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Dwarf stars have terrestrial sized planets orbiting in habitable zones very close to them. These exoplanets are often said to be tidally locked to their star, like the Moon is to Earth, and that they thus have one hot hemisphere and one cold.

But in the Solar system there's only one tidally locked planet, and that is Mercury which is asynchronously locked in a 2:3 relation. It does rotate relative to the sun anyway. And only one known planet which practically doesn't rotate at all, Venus. But Venus has a super-rotating atmosphere that distributes heat from insolation all around anyway.

Are there reasons to believe that asynchronous tidal locking and super-rotating atmospheres are less common for planets with a dwarf stars than in a planetary systems with a Solar like star?

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  • $\begingroup$ Are you defining super-rotating atmospheres against sidereal rotation or solar rotation? I think, as a rule, super-rotating atmospheres aren't applied to tidally locked planets because it's the solar rotation that's usually considered, but I'm not 100% sure and I tried to look up without success. Tidally locked planets have 0 solar rotation, so any trade-wind would be super-rotating. $\endgroup$ – userLTK Mar 26 '17 at 0:34
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I'm not exactly sure what you're asking, cause you touch on a few related points.

The reason planets around red-dwarf stars are thought to be tidally locked is because the tidal force is comparatively much greater for the habitable zone. Take, for example, a star with half the mass of our sun. It would have, roughly speaking, 1/16th the solar output, so a planet, to get the same amount of heat, would need to be 4 times closer or 1/4 AU.

The tidal force increases by the cube of the distance, or, 4^3, or 64, and the mass, 1/2, means that for just 1/2 the solar mass, the tidal force on a planet getting equal heat is 32 times greater. That's a ballpark ratio to the 5th power, which is highly significant. When you get into solar masses 25% the mass of the sun or less, the tidal force for a habitable zone planet can be thousands of times greater than the tidal force for the habitable zone in our solar system. Because of the high tidal forces, planets in the habitable zone of small stars are very likely tidally locked, at least for any near-circular orbits. That's pretty darn close to certain when the star is below a certain size.

There are some theories that thermal heating of a planet's atmosphere, which takes time, so it doesn't happen precisely at mid-day, but a couple hours after that, there's expected to be a tidal torque in the upper atmosphere and an equilibrium where the constant rotation of the atmosphere drags on the surface and keeps the planet rotating, so the planet never becomes tidally locked. Venus might be an example of that. But the articles below suggest that this is predicted to only happen in the larger red-dwarfs, 50% the mass of the sun or larger. Article here and here for more details.

In summary, for smaller red dwarf stars, tidal locking is probably very common within the habitable zone. For larger red dwarf stars, you might get a mix, growing less common for further out planets.

Rotations maintained by wind torque are probably, at least, to my thinking, not very rapidly rotating, similar to Venus, a slow rotation makes super-rotating trade winds easy. (I say trade winds because I don't think weather-wind or local wind is considered super-rotating), so I think we should just consider relatively permanent wind speed and direction).

And for any slowly rotating planet, Super-rotating wind should be quite common.

For the very smallest stars, like Trappist 1, which at .08 solar masses isn't far off from the minimum size for a red dwarf, it's inner most planet has a period of just 1.5 days, it's corresponding rotation (Sidereal, not solar) has a 1.5 day period too. That's probably a fast enough rotation to generate a significant Coriolis effect and some interesting weather (provided the planet hasn't lost it's atmosphere - which is also possible with close orbits around small stars). That's an equatorial surface velocity of over 600 km/h, so for very close orbit planet around the smallest red dwarfs, super-rotating winds may not happen.

Looking at the planets orbital periods around Trappist 1. The inner 2-3 planets might rotate too fast to have super-rotating winds. The 5th one, for example, with an orbital period of 9 days, corresponding to a sidereal rotating speed at the equator of not much more than 100 km/h, it's probably likely to have super-rotating winds. The longer the orbital period, the more likely super-rotating winds are to happen. Any tidally locked planet with an orbital period over 10 days, should be statistically likely to have super-rotating winds (compared to sidereal rotation). Solar rotation, well, by that measurement, all tidally locked planets with atmosphere have super-rotating winds.

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Mercury is in a spin-orbit resonance other than 1:1, hence is not tidally locked. This can occur in eccentric orbits and when the tides are weak (so that the orbit remains eccentric). The recently discovered system of planets (Trappist-1) has 7 planets in orbits with very small eccentricity, so the Situation as for Mercury will not occur.

Edit See also this recent question regarding the spin-orbit locking. The eccentricity and spin-orbit evolution are closely coupled (because of conservation of total angular momentum), but the time scale for the latter is much shorter. Therefore, the ratio between spin and orbital frequency quickly reaches an equilibrium (which depends on the eccentricity), but if the tides are weak the eccentricity may not change and the system hardly changes. This is the situation for Mercury.

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  • $\begingroup$ With what certainty is the eccentricity of the exoplanetary orbits constrained? Are there any assumptions about orbital precession involved? (Mercury being called tidally locked or not seems to be a matter of semantics, something the IAU has had big problems with defining lately). $\endgroup$ – LocalFluff Mar 25 '17 at 18:59
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    $\begingroup$ A closely packed system never has significant eccentricities - otherwise it would be unstable. $\endgroup$ – Walter Mar 25 '17 at 19:13
  • $\begingroup$ I suppose that is in co-planar planetary systems. Moons of the gas giants have varying eccentricity, but also varying inclination. Some moons, like Hyperion, have chaotic rotation because of the gravitational influence of their neighbors. Are orbits/rotations like those of Mercury, Venus and Hyperion just freak outliers, possible only in Sun-like planetary systems? $\endgroup$ – LocalFluff Mar 25 '17 at 19:55
  • $\begingroup$ One shouldn' t call something locked, unless it is. Mercury's eccentricity and spin-orbit ratio may change in the (very) long run because of tides. $\endgroup$ – Walter Mar 25 '17 at 20:34
  • $\begingroup$ @Walter, I thought tides is what keeps Mercury in its 3:2 ratio, but I might be wrong on that. I agree with your other point. Calling Mercury tidally locked is inaccurate, but it may be tidally bound to a 3:2 resonance. $\endgroup$ – userLTK Mar 25 '17 at 20:50

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