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If we ever thought it would be easy to tell whether a planet was ‘habitable’ or not, Stephen Dole quickly put the idea to rest when he considered all the factors involved in his study Habitable Planets for Man (1964). In this second part of his essay on habitability, Dave Moore returns to Dole’s work and weighs these factors in light of our present knowledge. What I particularly appreciate about this essay in addition to Dave’s numerous insights is the fact that he has brought Dole’s work back into focus. The original Habitable Planets for Man was a key factor in firing my interest in writing about interstellar issues. And Centauri Dreams reader Mark Olson has just let me know that Dole appears as a major character in a novel by Harry Turtledove called Three Miles Down. It’s now in my reading stack.

by Dave Moore

In Part I of this essay, I listed the requirements for human habitability in Stephen Dole’s report, Habitable Planets for Man. Now I’ll go over what we’ve subsequently learned and see how this has changed our perspective.

Dole, in calculating the likelihood of a star having a habitable planet, produced his own ‘Drake equation.’

Image: Dole’s ‘Drake Equation.’

Dole assigns the following probabilities to his equation: PHP=Nsub>S Pp Pi PD PM Pe PB PR PA PL:

Pp = 1.0, Pi = 0.81, PM = 0.19, Pe = 0.94, PR = 0.9, PL = 1.0, PB = 0.95 for a star taken at random, 1.0 if there is no interference with the other star in a binary system. He calculates that for stars around solar mass there is a 5.4% chance of having a habitable planet.

I’ll only summarize his calculations as this is not the primary thrust of this essay. Some of his estimates such as Pp = 1.0, the number of stars with planets, have held up well. Others need adjusting, but by far the biggest factors that determine the likelihood of a planet being habitable for humans are those he didn’t consider in depth.

Since Dole’s report, we’ve learned a lot more about the carbonate-silicate cycle and atmospheric circulation. The carbonate-silicate cycle provides a stronger negative feedback loop over a wider range of insolation than thought at the time of his report. Atmospheric and oceanic heat transport have been shown to work more efficiently also. This leads to a more positive assessment to the range of habitability. Planets with high axial tilts and eccentricities, which Dole had excluded, are now considered potentially habitable; and more importantly, there’s the possibility that tidally-locked planets around M-dwarf stars may be habitable. M-dwarf stars being the most common in the galaxy, this makes a big difference to the number of potentially habitable planets. Nsub>S, the mass range of stars, is now opened up. Pi, the range of inclination, is probably 1.0, and PD, the probability that there is a planet in the habitable zone, which he gave as 0.63 and is still a good estimate, is now extended to M dwarfs. And given that tidally locked planets are no longer excluded, PR, the rate of rotation is not a limiting factor.

On PM, Dole’s assumptions for the size of a habitable Earth-like world have held up well. His calculations on atmospheric retention and escape conclude that planets between 0.4 Earth mass and 2.35 Earth mass could be Earth-like. Planets below 0.4 Earth mass would lose their atmospheres. Planets above 2.35 Earth mass would retain their primordial Hydrogen and Helium atmospheres and become what we now call Hycean planets or Super-Earths.

This gives a range of surface gravities, assuming a composition similar to Earth’s, of between 0.68 and 1.5 G, which would mean from a gravitational perspective most of the range is within what humanity could handle. Dole puts the upper limit at 1.25 G based on mobility measurements made in centrifuges from that time. I would agree with him even though there are a lot of people walking around today with one and a half times their ideal weight. The limiting factor for high G is heart failure at an early age, a condition extremely tall people here on Earth suffer from. If you are a six-foot person on a 1.5 G world, your heart is pumping blood equivalent to that of a nine-foot person. In this case, people of short stature have a distinct advantage. A five-foot person would have the blood pressure equivalent of being seven foot six on a 1.5 G world and six foot three on a 1.25 G world.

However, when it comes to the frequency of Earth-sized worlds in the habitable zone, Dole’s guess at PM = 0.19 is probably too high even when we now include tidally-locked planets around red-dwarf stars. He, like the rest of us until recently, had no clue that sub-Neptunes and super-Earths would be the most frequently-sized planets in the habitable zone of a roughly Sol-mass star.

From our observations, Dole’s guess on orbital eccentricity, Pe, looks like it’s in the ballpark, again due to the inclusion of red-dwarf stars with their tidally circularized orbits. With a lot of these factors, though, slight changes in probability do not make a big difference in the frequency of habitable planets. The big differences come from those he didn’t consider.

Dole noted that water coverage on a planet could determine its habitability. He did not go over this in any detail, however, mainly I suspect because he had no information to go on. He didn’t include a term for it in his calculations. But, we do know from density determinations of transiting Earth-sized planets that there’s a significant possibility that a large percentage of them may be excluded due to being covered by deep oceans. This would mean, even if they had breathable atmospheres, they would not meet Dole’s criteria for habitability.

While Dole went carefully over the range of breathable atmospheres humans could tolerate, he essentially assigned a probability of 1.0 to the formation of this atmosphere once life appears on the planet, PL, and sufficient time has passed, PA, to which he arbitrarily assigns a period of 3 billion years. He made no consideration of how likely it would be for this process to go off the rails.

Yet, if you consider the range of possible atmospheric compositions and pressures on Earth-like planets, those that meet the requirements of human habitability are narrow. This is the one factor that is most likely to winnow the field with the possible exception of average water composition.

When considering what percentage of Earth-like planets could have a breathable atmosphere: Oxygen between 100 and 400 millibars, Nitrogen less than 2.3 bar, CO2 less than 10 millibars, and no poisonous gasses, we are helped by a natural connection of these parameters. Oxygen destroys most poisonous gasses. The Carbonate-Silicate cycle will draw down CO2 to low levels. With Nitrogen we note that Venus has 3 bars of Nitrogen. Earth has a similar stock, but most of it is either dissolved in the oceans or mineralized as nitrates. Mars still has a 2.6% by volume trace of its primordial Nitrogen atmosphere. This points to a certain consistency for terrestrial planets with regard to their Nitrogen stock; however, Oxygen to Nitrogen ratios do vary from star to star. Getting the level of Oxygen within breathable parameters is more problematic, though. It’s a reactive gas that disappears with time. I can see two possible pathways that can lead to a breathable atmosphere, one abiotic and one biotic.

On the abiotic front, there’s a robust mechanism available for generating Oxygen. If the planet is warm enough to have significant quantities of water vapor in the upper atmosphere or has a steam atmosphere, then photolysis and subsequent Hydrogen escape will result in the build-up of Oxygen.

Planets less massive than the Earth-like range lose their atmospheres. Planets more massive retain their primordial Hydrogen, which means any Oxygen resulting from photolysis will recombine to form water. Intermediate-sized planets, however, can build up Oxygen via Hydrogen escape.

How much it builds up depends on the balance of production and removal. The amount produced depends on stratospheric water vapor and UV levels. The rate of removal is determined by three main processes: Oxygen escape, which is dependent on planetary mass, magnetic field strength and the strength of plasma wind from its primary; chemical reaction with reducing gasses, which is proportional to the level of volcanic emissions; and the oxidation of exposed regolith due to volcanism and weathering, the first being proportional to the level of volcanism and the second being proportional to the planet’s temperature.

Abiotic Oxygen atmospheres are probably transitory in nature over geological time periods, but I do see sufficient Oxygen being generated at various stages in an Earth-like planet’s history. The first is from the time when a planet’s red-dwarf primary is sliding down its Hayashi track towards its position on the main sequence. Due to the star’s greater luminosity at this time, an Earth-like planet destined for the habitable zone will spend 100 million to a billion years with a steam atmosphere. Models of this process indicate it could lose up to several Earth oceans of water through photolysis and Hydrogen loss. The loss of an Earth ocean translates into roughly 300 bar of Oxygen, most of which, as with Venus, will finish up oxidizing the crust. If, however, the various factors balance out, so that when the planet’s steam atmosphere condenses as the star arrives at its main sequence position, the water fraction is sufficient to provide both oceans and continents, and the Oxygen production and removal hove balanced out to produce a breathable but non-toxic level of Oxygen, then we should get a habitable planet, albeit one with a highly oxidizing surface chemistry like Mars.

If this all sounds highly unlikely, you are probably right, but there are a lot of red dwarf stars in our galaxy.

Image: Artist’s impression of the ultracool dwarf star TRAPPIST-1 from the surface of one of its planets. We’re beginning to learn whether the inner worlds here have atmospheres, but will we find that any of the seven are habitable? Credit: ESO.

Oxygen generation through photolysis occurs anytime an Earth-like planet has a high level of water loss. Mars is thought to have lost an ocean of water corresponding to 1.4% of Earth’s ocean early in its history, which translates into a total partial pressure of 4.2 bar of Oxygen (under 1 G.) This Oxygen generation would have occurred over a long period, so the partial pressure at any given time was probably low; but you’ll notice that the mineralogy of Mars from around 4 billion years ago is highly oxidizing whereas Earth’s surface didn’t become oxidizing until 2.2 billion years ago.

Also an Earth-like planet suffering from runaway greenhouse such as Venus did two billion odd years ago would also experience a build-up in Oxygen.

If the presence of life in the galaxy is sparse, then this mechanism may result in more planets having Oxygen in their atmospheres than those that get it through biotic means, so Oxygen lines in the spectra of a planet’s atmosphere would not be a good indication that it harbors life.

We are familiar through descriptions of the history of life on how the biotic process leads to a breathable atmosphere. This has implications, however. To frame this, I’ll use a model in which planets become habitable at the rate of one per million stars starting nine billion years ago. (The figure I selected is arbitrary. You are welcome to adjust it and see what sort of results you get.) Given that star formation in our galaxy is about one star per year (star formation rates have varied over time but an average of one per year will suffice for this model), this will result in the total of 9000 planets that will be habitable to humans at some point in their lifetime. There may well be many more life-bearing planets than this, but this model is only interested in the ones that become habitable to humans.

If we assume these planets have a similar evolutionary track to Earth, then the youngest 5% of these will be at the prebiotic stage. Until about 2.2 billion years ago Earth was dominated by anaerobic life, so the next 20% will have anaerobic atmospheres full of toxic gasses. Hydrogen Sulfide in particular is lethal, killing at 1000 ppm. Intrepid explorers will have to live in sealed habitats with airlocks and go around on the surface in spacesuits. Does this meet your definition of habitable?

About 2.2 billion years ago on Earth, photosynthetic aerobes got the upper hand in Earth’s chemistry and the surface became oxidized with an atmosphere of 1-2% of oxygen. If their timeline is similar to Earth’s, then 20% of these planets would fit this condition.

These planets would be a far more pleasant place to explore. Toxic gasses would be removed by the Oxygen. You could probably go around with just an oxygen concentrator on your back feeding a tube to your nose. Habitats wouldn’t need airlocks; double doors would do. How would you classify these planets?

Then 500 million years ago Earth became fully habitable when the Oxygen concentration crossed 15% and the air became breathable. This period represents 5% of the sample. However, there’s a side effect to this. Oxygen is not very soluble in water and O2 concentrations fall off rapidly with distance. This is why the macroscopic lifeforms from the Pre-Cambrian age (>500 mya) were either flat leaf-like shapes or sponges, both of which give short diffusion distances throughout the organism. Once the oxygen concentration rose, however, lifeforms could develop thickness, and with thickness, they could develop organs such as hearts and circulatory systems, which could then circulate an oxygenated fluid throughout their bodies. A breathable atmosphere allows for the development of complex macroscopic life.

And, over time, complex macroscopic life gives rise to the second side effect of breathable Oxygen levels – sapience. This has often been considered a rare possibility, a fortuitous combination of circumstance, and in the Drake equation it is assigned a low fractional value, but the idea that intelligent life is rare and unique derives from our historical and religious concept that mankind is something unique and apart from the animal kingdom. However, studies show a steady increase in encephalization over time and its widespread occurrence in different phyla and classes: octopi in the mollusks, parrots and corvids in the birds, and dolphins, elephants and apes in the mammals.

Varying levels of communication signaling have been found in numerous species. Just recently, a troop of Chimpanzees has been found to have a 390-word vocabulary constructed by combining grunts and chirps in various sequences. It therefore seems that our ability with language is merely a development of existing trends rather than something that came out of nowhere. And language is the abstract representation of an object or action, so the manipulation of language leads to abstract reasoning.

Encephalization is a tradeoff between the energy consumption of neurons and the benefits they produce in reproductive fitness. Increasing the number of neurons in an organism is easy. A simple mutation in the precursor cells allowing them to divide one more time will do this; however, organizing those extra neurons into something useful enough to justify their extra metabolic cost is a lot more difficult. But increases in neural complexity can lead to more complex behaviors, which can increase fitness or allow the creature to colonize new niches. In addition, neurons, over time, have evolved to become more efficient. Moore’s law operates, but with a doubling time on the order of 100 million years. Parrots’ neurons are both smaller and three times more energy efficient than human ones. So, not only does encephalization increase with time, but the tradeoff moves in its favor. However, like any increases in biological complexity and sophistication, this does take time.

This points to the conclusion that on planets habitable to humans, the evolution of sentience is not so much a case of if, but when.

An atmosphere breathable to humans is also flammable over most of its range, so a good proportion of these sapients would have access to fire allowing smelting technology to develop. What the model I used implies is that 50% of habitable planets will by now have had intelligent life forms evolve on them, a majority of which could develop technology.

I would support this argument by applying the Law of Universality that states that no matter where you are in the universe the laws of nature operate in the same way. This means that a planet like Earth would produce intelligent life forms. There is a certain contingent element in evolution, so the timing and the resulting life forms would not be identical; however, the broad driving forces of evolution would produce something similar. This can be seen in the many cases of convergent evolution that have occurred on Earth. How different from Earth a planet has to be before it stops producing intelligent life forms is a matter of conjecture, but if these changes cripple the evolution of intelligent lifeforms, there’s a good chance they cripple the formation of a breathable atmosphere.

What these intelligent life forms would do to their planet over the eons is a matter of speculation, but if for some reason intelligent life did not arise, then complex life could thrive and the planet would be habitable for another billion years or more – depending on the star’s spectral type – before the star’s increasing luminosity sets off a runaway greenhouse. This means that of the planets that are habitable for humans at some stage in their life approximately 15-25% will be habitable at any given time. (The upper bound assumes that there are a high proportion of them around lower mass stars with longer lifetimes.)

If, however, intelligent life develops on planets as a matter of course, then the model indicates that for every habitable planet we have now (5% of the total) approximately ten planets had intelligent lifeforms at some stage in their history (50% of the total.) And if intelligent life is a side effect of habitability, then there will be a correlation between the number of habitable planets and the number of exosolar technological civilizations in our galaxy. So, in an inversion of the usual order of things, we can estimate the number of planets habitable for humans from the number of alien civilizations in the galaxy. The model I’ve been using points to them being within an order of magnitude of each other.

Adding in the fact that we have no information on the evolution of intelligent life on non-habitable planets, then calculating the number of habitable planets from evidence of alien civilizations is an upper bound. On the other side of the scales, there’s the number of planets that are habitable through abiotic means. Planetary atmospheric spectra within the next couple of decades may give us some indication of this. If, however, we use Hanson’s estimate where he deduces that from the lack of evidence of alien civilizations in our galaxy that the number of technological life forms is just one – us – then this would also point to the number of habitable planets in our galaxy being just one: Earth.

As a final point I would like to add that while I have not done a full literature search, I have read widely in this field and have not come across as rigorous consideration as Dole’s work on defining habitability for humans and considering the likelihood of finding planets that match that criterion. The field’s general mindset seems to focus on finding the conditions upon which life arises; then it just assumes evolution will automatically lead to a habitable planet for humans. We have learned a lot since Dole wrote his paper, but there does not seem to have been much reexamination of the topic. It is perhaps time we applied our minds to it.

References

Stephen Dole, Habitable Planets For Man, The Rand Corporation, R414-R
https://www.rand.org/content/dam/rand/pubs/reports/2005/R414.pdf

Dave Moore, “’If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare’: A review”
https://www.centauri-dreams.org/2022/05/20/if-loud-aliens-explain-human-earliness-quiet-aliens-are-also-rare-a-review/

Robin Hanson, Daniel Martin, Calvin McCarter, Jonathan Paulson, “If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare,” The Astrophysical Journal, 922, (2) (2021)