Centauri Dreams regular Dave Moore just passed along a paper of considerable interest for those of us intrigued by planetary systems around red dwarf stars. The nearest known exoplanet of roughly Earth’s mass is Proxima Centauri b, adding emphasis to the question of whether planets in an M-dwarf’s habitable zone can indeed support life. From the standpoint of system dynamics, that often comes down to asking whether such a planet is not so close to its star that it will become tidally locked, and whether habitable climates could persist in those conditions. The topic remains controversial.

But there are wide variations between M-dwarf scenarios. We might compare what happens at TRAPPIST-1 to the situation around Proxima Centauri. We have an incomplete view of the Proxima system, there being no transits known, and while we have radial velocity evidence of a second and perhaps a third planet there, the situation is far from fully characterized. But TRAPPIST-1’s superb transit orientation means we see seven small, rocky worlds moving across the face of the star, and therein lies a tale.

The paper Dave sent, by Cody Shakespeare (University of Nevada Las Vegas) and colleague Jason Steffen, picks up on earlier work Shakespeare undertook that probes the differences between such scenarios. We know that conditions are right for a solitary planet, unperturbed by neighbors, to orbit with a spin rate synchronous with its orbital rate, the familiar ‘tidal lock.’ On such a world, we probe questions of climate, heat transport, the effects of an ocean and so on, to see if a planet with a star stationary in its sky could sustain life.

Image: This illustration shows what the TRAPPIST-1 system might look like from a vantage point near planet TRAPPIST-1f (at right). Credit: NASA/JPL-Caltech.

But as TRAPPIST-1 shows us in exhilarating detail, multi planet systems are not uncommon around this type of star, and now we have to factor in mean motion resonance (MMR), where the very proximity of the planets (all well within a fraction of Mercury’s orbit of our Sun) means that these effects can perturb a particular planet out of its otherwise spin-orbit synchronization. Call this ‘orbital forcing,’ which breaks what would have been, in a single-planet system, a system architecture that would inevitably lead to permanent tidal lock.

The results of this breakage produce the interesting possibility that planets like TRAPPIST-1 e and f may retain tidal lock but exhibit sporadic rotation (TLSR). Indeed, another recent paper referenced by the authors, written by Howard Chen (NASA GSFC) and colleagues, makes the case that this state can produce permanent snowball states in the outer regions of an M-dwarf planetary system. What is particularly striking about TLSR is the time frame that emerges from the calculations. Consider this, from the Shakespeare paper:

The TLSR spin state is unique in that the spin behavior is often not consistently tidally locked nor is it consistently rotating. Instead, the planet may suddenly switch between spin behaviors that have lasted for only a few years or up to hundreds of millennia. The spin behavior can occasionally be tidally locked with small or large librations in the longitude of the substellar point. The planet may flip between stable tidally locked positions by spinning 180°so that the previous substellar longitude is now located at the new antistellar point, and vice versa. The planet may also spin with respect to the star, having many consecutive full rotations. The spin direction can also change, causing prograde and retrograde spins.

Not exactly a quiescent tidal lock! Note the term libration, which refers to oscillations around the rotational axis of a planet. What Shakespeare and Steffen are analyzing is the space between long-lasting rotation and pure tidal lock. Indeed, the authors identify a spin scenario within the TLSR domain they describe as prolonged transient behavior, or PTB. Here the planet moves back and forth in a ‘spin regime’ that is essentially chaotic, so that questions of habitability become fraught indeed. Instead of a persistent climate, which we usually assume when assessing these matters, we may be looking at multiple states of climate determined by present and past spin regimes, and their necessary adaptation to the ever changing spin state.

Such global changes are reminiscent, though for different reasons, of Asimov’s fabled story “Nightfall,” in which scientists on a world in a system with six stars must face the social consequences of a ‘night’ that only appears every few thousand years. For here’s what Shakespeare and Steffen say about a scenario in which TSLR effects kick in, a world that had been tidally locked long enough for the climate to have become stable. The scenario again involves TRAPPIST-1:

Such a planet in the habitable zone around a TRAPPIST-1-like star could have an orbital period of around 4-12 Earth days – the approximate orbital periods of T-1d and T-1g, respectively. Due to the TLSR spin state, this planet may, rather abruptly, start to rotate, albeit slowly – on the order of one rotation every few Earth years. The previous night side of the planet, which had not seen starlight for many Earth years, will now suddenly be subjected to variable heat with a day-night cycle lasting a few years. The day side would receive a similar abrupt change and the climate state that prevailed for centuries would suddenly be a spinning engine with momentum but spark plugs that now fire out-of-sync with the pistons. In this analogy, the spark plugs and the subsequent ignition of fuel correspond to the input of energy from starlight. The response of ocean currents, prevailing winds, and weather patterns may be quite dramatic.

Not an easy outcome to model in terms of climate and habitability. The authors use a modified version of an energy release modeling software called 1D EBM HEXTOR as well as a model called the Hab1 TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) Protocol as they analyze these matters. I send you to the paper for the details.

Science fiction writers take note – here is rich material for new exoplanet environments. Notice that the TLSR spin state is different from the one-way change that occurs when a rotating planet gradually becomes tidally locked over large timescales. This is a regime of sudden change, or at least it can be. The authors consider spin regimes lasting less than 100 Earth years, with the longest regimes (these are classified as ‘quasi-stable’) lasting for 900 years or more and perhaps reaching durations of hundreds of thousands of years. The point is that “TLSR planets are able to be in both long-term persistent regimes and PTB regimes -– where frequent transitions between behaviors are present.”

We learn that all tidally locked bodies experience libration to some degree even if no other bodies are found in the system being examined. Four spin regimes are found within the broader spin state TLSR. Tidal lock with libration can occur around the substellar point, as well as around the substellar or antistellar point, or as noted a planet may be induced into a slow persistent rotation. Much depends upon how long any one of these ‘continuous’ states lasts; given enough time, a stable climate could develop. The chaotic behavior of the fourth state, prolonged transient behavior (PTB), induces frequent transitions in spin. Such transitions would be expected to produce extreme changes in climate.

The spin history of a given system will depend upon that system’s architecture and the key parameters of each individual planet, an indication of the complexity of the analysis. What particularly strikes me here is how fast some of these changes can occur. Here’s a science fiction scenario indeed:

The more extreme change is in the temperature of different longitudes as the planet transitions from a tidally locked regime to a Spinning regime or after the planet flips 180 and remains tidally locked. Rotating planets experience temperature changes at the equator of 50K or more over a single rotation period. The exact effects require more robust climate models, like 3D GCMs [Global Circulation Model], to properly examine. However, using comparisons with climate changes on Earth, it is likely that erosion of land masses would increase and major climate systems would experience significant changes.

As if the issue of habitability were not complex enough…

The paper is Shakespeare & Steffen, “Day and Night: Habitability of Tidally Locked Planets with Sporadic Rotation,” in process at Monthly Notices of the Royal Astronomical Society and available as a preprint. The Chen paper referenced above is “Sporadic Spin-Orbit Variations in Compact Multi-planet Systems and their Influence on Exoplanet Climate,” accepted at Astrophysical Journal Letters (preprint).