary space. The corrected text now adheres to the standard guidelines.

Q5. Line 257, all most of these regions -> most of these regions

R5. We have revised the text to correct the phrase 'all most of these regions' to 'most of these regions,' as suggested.

Q6. Line 293, Figs.9(a-f) -> Figs. 9(a-f), missing space. Please check similar typos throughout the manuscript.

R6. We have rectified the missing space in the reference to Figures 9(a-f) at Line 293. Furthermore, we have conducted a comprehensive search for similar typographical errors throughout the manuscript and have rectified any instances found.

Round 2

Reviewer 1 Report

I would like to thank the author to address my comments