This is the second part of a series where I discuss my thoughts on the Fermi Paradox: the seeming contradiction between the fact that the universe is so incredibly vast and full of places where intelligent life could, in principle, arise, and the fact that we don’t see any evidence of its existence. The most recent estimates put the total number of stars in the Milky Way galaxy at somewhere between 200 and 300 billion, and we now have evidence that most of those stars have a system of planets around them. The odds of not a single one of those planets being suitable for intelligent life would be truly astronomical. But, we do know that a very specific set of circumstances led to the formation of the Earth as we see it today, and the odds of any particular planet being a nearly exact copy of Earth might be just as astronomical. The real question is: just how many of these conditions really are necessary for the existence of complex life?

The Rare Earth Hypothesis

Probably the most comprehensive argument for scarcity of habitable planets was made by Peter Ward and Donald Brownlee in the book Rare Earth: Why Complex Life is Uncommon in the Universe. Although it was written before the recent boom in exoplanet discoveries, many of its arguments do still hold up. Ward and Brownlee argue that complex life was only able to evolve on Earth due to a set of specific circumstances that could be highly improbable. Perhaps improbable enough that Earth is the only planet in the galaxy or even the visible universe to have intelligent life.

Galactic Habitable Zone

One of these circumstances is our sun’s position in the galaxy. If we were too close to the center of the galaxy, the high density of stars could cause extinction events at a frequency too high for complex life to develop. A nearby star passing through the Oort cloud at the edge of the solar system would unleash a hailstorm of comets on the inner solar system; and, if it got closer, it could perturb the orbits of the planets, causing catastrophic climate change or even ejecting planets out of the solar system entirely. In addition, sources of high-energy radiation, like neutron stars and supernovae, become more common as you get closer to the galactic core. These dangers represent the inner edge of a galactic habitable zone somewhat analogous to the habitable zone around a star, where a planet is neither too hot nor too cold to have liquid water. The outer boundary of this galactic habitable zone is governed by stellar metallicity, the fraction of heavy elements in a star. In astronomy, anything besides hydrogen or helium is considered a heavy element. These heavy elements are produced by supernovae, so they become less abundant as you move further away from the core. Therefore, rocky planets should be rare near the edge of the galaxy.

Unlike the stellar habitable zone (or circumstellar, more accurately), the galactic habitable zone doesn’t have defined edges. It is essentially just a set of probability distributions, but that hasn’t stopped people from trying to guess at what set of boundaries would give a fairly accurate estimate for the number of stars that fit these habitability criteria, and it’s not going to stop me either. Some of these estimations narrow the galactic habitable zone down to a thin strip around where our sun is. They argue that the vast majority of the galaxy is completely desolate and devoid of habitable planets. But is this really the case?

Many estimations of a galactic habitable zone are based on the assumption that any planet would be sterilized by a nearby supernova, but how would this actually happen? At a distance of several light-years, an explosion, even one as powerful as a supernova, isn’t strong enough to destroy a planet or remove its atmosphere. The primary damage mechanism is destruction of the ozone layer by X-rays and gamma rays. The dramatic increase in UV radiation could kill off pretty much all plant life on land, and animal life would soon follow. However, UV light does not penetrate very far in water, so marine life would be left relatively unscathed. Far from sterilizing a planet, a supernova would not even kill all complex animal life. This would be a mass extinction, perhaps larger than any in Earth’s history, but it would be something that life could certainly recover from. These events would have to occur very frequently to keep complex life from advancing at all, but even if they do, it is conceivable that life, simple and complex, could eventually adapt to higher levels of UV radiation.

*Correction: [Gamma-ray bursts, LGRBs in particular, are another threat that is functionally similar to supernovae. The main difference is that they can effect planets at much longer distances because they produce a more focused beam of radiation. Marine life beyond a few meters of depth would not be directly affected but would be put under stress by a sudden dieoff of phytoplankton near the surface. It is believed that a GRB is a likely cause of the Ordovician-Silurian mass extinction which killed about 85% of marine species.]

I think star density is a much better factor for establishing the inner boundary of a galactic habitable zone. There are a little over 7 cubic parsecs of space for every star in our region of the galaxy, which is 8 kiloparsecs away from the galactic core. The increase in the density of stars as you move toward the core can be approximated by an exponential, until you get to the galactic bulge at around 3 kiloparsecs from the core, where star density increases sharply. This is, of course, ignoring local variations in density caused by star clusters and the galaxy’s spiral arms. One 2010 paper created an analytical model to estimate how many disruptive encounters a star system would experience depending on star density and velocity dispersion (which also decreases with distance from the galactic core). It does not explicitly state what distance would give an average of one encounter for every 4.5 billion years, but I have been able to glean that information from one of its plots. The boundary of the safe zone (in green) is somewhere between 4 and 5 kiloparsecs, so I’ll set my inner boundary to 4.5 kiloparsecs. There will of course be stars outside of this boundary that have disruptive encounters and stars inside that do not, but these should roughly average out.

Plot from Jiménez-Torres et al. showing average number of encounters experienced by a star system in different regions of the galaxy.

The outer boundary, governed by stellar metallicity, is not as easy to set. We have discovered planets around stars with very high and very low metallicity, but far fewer of them compared with planets around stars with metallicity similar to the sun. However, in the case of small rocky planets, this may just be a result of observation bias, since there are few low-metallicity stars in our region of the galaxy. Even so, it stands to reason that fewer rocky planets will form if there are fewer materials with which to form them, we just don’t know exactly what that relationship is. However, we do have much better data on the metallicity dependence of another limiting factor for life. We have been able to detect many gas giant planets in other regions of the galaxy, even near the galactic core, and a 2018 statistical study showed a strong correlation between metallicity and the presence of giant planets.

The presence of gas giants like Jupiter in a star system is important for habitability because they sweep the star system clean of debris in moderately eccentric orbits. A 2017 simulation study showed that without gas giants, the inner planets would experience a high rate of large impacts for billions of years. Habitable planets without gas giant companions would have a rate of mass extinctions orders of magnitude higher than Earth experiences. Since it took roughly 10 million years for ecosystems on Earth to recover their former complexity after major mass extinctions, the chance of life becoming complex enough to develop intelligence could be much lower on these planets. Planets in systems without these “comet catchers” would also have a significant chance of experiencing a sterilizing impact long after the planetary system is finished forming.

Since the equation in the 2018 paper gives the probability of gas giant formation as a function of metallicity, simply setting an outer boundary for the galactic habitable zone would not capture the whole picture. I am able to estimate this whole picture, the number of planetary systems that are safe for life, with the following equation:

Where R is the distance from the center of the galaxy, Hd is the approximate height of the galactic thin disk (350 parsecs), n(R) is the density function, and fgg(Z) is the probability of gas giant formation, dependent on metallicity. Metalicity (Z(R,T)) is dependent on distance from the galactic center R and on the stellar age T. Here, I’ve used the approximation that all stars formed 4.5 billion years ago. When I integrate this from my inner boundary to the generally accepted value for the radius of the galactic disk, I get a total of 5.43 billion star systems. A far cry from the 200 billion stars I started with.

4.5 billion years is fairly close to the average age of population-1 (high-metallicity) stars in the Milky Way, but in reality, the different ages of stars give different metallicity distributions. Later in this series, I’ll try to quantify the effect of age on the possibility of complex life existing and factor an age distribution into this calculation. That will bring down the number of stars, but it still will be a very large number.

Other Galaxies

The canonical method of categorizing advanced civilizations by energy use was created by Nikolai Kardashev in 1964, and subsequently called the Kardashev scale. There are three reference points on the original scale. A Kardashev type-1 civilization would use all the energy available on a planet, a type-2 would use all the energy produced by a star, and a type-3 would use all the energy produced by an entire galaxy.

As I mentioned in part 1, the possibility of alien civilizations constructing megastructures to utilize most or all of the energy of a star means that a consideration of the Fermi Paradox needs to take other galaxies into account as well as our own. These megastructures, known as Dyson Spheres, or more accurately, Dyson Swarms, would absorb energy from a star and re-radiate it as infra-red waste heat. Because of the sheer number of stars in our galaxy, let alone others, it is unlikely that we would detect one of them individually, but if another galaxy was filled with enough of them that they used up a large portion of the galaxy’s total energy output, we would see the galaxy as unusually bright in the mid infra-red. We should be able to detect civilizations at or near type-3 status across vast distances.

The G-HAT study, which I also mentioned in part 1, attempted to do just that using the WISE space telescope. Out of 100,000 galaxies, it found none with spectra that did not correlate with known natural phenomena, such as dust. The authors also considered the possibility that a highly advanced civilization could find ways of producing energy other than by using stars. No matter what these methods are, they would very likely produce waste heat that would show up in the frequency range detectable by WISE.

I was not able to find exactly which galaxies were used in this study, but I can make some guesses of what the population of galaxies is like based on some clues in the paper. One of the plots from the paper indicates that the majority of the galaxies in the G-HAT sample are spiral galaxies, with a minority of ellipticals. It also mentions that all galaxies are within the “local universe,” usually defined as the space within one billion light-years from Earth. Since large galaxies are more visible at long distances than smaller galaxies are, large spiral galaxies like the Milky Way probably make up the majority of the sample. Using numbers from several different sources, I estimate that there are somewhere around 500,000 large spiral galaxies in the local universe, ignoring the fraction of the sky that WISE did not survey. Assuming uniform density, the average distance of the 100,000 closest of these galaxies is 440 million light-years. This means that any galaxy-spanning super civilization in the far end of this sample would have to have been using enough energy to have qualified as near type-3 for a longer time than the entire history of complex life on Earth for them to be detectable by us today. Eventually, I’ll revisit the effect of distance and age on the number of civilizations we should expect to see once I have an estimate for how long it would take for this kind of super civilization to develop.

The Milky Way is on the high end of this category of large spiral galaxies, but there are some elliptical galaxies that are far larger. In Rare Earth, Ward and Brownlee argued that elliptical galaxies were inhospitable for life, because they contain very old stars with low metallicity. However, more recent studies have shown that very large elliptical galaxies have both high metallicity and active star formation, although this ongoing star formation is at rates much lower than in large spiral galaxies. Since this low star-formation rate corresponds to a low rate of supernovae, some have argued that very large ellipticals could be even more habitable than spirals like the Milky Way.

Given that I am not convinced that the rate of supernovae is a strong limiting factor for life, I am not so sure that this one factor is important for habitability. These chaotic galaxies have greater velocity dispersion than spirals, which would increase the probability of disruptive interactions. However, the outer regions of large ellipticals also have lower star density than corresponding regions of spirals, because the stars are more spread out in the vertical direction (using the galactic plane as a horizontal). Additionally, the vast majority of stars in these large ellipticals are still very old population-2 stars. The equation I found for the probability of gas giant formation gives only a few percent probability for the metallicity values typical of population-2 stars, but these galaxies have so many stars that each could still host billions of habitable planets that are as much as 12 billion years old. The small but still significant population of young stars in these galaxies would also contribute to their habitability.

IC-1101, The largest known elliptical galaxy with somewhere around 100 trillion stars.

Because elliptical galaxies are a minority in the G-HAT sample (even though they are a majority in the real universe), I will focus on spiral galaxies. Assuming that the sample only (or mostly) includes galaxies in the top 5% of mass, I estimate that an average galaxy in it will be about 75% of the mass of the Milky Way. Then, taking that and assuming mass directly correlates to the number of safe star systems, I estimate that the G-HAT sample includes 407 trillion safe systems. However, I am not very confident about this estimate, and am only comfortable using it within one order of magnitude; meaning I will use an absolute minimum value of 40.7 trillion safe systems from here on. If I am going to be able to explain why not one planet in any of these trillions of star systems produced a civilization that ascended to Kardashev type-3 status, I am going to find a lot more factors standing in the way of life arising, or roadblocks preventing it from progressing from single cells to galactic empires.

Next time, I will continue with the Rare Earth hypothesis, looking at the concept of the circumstellar habitable zone and how it varies for different types of stars. I will look at data on exoplanets to try to figure out just how likely it is for each stellar type to host a habitable planet, and get an estimate for how many habitable planets there are in our galaxy and, by extension, all the other galaxies we’ve investigated.

References:

P. Ward, D. Brownlee. (2000). Rare Earth: Why Complex Life is Uncommon in the Universe. New York, Copernicus Books.

G. Gozalez, P. Ward, D. Brownlee (2001). The Galactic Habitable zone I. Galactic Chemical evolution. Icarus. https://arxiv.org/pdf/astro-ph/0103165.pdf

N. Prantzos, (2006). On the “Galactic Habitable Zone” Strategies for life detection. https://arxiv.org/pdf/astro-ph/0612316.pdf

J. J. Jiménez-Torres, et al. (2010). Milky Way Habitability: A Stellar Interaction Dynamical Approach Astrobiology. https://www.researchgate.net/publication/236673845_Habitability_in_Different_Milky_Way_Stellar_Environments_A_Stellar_Interaction_Dynamical_Approach

Cool Worlds Laboratory, Jupiter : Friend of Foe? | Elisa Quintana. (2017).  https://www.youtube.com/watch?v=_nwx0i3tnKM

E. V. Quintana, et al. (2016). The frequency of Giant Impacts on Earth-Like Worlds. The Astrophysical Journal 821,2. https://arxiv.org/pdf/1511.03663.pdf

J. A. Johnson., et al. (2018). Giant Planet Occurrence in the Stellar Mass-Metallicity plane. Earth and Planetary Astrophysics. https://arxiv.org/pdf/1005.3084.pdf

Atlas of the Universe: http://www.atlasoftheuniverse.com/superc.html

J. T. Wright, et al. (2014). The G-HAT Infrared Search for Extraterrestrial Civilizations with Large Energy Supplies II. Framework, Strategy, and First Result. The Astrophysical Journal https://arxiv.org/pdf/1408.1134.pdf

A. F. Crocker, et al. (2010). Molecular gas and star formation in early-type galaxies. Monthly Notices of the Royal Astronomical Society. https://arxiv.org/pdf/1007.4147.pdf

P. Dayal, et al. (2015). The Quest for Cradles of Life: Using the Fundamental Metallicity Relation to Hunt for the Most Habitable type of Galaxy. Journal of the American Astronomical Society. https://arxiv.org/pdf/1507.04346.pdf

References for Corrections:

B. C. Thomas, et al. (2005). Gamma-Ray Bursts and the Earth: Exploration of Atmospheric, Biological, Climatic, and Biogeochemical Effects. The Astrophysical Journal 634, 1. https://arxiv.org/pdf/astro-ph/0505472.pdf