This is the third part of a series in which 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. In part 2, I introduced the Rare Earth Hypothesis: a proposed solution to the Fermi paradox, which argues that complex life was only able to arise on Earth due to a specific set of highly improbable circumstances. In particular, I examined the first of these circumstances: our sun’s position in the galaxy. In this part I’ll look at two more of them: Earth’s distance from the sun, and the type of star that the sun is.

Exoplanet Discoveries

The idea that habitable planets are extremely rare has been a popular Fermi paradox solution for a very long time. Before the first extrasolar planets were discovered in the 1990s, it was an open question in astronomy whether planets of any type were common. The first exoplanets discovered were gas giants that orbited very close to their stars. Planetary formation models show that these “hot Jupiters” must’ve spiraled into their current positions from farther away from their stars, destroying or ejecting any rocky planets in their way, but the abundance of these planets in early data turned out to be a result of observation bias. The primary method used at the time for finding planets, known as the radial velocity method, involved looking at doppler shifts in the light from a star, caused by motion induced by the planet’s gravity. These signals are the strongest and easiest to detect when you have a large planet orbiting close to a star. Planet detection by radial velocity has improved dramatically since those early days. Telescopes using this method have found large numbers of gas giants far from their stars, as well as many rocky planets orbiting small nearby stars; but we started to get a much better sample of what types of planets there are in the galaxy with the launch of the Kepler space telescope in 2009.

Kepler used a different method: constantly keeping track of the brightness of a large number of stars, watching for periodic drops that would occur when planets transit in front of their stars. Kepler, along with other telescopes using the transit method, have discovered thousands of new planets. These largely fall into two populations: gas giants with masses similar to Jupiter, and planets with masses between that of Earth and Neptune. The latter category are termed “super earths,” and their likely composition is hotly debated, since these planets are unlike anything we have in our own solar system. Kepler did find some planets similar in size to Earth and a few even smaller, more like Mars; but the transit method clearly has an observation bias of its own. Transit signals are the strongest when large planets pass in front of bright stars. Additionally, to be confirmed as a transit, a signal must be observed multiple times, which is difficult if the planet has a long orbital period. For these reasons, most of the smaller planets discovered by Kepler closely orbit bright sun-like stars.

Circumstellar Habitable Zone

The circumstellar habitable zone (usually just called the habitable zone) is the region around a star in which an orbiting planet could have liquid water on its surface. Since factors besides the intensity of light illuminating a planet can affect planetary temperature (like greenhouse gasses and reflective surfaces), trying to predict the temperature knowing only the stellar intensity is very speculative. Therefore, there are several different ways of defining the habitable zone that are used, sometimes referred to interchangeably.

All of these definitions are based on the assumption that the type of life that we are looking for habitats for is life as we know it, based on carbon and water. I will stick with this assumption in my analysis since hypothetical alternative biochemistries based on ammonia and methane can only exist in very cold environments where the amount of energy available would be very limited. I think it is highly doubtful that complex life could emerge from such biochemistries, even if they were viable. The sci-fi staple of silicon-based life is also highly speculative, since silicon is far more limited than carbon in terms of what it can form chemical bonds with.

There are several environments in our own solar system where extremophile bacteria could survive, or even thrive, including the subsurface oceans of ice-shell moons, the cloudtops of Venus, and deep aquifers on Mars. However, none of these environments have liquid water exposed to sunlight. It’s this combination of a universal solvent and an abundant energy source that allowed life on Earth to develop into a complex ecosystem with large multicellular organisms. It is very possible that life of some sort could arise far outside any of the following definitions of the habitable zone, but since I am only concerned with the kind of life, as we know it, that could eventually produce technology, I’ll look for a definition of the habitable zone that only includes Earth-like conditions.

One empirical definition of the habitable zone, known as the optimistic habitable zone, uses Mars and Venus, the two data points that we are able to study in detail as boundaries. We now know that liquid water did exist on the surface of early Mars, validating its use as an outer boundary. There are also some climate models that suggest Venus may have had liquid water as recently as 700 million years ago. However, this result is based on a set of specific properties that Venus has (or was assumed to have had at that time).

Another definition that is based entirely on climate models, albeit simplistic ones, is called the conservative habitable zone. Its inner edge is the “moist greenhouse limit” where a runaway greenhouse effect will occur in an atmosphere dominated by CO2 and water vapor, superheating the planet into a state like Venus today. It is expected that most terrestrial planets will have this atmospheric composition very early in their history, since impacts with large asteroids and planetoids would frequently vaporize the oceans, as they did on Earth during the period known as the late heavy bombardment. The outer edge is the “maximum greenhouse limit” where an atmosphere dominated by CO2 would keep a planet just warm enough to have liquid water.

*Correction: [More thorough climate models that include clouds cast doubt on the boundaries of the conservative habitable zone. Clouds made from CO2 on the outer edge case and water on the inner edge case reflect light, effectively moving both habitable zone boundaries inward. The statistical studies I’ve found on the occurrence rate of habitable planets tend to stick with the simple conservative habitable zone. Since factoring in clouds moves both boundaries in the same direction, I don’t think that this changes the fraction of planets in the habitable zone by a factor significantly greater than the (rather large) error bars from the statistical studies, so they are still useful. Planets could also have liquid water at much farther distances from their star if a significant fraction of their atmosphere is made up of methane or hydrogen. However, this is incompatible with a significant concentration of oxygen in the atmosphere.]

Using the observation that sun-like stars get brighter as they mature, Michael Hart, whose more famous conjecture was explained in part 1, defined another habitable zone called the continuous habitable zone, a much narrower band where the planet is able to maintain habitable conditions for the entire lifetime of its star. However, the climate of a planet will change over time, just as the star does. Earth today is very close to the moist greenhouse limit, but billions of years ago, when its atmosphere actually was a moist greenhouse, the sun was dim enough that it was still comfortably within the conservative habitable zone. Over time, CO2 in the atmosphere was sequestered by chemical weathering: reactions between rocks and rainwater containing dissolved CO2. This process, part of the geological carbon cycle, forms a negative feedback mechanism that stabilizes the climate, since rising temperatures increase humidity and storm activity, increasing rainfall and sequestering more CO2.

In parts 4 and 5 of this series, I’ll get into how these feedback processes affect the chances of complex life evolving, and how they might narrow down the habitable zone; but, for the purposes of this analysis, I’ll just stick with the conservative habitable zone. I’ll start with the number of star systems that are safe from cosmic hazards that I estimated in part 2, which is 5.43 billion.

Stellar Types

Another factor in whether a star can host habitable planets is its size. Excluding dying stars and stellar remnants like white dwarfs and neutron stars, larger stars are generally hotter, which shifts their light output towards the blue end of the spectrum. For this reason, main-sequence stars are classified by their spectral type (M, K, G, F, A, B, and O). Size influences two key factors when looking at habitability of planets: stellar activity and stellar lifetime. Small stars have habitable zones very close in, with serious consequences for planets around them. Larger stars have shorter lifetimes, but they have an advantage in that they also have shorter active phases. All stars, including the sun, go through a phase early in life where they emit much higher levels of high energy UV and X-ray radiation. It is estimated that if the Earth during that period had the same atmosphere it does today, the sun would have stripped off the atmosphere entirely within a few million years. I will now assess the habitability of planets around each stellar type, with emphasis on the smaller ones, simply because there are many more of them. It is estimated that as many as 76% of main-sequence stars in the galaxy are M-type, and most of the rest are K-type. The only reason that the sun (a G-type star) is known as a “yellow dwarf” is that most of the stars we can see in the night sky are very large.

M-Type

As mentioned earlier, M-type red dwarfs are the most common type of star, and have very long life spans, as well as long active periods. Because these stars are dim, planets would need to be very close to them to have liquid water. The serious consequences of this are that these planets would be especially hard hit by the enhanced radiation and solar flares that these stars emit during their active phases, stripping off their atmospheres in most cases. Also, they would likely be tidally locked, meaning that one side always faces the star. That side would be perpetually baked, while the night side stayed frozen in perpetual darkness. Assuming these planets held onto an atmosphere, a narrow strip of moderate temperatures between the two sides would be wracked by extreme weather, as the atmosphere transfers vast quantities of heat energy from the day side to the night side. These factors paint a very poor picture for habitability, but can we imagine any scenarios where planets could avoid these fates? Because of how common M-type stars are, even rare edge-cases for habitable planets might be more common than Earth analogues orbiting G-type stars.

*Correction: [There are some climate models which indicate that, given the right set of climatic conditions, tidally-locked planets may have large habitable regions, including windspeeds similar to those on Earth]

Avoiding tidal locking is fairly straightforward: a planet simply needs an orbital eccentricity high enough to enter a spin-orbit resonance. This is how Mercury avoids being tidally locked to the sun. Its orbital period (year length) is exactly 1.5 times its rotational period (day length). About 30% of planets in the Open Exoplanet Database have an eccentricity higher than Mercury’s, so this appears to be fairly common. Proxima-b, the closest exoplanet to earth, has an unknown eccentricity that could be as high as .35 (Mercury’s is .21). If it was in the same 3:2 resonance, it would have a day length equal to 7.5 Earth days. This would result in much more extreme daily temperature variations than Earth experiences, but it would avoid tidal locking. Another way to avoid tidal locking would be if the habitable world was actually a moon orbiting a far more massive planet. It would be tidally locked to the host planet but would rotate with respect to the star as it orbited the host. Exomoons are very difficult to detect, and only a few have been found so far. The first was a Neptune-sized moon orbiting a planet larger than Jupiter. Although that particular configuration is probably not common, it does show that very large moons are possible.

An oxygen-rich atmosphere is a necessity for complex life (as we know it), and retaining one in the habitable zone of a M-star is more difficult than retaining liquid water. Even when they calm down after their long active phase, the output of extreme ultraviolet (XUV) radiation from M-stars is similar to that of the early sun, enough to remove oxygen from the atmosphere much faster than life could produce it. A planetary magnetic field would suppress this ion transport; but, because these planets are closer to their stars, the stellar magnetic field is stronger, and the planetary magnetic field would be suppressed. One 2016 paper estimated that a planet around an M-star would need a magnetic field 6.6 to 15 times stronger than Earth’s to keep the solar wind away from eroding its atmosphere, and would need to be many times stronger still, to resist the majority of the superflares that these stars produce.

Earth has an unusually large iron core for its size, because the cores of the two planetoids that collided during the moon-forming impact merged to form the core of the present-day Earth, while part of their mantles were blasted into orbit to form the moon. There is no clear consensus on whether planets larger than Earth would have stronger or weaker magnetic fields, because the exact process that creates Earth’s field is not fully understood. However, we can be fairly sure that slower spinning planets would have weaker fields. Even among the models that predict stronger fields for larger planets, a magnetic field greater than 10 times as strong as Earth’s is not feasible for any terrestrial planet rotating slowly enough to be in a lower-order spin-orbit resonance, even if it was completely composed of iron.

Gas giants can have far more powerful magnetic fields than terrestrial planets, so a habitable moon orbiting a gas giant could be protected from stellar activity. However, it would also need to generate its own magnetic field to protect itself from the magnetic field of the parent planet. To explain: the magnetic fields of gas giants rotate with them on a rotational period far shorter than the orbital period of a large moon would be. This means that the moon is effectively moving perpendicular to the magnetic field lines. That motion would create a Lorentz force, pushing ions generated by solar XUV rays out away from the planet. However, the field strength generated by the moon that’s necessary to keep the planetary field away from its atmosphere would be significantly less than what Earth generates.

We could imagine a moon as small as Mars retaining an atmosphere in the habitable zone of an M-star over very long timescales. It is believed that Mars lost its magnetic field due to its core cooling down; but, If it were orbiting a larger host planet, it would be continuously heated by tidal stresses. At this point, it is pure speculation how likely this scenario is, but it is a rather specific scenario. A large moon needs to either form or be captured into an orbit close enough to be inside the magnetosphere of the gas giant, but not close enough to get ripped apart by the tidal stresses.

According to a 2015 statistical analysis of the Kepler data, 16%, or one out of every 6.25 M-stars, should have a planet between 1 and 1.5 times the size of Earth in the conservative habitable zone. Gas giants, on the other hand, are quite rare around M-stars. A set of studies using several different planet-hunting methods, including radial velocity, microlensing and direct imaging, determined that only about 15% of M-stars have them. When I assume  the same 16% chance of an existing gas giant being in the habitable zone, and that there is a 5% chance of such a planet having a right-sized moon in the right orbit, I get a total of 1.3 million of these habitable moons in the galaxy.

K-Type, G-Type and F-Type

Spectral types K, G, and F fundamentally differ from M-stars in that they are not fully convective. M-stars can live for trillions of years because convection currents flow throughout the entire star, circulating fresh hydrogen fuel to the core. These convection currents also create very strong magnetic fields which create superflares, as well as the atmosphere-destroying XUV and X-ray radiation. K-, G-, and F-stars are only partially convective, meaning they have convective zones in the core and near the surface, separated by a radiative zone where no convection occurs. These stars live much shorter lives because hydrogen in the outer layers is not circulated to the core, but they provide a much more hospitable environment for life.

K-stars, or “orange dwarfs” make up 12.1% of the population of main-sequence stars. They are sometimes called “Goldilocks stars” because they are large enough to avoid most of the adverse effects of M-stars, but more stable and long-lived than G-stars like the sun. However, they still have a long active phase of a few hundred thousand to a billion years. A planet would need a strong magnetic field to keep its atmosphere, but not a freakishly strong one like what would be necessary for an M-star. A combination of distance from the star and lack of the superflares produced by young M-stars means that a planetary magnetic field would never be compressed to the point that the solar wind would directly contact the atmosphere. As long as a planet is large enough to not cool down too quickly, and has an iron-rich core, I’m going to assume that it will do just fine.

G-type “yellow dwarfs” like the sun make up 7.6% of all main-sequence stars. They have very short active phases of a few million to a few hundred million years. Planets around G-stars still need magnetic fields to retain an Earth-like atmosphere over long periods of time. These stars are large enough that lifespan starts to be a problem. I mentioned earlier how the geological carbon cycle can regulate a planet’s temperature by removing CO2 from the atmosphere over time, but I didn’t mention its limits. At some point, the CO2 levels required to keep the climate livable will be too low for plant life to survive. It is estimated that this will occur about 900 million years in Earth’s future, which is longer than the entire history of complex life on Earth, but is a smaller fraction of the history of life in general. If there was one major delay or setback in life’s progress toward becoming multicellular, Earth could have become uninhabitable before anything as complex as us had time to evolve.

F-type stars are essentially just larger and shorter-lived versions of G-stars. They make up 3% of the main-sequence population and live for between 2 and 3.2 billion years. Since it took 4 billion years for complex life to arise on Earth, these stars should only be considered if it is possible for complex life to develop much more quickly than it did on Earth. Later in this series, I’ll examine major events in the history of life on Earth, and revise my calculations with the time for life to develop as an additional factor.

Stars of types K, G, and F are much more likely to have gas giants than M-stars. A 2018 radial velocity survey found them in 8.5% of all cases. This particular survey was only capable of detecting gas giants within 2.5 AU from their stars, which is half the orbital radius of Jupiter. According to most planetary formation models of our own solar system, all of the gas giants formed between 3 and 8 AU from the sun, so I feel relatively safe multiplying this number by 4.  Adding in my factor of 4, I get 34% for the fraction of these stars that have “comet catcher” gas giants. Another statistical analysis of the Kepler data suggests that terrestrial planets are much less common in the habitable zones of K-, G-, and F-stars: that 8.6%, or one in every 11.6, of these stars has such a planet. However, there are some issues with this number. Putting aside the huge error bars for the moment, this analysis includes planets with radii between 1.5 and 2 times that of Earth. Assuming they are terrestrial, these planets would be 3.3 to 8 times the mass of Earth, and possibly too large to have a dipole magnetic field. The analysis I cited earlier for M-stars predicts roughly equal occurrence rates for these super-Earths and smaller, more Earth-like, planets, so I’ll cut this factor of 8.6% in half. That gives a total of 99 million planets around these stars.

A-Type

A-Type stars make up only 0.6% of the main-sequence population. They are interesting because they have very little convection and therefore little to no flare activity. A planet around an A-star might be able to retain an Earth-like atmosphere even with a weak magnetic field. However, these stars only last between 2 billion and a few hundred million years, so life would have to develop far more quickly than it did on Earth for one of them to produce a technological civilization.

Not many planets have been discovered around A-stars, and the vast majority that have been are gas giants. The 2018 radial velocity survey found gas giants around 20% of A-stars surveyed, a figure which I will extrapolate to 80%. Since only a few terrestrial planets have been discovered around these stars, It’s hard to do any kind of statistical analysis to determine what fraction of these stars have terrestrial planets in the habitable zone. Because there seems to be a trend of fewer terrestrial planets with increasing stellar mass, and because a wider variety of planets could retain an atmosphere around these stars, I’m going to assume  that 4.3% of these stars have habitable planets, just like with K-, G-, and F-stars. This gives a total of 6.2 million habitable, albeit short-lived planets around these stars.

B-Type and O-Type

B- and O-stars, called blue giants and supergiants, are, as the name suggests, very large, and live very short lives. The smallest, and therefore longest lived, B-stars only last for about 150 million years; a shorter time than it took for Earth to cool down after formation. O-stars live even shorter lives. Because of this, and because these stars make up only 0.13% of the total stellar population, I think I can safely exclude them from the analysis.

Adding it all up

I get a final total of 106.5 million habitable planets in the galaxy, when looking at all seven spectral types of main-sequence stars, but it’s probably a stretch to even say that this is an order of magnitude estimate. All these calculations are based on my estimate from part 2, that there are 5.43 billion planetary systems in the galaxy that are safe from cosmic hazards. I used a very unrealistic assumption in that calculation, and I will revise it once I finish investigating all of these “Rare Earth” factors that narrow down the number of planets we could expect to develop intelligent life. I will also do an error analysis to see exactly how viable the rare Earth hypothesis is.

However, these planets are only being qualified as habitable in the sense that they could have liquid water on their surfaces, and could retain an oxygenated atmosphere. There are many factors that are important for complex multicellular life beyond the type of star a planet orbits and how far it is from that star. Next time, I’ll get into the core of the Rare Earth hypothesis, and look at the specific planetary characteristics of Earth that allow it to have complex life.

References:

R. K. Kopparapu, et al. (2013). Habitable Zones around Main Sequence Stars: New Estimates. Earth and Planetary Astrophysics. https://arxiv.org/pdf/1301.6674.pdf

A. Mendez (2013). Summary of the Limits of the New Habitable Zone. University of Puerto Rico Planetary habitability Laboratory. http://phl.upr.edu/library/notes/summarylimitsofthenewhabitablezone

M. J. Way, et al. (2019). Was Venus the First habitable World of our Solar System? Geophysical Research Letters. https://arxiv.org/ftp/arxiv/papers/1608/1608.00706.pdf

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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

D. Kitzmann. (2017). Clouds in the Atmospheres of Extrasolar Planets V. The impact of CO2 ice clouds on the outer boundary of the habitable zone. Astronomy and Astrophysics. https://arxiv.org/abs/1701.07513

T. M. Merlis. (2010). Atmosphere Dynamics of Earth-like Tidally-Locked Aquaplanets. Journal of Advances in Modeling Earth Systems. https://agupubs.onlinelibrary.wiley.com/doi/full/10.3894/JAMES.2010.2.13