An Apple Pie From Scratch, Part IVc: Planets and Moons: Habitability

Building a habitable world is perhaps the trickiest bit of astronomical worldbuilding. Part of this comes from the dizzying array of factors involved: Both planetary systems and individual planets are complex, chaotic systems, and everything has to work out just right to allow for life, then continue to do so for billions of years to allow for complex life. But a big part of the problem comes from how little we know about what makes a planet habitable. We’ve only been able to spot planets outside the solar system—exoplanets—for a couple decades, and planets of similar size to Earth for less than half that time. Much of what we thought was secure knowledge before then has been overturned, and for all that we’ve discovered since then we won’t really be able to say what makes a planet habitable until we start finding other inhabited planets—assuming there are any in the neighborhood besides Earth.

Thus, I want to enter this discussion with the understanding that our goal here is not to determine which or how many actual planets are habitable or have life; I really don't know and I don't trust anyone who's confident they have anything close to an answer. As it stands, current estimates¹ are that about half of G- or K-type stars should have roughly Earth-sized planets within their conventionally defined habitable zones, but we currently know very little about the conditions on the surfaces of these planets, and even if we did, there are significant gaps in our understanding of which specific conditions are necessary for life.

My goal then is more to work out which sets of conditions could plausibly create a planet without any of the traits that would probably prevent it from developing complex life so far as we can currently tell, and how likely these conditions are. Whether or not any individual planet meeting these conditions will actually end up have life is largely an artistic choice on your part.

At any rate, the advantage of all this uncertainty is that we have a lot of freedom in constructing fictional habitable worlds. But too much freedom is no fun, so let’s see what the likely restrictions are based on what’s been discovered so far.

• The Habitable Zone
• Extending the Habitable Zone
• Contracting the Habitable Zone
• Seasons and Irregular Orbits
• Calculating the Habitable Zone
• Constructing a Habitable Planet
• Size
• Composition
• Other Habitability Factors
• Large Moons
• Neighboring Gas Giants
• Atmospheric Composition
• Day Length
• Luck
• Habitable Moons
• Superhabitability
• Our Little World
• In Summary
• Notes
• Appendix: A Simple Heat Model

Back to Part IVb 

The Habitable Zone

Concept of the Trappist-1 planets. NASA/R. Hurt/T. Pyle

For the purposes of this post I’m still defining “habitable” in terms of the ability to support complex life—life that has to potential to develop humanlike intelligence—and assuming that complex life requires liquid water and sufficient sunlight for photosynthesis. Again, we’ll discuss possible alternatives another time.

Note that this definition includes a temporal component as well; for a planet to develop complex life, it has to maintain habitable conditions for long enough for life to appear and evolve complexity. It’s hard to say exactly how long that might take given only one example (we’ll talk a bit more about estimating minimum timescale from that example in a later post) so for now we’ll use the current age of the Earth, 4.5 billion years, as a reasonable necessary period of habitability. Within our own solar system, Venus and Mars both likely had habitable conditions for at least hundreds of millions of years following the Late Heavy Bombardment, but only Earth has managed to stay habitable, so only Earth counts as “habitable” by our definition.

So really what we’re asking is, how do we get a planet with liquid surface water that remains in that state for billions of years?

Water itself is fairly common; it’s composed of the first and third most common elements in the universe. Even in the water-poor innermost regions of the protoplanetary disk, water could have been² delivered from planetoids flung in from beyond the iceline. Getting that water to be liquid requires a narrow range of temperatures, and the easiest way to constrain a planet’s surface temperature is to constrain the incident sunlight. Thus, the concept of the circumstellar habitable zone: close enough to the star to melt water, but not so close as to evaporate it.

The exact temperature of a planet depends on a balance between energy inputs and outputs. Solar insolation adds energy to a planet, excepting some amount that is immediately reflected away based on the planet's albedo, and the planet than radiates heat as thermal radiation at a rate that depends on its surface temperature. Thus, for any planet there is an equilibrium temperature where energy loss to thermal radiation is equal to energy gain from sunlight. We already discussed how to calculate equilibrium temperature in the last post, and the fact that its estimate for Earth is a severe underestimate at 255 K (-17 °C), compared to the actual average of 288 K (15 °C). Earth produces too little internal heat to significantly alter the surface temperature (and this will probably be true for most planets), so there must be an additional factor here.

The missing element is the greenhouse effect. For all the constructed controversy around it in recent decades, the physics is pretty straightforward: Certain gasses like CO₂, water, and methane are transparent to the visible wavelengths of most sunlight but opaque to the infrared wavelengths of thermal radiation. So visible light passes unimpeded through the atmosphere and is absorbed by the surface, but the thermal radiation emitted by the planet is partially absorbed by the greenhouse gasses, which then reemit it in all directions, such that much of it is absorbed by the planet again. This effectively reduces the rate at which the planet loses heat, and so heat accumulates on the surface and the temperature rises until the planet emits enough extra thermal radiation to reestablish an equilibrium.

Mechanism of the greenhouse effect, and humanity's influence on it. Australian Government

 
In terms of effect on temperature, water is actually the strongest greenhouse gas on Earth, accounting for over half³ of the total warming. But individual water molecules only remain in the atmosphere a few days, and so its concentration in the atmosphere is determined by temperature. Were there no other greenhouse gasses in Earth’s atmosphere, the water would quickly settle out of the atmosphere before it could cause significant warming, and with less water to cause greenhouse warming, temperatures would fall, causing more water to settle out of the atmosphere, and so on until the planet freezes over.

But if there are other greenhouse gasses present, water will tend to amplify their effect⁴. CO₂—which resides in the atmosphere for decades, longer if accounting for processes that tend to cycle it back into the atmosphere, and does not immediately react to temperature change—accounts for most of the rest of greenhouse warming (~20-30% of the total), so it is the CO₂ level that primarily determines surface temperature, and this should usually be the case for Earthlike inhabited worlds. Methane or hydrogen may have played⁵ bigger roles in Earth’s past, but neither can exist in high concentrations alongside oxygen (methane still accounts for ~5% of the total greenhouse warming, and ozone makes a similar contribution). If we want to warm a habitable planet, CO₂ is the best option.

But does this mean a planet has to form with just the right amount of CO₂ for habitable temperatures? And how does the concentration of CO₂ remain in this narrow range for billions of years, even as the star grows brighter?

To answer this, we have to see how the climate is controlled by a set of feedback cycles, which are ongoing processes where the end state of one instance affects the initial state of the next. There are two types: In a positive feedback, the process tends to reinforce changes in the initial state. Think of them like a pencil placed on its end; introduce a little tilt to the pencil, and it will become unbalanced and start to fall, tipping over more and becoming more unbalanced, until it topples over completely. Positive feedbacks are unstable, and a system dominated by them won’t last in its current state for long.

In a negative feedback, the process tends to counteract changes in the initial state. Think of them like a ball resting in the bowl; push the ball to the side, and it will roll back towards the center and lose energy to friction until it comes back to rest where it began. Negative feedbacks are stable, and a system dominated by them will last in its state indefinitely so long as the feedbacks continue to work. So if we want to keep a planet at a comfortable temperature and habitable for billions of years despite all outside influences, we need negative feedbacks to do the job.

Fortunately, we have quite a powerful one in the form of the carbon-silicate cycle, a.k.a. the “deep carbon” or “inorganic carbon” cycle. You may have heard “carbon cycle” used to describe the conversion of CO₂ to sugars and O₂ by plants and conversion of those compounds back to CO₂ by animals, but really that’s just a sideshow. The carbon-silicate cycle is a much larger, slower process that loops massive amounts of carbon through the atmosphere, oceans, crust, and mantle by geological processes. It can be aided by the presence of life, but doesn’t require it, and so it’s been going steadily since early in Earth’s history and through life’s appearance and many changes.

Stages of the carbon-silicate cycle on Earth. In principle it could also work by inorganic deposition without the need for animal shells. Source

It starts with volcanoes, which both release CO₂ stored in the planet’s interior and create vast tracts of new, exposed rock that contains, among other things, calcium. This exposed rock weathers quickly, and in the presence of water the calcium-bearing minerals will react with atmospheric CO₂ to produce calcium (Ca⁺) and bicarbonate (HCO₃^-) ions. Both ions dissolve in water and wash downstream to the ocean, where they combine to form calcite (CaCO₃) and other carbonate minerals that settle on the seafloor and also tend to trap some water with them—this is where marine life can help the process along by forming carbonate shells and then sinking to the bottom when they die. These minerals eventually make their way to subduction zones, where one tectonic plate is pushed under another and descends into the mantle (more on where and why this happens in the next post). Once in the mantle, the water helps to dissolve the minerals, splitting the calcium and CO₂ and creating a low-density magma that rises through the overlaying plate and bursts through to form volcanoes, closing the loop.

Now here’s the important bit: The rate at which CO₂ is released into the atmosphere is fairly constant, but the rate at which calcium-bearing minerals weather is tied to temperature. If there is excess CO₂ in the atmosphere, it will drive temperatures up, weathering will increase, and more CO₂ will be pulled out of the atmosphere and stored on the seafloor. If there’s a shortage of CO₂, the planet will cool and weathering will slow down while volcanic activity replenishes the atmosphere’s CO₂ supply. Whether the change in conditions is rapid or gradual, the concentration of atmospheric CO₂ will always trend towards the level necessary to maintain the temperature that best matches CO₂ production with CO₂ consumption, which happens to be a temperature that allows for liquid water on the surface and abundant life.

Interactions involved in the climate feedback. Green arrows indicate one effect increasing another, the yellow arrow indicates one effect decreasing another. Gretashum, Wikimedia

This elegant cycle is the prime factor that has kept Earth’s climate stable throughout most of its history. It is a long loop and so can take thousands of years to correct sudden upsets, as we are now discovering to our detriment. In the past unusual volcanic events have pumped extra CO₂ into the atmosphere—triggering brief warm periods and mass extinctions—or exposed vast masses of fresh calcium-rich rock—triggering cold snaps—but throughout Earth’s history the system has always returned to normal eventually. And so it should be do the same for other planets moderated by the carbon-silicate cycle even over a broad range⁶ of initial temperatures, CO₂ concentrations, and land areas. Thus, if we put an Earthlike planet with water and CO₂ in any orbit that could allow for habitable conditions with the right amount of greenhouse warming, there’s a good chance that it will become habitable without the need for further interference.

But robust as the carbon-silicate cycle is, it has to contend with positive feedback cycles affecting the planet’s climate as well. We already discussed one between greenhouse warming due to water and atmospheric concentration of water due to temperature. But even more potent is ice-albedo feedback, which is caused by the large difference in the albedos of ice (0.6-0.8) and open ocean (0.06). If a planet suddenly cools, it can cause the formation of sea ice that reflects away more of the incident sunlight, cooling the planet further; and the reverse can happen if a planet with some sea ice suddenly warms. Usually the carbon-silicate cycle overpowers the effects of ice-albedo feedback in the long term, but the latter cycle can operate on much shorter timescales—decades rather than millennia—and so can amplify brief upsets to the climate equilibrium. A sufficiently large upset could cause the oceans to evaporate away entirely, creating a “hothouse” world like Venus, or freeze over, creating a “snowball” world like Europa, before the carbon-silicate cycle can act. A planet could eventually recover from either condition (it’s easier for a snowball than a hothouse) but life may not.

Ice-albedo feedback loop; the same process can work in reverse, encouraging more freezing. Source

The ultimate limits on habitability are caused by two other positive feedbacks⁷ that kick in at certain levels of incident sunlight. To return to our feedback analogies, we might think of this like a ball placed in a bowl at the top of a hill. So long as the ball isn’t pushed hard enough to get it over the rim of the bowl, it’ll return to the center; but once it’s out of the bowl, it’s not going back in.

At the inner edge of the habitable zone, the sunlight is intense enough to keep a high concentration of water in the atmosphere even without the help of CO₂, and indeed CO₂ is expected to be largely absent on these worlds because of permanently high temperatures causing rapid consumption by weathering. But unlike with CO₂, no surface process can consume water as fast as its supplied by evaporation of the oceans. Some water is consumed by photolysis (breakup of water molecules into hydrogen and oxygen due to solar radiation in the upper atmosphere, with the hydrogen usually escaping to space), but this causes permanent loss, which can eventually lead to the planet drying out completely.

Thus, at sufficiently high insolation, a planet will either cross the moist greenhouse limit (generally⁸ when the average temperature crosses about 50 °C), at which point enough water reaches the upper atmosphere to warm the surface to near boiling and water loss by photolysis is fast enough to deplete the oceans entirely within 10s to 100s of millions of years; or the runaway greenhouse limit, at which point enough water evaporates to become the main component of the atmosphere: this effectively blocks all thermal radiation from the surface and the planet instead loses heat due to thermal radiation from the top of the atmosphere, but the temperature up there isn't closely tied to that of the surface; adding extra heat to the surface doesn't cause the whole atmosphere to heat up, it just adds more evaporated water to the bottom of the atmosphere. Thus, the planet cannot achieve equilibrium and just continuously warms until either the oceans have evaporated completely or the surface becomes warm enough to emit visible light that can penetrate the atmosphere.

It's generally agreed that planets of low-mass stars will experience a runaway greenhouse at their inner habitable limit, while those of high-mass stars experience a moist greenhouse, but which camp Earth falls into varies between models⁹. Either way, the ultimate result is that the planet ultimately dries out completely, which also means the weathering processes that sequester CO₂ stop, so that accumulates, and you end up with an extreme hothouse world like Venus with a thick CO₂  atmosphere.

Image of Venus. NASA/JPL

Going the other way, as distance from the star increases, the concentration of CO₂ necessary to maintain ideal temperatures does as well. Near the outer edge of the habitable zone, the concentration is so high (over 5 bar of just CO₂) that CO₂ clouds form. Though they may still contribute to the greenhouse effect, these clouds are reflective enough that, on balance, they cool the planet. Past the maximum greenhouse limit, an increase in CO₂ levels causes more energy loss due to reflection of sunlight by clouds than energy gain due greenhouse warming. This reverses the carbon-silicate cycle into a positive feedback (greater CO₂ causes lower temperatures causes less CO₂ consumption) and the planet cools to a snowball, and the CO₂ itself may eventually precipitate out in solid or liquid form. 

Concept of Earth in the Cryogenian. NASA.

These two(ish) limits define the edges of the “classical” habitable zone. The exact placement of these limits varies a little between models, with the dynamics of cloud cover¹⁰ near the inner HZ limit remaining a point of contention, but in our solar system they appear to fall at about 0.95 and 1.67 AU from the sun (1 AU being Earth's current distance from the sun). This puts Earth near the cusp of crossing the inner limit, and indeed we do expect¹¹ this to happen within the next 1.5 billion years.

Recognizing the limitations of current theoretical models, some researchers have designated these limits as the conservative habitable zone and also defined an optimistic habitable zone based on the assumptions that Venus and Mars had surface liquid water 1 billion and 3.8 billion years ago, respectively; accounting for the sun’s warming since then, this pushes the boundaries out to 0.75 and 1.75 AU. Both assumptions have their issues: in Venus’s case, we only have evidence that it couldn’t have had water less than 1 billion years ago and not that it did before that point (though there's some modelling to support this being possible; in Mars’s case, the evidence for a habitable climate is clearer, but we don’t know that it was at the outermost limit for water at the time, and neither do we know that any planet could manage to retain surface water longer than Mars did. But they’re decent ballpark estimates.

The optimistic and conservative boundaries of the "classical habitable zone", with some known exoplanets. Kopparapu 2018⁷

Extending the Habitable Zone

The classical habitable zone is defined for a very Earthlike planet; short days, large oceans, and a similar atmosphere. But ever since the zone was defined, researchers have been considering how more alien worlds may be able to retain habitable conditions outsize the typical limits.

First off, a thicker atmosphere can help by increasing the planet's albedo and altering the atmospheric temperature profile to more effectively radiate heat; with a 5-bar nitrogen atmosphere, the inner limit shifts⁹ to about 0.9 AU, with more dramatic improvements for hotter stars (the numbers I'll give in this section are all appropriate for a sunlike star; we'll discuss how to account for different stars later). though this depends on rotation rate¹² as well; slower-rotating planets may benefit from atmospheric pressures closer to Earth's. Atmospheric pressure also influences¹³ how efficiently heat diffuses over the surface and thus how much surface temperature varies; higher than 2-3 bar practically guarantees habitable temperatures across the whole surface (given a habitable average temperature), while at below 0.1 bar, poor heat transport means that a planet can have a boiling equator and freezing poles simultaneously, but a habitable temperate strip is still possible; 0.015 bar is around the minimum for sustained habitability anywhere on the planet’s surface given daily and seasonal temperature shifts.

A more substantial improvement can be made by slowing a world’s rotation, or make it fully tidal-locked. Such a world could develop¹⁴ large permanent cloud formations on its sun-facing side that substantially increase its albedo and so help keep it cool; the exact estimates vary but this might push¹⁵ the inner HZ limit to around 0.73 AU. Around K-type and early M-type stars, such planets could even¹⁶ pass the moist greenhouse limit with habitable temperatures and slow-enough water loss for oceans to survive billions of years, remaining habitable right up to the runaway limit. Once the orbital period drops below 5 days the climate essentially returns to that of a rapidly-rotating planet and the protective cloud formations no longer form, but even close to this inner limit that should only be a concern for stars below 0.1 solar masses.

But some of the most dramatic improvements can be made by counterintuitively getting rid of as much water as possible. Water is vital to both Earthlike life and the carbon-silicate cycle, but it’s a bit dangerous to have around because it both amplifies the greenhouse warming of CO₂ and causes ice-albedo feedback. Land typically has an albedo of 0.15 to 0.4, intermediate between ice and water, and so compared to an ocean-dominated planet, a land-dominated planet¹⁷ will be cooler near the inner edge of the habitable zone and warmer near the outer edge, extending the limits of the habitable zone. Thus the habitable desert planet, a long-time favorite of many authors, is not only feasible but may be easier to come by than a more Earthlike habitable world. They wouldn’t all be hot, marginal worlds, either; lakes and seas with forested shorelines could still exist on an otherwise dry world, and the range of surface temperatures would be much the same as for a wetter world.

Concept of Kepler-62f. NASA/Ames/JPL-Caltech

Still, such a world would likely have less total biomass than a similar-sized Earthlike world (depending on exactly how dry it is), and may have a tougher time developing complex life. Worse, the lack of ocean basins means it cannot experience subduction or plate tectonics, a vital component of the carbon-silicate cycle. Fortunately there are alternative tectonic modes that could sustain the cycle as well (more on them another time) but they may not do as good a job stabilizing the climate over the long term.

But assuming that the carbon-silicate cycle could operate even with extremely low surface water, the limits can be pushed to surprising extremes. A moist or runaway greenhouse requires an available source of water, so restricting all bodies of water to the cooler polar regions can push the inner limit¹⁸ to around 0.75 AU. If there is almost no surface water, such that a runaway greenhouse is impossible, the limit moves to¹⁹ 0.59 AU, and if one assumed a very high if questionably plausible surface albedo of 0.8 (perhaps due to vast salt flats from a former ocean, but even that's a stretch), it could be as close as 0.38 AU—inside the orbit of Mercury. In these cases most of the planet is dry and barren, but what little water there is collects in ice caps at the poles or on the nightside of a tidal-locked world and melts around the edges, forming a small habitable strip with liquid water. This marginal existence in the twilight zone between a glacier and a sweltering desert may not seem the ideal place to develop life, but all the elements are there.

Inner edge of the habitable zone for dry planets with N₂ atmospheres, albedo of 0.2, and humidity of Ф. Zsom et al. 2013¹⁹

Helpfully, a desert planet need not necessarily start out so dry; around sunlike stars, a planet with around 5-20% as much surface water as Earth (depending on its exact distance from the star) that passes the inner HZ edge may be able to lose enough of its water through atmospheric escape to avoid a full runaway state²⁰, thus gracefully transitioning to a habitable desert planet with some surface water remaining. Tidal-locked planets of K- and early M-type stars can remain habitable even during the moist greenhouse state¹⁶, giving them time to lose even Earth-equivalent oceans and transition to desert planets; planets of very small late M-type are also habitable through the moist greenhouse but lose water too slowly and so again would need small initial oceans.

Going the other way, we can extend the habitable zone outwards mostly by introducing other greenhouse gasses. Augmenting poorly-performing CO₂ with methane can push the outer edge²¹ to about 1.81 AU, but only for mid K-type stars and hotter (under the different light of cooler stars, it's actually a detriment). However, raising to methane level to more than about 1/10 that of CO₂ could form a haze that cools the planet, and methane cannot coexist in high concentrations with oxygen. Methane might be produced by geological activity, but a more stable climate may result if it is instead produced by life, which might produce methane until it reaches levels high enough to start forming a haze, creating a stable feedback where increased methane causes haze formation and cooling that reduces the activity of methanogenic life and decreased methane increases that activity.

A more dramatic improvement can be made with hydrogen, which can act as a greenhouse gas at sufficient pressure and condenses at much lower temperature. Just 0.05 bar of H₂ in an otherwise N₂/CO₂/H₂O atmosphere can push²² the outer edge to 1.94 AU, and 0.5 bar can push it to 2.4 AU.

Outer habitable zone limits for planets with given H₂ contents. "Effective flux" is a measurement of the sunlight the planet receives relative to Earth. Ramirez and Kalteneggar 2017²²

Maintaining such an atmosphere is a challenge given that hydrogen easily escapes into space and is not produced in large amounts on Earth currently. But a planet with different internal chemistry—closer to that of early Earth—might produce volcanic hydrogen and could reasonably reach H₂ levels in this range (though the same may not be true²³ for planets of M-type stars which have higher escape rates in their closer orbits).

But a sufficiently large planet may be able to retain an even thicker H₂-dominated atmosphere accreted as it first formed, and the chances of such an atmosphere happening to produce habitable surface temperatures are not actually too bad²⁴. At the extreme limits, 100 bar of H₂ could push the limit all the way²⁵ to 15 AU. Do note that very little visible light will pass through the thick atmospheres necessary for planets more than a few AU out, though even at the extremes at least some marginal photosynthesis is likely possible.

Atmospheric hydrogen necessary for a habitable climate (left) and flux of light appropriate for Earth-like photosynthesis reaching the surface of planets with such atmospheres (right; this is around 160 W/m^2 for Earth). Pierrehumbert and Gaidos 2011²⁵

If life appears on such a world, however, there’s a good chance it will metabolize the hydrogen into methane or produce oxygen that will react to form water, destroying its own environment. But if the rate of hydrogen consumption is linked to temperature and the planet is continuously outgassing more hydrogen, then a stabilizing negative feedback may result²⁶: Excess consumption of H₂ will cause temperature to drop and consumption with it, allowing the H₂ to be replenished by volcanic activity; and excess production will increase consumption. But unlike the carbon-silicate cycle, this feedback would be totally dependent on life, and if a sudden rise in H₂ and temperature caused a mass extinction—as has happened with CO₂ in Earth’s past—the dwindling population of survivors may be increasingly incapable of consuming enough hydrogen to prevent their own demise.

But even if these solutions aren’t viable in the long run, a planet that forms just past the conventional habitable zone might be kept warm by a hydrogen or methane atmosphere until the sun is warm enough that it can lose that atmosphere without issue.

Other possible alternative greenhouse gasses include hydrogen peroxide²⁷, ammonia²⁸, nitrous oxide²⁹, and carbon monoxide³⁰ but the potential limits of habitability with these gasses have not been formally explored and the plausibility of any becoming a major component of an atmosphere varies.

Expanded habitable zone with extremely dry and H₂-greenhouse planets accounted for, with the positions of some likely-rocky exoplanets shown. Seager 2013³¹

 

Taken altogether, combining the more plausible (though still unproven, I emphasize) options here might give us a more optimistic HZ range of about 0.6 to 2.4 AU.

Contracting the Habitable Zone

Before we get too optimistic about the prospects for habitability, we should also consider a couple possible issues that have been raised over the years that could limit habitability even past the initial conservative estimates.

One issue is that rocky planets essentially start life in a hothouse state, with a warm—perhaps even molten—surface and thick steam atmosphere. Achieving habitability requires the planet to cool enough for the water to condense to the surface, and this may not be possible³² for planets receiving more than about 95% Earth's current insolation, corresponding to an orbit at about 1.03 AU. Earth is habitable today because, when it formed, the sun was only about 70% as bright as today, placing the limit at about 0.83 AU; but Venus, at 0.72 AU, may indeed have been uninhabitable from the start. This could particularly³³ offset the proposed wider habitable zones of tidal-locked planets, because the atmospheric circulation of such hot steam atmospheres actually creates a cloudless dayside rather than thick cloud cover. As some consolation, researchers have delightfully proposed calling such young, hot, partially cloudless worlds mochi planets, with—quoting directly from an academic paper here—"the planetary surface represented by red bean paste, and the cloud layer represented by the sticky rice in which someone has taken a bite. Yummy!"

 

Maximum stellar flux (relative to Earth) to allow for a primordial steam atmosphere to collapse to the surface, and then likely current stellar flux of planets initially at this limit around stars of various ages (Gy = billion years), presuming standard main-sequence evolution. Turbet et al. 2023³³

Planets near the outer edge of the habitable zone may have a similar issue whereby if they enter a fully frozen snowball state, they may never be able to recover. In the inner HZ, a snowballed planet will experience very little surface weathering, and so volcanic CO₂ can simply accumulate in the atmosphere until high enough to force the ice to melt. But a planet receiving less sunlight requires more CO₂ to reach that point, potentially reaching levels high enough for the CO₂ to begin condensing at ice at the poles; at a certain point,  the CO₂ condenses as fast as it is produced, and if this happens at a level still too low to melt the ice, CO₂ levels stabilize, the CO₂ ice may become trapped under water ice, and the planet may never recover to a more habitable temperature.

For broadly Earthlike conditions this seems to happen³⁴ at about 1.3 AU, but the limit could vary considerably depending on the planet's axial tilt, rotation rate, and topography and the star's effective temperature. Desert planets may again be at an advantage here, as they may lack sufficient water for global ice cover, so albedo doesn't rise as much and CO₂ ice isn't buried under water ice. But even for wet planets, this may not be so bad as it sounds, as outer-HZ planets probably have more stable climates and are less prone to snowballing³⁵ anyway, as their higher CO₂ levels may more effectively buffer upsets from volcanic events or biological activity; rapidly removing 500 ppm of CO₂ from the atmosphere will have a big impact on a word that initially had 1,000 ppm of CO₂, but do barely anything to one with 100,000 ppm of CO₂.

But this may be more of a problem³⁶ for planets that initially form outside the HZ and then cross the outer limit as their star warms; with a star like our sun that was again initially only about 70% as bright as it currently is, a planet that formed beyond 1.4 AU would have been outside the HZ and might remain frozen today even if well inside it.

Even some planets that begin initially warm may struggle to maintain the high levels of CO₂ required for habitability in the outer habitable zone. High CO₂ levels drive high rates of weathering and CO₂ sequestration even at low temperatures, so high levels of volcanic outgassing are required to sustain the necessary CO₂. If a planet lacks sufficient CO₂ outgassing, it may enter a condition³⁷ known as limit cycling: CO₂ levels decline until the planet is plunged into a prolonged snowball period with global glacial cover; this stops weathering and allows CO₂ to rise again and eventually return the planet to habitable conditions (unless stopped by CO₂ condensation, as mentioned above), but only briefly before another crash back to a snowball. Each cycle, the cold period is longer and the warm period shorter, until the planet finally freezes over for good.

An example of temperature and CO₂ level shifts during limit-cycling of a planet in the outer region of the HZ for a sunlike star. Haqq-Misra et al. 2016³⁷

Whether or not Earth's current rate of volcanism would be sufficient to prevent this fate in the outer habitable zone at its current age varies between models, with some recent research³⁶ suggesting it may also depend on factors like land distribution, surface geology, and biological activity. A planet with a large equatorial continent may also be able³⁸ to settle into a marginally habitable but stable climate where most of the surface remains frozen but the continental interior thaws, allowing for enough weathering to balance CO₂ outgassing and preventing further warming. Tidal-locked planets and worlds with high obliquity³⁹ (I'll talk about them more in a moment) are also less prone to falling into a complete snowball because the areas with most intense heating (the substellar point and poles, respectively) can remain unfrozen as most of the rest of the planet freezes.

But at any rate, volcanic activity on all planets should decline as they age and cool, and so any habitable world that is not first pushed past the moist or runaway greenhouse limit by its warming star will meet this fate eventually (even the stable thawed continent climate state will eventually cool to a complete snowball), and the further out in the habitable zone they are, the sooner it will happen. Earth’s internal heat is only expected⁴⁰ to sustain plate tectonics for another 1.45 billion years (were it not likely to pass the inner HZ limit and lose its oceans first) and even the largest super-Earths are unlikely to last much longer⁴¹. Given that many stars last for trillions of years, this leads to the unsettling conclusion that in the far future the universe will be increasingly populated by dead, formerly-habitable planets.

Even for planets that have habitable climates in terms of average temperature and stability, the conditions for complex life may be limited only to some parts of the habitable zone. Some researchers have proposed⁴² that the high CO₂ levels in the outer habitable zone—as well as CO produced by photolysis of CO₂ in orbit of low-mass stars—could prevent the evolution of complex life. Humans can only tolerate up to about 10,000 ppm CO₂ for more than a short period and 50,000 ppm even briefly, levels which are likely to be exceeded for many planets past just 1.05 AU. There is some evidence vertebrates can acclimate to at least 0.1 bar of CO₂, but, to keep at least some part of the planet's surface above freezing, even that limit must be exceeded⁴³ past about 1.3 AU.

CO₂ levels necessary to maintain an average temperature of 15 °C in the sun's habitable zone, assuming Earthlike albedo (it should actually be higher near the outer edge as the atmosphere becomes more opaque and CO₂ clouds begin to form, which I didn't model here).

Personally, though, I’m skeptical that we can draw broad conclusions based on the tolerances of life on Earth that has developed in a low-CO­₂ environment. But, while we're at it, there's also a thin region near the inner HZ edge where the very low CO₂ levels may be problematic⁴⁴ for oxygenic photosynthesis, which becomes less efficient at such low CO₂ levels and functionally impossible when it reaches around 0.00001 bar (10 ppm in Earth's atmosphere).

Photosynthesizers may also struggle with the lower light available at the outer edge of the habitable zone. Again, some kind of photosynthesis should be possible even with very little light, but production of oxygen requires a fair bit of input energy; below a certain threshold, photosynthesizers may not be able to produce enough oxygen by day to offset what they must consume by night. But we don't have a good idea⁴⁵ of what that threshold might be; it may not be a real issue at all, or it may prevent buildup of oxygen produced by life in the outer habitable zone of sunlike stars and completely for smaller stars (which have dimmer light in their habitable zone—though this might be offset by tidal-locking, which provides constant light exposure to one hemisphere).

One final bit of late-breaking news is that a paper⁴⁶ that came out as I was making some edits to this post suggests that the stabilizing carbon-silicate cycle may not operate as well in the outer regions of the habitable zone. In short, evaporation rates are largely driven by direct sunlight rather than ambient air temperature, so a world with low sunlight and high CO₂ might be as warm as Earth, but will likely have lower evaporation and precipitation, which may bottleneck the weathering processes that draw down atmospheric CO₂. Increased CO₂ levels may thus not cause increased weathering and CO₂ drawdown (because precipitation doesn't increase), and so nothing prevents CO₂ from just accumulating to ever higher levels and warming the climate. These results are still quite limited, though, so it remains to be seen exactly how much of the conventional habitable zone this issue applies to (the paper suggests at least planets beyond 1.2 AU from a sunlike star may be at risk); whether there might be more stable warm or cool climate states that are still at least marginally habitable; and whether this issue applies over various possible ranges of planet rotation rate, obliquity, volcanic activity, and landmass distribution.

Seasons and Irregular Orbits

One caveat for these habitability models is that they mostly only consider planets in stable, circular orbits, and many basically treat planets as boxes with a single uniform albedo and average surface temperature. This doesn't necessarily make them unreliable—various parameterizations are included in these models to try and account for the behavior of real planets (though clouds are particularly hard to model well)—but they may not reflect the way in which conditions may vary over a planet's surface or across its orbit. We'll leave most of the details of that discussion to the later section on climate, but it's worth quickly discussing here how they might impact a planet's overall habitability.

On Earth, seasons are driven primarily by obliquity; the planet's rotation axis is tilted relative to its orbit, such that, as the planet moves around the sun while holding a constant rotation axis, the poles are pointed more directly towards or away from the sun, varying their insolation.

cmglee, Wikimedia/NASA

But in addition to varying insolation over the year, greater obliquity also increases overall heating of the poles relative to the equator. This may seem odd given that both winter nights and summer days will get longer and more intense with greater obliquity, but insolation in winter can never drop below zero, while in summer it can rise to as much as 4 times the global average (at the pole, at summer solstice, with 90° obliquity).

Thus, a planet with 0° tilt has no seasons and stark temperature contrasts between equator and pole, and then increasing obliquity both increases seasonal variation in solar heating and decreases variation in average heating by latitude. Once obliquity passes about 54°, the poles actually receive more heat on average than the equator, and even higher obliquities increase this contrast; it's even possible on high-obliquity worlds for an ice belt to form around the equator while the poles remain ice-free. The great shift in heating also complicates seasonal patterns; while each pole experiences one extreme summer-winter cycle each year, peaking during solstices, the equator experiences two equinox summers (when the sun passes directly overhead) and two solstice winters (when heating has shifted to either of the poles) in the same time.

What exactly this means for surface temperature and habitability depends on a number of factors, but particularly⁴⁷ on the efficiency of heat transport across the planet, which in turn depends to varying extents on the thickness of the atmosphere (a thicker atmosphere has more air working to move heat at any one time), rotation rate (faster rotation causes a stronger Coriolis effect that inhibits movement of air across latitudes), and size (a bigger planet means farther for heat to move between equator and pole). Efficient heat transport can moderate seasonal temperature swings and distribute heat across latitudes, allowing for the whole surface to remain habitable. Less efficient heat transport may imply more extreme temperature variation, but near the inner edge of the habitable zone this may be desirable; the poles of a low-obliquity planet or equator of a high obliquity planet may remain habitable even as the rest of the planet becomes unbearably hot.

The arrangement of continents also has a notable effect. Continents have less efficient heat transport than oceans and warm and cool faster with the seasons, so a polar continent may be more prone to freezing over and forming an ice cap on a low-obliquity planet and experience more extreme seasonal temperature swings on a high-obliquity planet, while a polar ocean (and nearby coastal regions) will see more mild seasons and could even remain unfrozen through the long polar night of a high-obliquity planet.

And, of course, the length of the year matters as well; average heating doesn't depend on year length, but longer years allow for more seasonal cooling and heating, so a high-obliquity planet with can expect to have a similar equator-pole temperature difference regardless of year length but less extreme seasons with shorter years.

Harsh as extremely seasonal high-obliquity worlds may seem, they may actually have some advantages; the intense summer heating of the poles may make them less prone³⁹ to completely freezing over in the outer HZ, and may also help encourage oxygenation⁴⁸. On the other hand, the intense heating of the polar atmosphere may also make⁴⁹ atmospheric escape of water easier and tend to warm the planet overall, likely slightly shifting out the inner edge of the HZ.

The other major factor that can drive seasonal temperature variation is orbital eccentricity; variation in the planet's distance from the star over its orbit. Unlike obliquity-forced seasons, eccentricity-forced seasons are uniform across the planet’s surface rather than offset by hemisphere, but they can be somewhat asymmetric by time; a planet moves faster near periapsis (closest approach to the star) than near apoapsis (farthest point from the star), so eccentricity-forced winters will be longer than summers.

People often assume that a planet has to remain within the habitable zone throughout the whole orbit, but planets take time to warm and cool in response to changes in insolation, so a brief episode of very high and low heating may not be an issue if the average heating is hospitable; much as with high-obliquity planets, broad oceans, a thick atmosphere, and shorter years can all help moderate seasonal temperature swings.

But eccentricity affects average heating as well, increasing it for a given semimajor axis (average distance from the star). Even though summers are shorter, the inverse-square relationship of insolation to distance from the star means that the increased heating near periapsis outweighs the lower heating near apoapsis. 

This means that the habitable zone is slightly further out⁵¹ for high-eccentricity planets, and so a frozen planet in a circular orbit just outside the typical habitable zone could conceivably be thawed out if the influence of another body increased its eccentricity.

NASA/JPL-Caltech

Of course, a planet can have both significant obliquity and eccentricity, and how that plays out for the surface depends in large part on how the two seasonal cycles coincide:

• If periapsis coincides with a solstice, this will intensify seasons in one hemisphere and moderate them in the other; if, say, northern summer coincides with periapsis, the northern hemisphere will have a short, hot summer and long, cold winter, while the south will have a long, mildly warm summer and short, cool winter. Tune the parameters just right and you might get a strip of latitudes in the south that essentially lack seasons, as the obliquity and eccentricity cycles cancel out.
• For a high-obliquity world, all this will hold true for the poles, but the twice-yearly equatorial season will be more complex: one short, hot summer at periapsis, a longer, cooler summer at apoapsis, and winters in between—though at high eccentricity the apoapsis summer may be quite weak, leaving the equator with essentially one brief summer at apoapsis and a long winter the rest of the year.
• If periapsis coincides with an equinox, heating is more symmetric but still falls at different parts of the year; one hemisphere will have a short, hot spring and long, cool fall, and the reverse in the other hemisphere. Given the right combination of parameters, you might essentially have high latitudes experiencing an obliquity-driven seasonal cycle peaking at the solstices and low latitudes experiencing an eccentricity-driven seasonal cycle peaking at the equinoxes.
• Different timings of periapsis can lead to intermediate results; this paper is a decent exploration of the range of possible insolation patterns, and the "irradiance fast rot" tab of my worldbuilding spreadsheet also allows you to play around with the parameters yourself and see the resulting insolation patterns.

But more than just messing with the calendar, a combination of high eccentricity and intermediate obliquity can help push out the outer edge of the habitable zone by preventing a cold planet from freezing over completely. A planet with an eccentricity of 0.5 and obliquity of 30° may be habitable⁵¹ with a semimajor axis past 2 AU around a sunlike star.

However, we should not expect these values to remain stable throughout a planet’s history. The Earth experiences periodic variations in obliquity, called “Milankovitch cycles” due to the gravitational influence of other planets. These cycles amount to little more than a 2° change in tilt, but this is enough to push the Earth between glacial and interglacial periods in our current ice age. Other planets may experience more extreme variations, both in obliquity and eccentricity, and these can cause similar shifts⁵² in ice cover at the poles. But changing ice cover can be dangerous due to ice-albedo feedback. Recent modelling⁵³ of this feedback and other climate-moderating effects for planets with large obliquity and eccentricity indicates that a point of critical instability is reached if the obliquity surpasses 35° while the planet is in a period of low eccentricity; either the polar ice caps will melt completely or they will expand to cover the whole planet, putting it in a snowball state. A later increase in eccentricity may help thaw the planet again, and an initial eccentricity over 0.2 will prevent the snowball from forming in the first place.

Note that both obliquity and eccentricity will be reduced⁵⁴ by tidal forces for planets in the habitable zone of low-mass stars, so unless they’ve been recently induced by other planets don’t expect them to be remain high by the time complex life appears in such systems.

Finally, there is one other way a planet to get seasons. A rapidly-rotating star will form an equatorial bulge, much as a planet does, with flattened poles. Because the material in this bulge is farther from the core and less dense, it is cooler and less bright than the poles. If a planet is in an orbit highly inclined from the star’s equatorial plane, then the planet will receive more light when over the poles than when over the equator. This can lead⁵⁵ to as much as 15% variance in surface temperatures, on par with eccentricity or obliquity-forced seasons. As with eccentricity-forced seasons the luminosity changes would be applied across the whole planet, but summer wouldn’t necessarily be shorter than winter, and in this case each year has 2 summer and 2 winters. I shudder to think of what the seasonal calendar might look like for a mix of all 3 types of seasons.

Calculating the Habitable Zone

As mentioned, all the numbers I've given so far for habitable zone boundaries have assumed a star identical to the sun. Dimmer or brighter stars will have HZs closer or further away, respectively. In a pinch, we could assume that the HZs of these stars should shift to distances with equivalent stellar flux (light passing through space) as in the sun's HZ:

B_n = boundary distance in new system

L = luminosity of star (ratio to sun)

B_s = boundary distance in solar system

However, hotter or cooler stars produce different spectra of light, and in particular water and ice reflect less of the red light from a cooler star, and so a habitable planet requires less insolation to reach a given temperature—and the reverse with the blue light from a hotter star. So it takes about 111% of Earth's insolation to reach the inner limit of the conservative HZ for planets of a sunlike star with an effective temperature of 5780 K, but only 92% for a planet of an M-type star at 2600 K and 163% for a planet of an A-type star at 10,000 K.

Determining the exact HZ limits for different stars requires complex atmospheric models, but for convenience researchers will fit a simpler formula to their results; in essence, they find an equation that coincidentally gives the same answers as their more complex model within a given range of parameters; emphasis on that last point, because outside that intended parameter range there is no guarantee that these formulas will be accurate or even physically sensible. In this case, the formulas are all fitted for a range of stellar effective temperatures.

Most of the habitable zone types I mentioned above have been fitted with the same standard type of formula:

B_n = boundary distance in new system (AU)

L = luminosity of star (ratio to sun)

S_eff = stellar flux at boundary for sunlike star, equivalent to 1/B_s² from above

T_* = star effective temperature – 5780 K

a, b, c, d = fit coefficients

Here's a selection of the appropriate stellar flux values and coefficients for a selection of the habitable zones we've discussed, some reported in the literature and a couple fits I could work out myself based on the reported results; for each I've listed the basic definition and the valid effective temperature range. All of these (and a few others) have been worked into the worldbuilding spreadsheet. ("E" is short for "*10^", e.g. "8E-4" is "8*10^-4")

Hab Zone	Distance from sun (AU)	Seff	a	b	c	d
Dry (high albedo)	0.38	6.925	8.497E-4	7.683E-7	4.357E-10	6.474E-14
Dry (low albedo)	0.59	2.873	7.73E-5	7.842E-8	4.43E-11	6.465E-15
Slow Rotation	0.73	1.883	2.713E-4	-1.2E-8	0	0
Recent Venus	0.75	1.768	1.315E-4	5.87E-10	-2.89E-12	3.217E-16
Water Condensation	0.83	1.435	8.577E-4	5.638E-7	1.819E-10	2.162E-14
Runaway/Moist Greenhouse	0.95	1.105	1.192E-4	9.593E-9	-2.619E-12	1.371E-16
Human Tolerance	1.14	0.766	2.928E-5	-4.981E-9	-1.774E-12	-3.297E-17
Cold Start	1.39	0.518	9.751E-5	-1.491E-8	0	0
Maximum Greenhouse	1.67	0.359	5.809E-5	1.539E-9	-8.355E-13	1.032E-16
Early Mars	1.75	0.325	5.213E-5	4.525E-10	1.022E-12	9.638E-17
Methane	1.81	0.305	2.216E-5	4.191E-9	-1.318E-12	1.18E-16
Volcanic Hydrogen	2.41	0.172	1.403E-5	-3.232E-10	-2.869E-13	4.293E-17

Dry (high albedo)¹⁹: Inner limit for polar habitability with negligible water and (questionably plausible) 0.8 albedo; fitted by me based on the provided distance-luminosity curve of 0.38 * [luminosity]^0.474 and the cited source for stellar parameters; 2700-6000 K.

Dry (low albedo)¹⁹: Inner limit for polar habitability with negligible water and 0.2 albedo; fitted by me based on the provided distance-luminosity curve of 0.59 * [luminosity]^0.495 and the cited source for stellar parameters; 2700-6000 K

Slow Rotation¹⁵: Inner limit for planets with very slow rotation (over ~100x day length); formula modified by me to fit this format; 2500-4500 K

Recent Venus²¹: Inner limit based on (questionable) assumption that Venus was habitable ~1 billion years ago; 2600-10000 K

Water Condensation³³: Inner limit for a planet in a system that is currently 4.5 billion years old to have been able to cool from an initial hothouse state after forming based on the star’s likely initial luminosity assuming standard main sequence evolution; see paper for similar estimates at different system ages; fitted by me based on reported values for 2300-6000 K

Runaway/Moist Greenhouse²¹: Inner limit for Earth-like planet with a carbonate-silicate cycle, due to runaway or moist greenhouse; 2600-10000 K

Human Tolerance⁴²: Outer limit for CO₂ levels below 0.01 bar (roughly the limit of human tolerance) to maintain a global average temperature of at least 273 K; see paper for limits with 0.1 and 1 bar CO₂; 2600-7200 K

Cold Start⁵⁶: Outer limit where recovery from snowball is possible, due to CO₂ condensation; likely varies considerably with planet characteristics; fitted by me from reported results at 4400, 5800, and 7200 K

Maximum Greenhouse²¹: Outer limit for Earth-like planet with a carbonate-silicate cycle, due to formation of CO₂ clouds; 2600-10000 K

Early Mars²¹: Outer limit based on assumption that Mars was habitable 3.8 billion years ago; 2600-10000 K (exceeds maximum greenhouse limit only below ~9100 K)

Methane²¹: Outer limit using a 1:10 mix of atmospheric CH₄ and CO₂; see paper for limits with 10 ppm and 1% CH₄; 2600-10000 K (exceeds maximum greenhouse limit only above ~4500 K)

Volcanic Hydrogen²²: Outer limit with 0.5 bar H₂, a reasonable maximum for volcanic production; see paper for limits with 0.01, 0.05, 0.1, 0.2, and 0.3 bar H₂; 2600-10000 K

Here's how all these boundaries look plotted in terms of stellar flux (on a log-2 scale) and star effective temperature; each boundary is truncated to the appropriate temperature range, and the Early Mars and Methane boundaries are truncated where they pass within the Maximum Greenhouse boundary; I've also marked a few boundaries as dotted where they're based on (what I somewhat subjectively deem to be) weak assumptions and dashed where the actual boundary may vary significantly depending on a planet's properties.

 

For these purposes, eccentric orbits can be treated as effectively equivalent to a circular orbit with a somewhat larger semimajor axis, though a habitable average temperature doesn't necessarily guarantee that life will survive the seasonal temperature swings.

 

B_e = boundary distance for eccentric orbit

B = boundary distance for circular orbit

e = eccentricity

 

As one extra formula, here's how to calculate the irradiance (sunlight exposure without accounting for atmospheric effects) for a given latitude, declination of the sun, and distance from the star relative to the semimajor axis; most of you probably won't need this but it might be convenient to the programmers or developers among you:

Q_day = average irradiance across the day (W/m²)

S₀ = solar constant; 1367 W/m²

L = stellar luminosity (ratio to sun)

d = current distance from sun (AU); a(1 + e) ­ at apoapsis and a(1 – e) at periapsis where a is the semimajor axis and e is the eccentricity

φ = latitude; negative in the southern hemisphere

δ = declination of the sun; the angle from directly overhead that the sun appears at noon on the equator; 0° at the equinox, ε (the planet’s obliquity) at the northern summer solstice, -ε at the northern winter solstice.

h₀ = hour angle of sunrise (°); cos^-1[-tan(φ) tan(δ)] except where [tan(φ) tan(δ)] > 1, in which case the sun doesn’t set and h₀ = 180°; or [tan(φ) tan(δ)] < -1, in which case the sun doesn’t rise and Q_day = 0.

(where the year length is much longer than the day length and so d does not vary significantly in one day)

This is a pretty hideous formula, so to save you a lot of time I’ve included a calculator for irradiance at different latitudes throughout the year in the worldbuilding spreadsheet. We can see that on Earth at 45° north latitude Q_day varies from 502 W/m² at northern summer solstice to 117 W/m² at northern winter solstice. Were Earth to have 0° obliquity, it would require a semimajor axis of 1.2 AU and an eccentricity of 0.42 for similar maximum and minimum Q_day at the same latitude. This isn’t to imply that this eccentric Earth would have an equivalent climate, and indeed this is a criminally oversimplified model of seasonal change (because it doesn’t account for surface albedo, thermal inertia, heat flow between latitudes, and various feedbacks)—but it’s a decent starting point.

Constructing a Habitable Planet

Being in a suitable orbit in the habitable zone is, unfortunately, no guarantee that a planet will be habitable. Mars, for example, orbits comfortably within even the conservative habitable zone estimate, and stubbornly remains dead. We thus need to consider more than a planet's orbit and rotation to make it habitable.

Size

As we've provisionally defined it, habitability requires an atmosphere, and, as discussed in the last section, that becomes difficult for a smaller planets which tend to experience faster atmospheric escape. At 0.107 times the mass of Earth, Mars retains only a thin atmosphere today, providing too little pressure and greenhouse heating for surface water.

But a Martian atmosphere shouldn’t be impossible; give Mars an Earthlike atmosphere today, and it’ll hold onto it for an impressively long time, and we discussed estimates last time that even a planet of 0.07 Earth masses could conceivably retain an atmosphere for billions of years by some estimates.

The real issue is that Mars lacks any volcanic activity that could produce enough gasses to replace its losses. The modern surface shows the scars of plentiful volcanism when the planet was young and what may even be⁵⁷ the early stirrings of plate tectonics, but the volcanic activity declined over time and these scars only remain because the surface has been largely dormant for billions of years. No volcanic outgassing means no thick atmosphere and no carbon-silicate cycle, so we can treat active volcanism as at least a soft requirement for habitability.

Volcanism and tectonic activity are driven by motion in the planet's interior; the heat of the core and mantle drive convection of hot rock towards the surface, and this either bursts directly through the surface, releasing any volatiles that happen to be trapped in the rock, or helps drive tectonic motion in the crust, which may create the conditions for rock to melt and rise to the surface. On Earth this manifests mostly as plate tectonics, and I've already discussed how the cycle of subduction and volcanism helps drive the carbon-silicate cycle, but there's some reason to believe⁵⁸ that other types of tectonic activity could allow for similar cycling so long as there is both volcanic outgassing of CO₂ and some amount of burial of surface sediment in a way that might allow it to eventually sink back into the mantle. These alternate tectonic regimes may be less stable and favorable to complex life, but we'll discuss all that another time; regardless, they all still require significant heat from the interior.

As an added bonus⁵⁹, interior convection drives the outer core dynamo, which produces Earth’s magnetic field. As mentioned in the last post, a magnetic field isn't nearly as important for survival of a planet's atmosphere as often supposed, but it could help and may be more important for young planets⁵⁹ with more hydrogen in their atmospheres or for planets near⁶⁰ the inner habitable zone boundary in danger of losing their water to a moist greenhouse.

So if we want tectonic activity on our habitable worlds, we need enough heat to drive internal convection. Earth's interior produces around⁶¹ 47 TW of heat continuously (though this includes heat from the crust, which doesn’t contribute to mantle convection). So far as we know it has two main sources: primordial heat, left over both from the impacts that first formed the Earth and from friction when heavier elements separated from lighter ones and fell to the core; and radiogenic heat, resulting from the decay of unstable isotopes like uranium, thorium, and potassium. How much each source contributes is a long-running debate, but observations of geoneutrinos⁶²—particles produced by radioactive decay that rarely interact with matter and so flow freely through the Earth—indicate that roughly 30 TW is radiogenic, with the rest presumably being primordial. But that’s just today; radioactive isotopes are depleted over time as they decay and primordial heat is lost as it is radiated into space, meaning that heat production declines over time. Nothing short of a gigantic impact that melts the surface can add more of either, so however much a planet starts with has to last for billions of years.

Which brings us back around to the matter of size. The rate at which a planet radiates heat to space is determined by its surface area, while—for a given composition and density—the heat capacity and total amount of radioactive isotopes is determined by volume. As a planet gets smaller, the volume declines faster than the surface area. A planet with 1/2 the radius of Earth will have 1/4 the surface area and 1/8 the volume—twice the surface area per volume. This relationship, called the square-cube law, turns up in a lot of contexts, so take note of it. This means that a smaller planet will lose primordial heat faster and have a cooler interiors for proportionally similar levels of radioactivity. This is what ultimately killed Mars: its interior cooled, its crust thickened, mantle convection slowed, and today it experiences only sporadic volcanism. It cannot replace its atmospheric losses, and even if it did have a thick atmosphere it couldn’t sustain warm temperatures without an effective carbon cycle.

Exactly what the minimum mass is for a planet to sustain tectonic activity for billions of years has not been studied in depth. A rough estimate⁶³ based on the decay rate of uranium—the most important of Earth’s radiogenic elements—and the observation that Mars’s tectonics appear to have halted 2 billion years ago (implying that the heat flow then was the minimum necessary for tectonic activity), results in a critical mass of 0.23 Earth masses. It’s a simple model with old figures, but it does about match with more recent studies showing that volcanism on worlds with plate tectonics should continue⁴¹ for up to 10 billion years on 0.25 Earth mass planets and that 0.1-Earth-mass planets cool too quickly⁶⁴ for plate tectonics to ever set in. 

 

Somewhat confoundingly, though, interior cooling rates don't necessarily depend directly on surface area; different types of surface tectonic activity might cause different rates of cooling, so the geologically active lifetime of a small planet may vary depending on its exact tectonic history, and it's even conceivable⁶⁵ (though quite uncertain) that in some cases a smaller planet may even outlast a larger one.

But even if a planet can't last long on its own heat, there may be a way to give it more from outside. Light won’t do it; if you can't heat the surface to more than a few hundred K to keep it habitable, you won't get the interior to thousands of K. But if a planet experiences strong tidal forces from its star, pulling up a tidal bulge on its surface and it has some obliquity, eccentricity, or non-synchronous rotation—all of which cause the tidal bulge on the planet to turn away from the star—then the tidal forces will drag the bulge back towards the star, causing internal friction and producing a good deal of heat. For an Earthlike planet with high eccentricity orbiting in the habitable zone of a star below 0.3 solar masses, the tidal heating alone could be enough⁶⁶ to drive plate tectonics even in the absence of other heat sources. Freed from the need to produce and retain heat, the minimum size of such a world is set by the requirement for the escape velocity to be high enough to prevent excessive loss of atmospheric gasses—which, as discussed last time, should put it somewhere around 0.05-0.1 Earth masses.

One important caveat, though, is that this heating doesn't come free; as the planet is heated, its eccentricity or obliquity or whatever else will be reduced in turn. To maintain heating for long periods requires some other body to continuously alter the planet's orbit or rotation such that tidal heating continues. Io, for example, retains high rates of tidal heating due to the influence of Jupiter's other moons. A planet could similarly maintain heating thanks to a large neighboring planet or star (the energy still isn't free, but in these cases it usually ultimately comes out of the neighboring body's orbit, which can contain huge amounts of energy).

So much for small planets; how big can a habitable world be? Here, there's a bit more research to draw on, perhaps too much; super-Earth planets of 1-10 Earth masses have attracted a fair bit of interest since they appear to be fairly common, but models of their interiors have yielded wildly⁶⁷ different⁶⁸ results⁶⁹. As a brief summary, the initiation of plate tectonics requires that the crust fracture and be pulled down into the mantle, but whether or not that happens depends on a balance between the stresses imposed on the crust by convection in the mantle and the resistance of the crust to breaking. All else being equal, greater pressure and heat on a larger world should lead to greater stresses, but they may also lead to a stronger crust as well. And the greater temperature and pressure may increase the viscosity of the mantle, which will reduce the stress, and water content may play a vital role⁶⁹ as well, and the more complex the models become the more assumptions we have to make and the more clear it becomes that we don’t really understand exactly how plate tectonics works on Earth, let alone how it might work on an alien world.

Still, even lacking plate tectonics, a super-Earth should, by the square-cube law, tend to have more internal heat than a smaller planet, so we can assume it will likely have some kind tectonic activity that might sustain a carbon-silicate cycle.

NASA/Ames/JPL-Caltech

If we’re willing to make that assumption, then setting the upper limit returns to a matter of atmospheres. Where a small planet has trouble holding onto any atmosphere, a large planet holds onto too much. Planets even slightly larger than Earth are at risk⁷⁰ of retaining their primordial hydrogen/helium atmospheres and experiencing too much greenhouse heating for habitability within the typical habitable zone; as mentioned, these planets could be habitable in wider orbits, but they may be less suitable for complex life and unstable in the long term, and a sufficiently thick hydrogen atmosphere eventually produces surface pressures and temperatures too great for any known biochemistry. Observation of exoplanets⁷¹ indicates that, past 4 to 5 Earth masses, most planets transition from super-Earths to sub-Neptunes that can basically be regarded as small gas giants.

If we use 0.25 to 4 Earth masses as our approximate habitable range and assume an Earthlike composition, that gives us an approximate planet radius range of 0.66 to 1.45 Earth radii, and thus a surface gravity range of 0.57 to 1.91 Earth g. If we assume the mass of the metallic core could vary between, say, 10 and 60% of the planet's total, we can expand the radius range to 0.61-1.55 Earth radii and the gravity range to 0.51-2.31 g.  If we’re more optimistic and extend the mass range to 0.05-10 Earth masses (and similarly vary core mass fraction) the radius range extends to 0.36-1.93 Earth radii and the gravity range to 0.30-3.78 g.

Relative sizes of planets with Earthlike compositions and a plausible range of habitable masses.

As a simpler rule of thumb, we might easier to remember a conservative range of habitable planet surface gravities of about 1/2 to 2 times Earth's gravity, and and an optimistic range of 1/3 to 3 times. Exactly what such varying surface gravity might mean for topography and life is a subject for another time, but given the range of masses and sizes of life on Earth, I doubt even a 4-fold increase in surface gravity would prevent complex life.

Composition

Many of these size limits are based on the assumption of an Earthlike composition, but we have good reason to believe potentially habitable planets could vary significantly.

To start off, I assumed in the last section that the differently-sized planets all have similar concentrations of radioisotopes of uranium (U-235 and U-238), thorium (Th-232), and potassium (K-40) producing internal heat, but in reality this could vary; presuming that surface flux of geothermal heat is the critical factor and going by simple square-cube scaling, doubling the radioisotope concentration should decrease the minimum habitable planet mass by a factor of about 1.41. So if our minimum was 0.25 Earth masses before, it would now be 0.18 Earth masses—with another doubling of radioisotope concentration, it goes down to 0.125 Earth masses.

Higher radioisotope levels could also help Earth-mass planets retain habitable conditions for longer; were the brightening sun not an issue, Earth's internal heat sources probably couldn't sustain habitable geological activity for more than another 4-5 billion years but doubling the initial radioisotope concentration might extend this by another 6 billion years (see the appendix at the end of this post for how I got these numbers). But we can't push this too far: higher radioisotope concentrations also implies higher initial internal heating and volcanic activity. We don't have any good sense of how much higher this internal heating could become before compromising habitability, but at the very least it might delay the onset of a stable tectonic regime like plate tectonics and increase the likelihood of a catastrophic volcanic event⁷² that pushes the planet into a runaway greenhouse state that it may not recover from.

There is probably some random variation in initial radioisotope composition between planets just due to different formation conditions, but it also appears to be generally declining as the galaxy ages⁷³; though they are continuously produced along with other heavy elements by the deaths of massive stars, the radioisotopes decay while other elements simply accumulate, so the radioisotopes are becoming increasingly diluted by those other elements. On average, Earthlike planets that formed 12.5 billion years ago in the young galaxy would've formed with about twice as much radioisotopes as Earth did (varying by isotope; there was only about 20% more Th-232 but over 5 times as much U-235) while those forming today have about 1/4 less—though the current radioisotope composition is still highest in the youngest planets.

Also, Earth and several other solar system planets seem to have lost most of their potassium as they formed; exactly why is still unclear, but if another planet retained more, it could have substantially more heating⁷⁴, at least initially; K-40's relatively short half-life (1.4 billion years compared to 0.7 for U-235, 4.5 for U-238, and 13.9 for Th-232) means it wouldn't much help in extending a planet's habitable lifetime, except perhaps for the smallest worlds.

I also tend to assume an Earthlike mix of 1/3 iron-nickel core to 2/3 rocky mantle and crust, but within our own solar system the core mass fraction is as little as 0.03 for the moon and as high as 0.69 for Mercury. A larger metallic core makes a planet overall denser, thus more resistant to atmospheric escape (because escape velocity at the surface is higher), and differentiation of the core from the mantle is a major source of internal heat, so a large core may be beneficial to the habitability of a small planet. You might expect a larger metal core would also imply more heavy-metal isotopes, but it isn't so straightforward: the same overall processes of star death produce both, so on cosmic scales we might expect them to appear together, but in the actual process of planet formation, uranium and thorium mix into the rocky mantle and crust, not the metallic core. How these different trends might balance out in any particular case, I'm not sure.

Even ignoring any effect on overall internal heating, the size of the core also influences convection in the mantle⁷⁵; a very large or small core may make plate tectonics less likely, and a planet with a large core may also not outgas enough CO₂⁷⁶ to maintain a warm climate in the outer habitable zone. You may also remember the possibility I mentioned in the last post that a rocky planet might have a small core not because of an overall shortage of iron metal but due to mixing of the iron into the core; this sort of iron-rich mantle and crust will tend⁷⁷ to absorb more water from the surface, drying it out, though given our previous discussions of desert worlds, this may or may not be detrimental to habitability in any particular case.

Speaking of the rocky mantle and crust, our limited evidence⁷⁸ suggests that there's not much variation in the bulk composition except in the ratio of silicon to magnesium. Given how much our crust's chemistry varies, this probably doesn't make a huge difference for habitability, but a very silicon- or sodium-rich crust may be too buoyant to subduct⁷⁹ or otherwise bring material into the mantle to drive the carbon-silicate cycle. Also, the presence of calcium in volcanic rocks is a major element of the carbon-silicate cycle through deposition of calcite (CaCO₃) minerals, but in its absence magnesium and iron could also help⁸⁰ deposit other carbonates (MgCO₃ and FeCO₃).

Continuing upwards, Earth's water oceans only make up about 0.02% of its total mass (though there might be a few times more water mixed into the mantle), but many observed exoplanets appear to be waterworlds, with deep layers of water accounting for as much as half of their mass, though liquid oceans typically only extend no more than a couple hundred km deep; beyond that, the water is compressed into high-pressure ice. So much water may sound like a boon for life, but again, remember that it's water that drives runaway greenhouse heating and snowball cooling. The carbon-silicate cycle requires some exposed land for weathering to occur, though exactly how much isn't clear, with some studies⁸¹ suggesting as little as 1% of the surface needs to be land and others⁸² suggesting as much as 15% (though heavily dependent on a number of other factors). Either way, if there is even less land area or the planet is inundated entirely, or if volcanism on this planet produces CO₂ at a much higher rate, then there may simply be too little weathering⁶ to counter CO₂ production, and the planet enters a moist greenhouse state. If the oceans aren't too deep, loss of water to space may expose enough land for the climate to recover, but otherwise the planet will likely enter an irreversible runaway greenhouse (or in the outer HZ, build up enough CO₂ to begin condensing out on the surface and freeze over).

Still, there might be some hope for habitability; the high-pressure ice layer may effectively block⁸³ both CO₂ release from the interior and CO₂ sequestration from the atmosphere, so if the planet happens to form with the right amount of atmospheric CO₂ for habitable temperatures (the chances for which aren’t excellent but aren’t vanishingly small either) then a planet could remain habitable for billions of years—especially if it orbits a small, slowly-evolving star. This is long enough to possible form life, though once it does it might start sequestering carbon on its own and so cause its own demise. Feedbacks between surface temperature and levels of dissolved CO₂ in the oceans might also⁸⁴ destabilize the climate of such a world.

 

Alternatively, on waterworlds with short days (<8 hours) in the outer regions of the typical habitable zone (~1.23-1.65 AU for a sunlike star), sea ice may be able⁸⁵ to absorb CO₂ and sink to the ocean floor at a rate proportional to atmospheric temperature, providing a stabilizing negative feedback⁸⁶ (presuming there is also an available source of CO₂ from the interior not totally blocked by a thick ice layer to replace the frozen CO₂) favoring a moderate climate state with large ice caps, an unfrozen subtropical ocean, and an atmosphere with several bar of CO₂.

Neither of these options works quite as well as the carbon-silicate cycle on a continental world, and there’s still the issue that the ice on the ocean floor may block access to vital nutrients for life—particularly phosphorus, a shortage of which in turn may prevent⁸⁷ production of atmospheric oxygen—so overall waterworlds shouldn’t be considered ideal for life. Fortunately, negative feedbacks between pressure on oceanic crust and production of water from the mantle should ensure⁸⁸ that even worlds with as much as 0.2% water content by mass—5-10 times that of Earth—have exposed continents.

Similarly, a carbon planet like we discussed last time might sound ideal for carbon-based life, but they'll likely have a diamond-dominated mantle that is both more viscous and more conductive than a silicate mantle, meaning such a world will cool quicker⁸⁹ and may not be able to maintain geological activity for long; even before cooling, the interior chemistry⁹⁰ should be less favorable to the emergence of liquid lava on the surface, possibly preventing volcanism entirely, and any nutrient supply or climate-stabilizing geochemical cycles that might come with it. Still, we might optimistically imagine there may be some prospect for the potentially complex surface chemistry to provide opportunities for stabilizing feedback cycles and life, and if not there is also the possibility I mentioned last time for a carbon-rich crust to form over a more familiar silicate interior.

Other Habitability Factors

So let’s assume we have a planet or moon of the right size in the right sort of orbit, and it has the right composition to maintain plate tectonics for a decent amount of time. Are we good? For the most part, yes, but there’s a few other factors we might want to consider.

Large Moons

First off, Earth is unique amongst observed terrestrial planets for having a fairly large moon, though it’ll be a while before we can determine how common that is for exoplanets. Researchers have long supposed that the presence of the moon could help stabilize Earth’s obliquity, reducing the occurrence of snowball episodes. But recent modelling has shown that a moonless Earth is perfectly capable⁹¹ of sustaining reasonable obliquity for long periods (and incidentally that retrograde-rotating planets are more stable) and that in fact⁹² the moon is close to the maximum size it can be without destabilizing Earth’s obliquity. And, as we saw earlier, variable obliquity may not be a showstopper for habitability anyway. 

A large moon may even be dangerous if there's some prospect for it to escape the planet's orbit, as an escaped moon has a good chance⁹³ of eventually returning and colliding directly into the planet.

Another proposed role for the moon is to cause tides that may have played a role in the origin of life (we’ll discuss that more when we tackle models for abiogenesis) but the sun’s influence alone can cause significant tides. It’s possible that the extreme tides shortly after the moon’s formation—when it orbited much closer to Earth—may have been necessary, or at least helpful, in getting life to appear as early as it did or that the moon-forming impact may have had⁹⁴ a beneficial effect on the Earth’s internal evolution, but neither proposal has been modeled in detail nor do they require that the moon remain in orbit after performing its vital task.

Neighboring Gas Giants

Another long-held belief is that a neighboring gas giant like Jupiter is well-placed to “shepherd” the asteroid belt and reduce the rate of destructive asteroid and comet impact events on Earth. Again, more recent modelling⁹⁵ has shown a more nuanced picture: It appears that the presence of Jupiter actually increases the rate of asteroid and comet impacts on Earth, by exciting their eccentricities such that they cross Earth’s orbit. The rate at which this occurs is notably lower than would be the case if there were a Saturn-massed planet in Jupiter’s place, but still higher than if there were no gas giant there at all. The only types of impacts that Jupiter helps reduce are those from long-period comets that enter the inner system from the Oort cloud, which it ejects out of the system, but these are the least frequent types of impacts (though also the most energetic) and even if there were no planet in Jupiter’s place, Saturn would do almost as good a job ejecting comets on its own. And given that, at this point, only one of the five major mass extinctions of the last half-billion years is still associated with an asteroid impact (the End Cretaceous extinction, which is considered likely⁹⁶ to have been caused by an asteroid rather than a comet and so is not the sort of impact Jupiter might help avoid), it's not clear that moderately more impacts would be a dealbreaker for habitability anyway.

However, though these models compensate for the bias in currently surviving asteroids and comets due to Jupiter’s presence, they cannot account for the competing models of how Jupiter’s presence may have massively changed the architecture of the early solar system. Some of these models predict that Jupiter’s influence helped deplete the asteroid and Kuiper belts early on, leaving us with fewer potential impactors to worry about.

And Jupiter could help in a couple other ways. It may have prevented Saturn and the ice giants from migrating into the inner system, and large giants in other systems may similarly prevent⁹⁷ the formation of super-Earths that would consume or eject more habitable Earth-mass planets. It may also have⁹⁷ scattered icy planetoids into the inner system early in plant formation and then halted their inner migration later, resulting in an Earth that’s wet enough for life and the carbon cycle but not so wet that it lacks exposed landmasses.

Well, good or bad though Jupiter may be in its current position, we’re certainly lucky it stays there. Were Jupiter’s orbital eccentricity increased to 0.2, it would significantly increase⁹⁸ the chances of the inner planets either colliding or being ejected from the system. At an eccentricity of 0.4 the long-term survival of Earth becomes almost impossible. Exoplanets with eccentricities this high aren't rare, and are probably more likely for systems that begin with multiple Jupiter-mass giants. Indeed, a large number⁹⁹ of observed exoplanets appear to be in single-planet systems due to past periods of instability, collisions, and ejections.

(A quick detour: if multiple-giant systems are less favorable to life, and high metallicity favors the formation of gas giants, this might imply that habitable planets will become rarer in the future as metallicity rises—another issue for the future habitability of the galaxy. However, we’d have to compare this to the trend for more low-mass stars to form, which disfavors the formation of giants. I don’t think we have the data yet to make that comparison.)

Anyway, you might think that this would mean that systems with hot Jupiters, which would have had to migrate through the inner system, would also lack habitable worlds. But so long as the migration occurs early and then the hot Jupiter stays in a low orbit, this is not necessarily so. Some of the material¹⁰⁰ in the inner system is consumed by the giant as it migrates inward or pushed ahead of it by resonances to later form hot terrestrial planets, but most of it is scattered into high-eccentricity orbits, allowing it¹⁰¹ to later return to the inner system and resume forming terrestrial planets. Scattering material like this may even help mix up the disk and deliver more water to the inner system, though given the issues with waterworlds this may or may not be a good thing.

Atmospheric Composition

Aside from the already-discussed impact of a thicker atmosphere on the habitable zone, another potential benefit we discussed in the last post is the cold trap helps prevent water reaching the upper atmosphere and escaping; nitrogen does the job in our atmosphere, but oxygen, argon, or neon could feasibly do the job as well. Oxygen is, of course, vital to aerobic life on Earth, and allows for high-energy reactions that might be hard to achieve otherwise—but we’ll leave a more in-depth discussion of oxygen’s utility to another time. Atmospheric nitrogen is an important source of nitrate nutrients for plant's life, but for what it's worth plant life on Earth appears capable¹⁰² of tolerating as little as 20% Earth's atmospheric pressure with little trouble, and can continue to grow with as little as 10%; alien life may be able to adapt even better.

Day Length

In general, for days shorter than multiple months long (which allows for formation of planet-cooling permanent dayside cloud formations), the exact length of day shouldn't have much influence on whether a planet's overall climate is habitable but does influence how hospitable particular areas of the surface may be: faster rotation (and so shorter days) causes a stronger Coriolis force, inhibiting transport of heat between different latitudes, so planets with very high or low obliquity or high eccentricity may benefit from slower rotation, allowing more even distribution of heat. Slower rotation also tends to cool down a planet overall due to more cloud formation over the tropics or other areas of intense heating, and very slow-rotating planets may have a similarly expanded HZ to tidal-locked planets, though the swings in temperature due to long days and nights may be challenging for complex life. In Earth’s current orbit, a day 16 times longer than our current one appears to be the ideal¹⁰³ to maximize habitable surface area.

 

It has also recently been proposed¹⁰⁴ that day length may have influenced Earth's oxygenation. Photosynthetic life can only produce oxygen by day, and such life on Earth can be slow to increase production in the morning; a longer day allows it to maintain peak oxygen production for longer, so as Earth's rotation has gradually slowed its rotation over time, this may have allowed for oxygen production to increase.

Luck

Finally, we shouldn't discount the influence of sheer dumb luck. Given the complexity of climate feedbacks (especially once life gets involved), we may simply be lucky¹⁰⁵ that Earth happens to be dominated by stabilizing negative feedbacks rather than destabilizing positive ones. And even with a stable climate, random events like orbital instability, large impact events, close passes from other stars, and extreme volcanic events have always posed some risk of wiping out life on our world by chance; so when it comes to other worlds, we probably shouldn't treat even apparently ideal conditions for habitability as a guarantee of inhabitation.

Habitable Moons

I’ve been using the term “planet” for our habitable world but there’s no particular reason it couldn’t be a moon, either of a larger terrestrial planet or a gas giant (or one of a binary pair of similar-mass planets, for that matter). I’ve left this subject to last because in most respects there’s no inherent difference in the possible physical characteristics of planets and moons, and just about everything I’ve said so far can apply to moon just as well as a planet (though with comments regarding the orbit applying to the planet’s orbit, and—for a moon with 0 obliquity, which is likely—the relative inclination between the moon’s orbit and the planet’s orbit having the same effect as obliquity would for a planet). We did establish in a previous post that moons formed in place around giant planets are unlikely to be larger than Mars-sized, but capture is a perfectly acceptable formation mechanism. Even "moonmoons" that orbit especially large moons have some prospects¹⁰⁶ for habitability. However, there are a few factors that we should consider.

 

"Effective obliquity" for a moon in an inclined orbit of a planet but with no tilt relative to that orbit.

 

First off, in most cases the semimajor axis of the moon’s orbit around the planet should be small compared to that of the planet’s orbit around the star, given that the Hill radius decreases closer to the star. But for the extreme case of a 13 Jupiter mass planet orbiting a 0.08 solar mass star, the hill radius will be 0.37 times the semimajor axis, meaning a retrograde-orbiting moon at the limit of stability could range between 0.66 and 1.34 times its planet’s distance from the star—similar to having an eccentricity of 0.34, but without the large variation in orbital speed (which gives us yet another method for giving a world seasons, though intriguingly for a tidal-locked moon the side facing the planet would consistently get less sunlight than the side facing outward).

Once a moon forms or is captured, it is very likely to become tidal-locked to the planet, tying the day length to the orbital period and thus the semimajor axis. For a wide-orbiting moon, this means very long days, but as already discussed this isn't a big issue for habitability. People often seem concerned with the potential climate effects of eclipses of a moon by its planet, but these should usually be quite subtle: In the most extreme case, a moon orbiting close to the Roche limit of a roughly Saturn-sized planet might lose as much as a quarter of its day to eclipses on a portion of its surface, but for most moons eclipses should only occupy a small portion of the day, and individual eclipses shouldn't usually last more than a couple hours at the most (with the longest eclipses tending to be for far-orbiting moons of less massive planets, which will have long orbits and so infrequent eclipses). If the moon's orbit is significantly inclined relative to its planet, eclipses might actually be quite rare (as they can then only occur at two points in the planet's orbit when the moon's orbital path passes through the planet's shadow, and the moon may not even pass through that part of its path in that window if it has a long orbit).

 

During the moon’s night, it may also receive significant reflected light from the planet, but though this might be bright enough to allow for significant activity by night, it's unlikely to be enough to actually impact climate or photosynthesis. However, a large gas giant can remain quite hot for a long period after initially forming, enough to radiate significant heat¹⁰⁷ onto a very close-orbiting moon for the first couple hundred million years of its life; this might slow cooling of the moon's surface and condensation of an initial steam atmosphere long enough to cause escape of much of its water or other atmospheric gasses—though given how tumultuous our planet's infancy was, this may or may not permanently render a moon uninhabitable.

 

For a tidal-locked moon, eclipses and reflected light will only affect the planet-facing side of the moon anyway; the far side of the moon will never see the planet. This suggests the intriguing possibility of a society developing on the far side of a moon, completely unaware of the planet or their world’s status, then sending out explorers and making some startling discoveries.

But if we want short days and so need a close orbit, there are other reasons to be careful about placing the moon too close to the planet. A moon can be tidally heated by a planet just as a planet is by a moon or star, and even for low eccentricities the tidal heating can cause¹⁰⁸ surface heat flows similar to Io for moons orbiting within 5-10 times the planet’s radius. In the habitable zone of a low-mass star the star’s influence can increase the eccentricity of the moon, while the radius of a stable orbit around the planet decreases. For planets of stars below 0.2 solar masses, a stable, habitable moon becomes near impossible¹⁰⁸, and even stars up to 0.5 solar masses may cause issues with tidal heating¹⁰⁹ for moons in the inner HZ. But more moderate heating can be beneficial; I’ve already mentioned how it could extend the range of habitable periods and masses, and this is as much the case for moons orbiting planets as for planets orbiting stars.

The planet’s magnetic field is another double-edged sword. It may provide some protection¹¹⁰ from some types of atmospheric loss for a close-orbiting moon, but the magnetic field also holds large amounts of high-energy particles and plasma in radiation belts, which can erode moon atmospheres in wide orbits and bombard their surfaces with radiation in close orbit. But the facts that Titan has maintained a significant atmosphere and Callisto experiences fairly mild radiation indicate that there is an intermediate range of favorable conditions.

Taken together, the effects of tidal heating and protection by the planet’s magnetic field could mean the minimum habitable mass for a moon is lower than that for a planet, though only with fairly specific orbital conditions. If we also recall from the last post that a planet with higher atmospheric CO₂ levels should have a lower minimum mass to retain a thick atmosphere, then altogether the lowest-mass habitable world should be a moon in the outer regions of the habitable zone.

Superhabitability

One final idea that has been floated in the scientific literature is that, given all the factors involved in habitability, Earth may not actually be the most habitable possible world. A few ideas for how other planets might actually support greater amounts of life and biodiversity have turned up over the years:

• Earth is currently substantially colder than it has been for most of the last half-billion years at least, and also has some rather large deserts. Earth in the late Cretaceous around 80 million years ago was substantially warmer and had few deserts thanks to a fortuitous arrangement of continents, and so by some estimates may have¹¹¹ supported substantially more biomass compared to today (the Ordovician climate was similarly amenable but there were no land plants yet to exploit it).
• Given that Earth's biomass and biodiversity have generally increased over time, an even older planet (if that age brings no issues such as reduced geological activity or increased chance of global catastrophe) could have as-yet unseen evolutionary innovations that allow for even greater complexity and biodiversity.
  
• We’ve already discussed how slower rotation could lead to warmer poles, and in my own experimentation with climate models I've found that the shift in circulation favors vast tropical forests uninterrupted by the subtropical deserts of Earth. It may also encourage more upwelling¹¹² of nutrients in the oceans.
• Increased obliquity could also help warm the poles and reduce desert cover, and the increased productivity of polar seas in summer may better favor⁴⁸ oxygenation.
  
• We also discussed how a different star could allow Earth to be habitable for longer. A planet nearer to the center of the HZ would also remain habitable for longer, and decreased surface water and increased eccentricity would make it more resilient to climate upsets, though all these shifts have to be balanced against their immediate impacts on surface conditions.
  
• Should super-Earths have no major issues regarding their tectonic activity, their greater size could support more total biodiversity than an otherwise similar small planet.
• A thicker atmosphere (or lower gravity, though that would conflict with the previous point) might conceivably allow for a greater diversity of flying life, perhaps even whole new aerial ecosystems.

Our Little World

For Teacup A, our example system, the standard habitable zone model gives us a conservative habitable zone range of 0.39 to 0.72 and optimistic range of 0.31 to 0.76 AU. The inner boundary can be pushed to roughly 0.28 AU with a slow-rotating planet or 0.15 AU for a low-humidity, high-albedo planet, and the outer boundary to 0.99 AU with a 50% H₂ atmosphere (a dry surface or high eccentricity should give a similar effect) or 5.8 AU for a 100 bar H₂ atmosphere.

Considering these boundaries and the constraints on mass established earlier, there are 4 bodies with potential for habitability: Teacup Ac, Ad, Ae, and Af V.

Teacup Ac, as you may have put together by now if you've been paying close attention, is designed to fulfill our requirements for a marginally habitable low-humidity desert planet. At 0.25 AU, it’s well within the limits for such a planet, and has a reasonable albedo of 0.3. Low obliquity helps keep the poles cool, especially the north pole that experiences summer during the apoapsis of the planet’s eccentric orbit. Thus the planet has small ice caps with meltwater lakes around the perimeter. With half Earth’s mass and a small core it doesn’t have the warmest interior, and by 6 billion years (the age of the example system) it’s only producing 0.06 W/m² of interior heat, but in this case a lower rate of volcanic activity may actually be preferable to keep CO₂ levels low. It’s still a fairly harsh environment, so we’ll say that it’s inhabited only by microbes living off what sunlight and chemical energy they can get in the meltwater lakes, perhaps brought here by meteorites from a more hospitable world.

Teacup Ad is a waterworld within the optimistic habitable zone, but its seas are boiling and are underlain by a thick layer of high-pressure ice that block access to vital nutrients. We’ll leave it uninhabited.

Teacup Ae is, of course, our Earth analogue. It sits comfortably within the conservative habitable zone—closer to the inner edge but not as close to Earth—and is within the ideal size range. Though it has a smaller core than Earth, bumping the radiogenic metals abundance up to 1.5 times that of Earth’s gives it 0.086 W/m² of internal heat at 6 billion years, ideal for habitability and plate tectonics. According to a quick check in Universe Sandbox 2, 0.03 atm of CO₂ should give it Earthlike surface temperatures. That’s high by our standards, but I’m sure the local life can get used to it.

The average irradiance Teacup Ae receives from Teacup A is only 74% what the Earth gets from the sun, but that should be plenty for photosynthesis. I’ll give the planet an obliquity of 15°, somewhat less than Earth, but also an eccentricity of 0.1, meaning its distance from Teacup A varies from 0.405 to 0.495 AU. I’ll give it an argument of obliquity of 150°, which puts the periapsis somewhat before the northern winter solstice. This gives the planet stronger seasons in the south (30-40% more day-averaged irradiance in peak summer and less irradiance in winter at mid-latitudes) and a slightly warmer northern fall/southern spring than northern spring/southern fall. Northern summer/southern winter is longer than northern winter/southern summer—by about 14 days (10 Tdays) if we count equinox to equinox—but that’s not a huge difference.

Irradiance of Teacup Ae averaged across the day at different latitudes (shown on the left) in W/m² (also shown by color scale), at regular intervals throughout the year. Produced with my worldbuilding spreadsheet.

(Note: Since first writing this post I've altered Teacup Ae to have a much higher obliquity, around 28 degrees at time of writing, to encourage more seasonality in spite of the shorter year; don't be afraid to iterate on your designs as you explore different aspects of your world.)

Based on the likely luminosity evolution of Teacup A, Teacup Ae should stay within the conservative habitable zone until the system is 14.9 billion years old, and within the optimistic habitable zone until the star is about 32 billion years old. If we presume Teacup Ae will become tidal-locked by that time, it could conceivably last through Teacup Ae’s entire main-sequence lifetime and even into the red giant stage.

But internal heat becomes an issue long before sunlight does. Based on my simple heat model, the ideal period for plate tectonics should be roughly from 2.5 billion to 7.5 billion years after formation, and habitable tectonic activity should last at most 11.7 billion years after formation. Thus, unlike Earth, Teacup Ae’s carbon cycle will fail while it still orbits in the habitable zone.

As tectonic activity decreases and CO₂ outgassing with it, the polar icecaps will advance and eventually Teacup Ae will start limit cycling; alternating between periods of global ice cover and brief, warmer interglacials. Over time the glacial periods will become longer and the interglacials shorter, until the planet is permanently locked in an iceball state. What little internal heat remains may allow for microbial life to survive in the crust or perhaps pockets of liquid water in the deep ocean, but complex surface life will be wiped out. Eventually the growing luminosity of Teacup A will thaw the surface, but then the planet will skip right past habitable temperatures to a runaway greenhouse.

Teacup Af V is a substantial moon within the habitable zone for hydrogen-rich atmospheres, and is helped along by its arid surface. But it’s small—only 0.2 Earth masses—and orbits too far from its planet to receive significant tidal heating at its eccentricity, so we’ll leave it as a quiet, dead world but with some traces of a wetter, more active past.

As with any system, life in Teacup A will only last so long, and the system has already lost some once-hospitable worlds. But we’ve given ourselves a good deal of breathing space; Teacup Ae could remain habitable for twice as long as Earth is expected to be, giving us plenty of time to develop intelligent life.

This post about wraps up the astronomical portion of this worldbuilding journey, at least for now; eventually the inhabitants of Ae will leave home and explore this system we’ve set up for them (I’ll also talk a bit about astronomical factors in regards to climate and alternate biochemistry). And before then I’ll probably have one-off posts outside this series addressing some ideas on the subject I couldn’t get into here. But for now, it’s time to focus in on Teacup Ae, and similar Earthlike worlds. Next time we’ll look at tectonic processes—both plate tectonics and plausible alternatives—and see how we can use the “rules” to produce realistic planet surfaces.

In Summary

• To maintain a habitable surface for billions of years, a planet requires stabilizing climate feedbacks like the carbon-silicate cycle to compensate for changing star luminosity.
• The limits of the habitable zone are set by the stellar fluxes where these stabilizing feedbacks break down and allow runaway greenhouse warming or snowball cooling.
• Various factors could extend these habitable zone boundaries:
• Higher atmospheric pressure and slower planet rotation could both extend the habitable zone moderately inwards.
• Lower surface water could extend the habitable zone both ways, and at the extremes may allow habitability in Mercury-like orbits.
• Atmospheric methane or hydrogen may allow habitability beyond the typical limits for CO₂.
• However, concerns regarding initial cooling after formation or recovery from a snowball episode, declining volcanic outgassing as planets age, and challenges posed by high CO₂ or low light could all hamper habitability towards the edges of even the conservative the habitable zone.
• Seasons could be caused by:
• Planet obliquity/moon inclination
• Planet eccentricity
• High planet inclination around a rapidly-rotating star
• Wide moon orbit of a large planet in a tight orbit around a small star.
• Motion of stars in a short-period binary system with planets.
• Extreme seasonality may cause harsh climates, but could also favor habitability in otherwise hostile orbits.
•  Habitable planet size is restricted by the need to be large enough to retain heat and continue outgassing an atmosphere, but small enough to lose the primordial thick hydrogen atmosphere. A reasonable ideal range is 0.25-4 Earth masses, but in extreme cases it could plausibly extend to 0.05-10 Earth masses.
• Moderate variations in a planet's composition like different levels of radioisotopes in the mantle, different core sizes, and different rock composition might not hinder habitability or even be benign, but radically different waterworlds or carbon worlds have more fundamental habitability issues.
• A large moon orbiting the planet and a large gas giant outside the iceline may both have positive impacts on habitability, but no evidence so far indicates they are vital.
• All the habitability conditions that apply to planets should apply about as well to moons as well.

Notes

This post is a little image-bare compared to my previous ones, but I’ve blown a lot of my stock of nice NASA/ESA/ESO images I found a couple months ago, and a lot of the papers on the subject just have graphs that make no sense until you’ve read half the study. I might come back and add more later, but it seemed like a silly reason to delay for another week.

Terms like insolation, stellar flux, and irradiation are used a bit inconsistently in the scientific literature. My personal standard is that insolation refers to the energy distributed over a planet's surface while stellar flux refers to the energy passing through space (equivalent to what a flat surface facing the star would receive), in both cases measured as power per area (W/m²) ; for a spherical, rapidly rotating planet, average insolation over the surface should be 1/4 of the stellar flux at its orbit, while for a tidal-locked planet, average insolation over the lit hemisphere will be 1/2 the stellar flux (though because some heat inevitably diffuses to the unlit side, especially if there's an atmosphere, you can't necessarily treat a tidal-locked planet as if it was getting twice the insolation as a rapidly rotating one). Really I should use insolation and solar flux only in the solar system and instellation and stellar flux for all other stars, but I've opted to just use the terms you'll see most widely used elsewhere. Irradiation can be generally treated as synonymous with insolation but I usually use it to refer specifically to light reaching the top of a planet's atmosphere without accounting for how much is reflected away or scattered in the atmosphere.

I just want to give special recognition to Noack and Breuer (2014)⁶⁴ for concluding that “[Plate tectonics] on exoplanets is either more, less or equally likely compared to Earth.” It was a useful paper, though.

Sooner or later I’m going to have to come back around to this idea that habitable worlds may become rarer as the universe ages and throw some actual math at it. Just to reiterate the reasoning for now:

• Radiogenic elements become diluted in stable metals.
• The average age of planets increases, meaning more of them have cold interiors.
•  Lower-mass stars, which may have issues with habitability, will become more common.
• A larger portion of the planets within the immediate habitable zone of aging stars will have previously spent long periods outside the habitable zone.
• Higher metallicity will cause more formation of multiple giant planet systems, which will make instability events more likely.
• Older systems will have had more time to experience instability from internal or external factors. 

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Part Va

Appendix: A Simple Heat Model

This is a simple heat model I worked up for the first version of this post I made in 2019. Looking back during a revision pass in 2024, I'm feeling rather less bold in presenting a lot of my wild assumptions with so much confidence. The estimations here for radiogenic and tidal heating are still reasonable, the trouble is estimating primordial heat. I assumed some simple scaling with mass would work okay at the time, but on further reading the current level of primordial heat depends on how much heat has been lost over the planet's history, and the rate of loss depends strongly both on the temperature profile of the planet's interior over that history and the passage through different tectonic modes that allow for different cooling processes. Basically, to get anywhere near to a decent estimate would require making several assumptions about a planet's tectonic evolution and then iterating a model forward in steps over that evolution. I will not be attempting that here, but I leave the flawed model I have assembled here for the benefit of anyone who wants to work on it further.

The idea is to estimate the habitable period of an Earthlike planet based on internal heat generation. I will assume that ultimately the presence or absence of tectonic activity on a planet can be determined by the heat flow at the surface from interior sources. In reality this heat can emerge in several different ways (convection, plumes of melt) and a single value could correspond to different tectonic modes depending on the history of the planet, but even with these wrinkles abstracted out surface heat flow should provide a good first-order estimate. I will also assume that we can divide internal heat sources into the three main categories already mentioned: radiogenic, primordial, and tidal. Again, where this heat is generated in the interior matters, but we can assume that for planets of similar composition, similar total heat production will imply similar results. The aim here is not to predict the tectonic mode for a given planet, but to put reasonable soft limits on the period of habitable tectonics for a planet that otherwise has all the correct conditions for such tectonics.

 

h_tot = total surface heat flow

h_rad = radiogenic surface heat flow

h_prim = primordial surface heat flow

h_tid = tidal surface heat flow

Radiogenic heat is the easiest to determine, as it is based only on the initial concentrations of radioactive isotopes, the half-lives of those isotopes, the heat released by their decay, and the age of the planet. 99% of Earth’s radiogenic heat comes from 4 isotopes: Potassium-40, Thorium-232, Uranium-235, and Uranium-238, with half-lives of 1.4, 13.9, 0.7, and 4.5 billion years, respectively. Taking into account their individual half-lives, rates of heat production, likely initial concentrations¹¹³ in the mantle, and proportion of the planet’s mass that consists of mantle, we can express the total heat produced at any one time:

h_rad = radiogenic surface heat flow (W/m²)

P_man = proportion of planet mass that is mantle; 0.68 for Earth

M_p = mass of planet (kg); 5.97*10²⁴ kg for Earth

R_p = radius of planet (m); 6.37*10⁶ m for Earth

[⁴⁰K] = initial concentration of ⁴⁰K in mantle; 4.64*10^-7 for Earth

[²³²Th] = initial concentration of ²³²Th in mantle; 1.55*10^-7 for Earth

[²³⁵U] = initial concentration of ²³⁵U in mantle; 1.64*10^-8 for Earth

[²³⁸U] = initial concentration of ²³⁸U in mantle; 6.24*10^-8 for Earth

t = age of planet (billions of years); 4.5 for Earth today

e ≈ 2.71828

This predicts a current h_rad for Earth of 0.062 W/m² (32 TW total for the planet) which matches the predictions of geoneutrino surveys. As mentioned, these values could vary quite a bit for other planets, and ⁴⁰K in particular could be 50-100 times more abundant for a world that formed outside the iceline. Were we to assume that abundance of these isotopes was directly tied to the relative size of the core, this would imply that radiogenic heat production peaks when the core contains half the mass of the planet, but the two factors probably aren’t so perfectly correlated across all systems.

Estimating primordial heat production is a bit trickier, partially because rather than just being remnant heat from formation it is still being produced by continuing differentiation in the core and mantle, and partially because the rate at which a planet loses heat depends greatly on the tectonic mode. Attempts to fully model the Earth’s thermal history are hideously complicated¹¹⁴ and difficult to generalize to other planets, so instead I’ll be using a highly simplified model⁶⁴ which essentially models primordial heat as if it were an additional radiogenic heat source, but in this case distributed throughout the entire planet’s mass rather than the mantle:

 

h_prim = primordial surface heat flow (W/m²)

M_p = mass of planet (kg); 5.97*10²⁴ kg for Earth

R_p = radius of planet (m); 6.37*10⁶ m for Earth

h_prim0 = initial primordial heating (W/kg); 1.2*10^-11 W/kg in my model

t = age of planet (billions of years); 4.5 for Earth today

e ≈ 2.71828

Not that I’ve altered the h­_prim0 from my source as there were attempting to use this model for all sources, including radiogenic, and using a lower estimate of current surface heat flow. I’ve normalized my value to achieve 15 TW of primordial heating today, so that combined with radiogenic heating it gets us to 47 TW. Presumably I should be adjusting the decay constant (coefficient of t) as well, but I haven’t thought of a good way to do that and I don’t think it should make too huge of a difference in this case. I’ll proceed with the warning that this model is only meant for planets that experience plate tectonics for a large portion of their lives, and that it probably gets increasingly inaccurate for planets of significantly different size, composition, and age compared to Earth.

Tidal heating is, unlike the other sources, not strongly dependent on time. For a planet in an orbit close enough for significant tidal heating, the obliquity and rotation rate won’t take long to reach a tidal-locked state and won’t drift far from it afterwards. But eccentricity can take a long time to dissipate and will produce quite a lot of heat as it does. So surface heat flow from tidal heating for a typical star and Earthlike planet can be approximated⁶⁶ based on the properties of the two bodies and their orbit:

h_tid = tidal heat (W/m²)

G = gravitational constant; 6.67408*10^-11 m³ kg^-1 s^-2

M_s = star mass (kg); 1.988*10³⁰ kg / solar mass

R_p = planet radius (m); 6.371*10⁶ m / Earth radius

Q’_p = planetary dissipation parameter; 500 for earthlike planet

e = eccentricity

a = semimajor axis (m); 1.496*10¹¹ m / AU

Eccentricity will decay over time—faster the more heat is produced—but it can be induced by other planets, and determining exactly how much eccentricity is induced and when is not simple. For the purposes of this model I’ll leave it as a free parameter and say that any moderate value is reasonable for a system with other nearby planets.

Now perhaps the trickiest part is actually placing constraints on the total surface heat flux that could allow for habitable surface conditions. I’m going to follow the example of researchers marking out habitable zones of luminosity and define a conservative and optimistic habitable range.

I’ll base the conservative range on the history of plate tectonics on our own planet. The preceding and following tectonic modes may not necessarily be uninhabitable, and indeed the origin of life predates plate tectonics, but given that complex life is only known to have evolved in an environment with plate tectonics it’s good to keep in mind.

The best current evidence¹¹⁵ indicates that the Earth transitioned from earlier tectonic states to plate tectonics around 2-3 billion years ago; 1.5-2.5 billion years after formation. It may have taken more time for some of the features of plate tectonics that we observe today to set in, but we can be fairly sure that subduction, moving continents, and associated volcanism have been going on in some form since then. Based on my heat model, the Earth’s surface heat flux at the time would have been about 0.19 W/m².

Extrapolation of current trends predicts⁴⁰ the end of plate tectonics in roughly 1.5 billion years. Note that for a planet in the outer region of the habitable zone, limit cycling may settle in before this transition, or this transition may trigger it. Again based on my heat model, the heat flux will be about 0.067 W/m²

For our optimistic limits, we can look to two bodies in our solar system that have clearly left the range of healthy, habitable surface tectonics. Io, at 0.015 Earth masses, should have long ago cooled off to a frozen iceball, but tidal heating from Jupiter—caused by eccentricity induced by the other Galilean moons—gives it a surface heat flow¹¹⁶ of about 2 W/m², far above any Earth has experienced since the moon-forming impact. The result is extreme widespread volcanism that spews massive amounts of CO₂ and other gasses into the moon’s tenuous atmosphere; were a similarly-heated planet in the habitable zone, it would likely experience a runaway greenhouse effect in short order. But even setting aside that issue, the volcanic activity is accompanied by frequent lava flows across the surface. Based on the lack of visible impact craters, it’s likely that the entire exterior of the moon has been resurfaced¹¹⁷ by lava flows within the last few hundred thousand years. Though some life might potentially survive such frequent volcanic activity by staying on the move, this will also be accompanied by extreme rates of outgassing of greenhouse gasses, so it's unlikely any stable habitable climate could develop.

Really, setting the upper limit at Io’s current heat flow is too optimistic, because even far tamer conditions would probably be too violent for life. But lacking a better example and given the uncertainties of scaling up from Io to a planet tens of times its mass, it’s a decent ballpark number.

By the way, note that this limit is far below the heat received from sunlight at the outer edge of the habitable zone (~120 W/m² average over the whole surface) so I’m doubtful that surface habitability could be maintained through tidal heating alone, though it could support a subsurface ocean as is the case for Europa. A planet with a thick Hydrogen atmosphere (but still not a gas giant) might manage to retain enough heat from internal sources to have habitable surface temperatures, but such an atmosphere would also obscure light from outside. In both cases it’s hard to imagine the scant supply of geothermal energy supporting the evolution of complex life.

At the lower end, I’ll follow the example⁶³ of academic researchers in using the estimated heat flow on Mars when major tectonic activity ceased 2 billion years ago: 0.04 W/m². Below this value, we shouldn’t expect a planet to produce enough CO₂ to maintain the carbon-silicate cycle, and it may even risk losing its atmosphere. My model predicts the Earth will pass this range in about 4.5 billion years, but that’s ignoring the effect of transitioning to a different tectonic mode or losing its oceans to increased insolation.

I’d expect the realistic limits to be somewhere between those set here, so the prediction of this model is more a reasonable range of habitable lifetime than hard borders.

But, if we are willing to accept this model, then it implies that the minimum mass for a planet with Earthlike composition to sustain habitable tectonics for 4.5 billion years is between 0.1 and 0.35 Earth masses, which decently agrees with other estimates. This doesn’t quite agree with the predicted thermal evolution of Mars, which is 0.1 Earth masses, but that may be partially due to the fact that I assumed similar radioisotope proportions to Earth; Mars has a core mass proportion about 2/3 of Earth, so if we assume (perhaps naively) that its heavy metal abundance is similarly scaled, the result is closer to reality. It’s also probably worth asking if there’s an activation heat for certain tectonic modes that is above the shutdown heat, and if there’s a delay after formation before something like plate tectonics can initiate, but that’s beyond the scope of this model.

I’ve added this model to my worldbuilding spreadsheet as well.

 

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