In part 4 of my Fermi paradox series, I made an estimate that there are around 66,500 truly Earth-like planets in our galaxy. This figure is the end result of a set of factors narrowing down the total number of stars in the galaxy. You may remember that when I started this analysis all the way back in part 2, I used a very unrealistic approximation that all stars in the safe regions of the galaxy were 4.5 billion years old. I did this because I had not done the analysis to figure out how long it would take for complex life to emerge on a planet, so I used 4.5 as an average value for stellar age that would hopefully give a rough estimate of the number of habitable star systems, which I could then narrow down to the number of planets that could support complex life. However, the number of Earth-like planets that exist now is not especially useful for trying to estimate the number of alien civilizations in the galaxy. To produce a civilization smart enough to develop the technology that would violate my non-observability conditions from part 1 (things like starships, Dyson spheres and super-sized radio beacons), a planet needs to have been habitable for a long time in the past. The longer the time it takes for intelligent life to develop, the more stars can be excluded by the analysis, either because they didn’t exist back then, or didn’t live long enough for a civilization to develop. Additionally, older stars have lower metallicity which means they are less likely to have comet-catcher gas giants to sweep the solar system clear of debris that would endanger a habitable planet.

A Short History of Life on Earth

To get an idea of just how long intelligent life could take to develop on other planets, we need to go through some of the major events in the history of life on Earth: events that were necessary for the evolution of human-level intelligence to be possible. Some of these events will involve random chance, making it difficult or impossible to predict how often they would occur on other planets. Others are more deterministic, taking a known amount of time that can be directly extrapolated to other planets, and can be directly plugged into a calculation.

Genesis

The oldest clear evidence of life on Earth comes from 3.8 billion years ago (BYA), almost immediately after the end of the late heavy bombardment. There are several common conclusions that people take from this. Either life forms very quickly wherever the right conditions exist; it formed around deep-sea hydrothermal vents and survived by migrating deep underground; or, it formed on Mars and was later transported to Earth by meteorites. However, there is one other explanation. Earth could simply be a statistical fluke, a planet that developed life much earlier than most.

We have not been able to figure out the exact set of chemical processes that lead to the origin of life, but like any chemical process, it will have a random component. Since we have only one data point on how quickly life arises on a habitable planet, it is impossible to do any kind of statistical analysis to figure out how often and how frequently it will happen on other planets.

Oxygenation

Gaseous molecular oxygen is a strong oxidizing agent, so it can serve as a reagent for the chemical reactions required to drive the high-energy metabolisms of animals. On Earth, oxygen is produced as a waste product of photosynthesis, since water is the most readily available source of hydrogen with which to combine with CO2 to produce complex hydrocarbons. The other types of photosynthesis that we know of require either hydrogen sulfide or free hydrogen.

Anoxygenic photosynthesis evolved not long after 3.8 BYA, but the first evidence of oxygenic photosynthesis comes from iron oxide deposits from 3.2 BYA. It took 800 million years after that for what is known as the “Great Oxidation Event” (GOE) to take place at 2.4 BYA. This is when the atmosphere permanently became oxygenated, although at only a small fraction of current levels. Before the GOE, much of the oxygen generated by photosynthetic cyanobacteria was removed from the atmosphere by chemical reactions with methane, which made up a significant portion of the atmosphere at this time. This methane was produced by another type of bacteria, called methanogens. At some point that triggered the GOE, oxygen levels became high enough to kill off the vast majority of methanogens, leading to unchecked buildup of oxygen. Additionally, the formation of an ozone layer and subsequent reduction in UV radiation allowed cyanobacteria to live closer to the surface of the ocean.

It is not clear exactly what this trigger was, but the explanations that hold up the best are geological in nature. One idea is that a cluster of proto-continents, called cratons, produced large mountain ranges that rapidly weathered away, adding lots of iron and phosphorus to the oceans. Iron and phosphorus are some of the nutrients that cyanobacteria need to thrive. Another explanation is that, as the mantle cooled down, volcanic activity produced less ultramafic rock. This is a type of rock that is high in nickel, and contains several minerals that can react to produce hydrogen. For methanogens, nickel is an essential nutrient and hydrogen is an excellent energy source. There is fairly clear evidence for a dramatic drop in nickel levels in seawater starting around 2.7 BYA and continuing for some time after the GOE. It seems more likely that the trigger for the GOE was a combination of the two effects. There is evidence for temporary spikes in oxygen long before the GOE, which seem to be correlated with collisions between cratons. This means that collisions by themselves can cause blooms of cyanobacteria, but they weren’t enough to trigger a GOE on their own. Another mechanism, such as starvation of methanogens, likely must have played a role as well.

Could alien equivalents of methanogens and cyanobacteria use different nutrients? It’s hard to say, but microbial life on Earth does seem to be exceptionally good at finding the most efficient way of producing energy, given any set of available resources. Since my overall goal is to eliminate possible solutions to the Fermi Paradox, I’ll be as conservative as reasonably possible, and assume that alien microbes do have similar restrictions to their counterparts on Earth. The geologic process, or set of processes that triggered the GOE seem like they could take substantially longer on a planet larger than Earth, since it would cool down more slowly. Using the range of planetary masses I established in part 4, and the not-unfounded assumption that planet abundance is independent of mass in this regime, I estimate that the average Earth-like planet will actually take 37% longer than Earth to reach this milestone. Since roughly half of Earth’s history takes place before the GOE, this could drastically shorten, or in some situations even eliminate the time window in which intelligent life could develop on many planets.

After the GOE, oxygen levels in the atmosphere stayed roughly constant for about 1.5 billion years. This is because the highly reactive oxygen was now exposed to the vast quantities of previously non-oxidized rock on the seabed and in the growing continents, as well as dissolved minerals in the seawater. During this period, sulfate and hydrogen sulfide were very abundant in the oceans, due to the massive quantities of volcanic sulfur on the young continents being oxidized and washed into the oceans. Sulfur-based metabolisms during this era may have played a major role in the evolution of eukaryotes, single-celled organisms far more sophisticated than anything that came before them, and the ancestors of all multicellular life. Unlike the cooling-down of a planet, this process does not follow a square-cube law, so would not necessarily take a very different amount of time on a different sized planet. More surface area on a larger planet means more rock to oxidize, but also more habitat for oxygen-producing microorganisms.

Snowball Earth

The GOE had a profound effect on the planet’s climate. Methane is a powerful greenhouse gas, and the mass extinction of methanogens triggered the longest set of ice ages in Earth’s history. This event, known as the Huronian glaciations, is one of two events during the Proterozoic eon where the planet’s surface either mostly or entirely froze over. It is believed that during these “snowball Earth” events, the climate became cold enough to reach a tipping point, where, as sea ice spread, more sunlight was reflected out into space, cooling the planet even further. Once sea ice and glaciers covered the entire planet, mechanisms for carbon sequestration were greatly restricted. Cyanobacteria no longer had access to direct sunlight, and lack of rain on a frozen planet meant that chemical weathering of rocks no longer took place. Earth remained in this frozen state until enough CO2 from volcanoes could build up in the atmosphere  to melt the snowball.

There seem to be three individual snowball Earth events as part of the Huronian era, each followed by a short warm period where cyanobacteria gorged on the abundant CO2 and mineral-rich oceans. During these periods, frequent storms drove carbon sequestration through chemical weathering, which continued until it triggered another runaway glaciation. This cycle, which lasted around 300 million years, seems to have only been broken by the increasing luminosity of the sun, although the changing positions of the continents may have also played a role.

A second set of at least two snowball Earth events occurred much later, from 750 to 630 million years ago (MYA). In this time period, known as the Cryogenian era, the trigger seems to be the breakup of the supercontinent Rodinia, which caused all major landmasses to end up near the equator. Tropical seas are very effective at absorbing heat and distributing it around the planet via ocean currents, so the relative absence of them cooled the planet enough to set off another runaway glaciation. This is not long after all available oxygen sinks were filled up, and the gas started to build up in the atmosphere.

These snowball Earth events seem to have had a minimal impact on the rate of oxygenation. Increased rates of photosynthesis during the warm and wet interglacial periods seem to have compensated (more or less) for the near-total absence of photosynthesis during the snowball Earth periods. They may have actually helped to drive the evolution of life to higher complexity. Eukaryotic algae evolved some time before the Cryogenian, but it was only during the Cryogenian interglacial period that algae became dominant over cyanobacteria. Like many future mass extinctions, this glaciation leveled the playing field by killing off most of the population of the dominant species and opening up living space for more complex newcomers to take their place.

Some very simple animals like sponges are known to predate the Cryogenian glaciation, and must have survived it; but it is hard to see how a complex ecosystem, like what would develop in the later Cambrian period, could survive such an event. Planets that form closer to the outer edge of the habitable zone could get stuck in a cycle of global glaciation events for a much longer time than the two periods that Earth experienced.

Cambrian Explosion

Oxygen levels rose steadily after the Cryogenian era, accompanied by slow growth in macroscopic animal life until one point, about 524 MYA, when everything changed. Over only 20 million years or so, all of the phyla (general categories) of animal life emerged in the fossil record, including mollusks (squids and snails), arthropods (bugs), and chordates (vertebrates), along with many other often bizarre looking animals that have since died out. This is the first time that complex multi-layered ecosystems developed, driving a predator-prey arms race that produced a number of critical evolutionary innovations, like hard shells, eyes, and brains.

Artist’s impression of a Late Cambrian ecosystem, including jellyfish, trilobites and the meter-long super-predator Anomalocaris (top left)

Oxygen levels do correlate well with bursts of biodiversity during the Cambrian period, but other environmental factors have been proposed as triggers for the Cambrian explosion. These include increased levels of minerals like calcium, that are used to make shells, and a configuration of continents that created extensive shallow seas. However great a role these factors may have played, an explosion of complex life seems inevitable on a planet with high oxygen levels and active plate tectonics.

The Great Dying

There is one more notable event in the history of Earth that may be necessary for the evolution of intelligent life. A massive set of volcanic eruptions, known as the Siberian traps, occurred during the Permian period from 252 to 251 MYA, covering most of modern-day Siberia with lava flows. In a fatal stroke of bad luck for life at the time, this happened to be the same area as a massive coal deposit formed by the lush forests of the previous Carboniferous period. The release of greenhouse gasses from the volcanic vents and the coal triggered catastrophic climate change and a mass-extinction that killed off 95% of all life. This was the greatest mass-extinction in Earth’s history, known as “the great dying.” It is thought that a short-term cooling trend caused by volcanic ash and sulfur dioxide prevented plant life from expanding to sequester the CO2 that caused a longer-term warming trend. Ocean acidification, combined with the higher temperatures, lowered dissolved oxygen levels in seawater, creating especially lethal conditions for marine life. On land, the supercontinent Pangea became a massive desert.

During this extinction, oxygen levels reached their lowest point since the Precambrian. Two groups of reptiles, the sauropsids and therapsids, survived and thrived afterwards because they each came up with a more efficient way of absorbing oxygen from the air. Sauropsids, the ancestors of dinosaurs, developed a system based on multiple air sacs that branch out from the lungs. This system allows modern birds to have a metabolism energetic enough to achieve powered flight. The therapsids, ancestors of mammals, developed a system using a muscular diaphragm to pump air through large lungs. Large brains are oxygen hogs, so human-level intelligence may have been impossible without the evolutionary innovations made during this mass extinction.

Because the Permian extinction was caused by an essentially random convergence of several geological factors, we could expect something similar to happen eventually on any planet with active plate tectonics and complex ecosystems, so this goes into the category of random factors.

The End of the World

Our sun’s brightness increases by about 1% every 100 million years, but Earth’s carbon cycle has kept compensating to keep its temperature livable for complex life ever since the Cryogenian era. Hotter temperatures (usually) lead to more plant life and more chemical weathering, which sequesters carbon out of the atmosphere; and the opposite happens when the climate swings towards colder temperatures. However, this process has limits. Without intervention by a technological civilization, Earth will reach a point, estimated at around 900 million years in the future, where the CO2 level required to keep the climate stable will be too low for large plants to survive. Chemical weathering will continue sequestering CO2 after the plants (and the animals with them) are gone.

As the sun continues to grow in brightness, Earth will keep heating up despite near zero CO2 levels in the atmosphere. At some point, the greenhouse effect provided by water vapor will cause a runaway chain reaction, leading to conditions similar to those seen on Venus today. Long after that, some 6 billion years in the future, the sun will end its main sequence lifetime and expand into a red giant, making complex life impossible on any planet anywhere near the current habitable zone, including Mars.

In between the last snowball Earth event and this minimum greenhouse limit where the carbon cycle breaks down, Earth has a time window of 1.5 billion years in which it is habitable for complex life. It took less than half of that time for humans to evolve, after many mass extinctions and climatic shifts pushed animal life towards greater complexity.

Quantifying Habitable Time Windows

Several factors govern the time window for a planet to develop complex life. The starting point of the time window, following an Earth-like pattern, comes from two factors: the time it takes for the planet to become oxygenated, and the time it takes for the planet to no longer be susceptible to a snowball-Earth style global glaciation.

Time for oxygenation is fairly straightforward. It took Earth 2.1 billion years to cool down to the point that the Great Oxidation Event could occur, and this figure will scale up proportionally with planetary mass because it follows a square-cube law. After the GOE, it took an additional 1.9 billion years for oxygen to reach the level that triggered the Cambrian explosion.

Although oxygen was the limiting factor on Earth, planets closer to the outer edge of the habitable zone would likely go through much longer cycles of global glaciations. These may not kill off all complex life, but would almost certainly kill all large specialist organisms, and would likely delay the spread of complex ecosystems to the whole planet. The last snowball Earth event occurred when solar intensity was 94.6% of its current level, so I’ll use that as the boundary for the end of a glacial phase.

The ending point of this time window could be caused by one of several different factors. The most common would likely be the minimum greenhouse limit that may cause Earth’s climate to become uninhabitable in the far future. A paper I found on this estimates that it happen at a solar intensity of 108.5% of its current value, so that’s what I will use as a limit.

Close encounters between stars, as discussed in part 2, can bombard planets with a storm of comets that would sterilize the surface, perturb their orbits to cause permanent catastrophic climate change, or possibly even eject planets from their solar system entirely. Jiménez-Torres and colleagues developed a model for the average rate of these interactions at different locations within the galaxy. This represents a purely random factor that could end a planets’ habitable time window.

Up to this point, I have included planets even at the outer edge of the habitable zone, because, as their stars become brighter over time, they will go through the same habitable period as Earth. It will just happen later in their history. In some cases, it will be so late that the star’s red giant phase will be the limiting factor on how long the planet can stay habitable, rather than its steady increase in brightness over time.

The final limiting factor on the time available for intelligent life to evolve is the time that humans evolved on Earth, which is essentially the same as now in geologic terms. A large portion of stars are not old enough to have developed complex life yet, and since the Fermi paradox deals with the question of whether or not alien civilizations exist now, not whether they will in the future, the portion of any planet’s habitable time window that takes place in the future will be excluded. When considering life in distant galaxies, the time it takes for light to travel the distance in between also needs to be included here. To be detectable by us today, a civilization in a galaxy 100 million lightyears away would need to have achieved Kardashev type-3 status 100 million years ago. In part 2, I estimated that 440 million light years was the average distance of galaxies in the G-HAT study, which attempted to find these galactic super civilizations.

Recalculating

Because of all the conditionals involved, and the added complication of multiple variables changing with distance to the center of the galaxy, it is not possible to solve this problem as a simple analytical expression. Instead, I wrote a Monte-Carlo algorithm in Matlab to complete the computation. This code essentially creates a randomly generated galaxy, based on known distributions of stellar age, location, and metallicity. Each star that has a comet catcher gas giant and a habitable Earth-like planet is assigned another set of random variables for the mass and initial position of the planet.

I only included main sequence stars of types K, G, and F in this. M-type and A-type stars represent a small fraction of the total number of habitable planets I estimated previously, and both of these stellar types represent environments for life that are very different from what we are familiar with. M-stars last a very long time, but the only habitable worlds that I would expect to see around them would be large moons in very specific orbits around gas giants in the habitable zone. A-type stars last for under 2 billion years and produce a lot of UV radiation. Since I’m trying to be as conservative as reasonably possible, and just to simplify things, I’ll assume that some unknown factors reduce the likelihood of worlds around these stars being habitable to the point that the occurrence rate for them is negligible.

Once all of the random variables are generated, each of the limiting factors for the habitable time window are calculated, including a random factor based on the chance of disruptive stellar encounters. An average of 10 of these randomly generated galaxies gives a total of 8824 planets that have been able to support complex life for a longer time than it took for humans to evolve on Earth.

The fact that Earth, with a time window of 1.4 billion years is fairly average in this plot shows that this analysis is at least self-consistent. The results also predict that there are many planets that have been capable of supporting complex life for several billion years, meaning that the prevalent sci-fi concept of ancient precursor civilizations is not unreasonable.

Error Analysis

For the Rare Earth hypothesis to be a true Fermi Paradox solution, this final number of planets that are habitable for complex life for long periods of time would need to be at or near 1. My result of 8824 may seem far from that, but I ended up using 8 separate factors to narrow down the 200 billion stars in the galaxy to the 1.2 million stars that were simulated in my Monte Carlo algorithm. Many of those factors were based on incomplete data and a large amount of guesswork on my part, and if each one of them was off by a factor of 75%, the final result would be thrown off by a factor of 10. I think the factors that I discussed in part 4 are the most likely source of large errors, but I'd be very surprised if this error was much more than a factor of 100. This is the equivalent of two unknown factors that narrow down the population of planets by a factor of 10.

The various empirical relations and distributions that my algorithm is based on are imperfect approximations of real distributions that are difficult to measure; but, even though several of these impact the result, I don’t see it being thrown off by more than a factor of 2. The resulting number of planets is just not very sensitive to changes in these inputs.

Even with the many conservative assumptions that I’ve made throughout this analysis, and postulating large errors in the positive direction, 44 is the lowest I can reasonably get the total number of planets that could produce a technological civilization. Overall, I don’t see the Rare Earth hypothesis working as a Fermi paradox solution on its own. There must be at least some biological or sociological factors that prevent civilizations on these planets from developing the kind of technology that would violate my non-observability conditions from part 1. However, it still is very helpful. Explaining why advanced civilizations did not develop on 44 suitable planets is a lot easier than doing the same for millions of planets.

Josh is part of the Space Decentral network, an organization that seeks to become a decentralized, citizen-lead space program. To get involved, join our community on Keybase: https://keybase.io/team/spacedecentral.community

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