Hurried Thoughts: You're Wrong About Tidal-Locking

Space Engine

I've already talked about tidal-locked planets at length in the past (several times), and there won't be much new here for my regular readers, I just figured it'd be nice to have a single relatively short place to address the most common myths about tidal-locked planets, and particularly their climate, for easy reference.

 

The very short version is that the popular perception of tidal-locked planets—hostile worlds split between a burning desert on the lit hemisphere, ice on the dark side, and, at best, a thin "twilight strip" of habitable temperatures in between, wracked by gale-force winds—is not a strictly impossible scenario in all its particulars, but our current best climate models¹ predict (and have² for quite some time now) that tidal-locked planets in the habitable zone with Earth-like atmospheres and quantities of surface water can more typically expect far more hospitable conditions³, with comfortable temperatures and moderate prevailing winds across the lit hemisphere; that the hottest part of the planet will usually actually be the wettest⁴; and that this habitable climate state may actually be more stable⁵ in some ways than that of a planet more like our own.

 

For a more detailed explanation, let's back up a bit and set the scene. Tidal-locking describes a phenomenon whereby the tidal influence of a star on a planet (or between a planet and moon) causes the planet's rotation to slow until one side of the planet faces permanently towards the star, and the opposite side faces away. Because the planet still orbits in a loop around the star, this requires that it also rotates around once on its axis to keep that star-side face pointed to the star, so this is also sometimes called a 1:1 spin-orbit resonance; for every 1 orbit, the planet spins around exactly once. The tidal influence of the star helps ensure this exact timing, hence the "locking" aspect. There are other spin-orbit resonances that tidal forces might lock a planet into, like the 3:2 spin-orbit resonance of Mercury (the planet spins 3 times for every 2 orbits), but whether these planets should also be called "tidal-locked" varies between sources; in colloquial usage, "tidal-locking" is used almost exclusively to refer to the 1:1 resonance.

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

The strength of tidal forces is strongly dependent on the distance between the planet and star. Smaller red dwarf stars that are substantially dimmer than our sun have habitable zones that are correspondingly much closer to the star, so any habitable-zone planets of these stars are much more likely to be tidal-locked. These are by far the most common type of star in the universe, accounting for over 3/4 of the total number, so the habitability of tidal-locked planets is a major factor in the prevalence in habitability in the cosmos generally.

 

Unsurprisingly, keeping one side of the planet pointed at the star has a profound effect on how light from the star—and thus heat—is spread over the planet's surface. On Earth, a flat surface directly facing the sun (with no obstructions and ignoring filtering by the atmosphere) receives about 1360 Watts per square meter (W/m²) of light. But Earth's rotation and axial tilt spread out this light, such that the average light any single part of the surface receives across the whole year (averaging together summer, winter, day, and night) varies between a bit over 400 W/m² near the equator and under 180 W/m² at the poles (subtracting out the light reflected away by the surface and atmosphere leaves about 2/3 of that light on average being actually absorbed as heat).

 

On a tidal-locked world in the same orbit, the substellar point in the middle of the daylight side, which faces most directly towards the star, would get that full 1360 W/m² of light continuously. The heating would decline towards the edge of the dayside, falling to 0 W/m² at the terminator, the line dividing the day and night hemispheres; over 2/3 of the dayside hemisphere's area would receive more light than the average for Earth's equator. The entire nightside receives no light from the star at all, save perhaps some meager twilight at the edges refracting through the atmosphere.

Average insolation across the surface of Earth (left) and a tidal-locked planet in the same orbit (right)

It's understandable, then, that when the prospect of tidal-locked planets was first being considered⁶, such extreme contrasts in lighting and heating were expected to be accompanied by an extreme climate, split between a scorching hot dayside and bitter cold nightside. Perhaps somewhere in between, near the terminator, there should be at least a thin strip of more hospitable temperatures, but that didn't guarantee habitability either. A common concern⁷ was that any water on the planet's surface and perhaps even CO² would become trapped as ice on the nightside, leaving the dayside bone dry and even hotter for lack of the moderating influence of water. In the worst scenario, sequestration of ices on the nightside and heat-driven escape of atmospheric gasses to space on the dayside might remove such a planet's atmosphere entirely.

Even those who imagined a habitable strip imagined it dimly lit, being so close to the terminator, and wracked by vicious winds; the planet's strong temperature contrast would create a powerful convection cell, with air rising on the dayside, moving at high altitude to the nightside, and then descending and shooting back towards the dayside close to the surface; prospects for complex life in this constantly buffeted twilight strip would be, well, dim.

A cross-section through the atmosphere of a tidal-locked planet, showing air circulation from the center of the dayside to the nightside, with the terminator in the center; the "temperature inversion" shows a portion of the lower atmosphere where temperature rises with altitude, rather than falling. Stevenson 2019⁸

This picture of tidal-locked planets as marginally habitable at best but more likely prone to complete collapse into dry, sterile, perhaps even airless worlds prevailed well into the 1990s⁹, but as computing technology improved and we finally gained some capability to simulate the climates of such worlds in detail, which painted a far different picture².

As it turns out, even an atmosphere substantially thinner than Earth's could distribute enough heat to the nightside to prevent atmospheric freeze-out, and a more Earth-like atmosphere could keep temperatures globally within about the same range¹⁰ we experience on Earth. Water, too, can easily avoid¹¹ becoming completely trapped on the nightside, and global oceans could then help distribute heat even more evenly¹² across the surface.

In fact, in some circumstances, tidal-locking might even make a habitable climate more stable. Near the inner edge of the habitable zone, where the sun's light is more intense, the slow rotation and global convection may allow for warm planets to develop a permanent cloud formation that reflects away much of the star's light, keeping temperatures moderate even in orbits⁵ where a planet with Earth-like rotation would boil from runaway greenhouse warming. At the habitable zone's outer edge, this cooling effect would be weaker, and the sharp gradient in heating from the star on the dayside would help prevent¹³ runaway cooling and ice formation of the sort that may have caused Earth to freeze over completely in the past.

So, let's take a quick look at what modern modelling predicts the actual climate of a tidal-locked planet with otherwise Earth-like properties should look like. Temperatures across the dayside³ could easily vary by less than 30 °C, and the nightside would tend to be even more uniform. Ice could still cover much of the nightside, but it needn't stop exactly at the terminator; it could extend well into the dayside while still leaving a substantial warm region, it could be restricted only to some nightside pockets, or the nightside could even thaw out completely¹². Ice cover on Earth has varied considerably over its history through warmer and cooler climates, and much the same would be true here.

Modelled surface temperature and prevailing winds (key shows 5 m/s) of all-ocean tidal-locked planets with a range of indicated orbital periods, appropriate to the habitable zone of stars with the indicated effective temperatures. Haqq-Misra et al. 2018³

For most cases, near-surface winds would indeed tend to converge on the center of the dayside, but in speed and strength would typically be no worse than a stiff breeze, comparable to the trade winds in our tropics. Planets orbiting the very smallest stars, with short orbital periods of under 20 days, might have more complex patterns, but I'll point you elsewhere for that discussion.

Precipitation in a climate model of Proxima b with a nitrogen-dominated atmosphere; the black line indicates the limit of freezing temperatures in this model. Boutle et al. 2018⁴

Conversely to the image of a dayside desert, the warmest part of the dayside, near the center, will actually tend to be the wettest⁴. Those converging winds would pull in moisture from across the planet, and the rising convection would encourage frequent widespread rain. Though some climate models briefly predicted a single permanent cyclone in the center of the dayside, it now seems more likely¹⁴ to be a less organized mass of stormy and rainy weather, with frequent cloud cover but some prospect for occasional breaks. Farther from the center of the dayside, rain would taper off, but the unusual atmospheric structure (cool winds towards the dayside near the surface, hot winds towards the nightside at high altitude) would encourage frequent fog.

Ocean currents could shift around heat considerably: on a planet with no continents, they'd tend to carry heat east, north and south of the center of the dayside, such that rather than the typically expected "eyeball" pattern of a circular region of open ocean surrounded by ice, you might expect¹⁵ more of a lobster shape extending onto the nightside. This tendency may vary depending on orbital period, though, and the presence of landmasses blocking free flow of currents could weaken their overall influence.

Modelled ice cover (left) and surface temperature (right) of a tidal-locked planet without (top) and with (bottom) fully modelled ocean currents. Peking University¹⁵

Various additional factors could influence the climate in other ways, but I've discussed that all in detail elsewhere.

Exactly why the old image of inhospitable tidal-locked worlds has persisted this long, well after the scientific community has moved past it¹⁶, I couldn't say, though it certainly doesn't help when even recent high-budget media claiming scientific accuracy repeats the old myths. A planet of stark climate extremes is admittedly a fairly compelling image, capturing the imagination of speculative authors for over a century now, but a more hospitable world with vast regions of tropical climate under eternal sunshine have their own potential as well. 

But if you do like the concept of a habitable twilight strip between hemispheres of desert and ice, don't despair; though we shouldn't view this as the default climate of tidal-locked worlds, but it can still be achieved in the right circumstances. A lower total volume of surface water, larger nightside continents, and lower geothermal heat will all encourage¹¹ trapping of water in nightside ice, potentially allowing for drying out of the dayside. A dryer dayside and optionally a thinner atmosphere will weaken distribution of heat, allowing the center of the dayside to become hotter while still allowing the nightside glaciers to spread to the terminator (though they might not reach it evenly on all sides; expect them to more reliably appear to the dayside's western edge). Meltwater from these glaciers could feed into¹⁷ a fairly broad habitable strip; evaporated water would be carried by winds into the dayside, but so long as the overall supply isn't too high, too little would accumulate there to cause rain and would instead return with high-atmosphere winds to snow down on the nightside glaciers—and the habitable region might see some sporadic rainfall or fog as well (there could also be slightly wetter climates where only a small region in the center of the dayside receives rain, separated from the glacial meltwater region by vast deserts). Winds over this habitable strip would probably be stiffer than for the more moderate climate state, but still not relentless gales.

Beau.TheConsortium, Rare Earth Wiki

 

That about covers the main issues I wanted to cover today, but while I'm here, I might as well go over a few other common myths and misunderstandings regarding tidal-locked planets (and other bodies) as well.

Tidal-Locked Moons

Just as a planet can tidal-lock to its star, a moon can tidal-lock to its planet. Indeed, because tidal forces scale strongly with distance and moon-planet distances are generally far smaller than planet-star distances, almost all moons in the solar system are tidal-locked (the few known exceptions, like Hyperion, are due to the influence of a much larger neighboring moon causing chaotic rotation), and we can probably expect this to be the norm for other star systems as well.

But tidal-locking of a moon to its planet means that it points one face to that planet and so rotates once for each orbit of the planet. Relative to the star, the moon thus spins around about once per orbit of the planet, and so should experience a regular day and night cycle in about that time (because the planet is moving around the star as the moon orbits the planet, the moon needs to complete either slightly more or slightly less—depending on the orientation of the orbits—than one full orbit to rotate back around to face the star again; our moon, for example, completes an orbit every 27.3 Earth days, but requires 29.5 Earth days for one of its days). Tidal-locking to the planet can have interesting implications for the day-night cycle of the planet-facing side of the moon due to potential eclipses by day and reflected light from the planet by night, but in general the climate should resemble that of a planet with equivalently long days rather than that of a tidal-locked planet (because many moons have quite long orbital periods, these climates might still be quite different from Earth's).

Tidal-locking of a moon to the planet's star rather than the planet is, so far as I can tell, not possible. The physics governing whether a moon can be kept in orbit of a planet at all (i.e., the Hill radius) and those governing the strength of tidal forces are fundamentally related such that any moon in any stable orbit of a planet must necessarily experience stronger tidal forces from the planet than from the star. The star might still have some influence on the moon's motion, but the balance of forces should always drive the moon's rotation towards locking with its motion around the planet and not the star.

I've occasionally heard it proposed that a moon might have an orbit as long as its planet's year, such that it can be simultaneously tidal-locked to both planet and star, but this doesn't work out either; again, the physics works out such that no moon can have an orbital period longer than about 58% the length of the planet's year, and realistically we'd expect most to have orbits limited to about 1/5 the length of the year. There is a point directly between the planet and star (the L1 Lagrange point) where their gravitational influence balances out such that a body can remain temporarily locked between the two, following the planet's orbit, but it's unstable, like a pencil balanced on its tip; any small perturbation will nudge the body away, such that it eventually moves off into another orbit, either of the planet or star.

Incidentally, a planet can also be tidal-locked to its moon, facing one side towards it as it orbits around the planet. Whether or not the balance of tidal forces favors this is more variable, depending on the particulars of the relative masses and distances of the objects involved (and in some cases¹⁸ it may change over the planet's lifetime). If it does happen, much of what is true for the surface climate and conditions of a tidal-locked moon are true of this sort of planet as well. We can also generally expect that the moon is already tidal-locked to the planet at this point, such that they're mutually tidal-locked, permanently facing each other, as is the case for Pluto and Charon.

Motion of Pluto and Charon. Tomruen, Wikimedia

Polar Orientation

A common exchange I see online is one person asking what might happen if a planet had one of its poles pointed towards its star, and another person responding that this is equivalent to tidal-locking. In a very abstract and conceptual sense this is a reasonable response, in that tidal-locking is a realistic case for the idea of having a part of a planet permanently facing the star, but in the strictest sense it's not true; a tidal-locked planet still rotates, and so still has poles, which should usually be somewhere along the terminator, facing at right angles to the star rather than towards it.

Fair enough, but I sometimes also hear it proposed that perhaps a planet could actually keep one of its poles pointed towards the star if there was some secondary rotation turning the planet in addition to its main rotation around its poles. In isolation, this simply isn't geometrically possible; objects in 3-dimensional space can only ever rotate around one axis at a time. There would need to be some outside force continuously acting on the planet to alter its rotation to allow this to happen. Earth does experience some precession—continuous alteration of its rotational axis—due to the influence of the other planets, and this is partially responsible for our cycle of cooler glacial periods and warmer interglacials (as shifts in axial tilt alter the amount of heating the polar regions get). But this is a minor shift over thousands of years. To have one of the poles kept pointed directly at the star at all times would, in terms of momentum change and energy required, be the equivalent of of stopping Earth's rotation completely, starting it at the same rate in the opposite direction, stopping the rotation again, and restarting the initial rotation every single orbit.

Earth has a total of 2.14 * 10²⁹ J of energy bound up in its rotation; for a planet with similar properties and rotation, this twice-over stopping and starting would require 4 times this amount of energy, 8.56 * 10²⁹ J, every orbit. Assuming a year as long as Earth's, that's a continuous power input of 2.71 * 10²² W. The total power of sunlight striking Earth (before even accounting for what's promptly reflected away) is only 1.74 * 10¹⁷ W. Thus, even assuming there was some outside influence capable of providing that much power in that specific way, if even a tiny portion of that energy was ultimately released as heat (and really we wouldn't expect it to be an efficient process at all), it would be plenty sufficient to push the climate far past the bounds of habitability and roast the surface, perhaps even melting the planet entirely.

Setting that scenario aside, a planet that has one of its poles facing towards the sun at one point of the year and then continues on its orbit with a constant rotational axis—pointing each pole towards the sun in turn at opposite seasons—is a possibility (Uranus is close to this orientation) and has its own intriguing implications for the surface climate.

A tidal-locked planet also doesn't need to have its poles pointed at exact right angles from the star at all times. Usually we would expect that, because the same tidal forces that cause tidal-locking also reduce axial tilt, a tidal-locked planet should have no tilt, but the influence of multiple other planets or stars might lock one¹⁹ into a "Cassini state" with some constant effective tilt relative to its orbit. In this case, the star would seem to shift north and then back south in the sky over the course of an orbit, and the terminator would shift as well, allowing for parts of the planet to have periods of day and night. Orbital eccentricity can similarly²⁰ shift the terminator around over the course of the planet's orbit, with the combined effect of shifting orientation relative to the sun called libration.

Tidal-Locking Limits

As mentioned, tidal-locking is expected to be more common in the habitable zones of smaller stars, because of how much stronger tidal forces should be in the closer habitable zones of these stars. Because of doubts about the habitability of tidal-locked planets—which, even with better and more encouraging climate modelling, still cannot be entirely dismissed without empirical evidence—researchers investigating the limits of habitability around other stars have often found it prudent to indicate which stars are likely to have mostly tidal-locked planets. This is why you'll often see charts of the habitable zone marked with a line indicated as a "tidal-locking limit" or something similar.

A typical habitable zone chart (based on Kasting et al. 1993²¹) showing a "Tidal lock radius".

This is a convenient way to make the implications of these charts readable both for those skeptical and optimistic about the prospects for habitable tidal-locked planets, but I think non-researchers sometimes misunderstand that line as an absolute limit; all planets on one side of the line must be tidal-locked and all those on the other side can never be tidal-locked.

In reality, whether or not a particular planet becomes tidal-locked depends on a number of factors beyond just distance from the star. First off, tidal-locking takes time; usually these charts assume an age of 4.5 billion years, presuming that we're interested in habitable worlds with intelligent life and that might take about as long as it did on Earth. But depending on why you're interested in tidal-locking, you might be considering much younger or older planets.

 

Tidal-locking limits at different ages ("byr" indicates planet age in billions of years) for Earth-like planets (dissipation factor of 100) with 12-hour initial days. Dark green indicates the conventional habitable zone, light green is a very optimistic habitable zone allowing for very low surface water²² near the star or up to 50% atmospheric hydrogen²³ far from the star.

The time tidal-locking takes also depends strongly on the initial rotation rate of the planet after it has formed; usually something like 12-13 hour days are assumed for the purpose of drawing these limits in habitable zone diagrams (I'm not totally sure why, presumably based on some model of Earth's rotational evolution), but in reality it could vary greatly depending on random factors like the last few large impacts during formation. A planet might just happen to form with very slow rotation close to the synchronous rate, so in principle there's no strict outer limit where tidal-locking becomes impossible (though the further from the star, the more precisely the initial rotation has to happen to match the synchronous rate, so the chances of this happening drop pretty precipitously past a couple AU from a sun-mass star, for example). At the other extreme, a planet can only start out spinning so fast before it would tear itself apart with the centrifugal forces (in Earth's case the limit is about 2-hour days), so that gives us a more definitive inner limit where tidal-locking may be unavoidable (in this simple model, anyway).

 

"h" indicates initial rotation rate in hours.

Finally, the planet's size and the nature of its response to tidal forces also have a small influence on the tidal-locking rate. The latter is a bit hard to pin down in a model so often represented as a single "dissipation factor"; it's generally taken to be about 12 for modern earth, but based on some models of the Earth's orbital evolution, may have been as high as 100 in the past.

 

"M" indicates mass relative to Earth and "Q" indicates dissipation factor; assuming an Earthlike composition, the 0.1 M planet has 49% Earth's radius and the 10 M planet has 179%.

Altogether, combinations of these factors give us a pretty wide grey zone where tidal-locking may occur depending on the particulars of the planet in question (and this is all based on a fairly simplistic model of tidal-locking; more detailed modelling can complicate matters further²⁴).

 

 

This still leaves a significant range of stars below around 2/3 the sun's mass where tidal-locking seems inevitable across at least part of the habitable zone, but there are more complex factors that may play into that, which brings us to...

Maybe Planets Won't Tidal-Lock

This isn't a widespread claim but it has started appearing lately in response to a couple recent papers investigating how additional tidal influences might prevent tidal-locking of planets that—based on the sort of simple modelling we went over above—we would expect to lock otherwise.

First is a 2015 paper²⁴ modelling the influence of a planet's thermal tide, a bulging of its atmosphere due to thermal expansion by day, and finding that in some cases it could act against the influence of the gravitational tides to prevent full tidal-locking, instead settling a planet into rotation slightly faster or slower than 1:1 resonance. The implications have seemingly been a bit garbled in interpretation; I've heard it claimed that the paper implies that any planet with an atmosphere will avoid tidal-locking around stars more than 1/4 the sun's mass, but the paper itself claims that an atmosphere 10 times denser than Earth's could prevent tidal locking for planets in the outer edge of the habitable zone of stars about 28% the sun's mass, but a more Earthlike atmosphere likely wouldn't stop tidal-locking near the inner HZ edge even for stars almost 70% the sun's mass.

Limits at which thermal tides prevent tidal-locking for different atmospheric pressures (10 bar, 1 bar, and a Venus-like atmosphere of ~100 bar); you can see there's a nonlinear relationship between atmosphere and tidal-locking tendency. Dots are known exoplanets. Leconte et al. 2015²⁵

Finer complexities like the planet's climate (affecting the thermal tides) and ocean geometry (affecting the gravitational tides) likely have an influence as well, and could perhaps allow for a planet to resist tidal-locking for a period of its history only to fall into it later on.

A more recent²⁶ set²⁷ of²⁸ papers²⁹ has examined the tidal influence of multiple planets on each other in tightly-packed systems such as TRAPPIST-1. In these cases it seems that, though a planet may tidal-lock initially, the competing influences may cause chaotic shifts between synchronous and non-synchronous rotation, and substantial drift of the planet's orientation even when close to synchronous. Because such tightly-packed systems are expected to be common for small stars, this might indicate that such irregular rotation is the norm, rather than perfect tidal-locking. But the TRAPPIST-1 system is an extreme case, being near the minimum size for a main sequence star and so having its planets in very close orbits, with quite a few planets packed closely together even for a star of its type—the closest approach between the two innermost planets is less than twice the distance from the Earth to the Moon. For a more moderate case, say, a planet pair orbiting a star half the sun's mass, these chaotic interactions can still occur²⁶ but it seems to take a substantially larger neighboring planet orbiting quite close in something near to an orbital resonance. Planets in more loosely packed systems (or completely alone) could still experience tidal locking around any of these stars.

Still, because this mechanism is strongest for the smallest stars, it neatly fills the gaps left by the other mechanisms that could prevent tidal-locking; there is, it seems no range of stellar masses for which perfect 1:1 synchronous rotation is the only guaranteed outcome for habitable-zone planets, nor is there a specific range beyond which tidal-locking is forbidden, though the overall trends definitely still favor more frequent tidal-locking for smaller stars.

Besides these new proposals, it's been known for some time that planets with some initial orbital eccentricity could end up³⁰ locked into various other types of spin-orbit resonances, giving them a more regular day and night cycle—though a quite slow one. Such resonances aren't necessarily as stable, though; in the habitable zones of the smallest stars, they could be accompanied by intense tidal heating³¹, enough to partially melt their interiors and alter their tidal dynamics enough to break the resonance and settle into the more typical 1:1 resonance.

As mentioned, a large, close-orbiting moon could also outcompete a star's influence and force the planet to tidal-lock to it rather than the star, giving the planet more regular days and nights. However, in any such case the overall interactions between star, planet, and moon will cause the moon's orbit to migrate towards or away from the planet (more likely the latter for the mutually tidal-locked state), and the moon can only migrate so far before escaping the planet's orbit or falling below its Roche limit and breaking apart. The closer the planet to the star and the stronger the tidal forces involved, the quicker this will happen, so Earthlike habitable-zone planets orbiting stars less than about half the sun's mass are unlikely³² to be able to retain a moon for as long as Earth's current age.

Rough limits for where planets in Earthlike habitable orbits can retain moons of varying composition for at least 5 billion years. Sasaki and Barnes 2014³²

 

 

 

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