In this part, I’ll get into the core of the Rare Earth hypothesis, and look at the specific planetary characteristics of Earth that allows it to have complex life. Ward and Brownlee, the writers of the book Rare Earth, argue that, while microbial life may be extremely common in the universe, the kind of complex multicellular life that could eventually develop technology is very rare. My findings so far definitely back up the idea that life in general in very common. In part 3, I estimated that there were about 106.5 million planets in our galaxy able to have both liquid water on their surfaces and oxygen in their atmospheres, as well as being safe from the cosmic hazards I looked at in part 1. For those calculations, at least, I had some real data to work with, since the Kepler Space Telescope, among other telescopes, has discovered thousands of exoplanets and determined their size and orbital radius. However, that’s all the information we have on the vast majority of known exoplanets.

There is little to no available data on most of the planetary characteristics I will need to consider for long-term habitability for complex life, so I will essentially just be guessing exactly how far each of these factors cuts down the total number of planets. I’ll assign each of them a value of 50% or 10% based on how likely they seem to me. Since the objective is to see if the Rare Earth hypothesis is even valid as a Fermi paradox solution, I’ll try to cut down the starting number of 106.5 million planets as much as I can reasonably justify, given whatever data exists and the results of whatever analytical and computational models I can find.

Right Sized Planet

In Part 3, I used a definition of convenience for Earth-sized planets, which was 1-1.5 times the radius of Earth. As I mentioned in part 3, Earth’s core is larger than it would have otherwise been due to a freak planetary collision, so Venus is probably a better model for the internal composition of an average rocky planet. Using my radius range from earlier and the density of Venus, I get a range of masses from .86 to 2.9 times the mass of Earth. A 2011 paper that I found presented two models for the magnetic fields of planets larger than Earth but with similar composition. The more convincing of the two, in my opinion, predicted that planets 2 times the mass of Earth or greater would have multipole magnetic fields instead of dipole fields like the Earth, which would allow much greater atmosphere loss by solar radiation. Cutting my mass range in half, I get a maximum mass of 1.88 Earth masses. From looking at some of the plots in the paper, I think this mass would be enough for a planet to have a dipole field, so I’ll add a factor of 50% for this characteristic. It is believed that Venus itself doesn’t have much of a magnetic field, either because it rotates very slowly, because it does not have plate tectonics, or because of some combination of the two.

Planet Composition

There is some reason to think that a significant portion of planets in the galaxy may have a composition that is different enough from Earth’s that it could cause problems for life. All but one of the planets in the Trappist-1 system, some of the few terrestrial planets for which we know both the mass and radius of, have much lower densities than Earth. That, along with the unusual orbital resonance of the system strongly suggests that these planets formed much farther from their star than they are now and migrated inward into the habitable zone. Low density indicates that these planets likely do not have iron cores large enough to generate a strong magnetic field and have much more water than a similarly sized planet that formed in the habitable zone. As much as 5% of the mass of some of these planets may be water, which creates serious problems for life. Oceans this deep will reach pressures high enough to form an exotic substance called Ice VII. This is a crystalline form of H2O which can exist at room temperature and is denser than liquid water, so it doesn’t float like regular ice. A thick layer of this substance on the seabed would prevent dissolved CO2 in the ocean from reacting with rock, stopping the geological carbon cycle completely. As I explained in part 3, the geological carbon cycle is critical in regulating a planet’s temperature as its star increases in luminosity over time.

*Correction: [A mechanism has been proposed for a carbon cycle that would function to regulate the climates of ocean worlds, based on CO2 clathrate ices. However, these planets would probably still not be habitable for complex life because without direct contact between the lithosphere and the ocean, nutrients for life would be in very short supply.]

It is not clear exactly how many of the planets that look terrestrial in the Kepler data are actually snowballs that migrated inward at some point. One computational model on planet formation that I found predicts that planet migration is extremely frequent, and as many as 90% of terrestrial-sized planets may have a significant portion of their mass made up of water, so I’ll add in a factor of 10%. The most likely reason that we don’t see any of these water worlds in our solar system is that Jupiter formed fairly early and swept up the material that could’ve formed them.

It has also been argued that variations in the elemental composition of the nebulae that planetary systems form from could affect habitability. Planets that form with a higher concentration of carbon could have exotic geology based on carbides and carbon allotropes like graphite and diamond. However, most stars in our part of the galaxy actually have lower carbon content than our sun, and a very small fraction of stars have a carbon-to-oxygen ratio high enough for these carbon planets to form. Another idea that has been around for a while is that radioactive elements like Uranium and Thorium, which help to heat Earth’s core could be rare. However, all of the information I’ve been able to find suggests that super-heavy elements, which only come from type II supernovae and neutron star collisions, are spread fairly evenly throughout the galactic disk and correlate well with metallicity. This means there shouldn’t be many planets, if any at all, that have too few radioactive elements to keep their cores warm over billions of years. The ratio between iron and rock-forming elements like silicon and magnesium would also affect the ability of planets to generate strong magnetic fields, but the studies I’ve found show that the vast majority of stars do not deviate from the sun in these ratios by more than 20%.

Plate Tectonics

The process of plate tectonics on Earth is very important for life. Although the geological carbon cycle could still operate to a limited extent on a planet without plate tectonics, known as a “stagnant lid” planet, the constant recycling of Earth’s crust, pulling carbonate rocks from the surface down into the mantle, makes it much more effective at regulating Earth’s climate. Plate tectonic processes are responsible for the nitrogen that makes up most of Earth’s atmosphere, allowing the Earth to have a thick atmosphere without an extreme greenhouse effect. Chemicals from the mantle brought up by volcanism at oceanic rifts also provide food for chemosynthetic life, which some of the earliest life may have been. Later in the history of life on Earth, the constant reshuffling of the continents changed the climate drastically over geological time, driving evolution towards more complex life forms.

Would planets of significantly different mass and composition still have plate tectonics? The most detailed model that I’ve been able to find indicates that they would, as long as habitable conditions existed on the surface. This is because the hydrated minerals associated with liquid water dramatically reduce the friction between sections of the planetary crust. That model also predicts that larger planets are actually more amenable to plate tectonics than Earth. Slightly smaller planets the size of Venus would probably also be fine, since we have found evidence of past plate tectonic activity on Venus. However, these models assume a crustal composition similar to Earth. A large portion (~40%) of star systems have a magnesium-to-silicon ratio that should give their terrestrial planets a significantly different geological makeup to that of Earth. This may alter the viscosities of the crust and mantle enough to cause problems for plate tectonics, but I really don’t know for sure. Just to be safe, I’ll add in a factor of 50%.

*Correction: [There is evidence of extensive fault lines on Venus but not functioning plate tectonics at any point in the past]

Right Giant Impact

As I have mentioned before, Earth’s composition is unusual with respect to the other terrestrial planets in the solar system because of the moon-forming impact. We know now that at some point late in its formation, the proto-Earth collided with another planetoid roughly the size of Mars, named “Thea.” This impact was essentially a glancing blow which blasted off a part of the mantle of each proto-planet, which eventually coalesced to form the moon. This impact removed most of the water and atmosphere that the proto-Earth had accumulated so far. In addition to creating the moon, this impact sped up Earth’s rotation, giving the early Earth a 5-hour day and extreme tides.

We know that impacts of this magnitude are very common since we see evidence for them on every terrestrial planet in the solar system. Mercury has an extremely large core for its size, Venus has a very slow, backward spin, and Mars has the northern borealis basin, an impact crater that covers its entire northern region.

It has been argued that a large moon like ours is necessary for complex life, but I’m not so sure. An old explanation for the origin of life is that it formed in coastal tide pools, but the tides on the early Earth were more like tsunami than the tides we have today. Furthermore, the sun also produces significant tides. In any case, I tend to favor the deep sea vent hypothesis for the origin of life, since there were many more deep sea vents on the early Earth than coastlines. By slowing down Earth’s rotation, the moon makes Earth’s weather much less extreme than it would have otherwise been, but It’s likely that Earth’s day length would not be vastly different than it is today if the moon-forming impact never occured in the first place. Mars has a similar day length to Earth today, and Mars’ giant impact didn’t alter its spin much. Earth’s climate would have been dramatically altered by an impact that slowed its rotation too much (for the same reason tidally-locked planets are problematic for complex life), or by an impact that sped up its rotation but did not create a large moon. For these possibilities, I’ll add in another factor of 50%.

Axial Tilt Stabilization

The most important thing that the moon does for Earth is stabilizing its axial tilt, keeping the seasonal variations in the climate consistent and preventing any radical climatic disruption, like what would occur if Earth’s rotational axis ever pointed directly toward the sun. Tidal forces from the moon stabilize Earth’s tilt, but there are several other ways that can happen. According to a 2010 numerical model, if Earth had no moon, interactions with the other planets would still be able to stabilize its axial tilt to a limited degree. Clearly, this does not happen in every scenario since Mars has a wildly unstable axial tilt. That analysis also showed that planets which rotate backwards are more likely to be stable on their own. A planet like Mercury in a spin-orbit resonance or a moon around a gas giant would also have stable axial tilt, so the scenarios I discussed in part 3 for a habitable world around an M-type red dwarf would also be safe. For these reasons, I’ll add another factor of 50%.

Right Amount of Water

Because most of Earth’s original water must have been removed by the moon-forming impact, it is believed that the water it has today came from asteroid and comet impacts during a period known as the late heavy bombardment. It is believed that during this period, the inner planets were pelted with large objects from the outer solar system, possibly due to the giant planets rearranging themselves. Afterwards, when the oceans condensed for the final time, Earth’s crust was fairly uniform and oceans covered the entire planet, except for a few volcanic islands. Over time, regions of low density rock were added to by subduction zones, until they became fully-fledged continents.

If Earth accumulated much more water during the late heavy bombardment, or if it didn’t lose as much water during the moon-forming impact, there might not be significant land masses on Earth today. Land Masses are important for life because coastlines and estuaries provide nutrients for the most complex and active marine ecosystems. Land masses also provide a much greater diversity of environments than oceans, once life is able to adapt to them. Additionally, the weathering of rocks on land by rainwater is much more efficient at sequestering CO2 than absorption of dissolved CO2 by rocks on the ocean floor.

Alternatively, If there was too little water to form oceans, divergent plate boundaries and hot spots would not be covered by water, and therefore would not produce the hydrothermal vents, the locations where I think life most likely originated. Even if this theory about the origin of life is not true, the oceans provided habitat for the vast majority of early life. I’ve been pretty vague in setting limitations for the amount of water an Earth-like planet can have, but since the late heavy bombardment may have been an unlikely event, I’ll add a final factor of 10% for deviations in water content.

Final Result

When I multiply all of these rare Earth factors by my original planet count of 106.5 million, I get a final total of 66,535 truly Earth-like planets in the galaxy that will be habitable for simple and complex life. So far, I’ve excluded factors that shorten or lengthen the amount of time that complex life has to develop, before the planet reaches the minimum greenhouse limit. This is when stellar luminosity increases past the boundaries of what the geological carbon cycle can regulate. Although many of the evolutionary innovations that advanced the progress of life on Earth seem to be random, making it impossible for us to know for sure how long they would take on average, there are some processes that would take roughly the same amount of time for any planet with life. This makes it possible to establish a limited time window for any given Earth-like planet to produce a civilization that could violate my non-observability conditions from part 1.

Next time, I will quantify this time window and finally revisit my calculations from part 2. You may remember that when I calculated the number of “safe” star systems in the galaxy, I used the very inaccurate assumption that every star in the galaxy is 4.5 billion years old. When I establish how long this time window is, I will be able to eliminate large numbers of newer stars based on the logic that they have not had enough time for life to advance to the point of producing technology. Then, I will be able to factor in the true metallicity distribution of the remaining stars.

References:

S. N. Raymond, et al. (2018). Migration-Driven Diversity of Super-Earth Compositions. Earth and Planetary Astrophysics. https://arxiv.org/pdf/1805.10345.pdf

J. M. Brewer, D. A. Fischer. (2016). C/O and Mg/Si Ratios of Stars on the Solar Neighborhood. The Astrophysical Journal 831,1. https://arxiv.org/pdf/1608.06286.pdf

V. Adibekyan, et al. (2015). From Stellar to Planetary Composition: Galactic Chemical Evolution of Mg/Si Mineralogical ratio. Astronomy and Astrophysics 581,2. https://arxiv.org/pdf/1508.04970.pdf

N. C. Santos, at al. (2015). Constraining Planet Structure from Stellar Chemistry. Earth and Planetary Astrophysics. https://arxiv.org/pdf/1507.08081.pdf

B. J. Foley, et al. (2012). The Conditions for Plate Tectonics of Super-Earths: Inferences from Convection models with Damage. Earth and Planetary Science Letters.  https://www.researchgate.net/publication/256695143_The_conditions_for_plate_tectonics_on_super-Earths_Inferences_from_convection_models_with_damage

J. J. Lissauer, et al. (2012). Obliquity Variation of a Moonless Earth. Icarus 217,1. https://www.semanticscholar.org/paper/Obliquity-variations-of-a-moonless-Earth-Lissauer-Barnes/09dc72409cfb1bcdf63ce58a9c9ef75270a271b2

References for corrections:

R. M. Ramirez. (2018). A More Comprehensive habitable zone for finding life on other planets. Geosciences. https://arxiv.org/ftp/arxiv/papers/1807/1807.09504.pdf

M. J. Way, et al. (2016). Was Venus the first habitable world of our solar system? Geophysical Review Letters. https://arxiv.org/ftp/arxiv/papers/1608/1608.00706.pdf