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Open AccessArticlePost Publication Peer ReviewVersion 2, Revised

On Mautner-Type Probability of Capture of Intergalactic Meteor Particles by Habitable Exoplanets (Version 2, Revised)

Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia;
Received: 28 June 2019 / Accepted: 10 July 2019 / Published: 9 August 2019
(This article belongs to the Special Issue Molecules to Microbes)
Peer review status: 3rd round review Read review reports

Reviewer 1 Yvan Dutil independant researcher Reviewer 2 Dragos G Zaharescu Georgia Institute of Technology Reviewer 3
Version 1
Original
Not approved
Authors' response
Approved with revisions
Authors' response
Reviewer inviting
Version 2
Revised
Not approved
Authors' response
Approved with revisions
Authors' response
Reviewer inviting
Version 3
Revised
Not approved Reviewer invited Reviewer inviting
Version 3, Revised
Published: 19 October 2019
DOI: 10.3390/sci1030061
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Version 2, Revised
Published: 9 August 2019
DOI: 10.3390/sci1020047
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Version 1, Original
Published: 15 July 2019
DOI: 10.3390/sci1020040
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Both macro and microprojectiles (e.g., interplanetary, interstellar and even intergalactic material)
are seen as important vehicles for the exchange of potential (bio)material within our solar system as well
as between stellar systems in our Galaxy. Accordingly, this requires estimates of the impact probabilities
for different source populations of projectiles, including for intergalactic meteor particles which have
received relatively little attention since considered as rare events (discrete occurrences that are statistically
improbable due to their very infrequent appearance). We employ the simple but yet comprehensive
model of intergalactic microprojectile capture by the gravity of exoplanets which enables us to estimate
the map of collisional probabilities for an available sample of exoplanets in habitable zones around host
stars. The model includes a dynamical description of the capture adopted from Mautner model of
interstellar exchange of microparticles and changed for our purposes. We use statistical and information
metrics to calculate probability map of intergalactic meteorite particle capture. Moreover, by calculating
the entropy index map we measure the concentration of these rare events. We further adopted a model
from immigration theory, to show that the transient distribution of birth/death/immigration of material
for the simplest case has a high value. View Full-Text
Keywords: intergalactic meteor particle; extrasolar planets; astrobiology intergalactic meteor particle; extrasolar planets; astrobiology
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Kovacevic, A.B. On Mautner-Type Probability of Capture of Intergalactic Meteor Particles by Habitable Exoplanets. Sci 2019, 1, 47.

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1

Reviewer 1

Sent on 03 Aug 2019 by Yvan Dutil | Not approved
independant researcher

To the editor,

I have read this paper carefully, before submitting this comment.

First, I observe that the expression “Mautner-Type” is not common in English and should not be used in the title.

Second, I shall note than gravitation focusing is irrelevant at intergalactic speed. While, this is stated in the third paragraph of the section 2.3.2, this also means that the whole section should be rewritten accordingly.

Third, the whole statistical analysis is based on the false premise that the know population of exoplanets in the habitable zone is representative of the reality, which is not at all. Indeed, the list used by the authors to build their probability distribution comes mostly from the Kepler space mission. The planetary size and especially the distance distribution observed are a consequence of the observational technique used by this mission and not the true spatial distribution of exoplanets. For example, the increase of the planetary radius with distance is a direct consequence of the observational method and has no astrophysical basis. Hence, the whole paper is fundamentally flawed by using this distribution.

The probability values have no unit. Is it per particle encounter or per year? In the second case, the reported observation of a collision of an IMP with Earth is very unlikely to be true.

The whole discussion should be brought in the introduction section, since it does very little to discuss the results of the paper itself. The whole section “Some Parallels with Biological Immigration Models” is irrelevant to the paper topic.

I shall also point out that the distance to the Earth is not the same thing as the distance to the centre of the Galaxy. The Earth being at about 8,000 pc from the galactic centre. Hence distance to Earth has no physical relevance and the conclusion that “The clustering is increasing toward the inner region of Galaxy.” is fundamentally false.

While the statistical methodology might be appropriate, the fundamental assumptions are flawed. The whole paper would have to be reworked to make it physically correct. Hence, I would recommend rejecting this paper.

 

Response to Reviewer 1

Sent on 13 Aug 2020 by Andjelka Kovacevic

A:We thank the Reviewer very much for reading our work. We deeply appreciate the Reviewer’s comments and suggestions and answered them point by point. All changes in the manuscript are given in bold face.

A:We thank the Reviewer for the comment and acknowledge Reviewer's concern about our choice of expression 'Mautner-type'. We would like to let us mention some notable examples of papers with expressions '-type': - Dynamical astronomy Petr Pokorn and David Vokrouhlický, 'Opik-type collision probability for high-inclination orbits: Targets on eccentric orbits', Icarus Volume 226, Issue 1, September–October 2013, Pages 682-693 - Mathematics Kamenev-type function in Z. Han, T. Li, S. Sun & W. Chen 'Oscillation Criteria for Second-Order Nonlinear Neutral Delay Differential Equations', Advances in Difference Equationsvolume 2010, Article number: 763278 (2010) However if there is a possibility that audience will be broader than experts only then the title can omit expression '-type' from its formulation.

A: We thank the Reviewer for the comment. Gravitational focusing was not implemented in any calculations due to the reason Reviewer mentioned. We did not intend to indicate gravitational focusing and we have therefore altered the text to specify that as follows: $b=R(1+\frac{2GM}{Rv^{2}_{\infty}})^{0.5}$ (where $G$ is gravitational constant) {\bf converges} to planet's radius $ R$, while the planet mass $M$ does not play any role as it can be seen {\bf (i.e. the right parameter in the brackets is vanishing i.e. gravitational focusing is irrelevant)}.

A:A: We thank the Reviewer for the comment. We did not mention explicitly that observed planets are not representative of reality, actually at one point in the text we mention that there are estimates about number of exoplanets of order 10^10 in our Galaxy. Thus, we revised the text to be more specific with following sentence: We note that the known population of exoplanets are not representative of the reality, since expected number of them is aabout 10^10.

A: We thank the Reviewer for these comments. We agree that it is a scientific fact that each method of measuring something has an inherent sampling bias. It is one of the constraints in any scientific study. Because of that we need a new surveys and more data, to recalculate and adjust our theories. Since Kepler examined over 200,000 stars to detect dips in starlight caused by transiting exoplanets, much of the analysis of the Kepler data had to be done by computers. Standard search algorithms attempt to identify sudden drops in brightness, and the team of astronomers are constantly developing a smarter algorithm that takes into account more parameters in order to 'extract' exoplanets from the light curves. R. Heller, M. Hippke and K. Rodenbeck published in Astronomy and Astrophysics (2019) 'Discovery and validation of 17 new sub- to super-Earth-sized planets in multi-planet systems from K2'. We assume that any analysis of the data could help designers of missions to adjust and improve the instruments and algorithm pipelines. We agree that this explanation is speculative at this level of observational and computational technology of extracitng exoplanets data, and we have edited the text to state that our conclusion is only suggested by our results: Because our results reflect the underlying exoplanets observational bias, we caution readers to keep this in mind when assessing the results. For example, the planetary size and especially the distance distribution observed are a consequence of the observational techniques and not the true spatial distribution of exoplanets. The increase of the planetary radius with distance is a direct consequence of the observational method and has no astrophysical basis. Also we added follwoing lines in Conclusion: In our study we employed available data from previous decades of exoplanets observations which were dedicated to the constraining the exoplanet population in the Milky Way on zeroth level (orbital parameters, radii and densities). However, the next generation of telescopes (e.g., James Webb Telescope, the European Extremely Large Telescope; Ariel) will provide data on the atmospheric properties of exoplanets, and improve those already obtained. It is hoped that the calculations outlined in this article will be useful to make atlases (i.e. collection of maps) of interstellar and intergalactic transfer of material within our Galaxy, indicating possible hot spots of panspermia activity, because it builds on our empirical knowledge. The future observational evidence will improve the prediction both of the HZEP probabilites and IMPs influx probabilites, and thus our understanding of the habitability of the Universe.

A: We thank the Reviewer for this comment. We explained more thorughly how hit probabilities are calculated in the section Methods and Materials: {\bf A simple analogy with military operations theory \citep{Bin78}, can aid in understanding the overall process. The calculation of the probability that a bullet impacts a target is reduced to estimating the hit probability into some region of a certain geometric shape. The basic interaction between weapon and target is given by damage function (or lethal area) D(r), which is the probability that the target is hit by a bullet if the relative distance between them (the miss distance) is r. The simple assumption that target is a planar figure with the density distribution of the position relative to the weapon PD(x,y). Then the probability of hit is determined by the double integral over the whole combat plane $\iint D(r)PD(x,y) \mathrm{d}\,x \mathrm{d}\,y$. If the target was uniformly distributed within some large $\Delta y$ area then distribution of relative target positions reduces to $PD(x,y)=1/\Delta y$ and double integral becomes $\frac{1}{\Delta y} \iint\limits_{\Delta y} D(\sqrt{x^2+y^2}) \mathrm{d}\,x \mathrm{d}\, y$. However, in our case damage function would reduce to the area of exoplanet cross section ($A_t$) and $\Delta y= \pi (\delta y)^2$ where $\delta y$ is a resolution of target's uncertainity position. Thus, the double integral would reduce to the ratio $\frac{A_t}{\Delta y}$. This is an essence of estimate of impact probabilities by adopting \cite{MM79} method. Note, that such defined probability is dimensionless.}

A: We thank the Reviewer for the comment. We improved the results and discussion section. Also it is possible to unite them into one section Results/Results and Discussion.

A: We thank the Reviewer for the comment. We wrote following paragraph to connect this subsection with the main topic in the paper, i.e. IMP: {\bf Some recent studies on interplanetary transfer of photosynthesis organism \citep{Co08} and simple life forms or bio material \citep{LL17} employed analogies with Earth ecological models of 'immigration' to qualitatively explore the possibility of interplanetary material immigration. Namely, in these analogies planets are seen as islands and even continents, and ‘immigration’ would essentially amount to transfer of lifeforms (or genetic material) via vehicles such as meteoroids. This enables us to make some qualitative description of IMPs immigration, if we assume that galaxies are 'continents' and the material exchange could probably occur only within our Local Group of galaxies. For example, the large-scale distribution of the galaxies observed by VIPERS \citep[see Fig. 15 in][]{Sco17} shows quite clearly the abundance of structures, and the segregation of the overall galaxy population as a function of the local galaxy density.}

A: We thank the Reviewer for this comment! We corrected the sentence as follows: The clustering is increasing toward the Solar system.

AC: We thank the Reviewer for this comment. We corrected typos and grammatical errors, improved sentences, added paragraphs to better explain the methods, we added a new Figure 1 to better explain the geometric and kinematic concept of the problem, we rewrite the whole Conclusion section.

Reviewer 2

Sent on 02 Aug 2019 by Dragos G Zaharescu | Approved with revisions
Georgia Institute of Technology

The topic and paper is very interesting, relevant, and overall it was an exciting read.

Except for few grammatical errors, the manuscript is well written, and easy to read by someone with general math training.

The only major concerns I have are: (i) some of the more complex mathematical formulas have to be better explained in text, to help readers from different fields better follow the logic; (ii) the last sections (Parallel with...) needs better connection with the process addressed in the rest of the paper (parallel should not be taken in its mathematical sense); and (iii) conclusions also have to be rewritten. They are currently written more of a summary list rather than conclusive remarks.

I provide line-by-line comments throughout the PDF, that hopefully will help clarify aspects mentioned above.
Other than that, I greatly appreciate the author's imagination and effort to share it.

Response to Reviewer 2

Sent on 13 Aug 2020 by Andjelka Kovacevic

Response to the Reviewer 1: We sincerely thank the Reviewer for carefully reviewing our manuscript and providing insightful feedback throughout the review process. Their comments have vastly improved the quality of this study. Accordingly, the revised manuscript has been systematically improved with new information and additional interpretations. Our responses (A) to the Reviewer’s comments (RC) are given below. Changes in the manuscript are given in bold face. A: We thank the Reviewer for all grammatical corrections. The sentences are corrected, references are added as well as the whole text is revised to improve the flow as per the Reviewer’s suggestions.

A: (I) We agree with the Reviewer's comment. The mathematical formulas were better explained following detailed Reviewer's comments given in the PDF of version 1. The conceptualization of the geometry, kinematics and parameters used in the impact probabiliies formulas is schematized in newly-added Figure 1. We also added following lines in the section Materials and Methods to help reader to follow overall calculation process: {\bf The statistical impact probability of IMPs with HZEP, can be equivalently stated as calculating probability of cooccurrence of a planet being in the habitable zone and hit by an IMP. As the geophysical properties of potentially habitable exoplanets are currently unknown, it is not possible to determine exact HZEP probabilities. Instead, we calculated HZEP probabilities as a probability density function with respect to observationally constrained planet properties (distances and radii), assuming a very optimistic geometrical HZ boundaries. The probablity density function was estimated by machine learning implementation of 2D kernel density estimate (KDE) in Python. } and {\bf Calculated HZEP probabilities are small due to small sample of HZEP confined in very large parametric space. Also, hit probabilities are small as a ratio of exoplanet cross section area and IMP's letal area. The cooccurence of such rare events can not be calculated classically by their coupling, instead the information theory metrics must be employed. For this purpose we used Entropy index.}

A:(ii) We thank the Reviewer for this comment. The last subsection (Parallel with...) is connected with the rest of the paper by following lines and new references: {\bf Some recent studies on interplanetary transfer of photosynthesis organism \citep{Co08} and simple life forms or bio material \citep{LL17} employed analogies with Earth ecological models of 'immigration' to qualitatively explore the possibility of interplanetary material immigration. Namely, in these analogies planets are seen as islands and even continents, and ‘immigration’ would essentially amount to transfer of lifeforms (or genetic material) via vehicles such as meteoroids. This enables us to make some qualitative description of IMPs immigration, if we assume that galaxies are 'continents' and the material exchange could probably occur only within our Local Group of galaxies. For example, the large-scale distribution of the galaxies observed by VIPERS \citep[see Fig. 15 in][]{Sco17} shows quite clearly the abundance of structures, and the segregation of the overall galaxy population as a function of the local galaxy density.}

A: (III) We absolutely agree with the Reviewer's comments. We rewrite the whole Conclusion, emphasizing methods and explaining obtained results.

A: The Local Group is the galaxy group that includes the Milky Way. Local Group is the name, do not invite an astronomer to be a godfather..

A: We added following lines to clarify meaning: {\bf On the chemical space we assume the property space spanned by all possible molecules and chemical compounds under a given set of construction principles and boundary conditions}.

A: We agree with Reviewer comment. We added following lines: {\bf HIP 13044, a very metal-poor star on the red Horizontal Branch and a member of the Helmi stream, was probably bounded to the Milky Way several Gyr ago from a satellite galaxy}. {\bf Because of the long galactic relaxation timescale, it is most likely that its planet (HIP 13044 b with mass of 1.25 mass of Jupiter) was not captured by any Milky Way star.}

A: We added following line: {\bf (i. e. acceleration happens when the particle drift motion is in resonance with changes in the induction electric field caused by the variable magnetic field)}

A: We clarfy the sentence as follows: projectiles ({\bf of negligible dimensions, moving on Keplerian orbits around Sun})

A: We provided the unit and reference as follows: are $\lesssim10^{-8}$ {\bf per orbital revolution} Rickman et al. 2014

A: We added Figure 1 to clarify geometry of the problem and also we added following lines; For simplicity, we will assume that an IMP follows a straight line {\bf when} entering into our Galaxy from position of our solar system. {\bf Trajectory of an IMP is within ecliptic plane and perhaps further studies should make use of 3D probes}.

A: Thank you it is really nice comment! We added following analogy: {\bf A simple analogy with military operations theory \citep{Bin78}, can aid in understanding the overall process. The calculation of the probability that a bullet impacts a target is reduced to estimating the hit probability into some region of a certain geometric shape. The basic interaction between weapon and target is given by damage function (or lethal area) D(r), which is the probability that the target is hit by a bullet if the relative distance between them (the miss distance) is r. The simple assumption that target is a planar figure with the density distribution of the position relative to the weapon PD(x,y). Then the probability of hit is determined by the double integral over the whole combat plane $\iint D(r)PD(x,y) \mathrm{d}\,x \mathrm{d}\,y$. If the target was uniformly distributed within some large $\Delta y$ area then distribution of relative target positions reduces to $PD(x,y)=1/\Delta y$ and double integral becomes $\frac{1}{\Delta y} \iint\limits_{\Delta y} D(\sqrt{x^2+y^2}) \mathrm{d}\,x \mathrm{d}\, y$. However, in our case damage function would reduce to the area of exoplanet cross section ($A_t$) and $\Delta y= \pi (\delta y)^2$ where $\delta y$ is a resolution of target's uncertainity position. Thus, the double integral would reduce to the ratio $\frac{A_t}{\Delta y}$. This is an essence of estimate of impact probabilities by adopting \cite{MM79} method. Note, that such defined probability is dimensionless.}

A: We clarifed the term with following lines: {\bf We used KDE implemented in machine learning package of Pyhton scikit-learn. KDE can be considered as a form of machine learning \citep{WS19}, where we want to estimate density but not to predict a new data given certain set of known data}. {\bf KDE discretize user-defined evaluation space (or grid), computing the density in equally separated grid points. So, the evaluation space can be represented as a multi-dimensional matrix. We defined the separation between grid points, so that we have 800 points in each dimension of 2D parameter space defined by exoplanet distances and radii. The output is KDE of the same dimensions as defined grid \citep{IV14,LN15}}.

A: We provided following definition: the impact parameter {\bf (defined as the perpendicular distance between the velocity direction of a projectile and the center of an object that the projectile is approaching)}

A: We clarifed the sentence as follows: Entropy {\bf can be viewed as the expectation of $\log(f (X))$ where $f$ is the probability density function (PDF) of a random variable X},

A: We explained it as follows: {\bf It is not given per any unit of time since the probabilities of a planet being hit by an IMP are dimensionless and $V_{j}$ are probabilities}.

A: We explained it in the section Methods as follwos: {\bf KDE discretize user-defined evaluation space (or grid), computing the density in equally separated grid points. So, the evaluation space can be represented as a multi-dimensional matrix. We defined the separation between grid points, so that we have 800 points in each dimension of 2D parameter space defined by exoplanet distances and radii. The output is KDE of the same dimensions as defined grid \citep{IV14,LN15}}.

A: We thank the Reviewer for careful reading all lines in our manuscript. Our Ministry requiers to be mentioned in Acknowldg. only.

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