An Apple Pie from Scratch, Part VId: Climate: Tidal-Locked Planets

 

Space Engine

For our last foray into climates (for now), let’s finally look at a category of worlds I’ve been putting off due to their particularly bizarre patterns of climate; those worlds that are tidally locked to their stars. To understand these worlds we have to go all the way back to the beginning, and reassess the assumptions underlying our reference climate scenarios back in Part VIa.

First off, some clarification: The term tidal-locked applies to any planet that, under the influence of tidal forces from its star, becomes “locked” into synchronous rotation, such that the ratio of the planet’s period of rotation around its axis (its sidereal day) and its orbital period (its year) is a simple fraction. Mercury, for example, rotates exactly 3 times for every 2 orbits around the sun—a 3:2 spin-orbit resonance—and so can be said to be tidal-locked.

But the term is most often used to refer specifically to worlds with a 1:1 spin-orbit resonance, such that the rotational and orbital periods are exactly the same, with one side of the planet always facing the star and the other side always facing away (this is also the default on this blog; whenever I say “tidal-locked” with no further clarification, you can assume I’m referring to a 1:1 spin-orbit resonance). These are the worlds I’m mostly concerned with in this post, though I’ll talk a little about other synchronous rotators near the end.

Tidal-locking can also occur between moons and planets, or between binary planets. In a case like this the rotational period of the moon matches the orbital period around the planet, but not the orbital period of the planet around the star. There is no case where the two orbital periods can be the same, and a moon will always feel a stronger tidal force from its planet than from its star (because of ratios between the factors determining tidal forces and Hill radii). The presence of a large moon could also prevent a planet from tidal-locking to its star, though tidal interactions between all 3 bodies may tend to cause such moons to either fall into a collision with their planets or be ejected from their orbits. In terms of climate, tidal-locked moons can be treated just as planets with Earthlike fast rotation, with a day length determined by their orbital period (a planet’s rotation can also become tidally locked to its moon’s orbit, with much the same results).

Tidal forces are strongly linked to the distance between the relevant bodies, so planets orbiting closer to their star will be more quickly tidal-locked. Lower-mass stars have much closer habitable zones, even relative to their mass, and so are more likely to have tidal-locked habitable planets with short orbital periods. But the time to tidal-locking is also determined by the initial rotation period, which could be anywhere from a handful to thousands of hours. As such, there’s no strict upper limit for how far away a planet can be from its star and still end up tidal-locked.

But there is a minimum rotation period a planet can have without tearing itself apart; a while back I ballparked this at around 2 hours for an Earth-like planet, and determined that a planet with this initial rotation period and otherwise Earthlike properties and age (4.5 billion years) would necessarily be tidal-locked anywhere in the habitable zones of stars below 0.34 times the mass of the sun (barring extenuating circumstances like a large moon).

All that in mind, let’s get started.

•  Mechanisms of Tidal-Locked Climates
• Rotation
• Slow Rotators (>20 days)
• Intermediate Rotators (5-20 days)
• Fast Rotators (<5 days)
• Ocean Currents
• Other Forcings
• Obliquity
• Eccentricity
• Continental Drift
• Climate State and Stability
• Surface Conditions
• Winds
• Clouds
• Light and Shadow
• Example Worlds 
• Slow Rotator (>20 days)
• Intermediate Rotator (5-20 days)
• Fast Rotator (<5 days)
• Desert Worlds
• Other Synchronous Rotators
• 2:1 Resonance
• 3:2 Resonance
• Asynchronous Slow Rotators
• In Summary
• Notes
  

Back to Part VIc

Mechanisms of Tidal-Locked Climates

Much as with the rapidly-rotating planets we considered before, let’s look at a series of scenarios of increasing complexity. First, consider a planet that is static with a homogenous surface—though we’ll acknowledge from the start that the nightside will be mostly frozen over. Rather than a ring of lights, we’ll have a single light source over the dayside. In this scenario the equator and poles no longer matter (though they will in later scenarios) so instead we’ll talk about the substellar point (SSP) at the center of the dayside where insolation is highest; the antistellar point (ASP) at the exact opposite end of the planet, furthest from sunlight; and the terminator ringing the planet halfway between these points, separating dayside from nightside (it’s where the reach of sunlight terminates).

High insolation at the SSP warms the air there, causing it to rise and then spread outwards in all directions. It crosses over the terminator, loses heat, and starts sinking back to the surface, but some amount makes it all the way to the ASP and sinks there. Then it flows back at low altitude towards the terminator.

At the edge of the nightside ice cap (which is not necessarily close to the terminator), there will probably be strong katabatic winds; the ice cap gradually slopes down from the ASP to this edge, and as descending air follows this slope it gains ever-greater speed until it shoots off the edge and buffets the surrounding area. But contrary to some early, simple models of tidal-locked worlds, the entire twilight zone (region of low light on the dayside near the terminator) will not be constantly buffeted by gales; rather, they’d be comparable to prevailing winds on Earth.

Once on the dayside, these low-altitude winds begin to warm up and continue towards the SSP. There the air rises again and closes the loop.

A cross-section through the planet's atmosphere from SSP to ASP, with the terminator at the center; the "temperature inversion" is a region of the atmosphere actually warmer than the surface. Stevenson 2019.

 

So there’s one giant circulation cell over the entire planet, with a high-pressure zone at the ASP and a low-pressure zone at the SSP. Rather than a broad, wet ITCZ circling the planet, all moisture converges at the SSP, causing unending rain and cloud cover.

Rotation

Now let’s introduce rotation to this scenario, because tidal-locked planets do rotate; they have to in order to keep the dayside pointed at the star as they orbit around it. The rotational period is, again, the same as the orbital period, and this is linked to insolation and star type; but as before, we’ll try to consider the impact of rotational period as an independent factor. We’ll also be assuming again that every planet rotates to the east, for simplicity (the planet necessarily has to rotate in the same direction it orbits anyway for this kind of climate).

Rotation of the tidal-locked moon (left) as opposed to a truly non-rotating body (right). Stigmatella aurantiaca, Wikimedia.

Rotation induces a Coriolis effect, which alters the paths of airflow over the surface and does so in different ways depending on the cardinal direction they’re travelling in. In general this weakens winds travelling towards the SSP from the north or south—passing over the poles—and strengthens winds moving along the equator. Past that, the specifics depend on exactly how fast the planet is rotating, and thus how strong the Coriolis effect is.

Different models vary on the conditions they predict, but in general it seems that for wet planets with Earthlike dayside temperatures, we can expect 3 major regimes of atmospheric circulation at different rotational/orbital periods. Note that estimates for the critical rotation periods for the transitions between regimes varies a bit between models, and it’s not yet clear if they might shift under differing conditions of size, atmospheric pressure, insolation, greenhouse heating, or surface cover.

Slow Rotators (rotation period >20 Earth days)

Modeled surface temperature (color) and prevailing winds (arrows) of slow-rotating tidal-locked planets. Labels show the star effective temperature, planet rotation period, and insolation at the SSP used for each model. Haqq-Misra et al. 2018.

In this regime—plausible for habitable planets orbiting stars over 0.1 solar masses—the Coriolis effect is small enough that the climate resembles our prior scenario without rotation: low-altitude winds blow directly from the nightside to the dayside all along the terminator, and converge on the SSP from all directions with about equal strength. There is little to distinguish north and south from east and west. Precipitation should be mostly concentrated near the SSP, with both rainfall and temperature smoothly decreasing away from the SSP in all directions.

Near the lower end of this range (below ~50 days) easterly winds will become noticeably stronger than westerly winds. This is accompanied by stronger westerly winds in the upper atmosphere, resulting in slightly warmer temperatures to the east of the SSP, even extending into the nightside.

Intermediate Rotators (5-20 days)

Once rotation drops below 20 days—plausible for planets orbiting stars below 0.47 solar masses—the climate transitions to another state, called the “Rhines rotation regime”. The dayside becomes dominated by easterly and westerly winds, with the latter being stronger, and few winds directly towards the SSP from the poles. These winds no longer converge only at the SSP, but rather along a broad, crescent-shaped front, along which we can expect heavy rains (and hurricanes). Winds deflected by the front bring warmer air over the poles, while areas near the terminator at the equator are cooled by strong winds from the nightside.

Fast Rotators (<5 days)

For fairly short periods—plausible only for close-orbiting planets around the very smallest stars, below 0.1 solar masses—the climate transitions again: Distinct convection cells form in the north and south hemispheres, and something resembling an ITCZ (intertropical convergence zone) appears near the equator. But curiously, winds along this convergence zone behave differently in different areas. On the nightside the Coriolis effect causes easterlies just like on Earth, but on the dayside superrotation dominates (due to complex processes of atmospheric waves carrying momentum towards the equator) and so westerlies appear near the equator.

This long convection zone creates a band of precipitation along the equator, broadest near the SSP and to its east—where the dayside westerlies and nightside easterlies converge—but extending even to the nightside. It should also, like Earth’s ITCZ, detour away from the equator towards the center of landmasses, though only on the dayside and moreso east of the SSP.

The odd wind patterns also shift around the planet’s heat a good deal: The poles here are colder than in either previous scenario, even on the dayside, but conversely a warm region near the equator extends into the nightside, broader west of the SSP but circling all the way around. It’s very possible to have an ice-free and even fairly mild corridor crossing the nightside—though with no light, little rain, and probably not much life, it’s still not terribly hospitable.

Ocean Currents

Global ocean circulation seems to be a bit harder to simulate than atmospheric circulation, so hasn’t been modelled in quite so much detail for tidal-locked planets. As such, I’m less confident in my proscriptions here, but nevertheless:

Rather than several distinct regimes of circulation, the oceans appear to tend towards one state, which becomes more pronounced for faster-rotating planets. Strong currents flow from west to east all along the equator, creating a warm belt encircling the entire planet, though wider to the east of the SSP. On the day side, a pair of ocean gyres also form at mid latitudes, carrying some heat towards the poles.

General pattern of ocean currents on tidal-locked planets, with SSP in the center and nightside shaded.

On cool planets, the combination of these factors creates a distinct lobster-shaped region of habitable (above-freezing) conditions, with dayside lobes created by the gyres and a long “tail” extending onto the nightside created by the equatorial current.

Sea ice cover (left) and surface temperature (right) in models without (top) and with (bottom) fully modeled ocean circulation. Peking University.

From the models I’ve seen, these currents are fairly strong even at periods as long as 60 days. As the rotational period decreases, currents along the equator strengthen and poleward currents weaken. I’ve yet to see models of ocean circulation for rotational periods in the hundreds of days, so I’m just forced to extrapolate in the opposite direction and suppose they’ll have similar geometry but be overall weaker and less heat will be carried to the nightside.

This also has knock-on effects for the wind patterns; winds will no longer converge just at the SSP, but at all the warm areas created by these currents, and this may somewhat broaden the region of heavy rain for moderate rotation periods.

Note, however, that most of these models assume global deep oceans. Continents and shallow ocean floors can block these currents, allowing the nightside to remain much colder than implied here. Globally shallow waters seem to strengthen poleward currents and weaken equatorial ones, and even a fairly small landmass continent at the SSP or directly to its east can block the equatorial current and keep most heat on the dayside even at short periods, creating an “eyeball” world like we’re used to seeing in older models.

Sea surface temperatures for models of planets with different ocean depths and with obstructing "ridges" of land. Yang et al. 2019.

Other Forcings

That all gives us a general idea of what tidal-locked worlds should look like, but much as with more Earthlike worlds there are a variety of climate forcings that can subtly alter these global patterns. Many of these have much the same overall impact here: Greater volcanic outgassing will tend to raise global temperatures, greater weathering in warm regions will tend to decrease it; greater atmospheric pressure or greenhouse heating will tend to decrease the temperature contrast between warm and cold regions, and greater size or insolation will tend to increase it. But other forcings will have somewhat different impacts, which are worth discussing here.

Obliquity

The same forces that cause tidal locking should also usually reduce a planet’s obliquity to zero, so quickly that we should typically expect tidal locking to imply zero obliquity (note that, in the case of a moon tidal-locked to a planet, the moon’s orbit around the planet may be inclined relative to the planet’s orbit around the star, such that we can consider the moon to have an “effective obliquity” equal to that inclination for all purposes of climate).

Diagram showing that the "effective obliquity" for a tidal-locked moon is equal to its orbital inclination around its planet.

However, an external influence (such as another planet or star) can perturb both the planet’s orbital and spin axes, causing it to eventually settle into a Cassini state, wherein both elements shift in concert to effectively give the planet an obliquity as high as 100° (or 180°, flipped completely over and rotating retrograde to its orbit) which remains constant even with high tidal forces.

The effect of obliquity is to make the star appear to shift north and south in the sky, with the SSP and terminator following it. For example, at 30° obliquity, the substellar point moves from 30° south in northern “winter” to 30° north in northern “summer”; and the northern edge of the terminator moves from 60° north on the dayside in “winter”, to 60° north on the other side of the planet, the nightside, in “summer”. This effectively brings a day/night cycle to a ring of land along the boundary between dayside and nightside, broadest at the poles and thinning down to zero width at the equator.

Maximum (top), minimum (bottom), and average (middle) insolation compared to SSP insolation for a planet with 30° obliquity. Dobrovolskis 2009.

What this looks like in terms of climate depends in part on rotation period. For long periods, conditions near the poles may resemble the polar regions on Earth: summers of constant sunlight and winters of constant night, though there’d be no intermediary period of regular days and nights; the sun would rise once in spring and remain above the horizon until it set in winter. At shorter periods, it would be more of a long day and night, with life and civilizations perhaps treating them just as we treat days and nights here.

For greater obliquities, the region affected by this day/night cycle increases, up to the point that, at 90° obliquity, the entire planet sees sunlight at least briefly (the same is almost true for night, but because the star has some width there will still be a small area where it never completely sets below the horizon). Even so, there will still be a clear “dayside”, that receives light through most of the year, and “nightside”, that spends most of the year in darkness. And unlike for Earthlike rotators, average insolation throughout the year is always highest near the center of the dayside, not at the poles. As such, prevailing wind patterns aren’t actually all that much affected by obliquity.

Modeled average surface temperatures (colors, K) and prevailing winds (arrows) on planets with varying obliquity (and a 28-day rotation period). Wang et al. 2016.

Still, high obliquity could warm polar regions enough that they resemble temperate regions on Earth. The upshot of all this is that you can have a world with both regions of constant sunlight (though the star oscillates in the sky) and regions of more Earthlike day/night cycles (though the days are necessarily longer).

Eccentricity

Eccentricity is another orbital element that should usually be reduced by tidal forces, but less aggressively than for obliquity, and eccentricity can also be increased by the influence of other planets. Highly eccentric planets are more likely to end up tidal-locked in other spin-orbit resonance states, but it is at least marginally possible for planets up to 0.6 eccentricity to end up in a 1:1 resonance.

The effect of eccentricity is twofold: For one, the insolation the dayside receives will vary throughout the orbit, peaking at periapsis, the point when the planet is closest to the sun, and falling until apoapsis, when the planet is further away. But there’s also a subtler shift in how eccentricity affects the relationship between spin and orbit:

As a planet orbits around a star, from its perspective the star appears to be moving around it. We’re familiar with the daily apparent motion of the sun, but if Earth’s rotation were to stop completely, we would still see the sun appear to circle around the Earth once per year. On a tidal-locked planet with no eccentricity or obliquity, the rotation of the planet is perfectly synchronized to the apparent angular motion of the star, such that it appears to remain static in the sky. But with an eccentric orbit, the planet will move through its orbit faster near periapsis and slower near apoapsis. This causes the apparent angular motion of the star to change throughout the year, speeding up near periapsis and slowing down near apoapsis. But the planet’s rotation rate remains constant all throughout the year. From the perspective of an observer on the planet’s surface, this causes the star to appear to shift east near periapsis, when the star’s apparent motion outruns the planet’s rotation; and shift west near apoapsis, when the star’s apparent motion lags behind.

So if a planet’s orbital eccentricity were, say, 0.4 (with zero obliquity), then the substellar point would move about 49° longitude west and east of its position at periapsis, and the terminator with it (the motion is necessarily symmetric about the position at periapsis, which is also the position at apoapsis, though there is some asymmetry; areas to the east will have a short, rapid “morning” as the sun shifts east and long, gradual “evening” as the sun shifts back west, and the reverse for areas to the west). Much as with obliquity some areas near the edge of the dayside will alternate between day and night, and whether the effect on climate is more day-like or season-like depends on the orbital period—but the center of the dayside still receives the most average insolation and so overall climates shouldn’t be too altered.

Modeled average surface temperature (colors, K) and movement of the SSP (arrows) for planets of varying eccentricity. Wang et al. 2017.

And, of course, obliquity and eccentricity can be combined in myriad ways. If, for example, periapsis comes close to midsummer in either hemisphere, the substellar point will move in a loop around the center of the dayside (not a perfect circle, more of a squashed egg). The result is what we might call a “Clock world”, with areas of temporary day or night circling around the edges of the dayside over each orbital period, like hands of a clock. The motion won’t be totally consistent, though; one hemisphere will get brief days of intense sunlight, the other will get longer, milder days, though this does actually balance out to roughly equal values for average insolation in each hemisphere.

Hypothetical conditions on the dayside of a "clock world" with periapsis at northern summer solstice. This is just a suggestive representation; I haven't modelled the motion of the terminator in detail.

You can experiment with more patterns of insolation on tidal-locked worlds with both obliquity and eccentricity in the “Irradiance slow rot” tab of my worldbuilding spreadsheet.

Continental Drift

At our current level of knowledge, it’s hard to be certain that Earthlike plate tectonics could operate the same way on a tidal-locked world, but at any rate there’s no compelling reason to believe it should be impossible. But if it does happen, the interaction between the strong tidal forces and the mobile crust will add an extra flair to the process. Any bulge in the crust will tend to be dragged towards either the SSP or the ASP (a case of true polar wander, where the planet’s orientation changes relative to its rotational axis). Such bulges can be formed by rising plumes of hot rock in the mantle, such as those that tend to form under supercontinents; the upshot, then, is that whenever a supercontinent forms on a tidally-locked planet, the planet should tend to reorient itself to place the supercontinent at the SSP or ASP.

Behavior of a tidal-locked planet with large plumes of rising mantle rock. Leconte 2018.

Mantle plumes can form on worlds without plate tectonics as well, so similar reorientation events can happen there, though of course it won’t be associated with supercontinents. However, if such a world forms a permanent bulge in its crust, like the Tharsis highlands on Mars, this should be pulled to the SSP or ASP and then stabilize the planet against further reorientation.

This process won’t be quick, mind, probably occurring over tens to hundreds of millions of years. But that’s fast enough to have some interesting consequences for the long-term development of the planet’s climate and life.

On Earth, the drift of continents into and out of the tropics has a major influence on the transition between climate states: young mountains exposed to high temperatures and precipitation will experience increased weathering, which draws CO₂ out of the atmosphere and cools the planet. Much the same should be true should be true on tidal-locked planets, except that high temperatures and precipitation are mostly limited to a small area around the SSP (especially in the slow-rotating case), so the presence or absence of a continent there may have a profound impact on global climate.

With an ocean at the SSP, CO₂ will rise unimpeded until landmasses further from the SSP are warm and wet for enough weathering to match CO₂ production. Were a continent to then move into the SSP, weathering would rise dramatically, enough to draw down CO₂ levels by a factor of 10,000 before it’s balanced out by volcanism. This alone will have varied effects for surface chemistry and life (Even if occurs gradually over many millions of years, such a drop in CO₂ levels could be disastrous for photosynthesizing life depending on it, and an equal rise could be just as disastrous for oxygen-breathing life not adapted to high CO₂).

But of course, such a drop in greenhouse warming—as well as disruption of ocean circulation that carries heat away from the SSP, and lower evaporation at the SSP which would reduce atmospheric water vapor and so further decrease greenhouse warming—will cool the planet by perhaps 40 K or more. At least this cooling will mostly occur on the nightside an edges of the dayside; thanks to poor ocean circulation, the SSP temperature will actually increase with a continent there. Reduced evaporation will also cause reduced precipitation and cloud cover across the dayside—the associated drop in albedo will slightly offset the global cooling, and further contribute to warming the SSP.

So now consider how the climate of such a world will develop over long timescales. First, suppose a supercontinent forms and the planet reorients to place it at the SSP. Supercontinent formation on Earth is already associated with cooling due to decreased volcanism, and here this trend is amplified by the intense weathering at the SSP and drop in atmospheric water vapor. Given an Earthlike atmospheric pressure and insolation, CO₂ levels may drop to a few parts per million (compared to ~400 ppm today). Photosynthetic life dependent on that CO_2­ will die out, and the whole food web depending on that life comes crashing down—oxygen levels may also decline as production stops. This is further compounded by freezing over of many of the seas far from the SSP, killing marine life. Something will survive in the warm, wet region around the SSP—there are other biochemical pathways for photosynthesis and chemosynthesis that don’t rely on CO₂—and given how gradual this will be, perhaps even some complex life will make it through. But it will be a major bottleneck in the evolution of this world’s life.

Then, supercontinent breakup begins, bringing a sharp rise in volcanic activity and opening new ocean basins near the SSP. CO₂ levels shoot back up, precipitation rises, temperatures rise by tens of degrees, and the frozen-over regions of the dayside thaw. For a time, life is good.

But suppose this is an extroversion cycle, with the continents moving around and assembling a new supercontinent on the opposite side of the planet, near the ASP. In this case, the continents move ever further away from the SSP, become cooler and drier as a result. CO₂ levels continue to rise, peaking at 5% or more of the atmosphere (again, presuming Earthlike pressure and insolation) once the dayside is mostly free of land. Oxygen-breathing life (if any exists at this point) that survived the low-CO₂ bottleneck may have trouble adapting, and most life on land will be wiped out as the continents pass over the terminator. Meanwhile, as the oceans open, circulation patterns will transition from an “eyeball” to a “lobster” state, warming areas to the north, south, and east of the SSP, but cooling areas to the west, northeast, and southeast.

These alternating bottlenecks of cool, dry, land-dominated periods with low CO₂ and hot, wet, ocean-dominated periods with high CO₂ could prove a real challenge to the development of complex life on tidal-locked worlds. But supercontinent cycles are slow and not always as clean as presented here, so perhaps with some luck there can be windows of moderate climates for a few hundred million years or more.

Climate State and Stability

If the climate forcings of a tidal-locked planet really are bouncing about so violently, we might be concerned about it retaining a habitable climate at all, rather than tripping over some threshold into a snowball or runaway greenhouse state. Fortunately, compared to Earthlike rotators, tidal-locked planets appear to be more resistant to either transition, and even have a broader habitable zone.

Part of this comes down to the distribution of insolation. On Earth, a flat surface facing directly at the sun on a clear day receives over 1000 W/m² of sunlight, but rotation and obliquity spread that sunlight around such that no part of the planet receives more than around 350 W/m² averaged across the year (nights and winters also provide good opportunities for ice accumulation). This only drops by around 100 W/m² at 45° latitude, and even the poles get around 140 W/m². Thus once it’s cold enough for ice to form at high latitudes, the planet only needs to get slightly cooler for the ice to spread to low latitudes.

Were Earth tidal-locked with no obliquity or eccentricity, the substellar point would constantly receive 1000 W/m², areas 45°longitude or latitude away would receive around 300 W/m₂ less, and insolation would drop to 0 at the terminator. So ice may form at the edges of the dayside even under fairly warm conditions, but the planet needs to become substantially cooler for this to reach the SSP.

This steep insolation gradient reduces the strength of destabilizing ice-albedo feedback (as does the lower albedo of ice in redder light, if orbiting a red dwarf), the tendency for more ice formation to reflect away more sunlight and cause more ice formation. Thus, unlike Earth, there is no rapid transition from a hothouse climate to an icehouse climate, and then again to a snowball. A snowball state of total ice coverage is still possible, but it’s onset would be more gradual, and it would be somewhat easier to recover from.

Gradual onset of a snowball state for a planet with decreasing insolation. Checlair et al. 2019.

Now, high insolation at the SSP is somewhat offset by high cloud cover that blocks much of the sunlight from reaching the surface, but this itself acts as a stabilizing negative feedback, because the total cloud cover is linked to the dayside temperature. You may recall a while back I mentioned that such permanent cloud formations could reflect away enough light to allow a slow-rotating or tidal-locked planet to remain habitable well inside the edge of the habitable zone for Earthlike fast rotators (the limit would be around 0.66 AU from a sunlike star, rather than 0.95 AU for the traditional habitable zone). But increased cloud cover could help moderate any other forcing towards warming as well, and inversely a decrease in cloud cover when temperatures drop could moderate any cooling process (though this doesn’t affect the outer limit of the habitable zone).

And even when a tidal-locked planet does cross over the inner limit of the habitable zone, the results may not be as severe as for fast rotators. When an Earthlike rotator passes over the inner edge of the HZ, it enters a moist greenhouse state, where huge amounts of water enter the upper atmosphere and surface temperatures rise to near boiling. Water is rapidly lost to space and the oceans are drained in short order, which stops weathering and allows CO₂ to build up in the atmosphere until the planet resembles Venus.

But for tidal-locked planets the transition is much gentler: dayside temperatures remain well within the habitable range and ice still covers much of the nightside. Water is still being lost to space, but gradually enough that it may take billions of years for the planet to dry out.

And drying out may actually be beneficial to habitability in the long term; Once a planet reaches the moist greenhouse state, it doesn’t take much more warming to push it into a runaway greenhouse state, where the oceans evaporate and are completely lost to space within a few million years, and the gradually brightening star will provide the necessary forcing sooner or later (though for slow-evolving red dwarfs, it can still be many billions of years). But if a planet manages to lose enough water before then, the lower humidity will allow more dust to form and accumulate in the atmosphere, reflecting away light and slowing the warming of the planet. All of this may buy enough time for the planet’s interior to cool, decreasing volcanic CO₂ production, such that eventually there just isn’t enough water or CO₂ remaining to cause a runaway greenhouse effect. Instead the planet transitions to a marginally habitable desert world, a state that can survive to much higher insolation (as close as 0.38 AU to a sunlike star if the planet’s albedo is high enough), with life perhaps still surviving in meltwater lakes near the terminator around the last of the planet’s glaciers.

(Due to their different circulation patterns, planets with orbital periods under 5 days do not pass through the moist greenhouse state, and so do not have this opportunity for gradual transition to a desert planet; they transition straight from habitable to runaway greenhouse.)

But none of this is to say that tidal-locked planets can never suffer from climate-destabilizing positive feedbacks. For example, we can expect such planets to be more vulnerable to the possibility of atmospheric collapse. If some portion of the nightside becomes cold enough, atmospheric gasses will deposit to form ices. This lowers total atmospheric pressure, which weakens both the greenhouse effect and transport of heat from dayside to nightside, so the nightside cools and more gasses deposit until the atmosphere is nearly or completely locked away in ice.

For Earthlike atmospheric pressure and insolation, this isn’t much of a concern; heat transport should remain strong enough to prevent atmospheric collapse across a broad range of parameters. But it could happen to worlds with atmospheric pressures below around 0.1 atm, up to ~3 atm at the outer edge of the HZ (remember though that outer HZ planets already need several atm of CO₂ to remain habitable, so this may be a moot point for them).

Division between stable (red circles) and collapsing (black dots) CO₂-dominated atmospheres for different atmospheric pressures and SSP insolations. Wordsworth 2015.

Once we take weathering patterns into account, CO₂-dominated atmosphere below ~0.2 atm may be particularly vulnerable. Typically a drop in CO₂ levels will decrease weathering, but if a drop in CO₂ levels also represents a significant drop in pressure, then weaker heat transport will actually make the SSP hotter, and so weathering will increase, continuing to draw down CO₂ until the nightside is cold enough to allow CO₂ deposition and atmospheric collapse.

On the other hand, large water oceans may help prevent collapse and lower these thresholds by providing an alternate pathway for heat transport. Various other factors such as topography, geothermal heat, and other variations in atmospheric composition could also impact the probability of collapse.

But speaking of water, that too could be locked away in nightside ice, with a similar feedback of decreasing water causing decreasing heat transport. But nightside ice sheets will form on top of the oceans, insulating them and trapping in geothermal heat. Total loss of the dayside oceans should only happen on worlds with low geothermal heat, large nightside continents, and oceans holding only 10% the water of Earth’s oceans. And, of course, a dry dayside can still remain marginally habitable, though it will hold less life overall and have poorer prospects to develop complex life.

Yang et al. 2014.

Surface Conditions

Before we moved on to worked examples, Let’s pause a moment to think about aspects of life on tidal-locked worlds that can’t be summarized with climate zone maps.

Winds

For one, there are the winds: Early models of these worlds predicted constant hurricane-force winds near the terminator, but more recent modelling has suggested typical low-level windspeeds on the dayside of around 5-10 meters/second, perhaps up to 15 m/s in some areas; a stiff breeze but certainly no hurricane. The simpler convection patterns of slow-rotating worlds means that wind direction will be very consistent, and this may still have an impact on surface conditions; hills and mountains will have distinctly more wind erosion and rain on slopes facing away from the SSP, and we may perhaps even see life specializing into different niches on wind-facing and leeward slopes.

The nightside, on the other hand, will have very little wind across most of its surface, especially on slow-rotating worlds. Only near the terminator will winds towards the SSP become significant, and as mentioned earlier, strong katabatic winds may form at the edges of glaciers.

Clouds

One point I keep coming back to is the intense precipitation and cloud cover near the substellar point. Contrary to some earlier predictions, this probably wouldn’t appear as a gigantic rotating hurricane with a distinct eye; the circulation patterns are a little messier than that. But there should be near-permanent cover by multiple layers of clouds in a region about 15-30° latitude or longitude away from the warmest area (the SSP on slow rotators, somewhat to the east on fast rotators). So ironically, it may be rare to get a direct view of the sun in the area facing most directly towards it on the world of eternal day. Fortunately for life and agriculture, small-scale eddies should give some breaks in the clouds with reasonable frequency.

Modelled cloud cover for Proxima b (arrows are high-altitude winds, not prevailing winds near the surface). Boutle et al. 2018.

Far from the SSP, high-level clouds become rarer, though the exact distribution depends on the rotation rate (there will usually be more clouds to the SSP’s east in any case). But something curious happens to the lower atmosphere: with little heating of the surface, and huge masses of hot air moving out of the SSP at high altitude, temperature actually drops with altitude, peaking at a few kilometers above the surface. Thus, any descending air will become colder and any moisture it contains will precipitate out. This may add a bit of rain and snow, but for the most part it will result in frequent fog covering large regions near the edge of the dayside.

Modeled atmospheric temperature profile at the SSP (solid line) and ASP (dotted line) for Proxima b with an Earthlike (blue) or pure-nitrogen (green) atmosphere. Boutle et al. 2018.

Much the same is true for the nightside, with essentially no heating of the surface, but by this point the descending air is so dry that it only forms a thin icy fog. But lacking strong winds, this fog should be fairly persistent and cover much of the nightside.

Light and Shadow

For a tidal-locked planet with zero obliquity and eccentricity, a static sun will cast static shadows. On Earth at high latitudes, we can already see how ice and snow survives longer in spring on the north slopes of hills and mountains, due to less direct sunlight exposure. On this world these regions would be larger, more numerous, and more starkly divided from sunlit regions; ever hill near the terminator will have a cold side of eternal shadow, and a warm side where the slopes face more directly towards the sun. For substantial mountains the shaded regions can be quite vast, following this formula:

d = length of shadow cast at sea level by mountain (any unit so long as r and h are the same)

r = radius of planet

h = height of mountain

l = longitude or latitude away from substellar point (°)

So a mountain range 5 kilometers high on an Earth-sized planet 80° away from the SSP will cast a permanent shadow over 28 kilometers long. Given that prevailing winds towards the SSP are likely to produce rain on the side facing away from the SSP, we can expect pretty substantial glaciers to commonly form in these regions. But on a warmer world this area could remain above freezing, and exist just as wet but largely lifeless wastes.

Because of this shading, the terminator won’t form a straight line where it passes over land, but instead will swoop back and forth by potentially over 100 km due to topographical features, with additional “islands” of dark forming in valleys on the dayside and “islands” of light on mountain peaks on the nightside.

Example Worlds

All that in mind, let’s look at what climate maps on these worlds should typically look like in a few different example cases. To keep things simple I won’t worry about variations in climate state, orbital elements, or land distribution. I’ll just use the same topography of Teacup Ae as before—with the SSP placed in the center of the maps we’ve been using, in western Lyell—and assume obliquity and eccentricity to be zero, only varying rotation rate. Global average temperature I’ll assume to be about right to place the edge of the nightside icecap roughly near the terminator—though by no means will this necessarily be the case for all tidal-locked worlds.

However, the equirectangular map projection I’ve been using for climate maps so far rather awkwardly displays the terminator as a square, even though in reality it’s equally distant from the SSP on all sides. Because distance from the SSP is more important and cardinal directions are less important to climate patterns on tidal-locked worlds, and because all the most important stuff we’re concerned with is concentrated on one hemisphere, I’ve opted for a different map projection here: The somewhat obscure Ortelius Oval projection. I’ll talk at length about map projections in another post, but in short it correctly displays the dayside as a perfect circle, while not doing anything too weird to the orientation of areas on the nightside and preserving east-west directions throughout the map.

However, note that I'm aware of no way to convert a map in this projection back into equirectangular or any other projection. It may be wise, therefore, to use a map in this projection to build your climate zones, and then use it as a guide to transpose them back into equirectangular.

Tidal-locked Teacup Ae rendered in the Ortelius oval projection. SSP shown in red, terminator shown in purple, nightside shaded, and graticules at 30° intevals of longitude and latitude.

Conveniently enough, there are substantial regions of both land and sea near the SSP, which should perhaps help produce a moderate climate between the hot ocean world and cool supercontinent world we discussed earlier.

The Koppen classification scheme isn’t ideal for this type of world—without seasons, only 7 out of our usual set of 14 zones are even possible—but for purposes of comparison it’ll do fine.

Slow Rotator (>20 Days)

First, let’s look at the most straightforward case: A planet rotating slow enough to induce no significant Coriolis effect, aside from perhaps a slight tug towards the west for winds near the equator.

We’ll start with the ocean currents, though because of limited modelling we’ll have to be a bit fast and loose with the rules here. To start out, we’ll have an equatorial cold current coming into the dayside from the west. Were the equator clear of obstructions, this current would continue straight across the dayside and circle the planet. In this case, it’s stopped by Lyell’s coast just short of the SSP.

Warm currents then follow the coasts north and south, eventually looping around to form gyres centered to the northwest and southwest of the SSP. Gyres should still appear here even if there were no landmass at the SSP.

Again, without obstruction we’d expect the equatorial current to continue east around the whole planet; but here, instead we’ll fill in the oceans to Lyell’s east with an equatorial current to the west, with it’s own accompanying gyres.

That covers the most important elements of ocean circulation; we can add some secondary gyres around the edges of our main currents, but they probably won’t have a major impact on the climate of nearby landmasses. We also don’t need to worry much about currents on the nightside in this scenario; They’ll be fairly lethargic, isolated from the surface by thick ice sheets, and have little impact on surface conditions.

I’m going to switch up the order here a bit and tackle winds next, because they have a bigger impact on surface temperatures here than on Earthlike rotators.

In this case, wind patterns are easy; low-level winds pass directly over the terminator and converge on the SSP from all sides. These winds may be somewhat deflected by large mountain ranges, and needn’t converge exactly at the SSP but can end anywhere in the warm region created by ocean currents.

Wind will be weak across the nightside, so again there’s no need to worry about them much.

For temperature, Clima-Sim is no help; it’s simply incapable of modelling the circulation patterns at work here. We’ll just skip ahead to marking out climate bands, which is a little easier, and rely on a combination of intuition and a few reference models to help us out.

Unfortunately these models vary quite a bit on the expected surface temperature profiles, but it appears that for a slow rotator to have 0 °C near the terminator (such that the edge of the nightside ice cap will be there) requires a warm dayside with tropical temperatures reaching as far as 50° latitude or longitude from the SSP. Ocean currents and winds carrying air warmed or cooled by these currents will determine the exact shape of the edges of this zone, and to some extent topography will as well—but not quite as you’d expect.

Remember that in some areas, temperature actually rises with elevation. Near the SSP, high mountains will likely be colder than lowlands, but near the terminator mountains 2 to 4 kilometers high may actually be warmer than either lower or higher elevations.

Without seasons, there’s also no thermal inertia to worry about, so the overall effect is that landmasses may actually tend to be warmer near the terminator than nearby seas—though the extent to which this is true depends a good bit on the topography and nearby ocean currents of a particular region. For the most part, I’d say it should only be obvious where there are large mountainous regions, with plateaus close to that ~3 km sweet spot.

At any rate, this isn’t much of a concern for the tropical band…

…but it is moreso for the temperate band and tundra zone. These will form fairly thin concentric strips around the tropical zone following the same overall logic; the latter will be a slightly thicker strip, but of course it can vary with the various factors involved in each location. There should be some temperate areas between all tropical and tundra areas, and some tundra between temperate areas and the ice caps we’ll add next. Naturally, without seasons there are no hot-summer temperate or continental zones to worry about.

And of course the rest of the planet will be frozen over, encompassing most of the nightside and extending into the dayside here and there near cold currents.

Precipitation will be fairly straightforward in this case, and to keep things simple (and not overextend past the available modelling references) I’ll just mark wet and dry in this case: First, there will be a large region of convective rain near the SSP, extending out around 30° latitude or longitude in all directions, but excluding some areas with strong rainshadows (the extent of this rainy region seems to vary a bit between models for reasons hard to pin down—other than land cover near the SSP—so you could be more optimistic and have a wetter planet, but it shouldn’t cover the entire dayside).

We can perhaps extend out this zone a little further in areas with major warm currents and onshore winds.

There are no large fronts, because all prevailing winds are close to parallel to their neighbors. So we’ll just add some regions of orographic rain, on the windward slopes of major mountains…

And a few areas of lee cyclogenesis, where winds passing directly over mountain ranges create cyclones that pull moisture onto the downwind sides of these ranges.

We don’t need to worry about precipitation on the nightside, of course, and really we only actually need rain patterns in the tropical and temperate bands to mark climate zones. Speaking of which, we can mark out all dry areas in those bands as arid, mostly filled with desert but with a buffer of steppe around wet areas (only hot desert and steppe in this case

The last step is to add some rainforest in the wettest regions of the tropical band, near the SSP or on the windward slopes of high mountains (because we skipped marking “very wet” zones in this case, you’ll just have to judge the wettest areas by intuition, but it’s okay I trust you). In the warmest areas of the planet (strictly speaking, areas above 29 °C, compared to the 18 °C transition between tropical and temperate) rainforest transitions directly to steppe, with no intervening savanna.

Contrary to the common misconception of a habitable strip around a desert, this is almost the reverse case; a vast rainforest near the SSP, but little more than islands of hospitability across the rest of the desert- and tundra-covered dayside. It may not be quite as bad as it looks for those regions, however; orographic rains will feed lush river valleys crossing many of the deserts, life in the tundra regions shouldn’t be hampered by permafrost as it is on Earth, and regular thick fog should provide some moisture to life in even the driest deserts at the edge of the dayside.

Still, it’s a harsh world compared to Earth, and temperate climates are very much the exception rather than the rule here.

Intermediate Rotator (5-20 Days)

The broad strokes here will be similar to the slow rotator, but there are various important differences.

First off, the currents will be largely the same, but perhaps somewhat tighter around the equator; weaker north or south currents, stronger east or west currents (the currents outside the main gyres are really just guesswork in this and the next case).

The most obvious difference will be in wind patterns. Rather than a single convergence point around the SSP, there will be a broad crescent-shaped front, centered at the SSP but curving around to ends at roughly 60° poleward, 60° west in each hemisphere. It should lie roughly along the warmest areas, so may have a somewhat different shape depending on warm currents, but in Teacup’s case the position of oceans just complements the basic shape of this front.

Winds at low to mid latitudes will be predominantly east or west, converging at the front.

At high latitudes, a pair of anticyclones will actually form on the nightside, east of the terminator. Winds branching off of these anticyclones will pass over the poles , some converging back on the front and some looping around the end of the front to converge on it from the other side.

This pattern of winds makes areas north or south of the SSP warmer than areas east or west, which will give the climate zones a “squashed” appearance relative to the slow rotator. The edge of the ice cap will deviate a good bit from the terminator; reaching far into the dayside near the equator, but with ice-free poles.

For precipitation, we do still have a large region of convective rain around the SSP.

But in addition, a broad strip of rain exists along the crescent-shaped front, much as with static fronts on Earth.

And, of course, we can add in the orographic and lee cyclogenesis rains, accounting for the different wind patterns in this case compared to the slow rotator.

Marking out climate zones proceeds much the same, but we can have more rainforest spread out along the front, rather than just at the SSP.

The result is a somewhat wetter world than the slow rotator, with two great avenues of hospitability connecting the SSP to the terminator. The climate bands are somewhat less ring-shaped, but there’s still a clear sequence from dayside to nightside. This may be a good option if you want a tidal-locked world with roughly concentric rings of climate, but with large temperate regions at the edges of the dayside.

Fast Rotator (<5 Days)

This is the odd one out, with climate patterns more resembling Earth-like rotators in some ways than other tidal-locked planets. Unlike the other two cases, we do have to pay some attention to ocean and air circulation on the nightside.

To start out with, currents will again be fairly similar across the planet, though with faster rotation and westerly winds overhead, I’ll switch the direction of the current on the eastern part of the dayside, though there may still be a west-flowing current on the nightside where easterly winds dominate. Midlatitude currents may also be a bit more vigorous here, due to a greater heat gradient between the equator and poles (again, there’s a lot of guesswork here for lack of detailed modelling).

For winds, we can start out by drawing a convergence zone along the equator, similar to the ITCZ. It should stay fairly near the equator in the western part of the dayside, but may deviate from it pretty far in the east, detouring towards landmasses and mountains in particular.

A pair of anticyclones will form to the west of the terminator near the poles, likely centered in cold landmasses (though in this case, the coldest areas are actually in lowlands). From there, winds will converge on the convergence zone across the dayside, curving to the east near the equator to produce superrotation.

They also converge on the nightside, but in this case they twist to the west, and approach the equator at a shallower angle. East of the SSP, some small fronts may form where these opposing equatorial winds converge, though nothing as impressive as for intermediate rotators. They may also form at higher latitude to the east of the terminator, but wind speed is low there and temperatures very low, so they’re not really worth tracking for the purposes of marking out precipitation.

The climate bands will again be somewhat squashed, though in the opposite direction as for intermediate rotators and to a greater extent; The tropical band will occupy a large oval-shaped region in the dayside, but also extend into the nightside along the equator to the west of the SSP. This could even encircle the entire planet in some cases, though I’ll opt for something a bit more moderate here. Increased temperature with elevation at the edge of the dayside is still somewhat true here, but less so near the equator compared to the poles.

The temperate band and tundra zone will be very thin directly north and south of the SSP, covering only 10-15° latitude, but broaden out elsewhere, and occupy large stretches of the nightside. Bear in mind that there is no solar heating on the nightside; some hot air is descending from above, but wind and current patterns have a much clearer impact on temperature.

And of course, the rest is given to ice cap, forming two distinct ice sheets now, one over each pole.

High precipitation will be spread along the convergence zone and its associated fronts, but still broadest near the SSP and thinning out towards the terminator.

Far into the nightside, the convergence zone itself doesn’t cause rain, but air there carries enough moisture to allow for orographic rain where prevailing winds encounter mountains.

For the final touches, you can extend rainforest along much of the equatorial convergence zone, and add some step along the equator on the night side as there should still be a bit of occasional rain along most of that warm corridor.

The final result is a huge rainforest on the dayside, but very few temperate wet areas and large polar ice caps extending far into the dayside. Some of those wet temperate areas are spread along the nightside here, and there’s a belt of unfrozen ocean across the equator. But in this case the climate zones are deceptive; we can hardly expect a region of eternal night to support forests or crop growth. But a marginal ecosystem based on chemotrophs could survive here, perhaps—something akin to the seafloor ecosystems that appear around deep-sea vents on Earth.

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Though I’ll call it there in terms of climate maps, there are a couple other unusual cases worth considering that could produce vastly different climates.

Desert Worlds

By now it should be clear that the classic conception of all tidal-locked planets as “twilight worlds”, only habitable near the terminator, doesn’t hold up under modern climate modelling. But that isn’t to say such worlds are impossible. Back in Part IVc I mentioned that dry worlds with little CO₂ and almost no water could plausibly remain habitable even in very close orbit of their stars, well inside the conventional habitable zone for wetter worlds. Most of the surface would be inhospitable desert, but small meltwater lakes near the poles may provide islands of habitability.

The same climate scenario can work for a tidal-locked world as well, but here the small habitable region extends all the way along the terminator. It even helps, in this case, that large amounts of water can be trapped in ice on the nightside, as it keeps this water from contributing to the greenhouse effect, but allows for some meltwater to continue reaching the edges of the dayside. Of course, a fully ice-covered nightside and dry dayside, with the edge of the glaciers sitting neatly along the terminator, would require a very specific amount of water; fortunately, even with substantially less water there appears to be a tendency for glaciers to form near the edge of the terminator, to the SSP’s west (at least for slow rotators).

Distribution of ice on a dry planet with increasing heat transport to the nightside (in this case, provided by a thicker atmosphere). Leconte et al. 2013.

Modelling indicates that meltwater from these glaciers could produce a wet region hundreds of kilometers across, without putting enough water vapor into the dayside atmosphere to produce a runaway greenhouse effect. Any vapor produced won’t be carried to the SSP, but instead rise into the upper atmosphere and be return across the terminator to precipitate back down onto the nightside glaciers.

This wet strip wouldn’t experience much in the way of precipitation, save perhaps in mountainous regions, but a constant stream of meltwater could produce river valleys and even small seas. Though this region is arid, fairly thin by planetary scales, and may not cover the entire perimeter of the dayside, it does give us an option for the twilight habitable strip that have been popular in recent depictions of tidal-locked worlds.

Other Synchronous Rotators

Next, let us consider worlds that are tidal-locked to their stars, but not in a 1:1 spin-orbit resonance. 1:1 resonance is the only stable possibility for a planet in a perfectly circular orbit, but for planets with eccentric orbits there is some possibility to end up in a 1:2 spin-orbit resonance state (1 rotation around the planet’s axis for every 2 orbits around the star), a 3:2 state (3 rotations ever 2 orbits), 2:1, 5:2, 3:1, 7:2, and so on for every half-integer ratio of rotation period to orbital period (though a “0:1” state, with no rotation at all, appears to be impossible to produce through tidal-locking, and I’m not clear on the plausibility of Cassini states producing “negative” resonance, with retrograde rotation, for ratios other than -1:1). Each state is only possible for a certain eccentricity range, but random variations in the initial state and evolution of the system can allow for a planet with given eccentricity to end up in multiple states. Note as well that a planet’s eccentricity can change fairly rapidly under the influence of other planets, so even if a planet’s eccentricity makes a certain resonance state unlikely, it may have entered that state in the past when it was more or less eccentric.

Probability for a tidal-locking into each resonance state (stated here as spin/orbit ratios) for a planet with given eccentricity, depending on whether it initially spins faster than these resonances (left) or slower (right). A probability curve exists for every integer and half-integer resonance above 0.5, but most are omitted here for clarity. Dobrovolskis 2007.

For all resonance states other than 1:1, there is no longer a static substellar point, and all parts of the planet can expect to see at least some sunlight (save perhaps for shaded valleys near the poles of low-obliquity planets). But there can still be more average insolation at some longitudes compared to others, producing unusual climate patterns unlike those on Earthlike rotators. Bear in mind that for such planets, the synodic day length—the day length as measured by the apparent motion of the star as observed on the surface, from noon one day to noon the next—may be very different from the planet’s rotation period; for any resonance state (or any planet generally), there will be one less synodic day per orbit than rotations. So if a planet in a 3:2 state completes 1.5 rotations per orbit, it experiences just half a synodic day. A planet in a 1:2 state completes -0.5 synodic days an orbit, indicating that it completes half a synodic day per orbit but the star appears to move retrograde, rising in the west and setting in the east.

There are two resonance states other than 1:1 worth highlighting here, that set a pattern for all resonance states generally.

2:1 Resonance

These planets experience exactly 1 synodic day per orbit, so the same side always faces towards the star at periapsis, and the opposite hemisphere always faces towards the star at apoapsis. Because the planet necessarily has an eccentric orbit, this means that the sunlit side at periapsis will receive more insolation in its day, and even at fairly low eccentricity this can produce significant asymmetry in the average insolation received across the year. In short, though the sun passes over the entire planet, one side will be warmer than the other.

Given the right global climate conditions, this allows for such a planet to become an “eyeball world”, similar to 1:1 resonance planets; a warm, roughly circular region exists in the center of the warmer hemisphere, and the rest of the planet is covered in vast glaciers. A less stark contrast is also possible at moderate eccentricity: tropics along the equator in the warm hemisphere, and merely temperate conditions in the cooler hemisphere.

What the climate looks like is probably dependent in part on how strong this contrast is, but in general it should resemble 1:1 planets due to the warm hemisphere retaining more heat year-round. Bear in mind, though, that the planet rotates twice as fast, so the transitions between atmospheric circulation regimes will happen at twice the orbital period relative to 1:1 planets.

One thing to note, though, is that both the magnitude of orbital eccentricity and the position of periapsis within the planet’s orbit, can shift fairly rapidly due to the influence of other planets. The warm “eyeball” may circle around the planet in cycles of just a few thousand years, compared to perhaps tens of millions of years for the SSP on a tidal-locked planet to shift due to tidal interactions with the drifting continents. If a planet in a 2:1 state has some obliquity, this can also oscillate and produce even more complex patterns of climate evolution.

A broadly similar insolation pattern should appear for planets in other integer resonance states (they complete a whole number of rotations in each orbit) such as 3:1, 4:1, etc. Though they have more synodic days per orbit, there is still one hemisphere that always faces towards the star at periapsis and should be warmer than the other hemisphere. However, for higher-order resonances with more and shorter days the contrast is less stark; insolation is more evenly spread along the equator and if an “eyeball” does form, it will appear less like a circle and more a stretched oval, until it becomes just an uneven warm strip circling the equator (even the 2:1 “eyeball” is a bit stretched compared to the 1:1 case).

Maximum (solid line, center) and average (dashed line, right) insolation across the equator (left) and over the whole surface (center, right) for the (top to bottom) 0:1 (not actually achievable), 1:1, 2:1, 3:1, and 4:1 resonance states, all with 0.4 eccentricity. Dobrovolskis 2015.

3:2 Resonance

This is the resonance state of Mercury, and we can probably expect it to be the next most common resonance state after 1:1. Though the planet rotates 1.5 times each orbit, it still takes 2 complete orbits to experience one synodic day. Because of this, the hemispheres alternate facing towards the star at periapsis. For fairly low eccentricity (which is very much a possibility for this resonance state), this averages out to roughly even insolation across the equator, and circulation patterns may come to resemble that of an Earthlike fast rotator (though with such a long day, it may just have a single convection cell in each hemisphere stretching to the poles).

But with significant eccentricity, it may instead form a “double eyeball” pattern, with warm spots appearing in each hemisphere and cooler, possibly glaciated regions dividing them. These regions will even have winds converging on them like the SSP of a 1:1 resonance world, though as yet it’s not clear exactly how similar they are and if the same three circulation regimes will appear for different rotational periods.

Modeled average surface temperature (top), precipitation (middle), and prevailing winds and evporation (bottom), with average (solid line) and maximum (dashed line) extent of above-freezing temperatures indicated, for Proxima b in a 3:2 resonance state with 0.3 eccentricity. Boutle et al. 2018.

 

Similar “double eyeball” climate patterns may form for planets with other half-integer resonances (they complete 1/2 less than a whole number of rotations in each orbit) like 5:2, 7:2, etc.: their hemispheres will alternate facing towards the star at periapsis, and the centers of those hemispheres receive more insolation, though these planets have more synodic days per orbit—save for the 1:2 resonance, which has 1 synodic day every 2 orbits just like 3:2, but with the sun appearing to move in the opposite direction, rising in the west and setting in the east. Once again, higher-order resonances spread out insolation more evenly, making the “eyeballs” less distinct. 

Same chart as for the integer resonances, but for the (top to bottom) 1:2, 3:2, 5:2, and 7:2 resonance states.

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Aside from these specifics, one trait common to all worlds with long synodic days (and as such applying to asynchronous slow rotators and long-period moons as well) is a greater resistance to entering a full snowball state, and reduced severity and rapidity of transitions between climate states. So even though many of these worlds may have nights years long, they are actually less likely to become permanently locked in ice compared to worlds with day lengths similar to Earth.

Relative heating required for entry into (bottom of the purple region) and exit from (top of purple region) a snowball state for worlds with given synodic day length. Abbot et al. 2018.

Notably, however, the model I’m referencing doesn’t account for the effects of eccentricity on day and night length or intensity. A highly eccentric planet with an orbit that passes through the HZ may nonetheless be locked in ice through its long apoapsis winter, with at best brief thaws in the warmest area of the planet in the brief and infrequent summers.

Another issue with eccentric planets is increased tidal heating. For a planet orbiting in the HZ of a small red dwarf, the tidal forces produced by even moderate eccentricity may produce catastrophic levels of internal heat, tens to hundreds of times that experienced by Io. Even if the heat alone isn’t enough to render the planet uninhabitable, the huge amounts of greenhouse gasses released by widespread volcanism will almost certainly do the job (and frequent widespread lava flows aren’t exactly healthy for surface life either). Perhaps moderately greater volcanism and greenhouse warming could help the planet stay warm through winter (though only to an extent; the long winter may just cause the collapse of a CO₂-rich atmosphere) but it’s still better to have such eccentric, resonant planets in systems with more sunlike stars, if the intention is for them to be habitable (for Earthlike life, at least—such a volcanically active world might be ideal for life with exotic biochemistry that utilizes sulfur compounds and favors high temperatures).

Asynchronous Slow Rotators

Finally, some possibility exists for a planet to have a rotation period much longer than Earth’s, but not locked into a resonance with its orbital period. Planets can plausibly form with initial rotation periods hundreds of times longer than Earth. In close orbits of small stars such planets will be promptly tidal-locked, but more distantly-orbiting planets of larger stars may retain asynchronous rotation for much longer. A planet may also be tidal-locked to a distant-orbiting moon (or a moon tidal-locked to its planet) giving it long synodic days in no resonance with its orbital period around the star. But tidal interactions between all 3 bodies may make the orbit of any moon unstable around close-orbiting planets of small stars.

But asynchronous rotation could also be maintained for close-orbiting planets of relatively small stars, even without a convenient moon. As we’ve established, air tends to converge on the warmest part of a planet’s surface, and rise into the upper atmosphere from there, all of which creates a bulge of greater atmospheric mass, somewhat like the tidal bulge on the surface. But due to the surface’s thermal inertia, the hottest part of the day is not at midday, but some time afterwards, and so this thermal tide appears not over the SSP, but to its east (for prograde apparent motion of the star) or west (for retrograde apparent motion). The star’s gravity pulls this tidal bulge towards the SSP, and friction translates some of this pull to the ground.

The overall effect is still to despin fast-rotating planets, but once their rotation has slowed down, there are 3 stable rotation states they can be pulled to, with the exact result depending on the particulars of the system:

•  If a planet happens to start off very close to synchronous rotation, it can still land in a 1:1 resonance.
• If a planet starts off spinning prograde faster than 1:1, it will end up spinning slowly prograde, typically around 2 to 3 rotation periods per orbital period.
• If a planet starts off spinning retrograde or very slowly prograde, it will end up spinning very slowly retrograde, with a rotation period longer than its orbital period.
  

Venus is an example of the latter case, with its thick atmosphere causing its slow but asynchronous rotation. But a similar effect could happen for a planet with an atmosphere similar in mass to Earth, allowing for asynchronous rotation in the habitable zones of stars as small as 0.5 solar masses. An atmosphere 10 times thicker could extend this to stars of just 0.3 solar masses.

 

Limits of asynchronous rotation for different atmospheric pressures (~93 bar for Venus) compared to the classical habitable zone. Leconte et al. 2015.

This trend doesn’t continue forever, though; thicker atmospheres may have more cloud cover or distribute heat more efficiently and so have weaker thermal tides. It’s not yet clear what the exact limits are for asynchronous rotation caused by thermal tides.

The climate of such a world will depend on the exact rotation rate. For days even 16 or more longer than Earth’s, distinct circulation cells will still appear in each hemisphere and the whole equator should remain reasonably warm throughout the day. Somewhere before day length reaches around 100 times longer (I’ve yet to see research that clarifies when exactly that transition occurs), air circulation comes to resemble a tidal-locked planet, with winds converging on the warm, sunlight side, and producing heavy rains there. Even with days 128 times longer, though, there’s a noticeable lag between noon and the warmest time of day.

Snapshot of the modeled surface temperate (top, lines, K), cloud cover (top, colors), surface winds (bottom, arrows), and humidity (bottom, colors) for a planet with a 128-day asynchronous rotation period, and current SSP at the black dot. Yang et al. 2014.

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At long last, this brings a close to our discussion on climate, though naturally we may discuss its impacts on life and civilization later on. The Teacup A system contains no planets with atmospheres tidal-locked into a 1:1 resonance with the star. Teacup Ac is tidal-locked into a 3:2 resonance, but it has fairly moderate eccentricity (0.15) and is already mostly desert, so we don’t need to be too concerned about how its atmosphere circulates. We may want to refer back here, though, when we get around to fleshing out the Teacup B system.

At any rate, we can take the climate of Teacup Ae established a couple of posts ago (and the sketch of glacial extent during the most recent ice age in the last post), collate that with the world’s tectonic history, and finally get down to work mapping out its terrain in fine detail: Mountains, valleys, rivers, coastlines, and all. That will be our task for the next couple posts, coming hopefully fairly soon in the new year.

In Summary

• Tidal-locked, 1:1 synchronously orbiting planets have a rotational period equal to their orbital period, such that one hemisphere always faces the star and the other always faces away.
• On such worlds, air circulates not from the equator to the poles, but from the substellar point (SSP) to the antistellar point (ASP)
• The substellar point should typically have constant cloud cover and heavy rains, while areas near the terminator and on the nightside will be relatively dry.
• However, differing rotation rates create different patterns of air circulation:
• Rotational periods over 20 days allow for prevailing winds passing directly over the terminator on all sides, converging directly towards the SSP.
• Periods between 5 and 20 days produce a broad, crescent-shaped front on the dayside with broader rain patterns and warmer poles.
• Periods below 5 days will produce a long convergence zone along the equator, with a warm band stretching all the way around the planet and bitterly cold poles.
• Unobstructed ocean currents will tend to redistribute heat to produce a “lobster” pattern of surface temperature, rather than the more familiar “eyeball” pattern with constrained ocean currents.
• Cassini states can allow for tidal-locking planets to retain some obliquity, causing the SSP and terminator to appear to shift north and south over the course of a year.
• These planets can also have some eccentricity, causing the SSP and terminator to appear to shift east and west over the course of a year.
• Obliquity and eccentricity together can produce unusual patterns of day and night at the edge of the dayside, like “clock worlds”.
• Tidal forces should tend to pull supercontinents towards the SSP or ASP.
• The passage of landmasses across the dayside can produce dramatic shifts between a cold, dry, CO₂-poor state with a continent over the SSP, and a hot, wet, CO₂-rich state with an ocean over the SSP.
• Tidal-locked worlds should better resist both snowballing and runaway greenhouse effects, and may extend their habitable lifetimes by gradually transitioning to desert planets.
• However, planets with thin, CO₂-dominated atmospheres may be prone to atmospheric collapse, and relatively dry planets can have most of their water locked in ice on the nightside.
• Consistent winds, orographic rains, and permanent shadows may cause vastly different conditions to exist on either side of even small mountains.
• Far from the SSP, temperature rises with elevation in the bottom few kilometers of the atmosphere, creating widespread fog and allowing for regions with temperate highlands and tundra lowlands.
• Though they are not as ubiquitous as once thought, dry tidally-locked worlds can have vast deserts at the SSP with only a thin wet region near the terminator.
• Tidal locking can produce other resonance states for planets on eccentric orbits, which tend to have one of two climate patterns:
• Integer resonance states like 2:1 produce “eyeball” patterns like 1:1 planets with a warm spot in one hemisphere, even though the entire planet receives some amount of sunlight.
• Half-integer resonance states like 3:2 produce “double eyeball” patterns, with warm spots on opposite sides of the planet.
• Higher-order resonances or lower eccentricity will cause more even heating and these “eyeballs” will become less distinct.
• Thermal tides can allow some planets to retain asynchronous rotation even in the HZ of stars below 0.3 solar masses.

Notes

Now that I’ve got something of a settled style, I feel I should update some of the older posts to match. I’ve set myself the goal of updating two old posts for each new one. I’ll let you know when I’m done with this sweep, at which point you can check back on the old posts (most of the information should be the same aside from a couple small updates, it’s mostly just formatting) but until then you might notice some odd irregularities in formatting of old posts and the site map.

To keep track of this and other such updates, I've created a page tracking all major changes to existing posts, so that you don't have to keep checking them after you've read them.

Also, you may now notice there's now a little widget at the top of the sidebar allowing you to follow by email, so you can get email notifications whenever a new post comes out.

And finally, in case you’ve ever felt bad about slapping together elements of a project at the last minute, I present to you this figure, featured in a formal research paper, written by a collaboration of renowned experts and published in a prestigious journal:

I think it's demonstrating air motion above the SSP, if you're curious. Yang et al. 2019.

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Part VIIa