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Peer-Review Record

Multiverse Predictions for Habitability: Number of Potentially Habitable Planets

Universe 2019, 5(6), 157; https://doi.org/10.3390/universe5060157

by McCullen Sandora^1,2

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Universe 2019, 5(6), 157; https://doi.org/10.3390/universe5060157

Submission received: 14 May 2019 / Revised: 18 June 2019 / Accepted: 21 June 2019 / Published: 25 June 2019

(This article belongs to the Special Issue The Multiverse)

Round 1

Reviewer 1 Report

The author took on a topic with an enormous breadth, and she should be commended. However, I don´t know whether it is even possible to do each included research area justice, and particularly in regard to habitability and habitability evaluations there are some significant shortcomings.

First, the title, is a bit misleading and should be more appropriately something along: “A Multiverse Prediction for the Number of Planets in the Habitable Zone”, since there are many more factors affecting habitability and what would constitute a habitable planet than the parameters discussed in the paper.

Although it is referred to a definition of habitability in the paper at some places, none is given. It is not made clear what the author understands under “habitability”. It appears for the author this is a terrestrial-size planet in the habitable zone, but that does not mean that planet is habitable. Our Moon fits that definition (other than that it is a moon), but our Moon is clearly not habitable.

On the other hand there are the icy moons such as Enceladus, Europa, Titan etc, which are not terrestrial, but clearly could be habitable. This should be made clear in the Introduction – also that there may be life that in fact has a different biochemistry, so all terms used here are Earth-centric and constraint to life as know it. That should be clearly spelled out. Heading (3) should be modified accordingly to “Number of Planets in the Habitable Zone (HZ) per star”. On p. 16 the author shows some understanding of HZ versus habitable and notes that the term HZ has been replaced with “temperate zone”. The reason is precisely because habitable zone does NOT mean habitable.

In regard to HZ it should be mentioned in the discussion on p. 17 that Mars, which is by most accounts outside of the HZ, would be much more Earth-like if it would be the size of Earth or better a bit larger - meaning planetary size (and resulting internal heating and activity) plays a significant role. On the other side of the extreme the author discusses planetesimals (p. 14) - yet there is not even a paragraph of discussion whether life is even possible on a planetary body below a certain size limit. In this regard Enceladus should be mentioned, which is the smallest known moon currently considered as a abode of life. And to be even a bit more to the point: Enceladus is not a terrestrial planet.

Aside the clarification of the habitability issue:

Reference (1) is not a (peer-reviewed) published paper (only arXiv) which seems to be odd since so much science is based on this precursor paper.

It appears to me that whether a hot Jupiter would still allow habitability within a solar system being a rather insignificant point

p. 17, 3^rd line: surely not till eternity, for Earth this is about 4 billion years

p. 19, subchapter on Planet Migration: it should be mentioned that our gas giants moved as well and quite a bit – and yet we do have a habitable Earth (with possibly a habitable Venus and Mars for some time as well)

p. 20 (and before): it seems to be that a lot of the processes discussed don´t really relate to different universes, but rather simply different conditions in a solar system

p. 20, second line of discussion: “influence the habitability of a system” – that is nicely phrased (contrary to many other instances)

p. 21, Table 3.

a. what is yellow S. standing for ? This has to be explained. Is it yellow star, meaning a dG star? If so, then this is not correct and the discussion needs to be expanded. There is more and more evidence that dM stars have most likely habitable planets as well, and more suitable than dG or dM stars, are actually dK and dL stars. There are several recent publications that make this point.

b. photosynthesis criterion. Life can be entirely based on chemosynthesis as seen at the hydrothermal vents on Earth and also proposed by many for the subsurface oceans on the icy moons. Again, if these possibilities are not considered in the paper, then this has to be explicitly stated so (with repercussions for title and abstract)

p. 22, “biological timescale criteria” are popping up here, but are not discussed previously in the text (unless I missed it somehow)

p. 23, last paragraph: the implications laid out here seem to be quite far-reaching, yet the wording is not clear and seems partially convoluted. Please reword and clarify.

Appendix, Table 4 and continued. It seems that this is all one table and not several different ones (as implied by the numbering). All abbreviations, including those in column 1 should be explained and spelled out.

Author Response

I thank the reviewer for their suggestions on the draft, and find that incorporating them does improve the paper.

I don’t know whether it is possible to do this research area justice either, and agree that I have not come close in this work. It is my hope that this paper will be an early entry in a research program that may take decades to complete.

The title as it is refers to the fact that this paper deals with this factor in the Drake equation, as opposed to the others in this series, and so must remain. The alternate title the reviewer suggests only highlights one 3 page section in this work. Obviously, this 40 page paper cannot provide a comprehensive determination of the number of habitable planets in other universes- the thousands of papers addressing this issue in our universe have come nowhere close to this either. The reviewer’s criticism could equally well apply to any one of this slew.

I intend eqn 1 to define the habitability of the universe, but realize I did not explicitly state this in this paper, so I added a sentence beforehand to explain. This definition is general, and does not commit to the specific details of whether a planet has to be roughly Earth sized or not, or whether it must be in the temperate zone or not. The point of the paper is to explore all four of these alternative definitions (along with many others) to determine which are compatible with the multiverse.

This paper is very terrestrial-centric. I now explicitly state this in a separate paragraph starting on line 212, when the estimation of the number of planets is commenced. This is a major assumption in this paper, and I have concrete plans to examine both the possibility of alternative biochemistry and the habitability of icy moons in this context in two separate forthcoming publications.

This is rectified by including a paragraph on line 229 discussing the (im)possibilities of life on Mars or Neptune like planets. A mention of Enceladus is included in the paragraph on line 212.

Aside the clarification of the habitability issue:

Reference (1) is not a (peer-reviewed) published paper (only arXiv) which seems to be odd since so much science is based on this precursor paper.

It seems that it was not made clear to the reviewer that this paper is to be published as the second part of a four part series in this special issue of the journal Universe, along with reference (1) and two others.

It appears to me that whether a hot Jupiter would still allow habitability within a solar system being a rather insignificant point

I have to disagree: I believe the question of whether planetary systems that possess hot Jupiters are habitable or not to be of significant scientific interest. In this context, the question of whether these systems are more prevalent in other universes is also worthy of at least a short subsection here.

p. 17, 3^rd line: surely not till eternity, for Earth this is about 4 billion years

Reworded.

I included a short discussion of the solar system in the first paragraph of this subsection.

p. 20 (and before): it seems to be that a lot of the processes discussed don´t really relate to different universes, but rather simply different conditions in a solar system

Precisely! The logic is that we are in our universe because it is exceptionally habitable. By mapping out what other universes look like, we can tell that if most of the real estate is of a certain kind other than our own, then that must be uninhabitable. Then, we may check whether locales in our universe that mimic these other universes have life. If they do, then the multiverse must be wrong.

It will be helpful to consider the following, overly simplified, purely hypothetical example: suppose we find out that our universe is one of the only ones where oceans are possible. Then the vast majority of planets in the multiverse will be completely dry, yet we find ourselves on a wet world. The only explanation for this would be that oceans are crucial for life. The corollary is that we will never find life on a completely dry world within our universe. If we ever did (in this hypothetical example), we would have a serious conflict with the multiverse.

p. 20, second line of discussion: “influence the habitability of a system” – that is nicely phrased (contrary to many other instances)

p. 21, Table 3.

The S and yellow criteria were explained in the first paper and briefly recapped in the 2^nd paragraph on page 2. Given the displacement of this table, a reference to this explanation has been included in the caption. By ‘yellow’ I am referring to stars whose wavelengths lie in the photosynthetic range, defined conservatively. This does in fact exclude the smallest m dwarf stars from being habitable. In the first paper (and in the final table) I explore relaxing this condition, but there is little difference in outcome, as explained on page 2.

The relevant issue is whether complex life may be based on chemosynthesis or not. I agree, it is entirely plausible that it may. However, as explained in more detail in the first paper of this series (and as the values of the final table will attest), this is hard to reconcile with the multiverse. It is for this reason that I assume the photosynthesis criterion for the majority of this paper.

p. 22, “biological timescale criteria” are popping up here, but are not discussed previously in the text (unless I missed it somehow)

This has been rectified by introducing this term and others on line 473.

p. 23, last paragraph: the implications laid out here seem to be quite far-reaching, yet the wording is not clear and seems partially convoluted. Please reword and clarify.

The discussion in the final paragraph has been expanded and reworded for clarity.

Done and done.

Reviewer 2 Report

This paper considers the conditions for habitability in different parts of the multiverse, where different regions of space-time could have different laws of physics. The paper is worthy of publication, but should undergo significant revision before going to press.

One overall comment is that the paper is not very well defined. One part of this ambiguity is due to our lack of knowledge about the possibilities that are available in considering the multiverse, and this aspect is unavoidable. In addition, however, the writing style is rather vague and rambling. The first task is thus to clarify the writing. Given the current state of the manuscript, it is difficult to pin down a clear path forward. The following report includes both general and specific suggestions toward clarity.

The abstract poses a number of questions, but it never actually says what the paper assumes, what the paper calculates, and what the paper concludes. This information should be included in the abstract.

The paper introduces an enormous number of parameters. Many of these parameters don't seem to make any difference to the results, whereas others do matter. It might be useful to include a table with all of the parameters, their definitions, their values (or range of values) in our universe, etc.

It might also make sense to remove the extraneous parameters. In other words, why introduce parameters that do not affect the results? Instead, you could include a discussion of the parameters/effects that one could in principle use, but are not considered here because they don't matter. And explain why they don't matter. That way, the paper itself will be more clear.

One relatively large, and largely unnecessary, part of the paper concerns Hot Jupiters. First, the conclusion is that the consideration of Hot Jupiters is not important. This makes sense, as only about 0.5 percent of stars have Hot Jupiters, whereas the galaxy has more planets than stars. So, without doing any calculation, it's clear that the presence of Hot Jupiters won't matter. Moreover, Hot Jupiters would only affect habitability if their presence somehow precluded the existence of smaller planets on exterior orbits. But we also know that this is not the case. The (now somewhat famous) Hot Jupiter Wasp-47 has two close companions, both much smaller, where one is exterior (the system also has a second, Jovian companion in a somewhat Earth-like orbit, so it could have a habitable moon in principle). I suggest discussing the Wasp-47 result, arguing that Hot Jupiters [a] don't matter and [b] don't affect habitability, and shortening the paper accordingly.

Another general comment concerns the probability values that are presented and tabulated in the paper. Most of the paper discussions constraints on the parameters of interest (e.g., the fine structure constant \alpha) to define the range of habitability. Then the paper magically presents numbers that represent the probability the multiverse realizing values within that range (e.g, equation [13]). There are two problems here: [1] It seems that all of the explanation of where these values come from is given in previous papers. This paper should be readable without reading all of the previous literature, so some explanation is warranted. [2] The previous papers (apparently) use some particular set of priors to estimate the probabilities. In spite of claims to the contrary, the results must depend on the priors (see below). And given this sensitivity to the priors, and the fact that the priors remain completely unknown, the meaning of these probabilities is called into question.

Let's consider two cases for the priors: Suppose that the mass ratio \gamma can vary by a factor of 10. As one possible case, the Planck mass could be *the* parameter of the universe (the original hope of string theory was for this to be the case). If you then choose a uniform prior, then the value in our universe is \gamma = 10^{-19}. In this scenario, it could be as large as 10^{-18}. But with a uniform prior, where any number in the interval [0,1] is allowed, the odds of getting a good result is less than 1 part in 10^{18}. If you use a log-uniform prior, as I believe is used here, then \log\gamma might be a number between, say, -38 and 0 (assuming here that one has as the same number of decades below the observed value as above). Then the odds of getting a good universe are 1 part in 38. The point is that these two cases are markedly different, and we have no means of deciding which is better, or if some completely different prior is applicable. As a result, the probabilities used here do not seem to hold any meaning. I would suggest removing the probabilities from the paper and focus on the determination of the allowed ranges of the relevant parameters, which is something that is both well-defined and meaningful.

The following comments are more specific:

Equation (7): The mass required for mass retention does not include the gravity due to dark matter, which dominates the gravitational potential well of these structures. Moreover, in other universe, the

dark matter could in principle be even more dominant.

Line 117: The depletion time scale for star formation is equated here to the free-fall time scale. This expression is probably reasonable for the initial depletion. Over long time scales, however, secondary infall, slower star formation rates, and return of material to the interstellar medium allow for a much longer span over which galaxies can make stars (so that this simple picture no longer applies).

Line 118: The text says that the threshold in mass for burning carbon is `parametrically the same' as the minimum stellar mass. The latter corresponds to burning hydrogen (not carbon), so some additional

explanation should be given here.

Line 138: This discussion seems to confuse mass infall onto the disk with mass accretion through the disk. In general, these two rates will not be the same. And, in general, neither of these rates have the time dependence \sim t^{-3/2} given here.

Lines 140/141: The text says that ``This phase of evolution occurs on the viscous timescale of the disk, which is much smaller than the accretion timescale''. However, in most cases, the viscous timescale determines the disk accretion timescale. So, again, clarification is required.

Line 158/159: The text says that stellar fusion ``will not depend sensitively on the fundamental constants''. This statement cannot be completely true. If you increase \alpha too much, then fusion shuts down. If you decrease \alpha too much, then the star becomes a bomb. If you decreases the strong force too much, then nuclei become unbound. etc. So the paper must intend to say something different at this point in the text.

Line 214/215: The text mentions that planets have a range of 8 orders of magnitude in planetary mass. This range should be defined and clarified. The largest mass for a planet is about 10 Jupiters because larger objects are degenerate and generally considered as brown dwarfs (and those larger than 80 Jupiters are stars). So the range seems to include objects from 10 Jupiters down to about 10^{-7} Jupiters, which corresponds to rocks of size R = 200 km.

On a related note: If you consider objects to be planets this far down in mass/radius scale (200 km), then all of the discussion about a peak in the mass distribution at a few Earths is incorrect. In our solar system, for example, we have already discovered about 50 dwarf planets, so the mass function must increase sharply to smaller masses.

Lines 244-248: It is not clear if the mass accounting includes the fact that only about 1 percent of the mass of the disk is contained in rocky material that can make earth-like planets. This point should be clarified. The role of the snow line is also unclear. Some theories consider it easier to make planets beyond the snow line (and then have them migrate inward); in this case, the mass limit would not be

relevant.

Line 519, the Appendix: The relevant reference for the mass infall rate is Shu 1977, ApJ, 212, 488. The reference given here is simply one of the nearly 1400 papers that cite the original.

In light of all of the above considerations, I think that the final paragraph is worded too strongly: The text says that ``.... if any of the ones we have uncovered so far is shown to the correct condition for the emergence of intelligent life, then we will be able to conclude to a very high degree of confidence (up to 5.2σ) that the multiverse must be wrong.'' This conclusion would only hold if you know the full details of all of the habitability requirements and if you know the correct priors to compute probabilities.

Author Response

I thank the reviewer for their suggestions on the draft, and find that incorporating them does improve the paper.

This is a fair point, and I have made the edits the reviewer suggests to improve clarity.

The abstract has been updated to incorporate these suggestions.

This is a good idea. I have now included this table at the end of section 1.

To address this comment, I think having the broader context for this paper is important. As the 2^nd in a series of 4 papers to be published in this journal all involved with the question of “why are we in this universe?”, this focuses on the particular subquestion “Are planets generic in the multiverse?” The overarching answer to this question is “Yes”, the corollary being that neither the presence or properties of planets can be the main reason for our being in this particular universe (as is explained in the paragraph starting on line 75). There are several exceptions to this that are highlighted as they come up (and now in the abstract), but the broad brush conclusion is that the results of this paper just do not matter as much as the other ones. This itself is an important conclusion, and the main justification for this work: planets are a generic outcome of physics, in any universe. It takes going through all the potential pitfalls discussed in the text to arrive at this conclusion.

I included the hot Jupiter section because this was brought up as a question by several people I talked to, who wondered whether they would be more prevalent in other universes. Though the answer turned out to be no, I would not go so far as to say this is obvious. Had the fraction scaled differently with parameters, it may have been important. Given that this section is actually only a page and a half, I find it reasonable to include rather than omit, to spare anyone else who wonders about it from the work.

Though I commit to the planet-planet scattering scenario here, in an original draft I had included the planet-disk interaction model as well, which ironically doubled the length of this section, without yielding any interesting results. I have included in a reference to the WASP-47 system, though I have never met anyone bold enough to claim that it represents a typical HJ system, and even if smaller outer planets can exist in these systems, HJs may influence habitability in other ways.

The quantity computed is now explained more fully before eqn 13. The issue of the priors is addressed after the reviewer’s next point.

I gave an argument for the choice of priors in the first paper of this series, that since m_p is set by dimensional transmutation, both beta and gamma will naturally be log-uniform, and alpha should be approximately uniform. These arguments are all field theoretic, and do not sensitively depend on the details of the UV physics. However, I realize that this is not known for certain, and so I explored including different priors there.

The situation is not quite as dire as the reviewer makes it out to be. The probabilities I compute are all conditioned on the fact that the values must be less than the anthropic boundary. So, in the numerical example given, p(gamma)=.1 for a uniform prior, and .97 (reported as .03) for a log-uniform. This leads to an order of magnitude difference, which in some cases can be crucial, but the best I can do is to provide a framework for computing these values, given the stated assumptions I deem reasonable, and releasing the code so that anyone may feel free to modify it for their preferred assumptions. I stress the dependence on the prior more now, both when it is first introduced on line 41 and in the conclusions.

I must reject the reviewer’s suggestion to abandon the probabilities altogether, as these are key to deriving the actual predictions for what life needs. It is only by comparing alternate notions of habitability through their different likelihoods of being in our universe that we can differentiate between them, and check against future experiments.

The following comments are more specific:

dark matter could in principle be even more dominant.

The current paper holds the dark matter to baryon ratio fixed, for simplicity: I’ve only kept track of how the expression scales with the parameters I consider. It would be interesting to incorporate this as a variable as well, and indeed I plan to do so in the future, but this will have to be left for future work.

I agree with the reviewer that I certainly could have undertaken a more thorough account of star formation than was performed here, and I’ve updated this sentence to reflect that. However, given that this bound played almost no role, a more in depth analysis does not appear warranted. I do plan to revisit this issue in a future publication related to galactic habitability.

explanation should be given here.

Clarification added.

Reworded. I deleted referencing the t^-3/2, as it was unimportant to the rest of the paper anyway.

Amended. I meant the disk lifetime.

I changed the wording to be more accurate. Again, it is probably an oversimplification to assume that the asymptotic metallicity is independent of parameters, but given that this effect changes the probabilities by less than 1%, a more sophisticated treatment is not very high priority at this time.

Reworded. Here I was referring to spherical bodies that don’t undergo fusion, so this potato radius at 200 km is exactly what I had in mind

Yes, if one is prepared to consider these planetesimals as potentially habitable, the discussion on page 15-16 is more appropriate.

relevant.

Clarified. The cold trap mechanism is discussed briefly in the migration section, but I added a reference to that discussion here, and an explicit statement about the assumptions made.

Line 519, the Appendix: The relevant reference for the mass infall rate is Shu 1977, ApJ, 212, 488. The reference given here is simply one of the nearly 1400 papers that cite the original.

Fixed.

I have included the points the reviewer brings up to give a more rounded final paragraph.

Round 2

Reviewer 1 Report

The author did try to address my review comments and succeeded to a large extent. The remaining issues I believe stems mostly from the author´s astrophysical background, while habitability researchers consider the meaning of habitability to encompass much more than just temperate conditions and the possibility of liquid water on the surface.

For the paper to be cross-disciplinary correct, I suggest the following:

(1) On the title issue:

The author wrote as response: The title as it is refers to the fact that this paper deals with this factor in the Drake equation, as opposed to the others in this series, and so must remain. The alternate title the reviewer suggests only highlights one 3 page section in this work. Obviously, this 40 page paper cannot provide a comprehensive determination of the number of habitable planets in other universes- the thousands of papers addressing this issue in our universe have come nowhere close to this either. The reviewer’s criticism could equally well apply to any one of this slew.

I suggest as a compromise to just change the subtitle from “Number of Habitable Planets” to “Number of Potentially Habitable Planets”, because with this methodology there is no way to determine the number of planets that are truly habitable. I consider this as very important and would think that this is amenable to the author..

(2) On the Earth-centric issue:

The author wrote as response: This paper is very terrestrial-centric. I now explicitly state this in a separate paragraph starting on line 212, when the estimation of the number of planets is commenced. This is a major assumption in this paper, and I have concrete plans to examine both the possibility of alternative biochemistry and the habitability of icy moons in this context in two separate forthcoming publications.

Ok, so I would clarify it a bit more to on line 213-214 by adding three references:

“It should be noted that we are restricting our attention here to surface dwelling life on planets orbiting 213 their star. So, life in subsurface oceans and/or on icy moons like Enceladus (Taubner et al., 2018), or even more exotic types of life (e.g. Bains, 2004; Schulze-Makuch and Irwin, 2006), are not considered. It is our plan to consider these alternative environments in future work.”

Bains, W. 2004. Many chemistries could be used to build living systems. Astrobiology 4: 137-167.

Schulze-Makuch, D., and Irwin, L.N. (2006) The prospect of alien life in exotic forms on other worlds. Naturwissenschaften 93: 155-172.

Taubner, R.-S., Pappenreiter, P., Zwicker, J. et al. (2018) Biological methane production under putative Enceladus-like conditions. Nature Communications 9: # 748.

(3) On habitability and underlying assumptions

Some of the underlying assumptions in the paper are tenuous and really unknown such as whether photosynthesis is really needed to sustain complex life, for example it could be envisioned a planet with lots of hydrothermal vents on the ocean floor and near the surface with chemoautotrophs that support complex life. Anyhow, my point is to show the limitations and make clear what habitability really entails. The revised paragraph is already much better at the end of the paper (538-547), but I strongly suggest to cite two landmark papers what habitability all entails and means when put in a planetary context:

Line 538: It should be stressed that there is a great deal more that these conditions omit: nothing at all is said about how habitability is affected by things like planetary eccentricity, elemental composition, water abundance, or a host of other potentially paramount aspects of a planetary system (Schulze-Makuch et al. 2011; Cockell et al. 2016). The de facto stance on all omissions is that they have no bearing on habitability, and it will only be through future work, including all possibly relevant aspects, that a fully coherent list of predictions may be assembled. Further still, though we have placed a prior on the relative availability of each type of universe based on reasonably generic arguments, the precise probabilities, and the conclusions that follow, will tremendously benefit from a way of being able to derive this prior with absolute surety.

Schulze-Makuch, D., Méndez, A., Fairén, A.G., von Paris, P., Turse, C., Boyer, G., Davila, A.F., António, M.R.S., Catling, D., and Irwin, L.N. (2011) A two-tiered approach to assessing the habitability of exoplanets. Astrobiology 11: 1041-1052.

Cockell, C.S., T. Bush, C. Bryce, S. Direito, M. Fox-Powell, J.P. Harrison, H. Lammer, H. Landenmark, J. Martin-Torres, N. Nicholson, L. Noack, J. O'Malley-James, S.J. Payler, A. Rushby, T. Samuels, P. Schwendner, J. Wadsworth, and M.P. Zorzano (2016) Habitability: a review. Astrobiology 16, https://doi.org/10.1089/ast.2015.1295

That would nicely clarify things.

Author Response

I have updated the title and included the references, as the reviewer requests. I thank the reviewer for the suggested literature, and look forward to reading them.

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