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# Are exoplanets at dwarf stars less likely to have super-rotating atmospheres or asynchronous tidal locking?

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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?

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.

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.

## New Study Suddenly Makes Billions of Exoplanets Habitable

Astronomers hunting for habitable Earth-like planets now believe that the best place to look is not around stars like our Sun, but rather around smaller, cooler stars—orange and red dwarfs. These are by far the most abundant stars in our galaxy, and all of them have at least one exoplanet.

Artist representation of a red dwarf surrounded by 3 planets. Image via Wiki Commons.

Red Dwarfs are smaller and cooler than our Sun, ranging from a mass of of 0.075 solar masses to about 0.50 solar masses. Red dwarfs are by far the most common stars in the Milky Way galaxy and in the entire Universe, but due to their low luminosity they are pretty hard to observe. It’s estimated that some 75 percent of all stars in the universe are red dwarfs, and all of them host planets.

The habitability of red dwarfs has been discussed many times, and is still a matter of debate. Of course, knowing if the most common stars in the universe can host habitable planets is a big deal. Among the problems raised against habitability is the so called tidal locking: just like our planet sees only one side of the moon at all times, so do the red dwarfs they only see one side of the planet, which means that one side is likely a desertic landscape, while the other is a frozen nightmare.

This happens when the planet is close to its star, as planets would have to be closer to red dwarfs to be habitable. Naturally, in this case the chances for life are much smaller (though it’s not completely impossible). However, this new study challenges this idea, and claims that not all planets are engaged in tidal locking.

The simple existence of an atmosphere, researchers argue, is enough to ensure that the planet is rotating and revolving around its star, making it much more likely to be habitable. According to Jérémy Leconte, the theoretical astrophysicist at the University of Toronto who lead the study, this means that we may have already discovered many habitable planets – we just don’t know it yet.

“Planets with potential oceans could thus have a climate that is much more similar to the Earth’s than we’ve previously expected,” he says.

So how does the atmosphere play into this problem? Jeff Coughlin, a SETI astronomer working with Kepler planet-hunting mission, who was not involved in the study explains it like this:

“On Earth, light from the sun is what drives the weather in our atmosphere. And that weather, in the form of wind, constantly pushes against the planet—running into mountains, for example, or creating waves on the ocean. This friction is deposited in the rotation rate of our planet, helping to speed it up or slow it down.”

Astrophysicists have known this for quite a while, but according to initial calculations, the atmosphere would have to be incredibly massive to have this impact. We have a good case study very close to us: Venus. Venus’ atmosphere is just big enough to escape lockup, and Venus’ atmosphere is absolutely huge – about 90 times heavier than our own. So scientists discarded the idea.

But when Leconte and his team ran simulations to see how the atmosphere would play into gravitational locking, they surprisingly found that thinner atmospheres actually have a larger rotational effect on their planets. This may seem counterintuitive, but it happens because a thinner atmosphere scatters less sunlight. This creates extra heat which in turn creates a stronger atmospheric tide (a bulging of atmosphere, much like our ocean’s tides). This results in a stronger planetary rotation. If Venus were to have an atmosphere like Earth’s, it would spin 10 times faster.

Armed with the results of this model, the team showed that Earth-sized planets can spin quite healthily around a red dwarf if they have an atmosphere.

“More and more, we’re discovering that there’s a lot of ways to have a very nice, habitable planet around dwarf stars,” Coughlin says. But there’s something more at play here. “We really shouldn’t be so narrow-minded in our assumptions about what types of planets could or could not be habitable,” he says. Coughlin says that even a locked-up rotation is not necessarily a killer for a planet in terms of habitability—strong winds could help smooth out the temperature between the two sides.

It would be nice if we’d be able to confirm this model with some observed information, but until that, the results of this study are pretty convincing.

“Every time we’ve made simple assumptions about habitability,” he says, “we find out new ways why and how they don’t apply.”

Journal Reference: Jérémy Leconte, Hanbo Wu, Kristen Menou, Norman Murray. Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars. Science DOI: 10.1126/science.1258686

## Abstract

CO2 rich atmospheres have been considered for the outer limit of the classic water habitable zone. Here we provide a database for the outer limit of the life supporting zone consisting of a sulfuric acid, a water and a water/ammonia mixture (15 wt% ammonia) habitable zone for virtual exoplanets having CO2-rich atmospheres and orbiting G-, K-, or M-dwarf stars. We used recent CO2 line and continuum absorption data for CO2 pressures up to 100 bar for our simulations. Scenarios for different stellar spectra, stellar fluxes, planetary surface albedos, atmospheric pressures and planetary masses are explored. One notable result is that the surface temperature does not strongly increase if CO2 pressure is larger than approximately 25 bar, due to increased Rayleigh scattering or CO2 condensation at the surface and a thereby reduced greenhouse effect in these cases. The database is created for virtual exoplanets and applied to Kepler planetary candidates. All of the considered planetary candidates likely lie within the outer limit of the life supporting zone.

## Overcoming Tidal Lock around Lower Mass Stars

One of the big arguments against habitable planets around low mass stars like red dwarfs is the likelihood of tidal effects. An Earth-sized planet close enough to a red dwarf to be in its habitable zone should. the thinking goes, become tidally locked, so that it keeps one face toward its star at all times. The question then becomes, what kind of mechanisms might keep such a planet habitable at least on its day side, and could these negate the effects of a thick dark-side ice pack? Various solutions have been proposed, but the question remains open.

A new paper from Jérémy Leconte (Canadian Institute for Theoretical Astrophysics, University of Toronto) and colleagues now suggests that tidal effects may not be the game-changer we assumed them to be. In fact, by developing a three-dimensional climate model that predicts the effects of a planet’s atmosphere on the speed of its rotation, the authors now argue that the very presence of an atmosphere can overcome tidal effects to create a cycle of day and night.

The paper, titled “Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars,” was published in early February in Science. The authors note that the thermal inertia of the ground and atmosphere causes the atmosphere as a whole to lag behind the motion of the star. This is seen easily on Earth, when the normal changes we expect from night changing to day do not track precisely with the position of the Sun in the sky. Thus the hottest time of the day is not when the Sun is directly overhead but a few hours after this.

Because of this asymmetry in the atmospheric mass redistribution with respect to the subsolar point, the gravitational pull exerted by the Sun on the atmosphere has a nonzero net torque that tends to accelerate or decelerate its rotation, depending on the direction of the solar motion. Because the atmosphere and the surface are usually well coupled by friction in the atmospheric boundary layer, the angular momentum transferred from the orbit to the atmosphere is then transferred to the bulk of the planet, modifying its spin.

This effect is relatively minor on Earth thanks to our distance from the Sun, but is more pronounced on Venus, where the tug of tidal friction that tries to spin the planet down into synchronous rotation is overcome by the ‘thermal tides’ caused by this atmospheric torque. But Venus’ retrograde rotation has been attributed to its particularly massive atmosphere. The question becomes whether these atmospheric effects can drive planets in the habitable zone of low mass stars out of synchronous rotation even if their atmosphere is relatively thin.

Pressure units in a planetary atmosphere are measured in bars — the average atmospheric pressure at Earth’s surface is approximately 1 bar (contrast this with the pressure on Venus of 93 bars). The paper offers a way to assess the efficiency of thermal tides for different atmospheric masses, with results that make us look anew at tidal lock. For the atmospheric tide model that emerges shows that habitable Earth-like planets with a 1-bar atmosphere around stars more massive than

0.5 to 0.7 solar masses could overcome the effects of tidal synchronization. It’s a powerful finding, for the effects studied here should be widespread:

Atmospheres as massive as 1 bar are a reasonable expectation value given existing models and solar system examples. This is especially true in the outer habitable zone, where planets are expected to build massive atmospheres with several bars of CO2. So, our results demonstrate that asynchronism mediated by thermal tides should affect an important fraction of planets in the habitable zone of lower-mass stars.

Here is the graph from the paper that illustrates the results:

Image: Spin state of planets in the habitable zone.The blue region depicts the habitable zone, and gray dots are detected and candidate exoplanets. Each solid black line marks the critical orbital distance (ac) separating synchronous (left, red arrow) from asynchronous planets (right, blue arrow) for ps = 1 and 10 bar (the extrapolation outside the habitable zone is shown with dotted lines). Objects in the gray area are not spun down by tides. The error bar illustrates how limits would shift when varying the dissipation inside the planet (Q

100) within an order of magnitude. Credit: Jérémy Leconte et al.

The result suggests that we may find planets in the habitable zone of lower-mass stars that are more Earth-like than expected. Do away with the permanent, frozen ice pack on what had been assumed to be the ‘dark side’ and water is no longer trapped, making it free to circulate. The implications for habitability seem positive, with a day-night cycle of weeks or months distributing temperatures, but Leconte remains cautious: “Whether this new understanding of exoplanets’ climate increases the ability of these planets to develop life remains an open question.”

The paper is Leconte et al., “Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars,” Science Vol. 347, Issue 6222 (6 February 2015). Abstract / preprint available. Thanks to Ashley Baldwin for a pointer to and discussion of this paper.

Comments on this entry are closed.

Not sure it’s just tidal locking. Close enough to the star, and you’d have tidal heating problems as well.

This would seem to rule out Proxima Centauri (0.123 Solar mass) as having a planet that could rotate. So Baxter’s planet in his novel Proxima is likely safely correct in being synchronous.

I note this near the end: “On the other hand, the habitable
zone has been recently shown to be more extended for synchronous planets”.

Doesn’t this mean that the atmospheric reduction of synchronous rotation reduces the likelihood of finding a habitable planet for a red dwarf world?

Thanks Paul. This is a real Earth moving paper and has caused ripples in the exoplanet community. It opens up the possibility of life around M dwarfs ,which are common and also the easiest to view and analyse with missions like yesterday’s Twinkle ( or better) and TESS supported by JWST. The graph has been described as ” a work of art” by the most down to Earth astronomers . JWST might just have the power to spot life on Earth sized planets around M dwarfs . Another paper on M3 dwarfs , almost as exciting and overlapping with this paper, by Houdebine et al was released almost simultaneously and is also available through arxiv . Like this, it is a great read and shows for complex reasons why these stars have low chromospheric activity which makes them easier to view and characterise from Earth . Their tight habitable zone gives lots of deep transits for spectroscopic analysis . We know Sasselov has shown that Super Earths can maintain their oceans for long periods and Kite’s 2008 paper on Geodynamics and volcanism on Super Earths shows this can lead to the extended tectonics needed to maintain secondary atmospheres till long lived M dwarfs settle down. Taken together , all these papers give reason for optimism of historic discoveries in our lifetime.

Brett. You’re quite correct . Clearly non synchronous rotation is not the only factor to consider for life but this mechanism gives a pathway to more Earth like planets when other criteria are met . No atmospheric collapse on the permanently night side. If the orbits remain circular , this will mitigate tidal heating to some extent too.

I have a bit of a quibble with the Science editors. Yes the article is about (slightly) low-er mass stars than Sol, it is not about low mass stars. The fine distinction made in the title of the paper might escape the notice of some readers who are not astronomers.

In fact the mass range discussed is

the mass range of spectral class K stars. I like K stars for astrobiology even more than G stars. Also, K stars are

60% more common than G stars. As Alex has noted, this paper has no application to actual low mass M stars like Wolf 359 (mass = 0.09 M☉). That is unfortunate, as M stars are

3/4 of the stellar population.

Seems to me the best bet for a habitable planet around a very small star would be a moon of a gas giant. The giants magnetic field might also protect the planet.

I thought I read that the retrograde rotation of Venus was caused by Earth. Was that theory disproven?

One of the unfortunate things we have to live with is the legacy of the M spectral class which is quite a mixed bag. In the present time, it would not have been considered sensible to put Lalande 21185 in the same stellar class as Wolf 359. The larger near neighbor star has 5x the mass, 18x the luminosity, and visually is 6 magnitudes brighter than Wolf 359. Similar stars? Not at all.

@Ashley
I had a look at the Houdebine paper, nice work, so there is observational evidence of transition to convection at M3. If M3 is a sweet spot for astrobiology observations, this would increase the target list considerably as M3 stars are roughly as abundant as K stars.

In the Enterprising spirit, I am pleased to announce that I am taking deposits for habitats to be built in Phase 1 of my proposed property development in the lovely Gliese 687 system. Gliese 687 is a certified stellar-safe M3. Our idyllic system includes a Neptune class planet to grace your night sky. Buy now or be priced out forever! Construction will commence when Phase 1 is fully subscribed. Most major currencies accepted. (sorry no Hryvnias or Quatloos) Operators are standing by!

Don’t count on ALL habitable zone planets orbiting Proxima Centauri-like stars having synchronus rotation. Desert planets will, but Ocean planets MAY NOT, if the recently published paper on the effect of oceans on spin-down rates of planets orbiting close to M stars is correct. The authors of these two papers should now COLLABORATE, with the hope of eventually publishing a NEW paper which deals with this very complicated issue.

JOY: Thanks for the tip about Gilese 687…I hope you can become part of one of the teams to use the Giant Magellan Telescope in 2020…It would be ironic if you find a family of planets around that star…terraforming doesn’t come up much around here…and since no planet will likely be found perfect for human beings…extraterrestrials will live inside giant hollowed mountains, and recess will be under a mile wide transparent dome open to the heavens…We have to start somewhere…

‘Atmospheres as massive as 1 bar are a reasonable expectation value given existing models and solar system examples…’

This may not be correct, the Earth may be an exemption due to the early impact that formed the moon depleting the early atmosphere. If you look at Venus it has much more nitrogen

2-3 bars worth, so an atmosphere on average around an Earth massed world may be 2 to 3 times higher in pressure and thus aid the anti-tidal lock process down to lower massed stars.

@James Stilwell February 12, 2015 at 12:40

‘It would be ironic if you find a family of planets around that star…terraforming doesn’t come up much around here…and since no planet will likely be found perfect for human beings…extraterrestrials will live inside giant hollowed mountains…’

‘Techaliens’ are more likely to build very large space habitats than terraforming worlds and it these habitats we may find transiting their stars and/or reflecting-emitting light from that star.

@Michael: as regards the larger amount of nitrogen on Venus, as far as I am aware this could be a result of the lack of subduction processes rather than a difference in the initial nitrogen inventory. See e.g. Lécuyer, Simon and Guyot (2000). In addition, the lack of a large satellite does not mean that Venus never had a giant impact: not all such impacts would necessarily lead to the formation of a satellite.

@Michael February 12, 2015 at 12:40

‘It would be ironic if you find a family of planets around that star…terraforming doesn’t come up much around here…and since no planet will likely be found perfect for human beings…extraterrestrials will live inside giant hollowed mountains…’

‘Techaliens’ are more likely to build very large space habitats than terraforming worlds and it these habitats we may find transiting their stars and/or reflecting-emitting light from that star.

I wasn’t very exact…terraforming and living inside a sealed hollowed out mountain on an alien world aren’t the same thing at all…Please read “The City and the Stars” by Arthur C. Clarke for a more accurate reading of my thinking in its dreamy way…A short synopsis of his futuristic city, Diaspar, might also be found on Wiki…

@Michael: Not sure what the moon effect is with regards to nitrogen, but there is also the matter of carbon dioxide, which seems much more material to me. Earth’s atmosphere is depleted of it, and Venus has about 90 bars of it. Exoplanets could be expected to be anywhere in between, thus will tend to have much more than 1 bar of atmosphere.

Thanks for the paper link.

When we look at the Earth we suspect that there is an oceans worth of water in the mantle primarily due to sub-duction. If we also look at the amount of dissolved nitrogen in the water (15 ppm) which we will say is the major source and that it is pulled into the mantle with the water.

Now a little maths points the way to the fact that there is not enough nitrogen in the mantle, from the sub-duction, to even come close to the observed amount of nitrogen in Venuses atmosphere. I am taking into consideration that the heat on Venus led to significant out gassing and that the moon formation impact also degassed the earth to the same level.

@Eniac February 13, 2015 at 23:41

‘Not sure what the moon effect is with regards to nitrogen, but there is also the matter of carbon dioxide, which seems much more material to me. Earth’s atmosphere is depleted of it, and Venus has about 90 bars of it. Exoplanets could be expected to be anywhere in between, thus will tend to have much more than 1 bar of atmosphere.’

During the moon forming impact the temperature and momentum of the impactor would have removed a significant amount of CO2 and N2. On the Earth the CO2 is mostly locked up in carbonates at around 60 bars worth.

@Michael: I think you are incorrect in assuming that the nitrogen being subducted would mainly be from dissolved nitrogen in water, as ocean floor sediments themselves contain nitrogen from decayed organic matter. The main input of nitrogen to the mantle by subduction would likely be in the form of ammonium, but the behaviour of nitrogen in subduction is not particularly well constrained at the moment. For example, Marty & Daumas (2003) estimate that the nitrogen content of the silicate Earth could be comparable to the atmosphere, but other estimates of the nitrogen input into the mantle vary substantially and some subduction zones appear to be far more efficient than others at transporting nitrogen into the Earth’s interior rather than re-releasing it by volcanism.

This article below explains a little more than I can. An impact of the size that formed the moon would have an enormous effect on the atmospheric inventory of all volatiles. I am still in favour of the atmospheres of Earth massed planets been thicker than ours even when CO2 has been removed through carbonate formation, this may favour a thermal tide anti-tidal lock process down to lower massed stars.

@Michael: I’m not saying the moon-forming impact did not have an effect, the issue is that multiple giant impacts should be fairly common during terrestrial planet formation. Earth had one set of impacts, Venus received another. Can we actually assume that the Venusian impact sequence is more typical for terrestrial planets than Earth’s? There’s also no particular evidence against Venus experiencing giant impacts that formed moons that were subsequently destroyed (e.g. when further giant impacts changed the angular momentum of the system).

At present there’s not much information at all about how much volatile loss is typical on Earth-mass planets, the number of examples is too small (and that’s before you consider possibilities such as oceans enhancing atmospheric loss during giant impacts, which would tend to favour thinner atmospheres on terrestrial planets located further out). We need data on more planets before leaping to conclusions. It doesn’t help that you’ve also got the complication that the two planets have been undergoing very different geological (planetological?) processes over their history which is going to confuse things even more: different degrees of outgassing, atmospheric erosion and geological recycling are going to have their effects which can mask the evidence for the initial conditions.

It would be interesting to know if the axial tilt would have an appreciable difference on the spin rate or could it even create a chaotic one. But there is still that issue with the long contraction phase of low mass stars depleting a lot if not all of the water of close in planets, that to me is a huge stumbling block greater than the spin issue.

Speaking of moons, if the proposed theory is correct, why is Titan, with it’s thick atmosphere, in synchronous rotation with respect to Saturn? Am I missing something here?

@Harry R Ray: the mechanism is due to thermal tides in the atmosphere, i.e. it requires the primary to be supplying significant amounts of heat to the secondary. So for the mechanism to disrupt Titan’s locking to Saturn, Saturn would have to be a substantial heat source for Titan’s atmosphere. According to my quick back-of-the-envelope calculation, for Titan the heat flux from Saturn is roughly 3 orders of magnitude lower than that from the Sun, which is itself 90 times lower than that received by the Earth from the Sun. Titan’s atmosphere is not strongly heated enough to substantially disrupt the tidal locking effect.

@andy, @Michael: Andy rightly points out how little we really know about what gives a planet the size of Earth or Venus its atmospheric pressure. Consequently, we have to assume that the norm is somewhere in between the two, which would make the expectation value a great deal higher than 1 bar.

My favorite theory is that Earth is atypical, because biological fixation of carbon into limestone and carbohydrates has removed all CO2 from its atmosphere. My expectation is that when we start analyzing the atmospheres of Earth-sized planets in habitable zones, we will find them to typically have an atmosphere similar to Venus’, although with varying amounts of water. I suppose that would mean that planets around red dwarfs could easily avoid tidal lock by the above mechanism.

When we find one that has a thin atmosphere free of CO2, that is when we should really take a closer look…

Consequently, we have to assume that the norm is somewhere in between the two, which would make the expectation value a great deal higher than 1 bar.

No we don’t, that would be overinterpreting small number statistics. In fact there’s no particular reason to assume that the terrestrial planets in our solar system are particularly representative of terrestrial planet formation elsewhere. For example the low masses of Mars and Mercury suggest that the initial distribution of material in the inner solar system was rather odd, which may have led to a different growth history than in solar systems that grew from a less truncated initial condition.

@andy February 19, 2015 at 15:09

‘No we don’t, that would be overinterpreting small number statistics. In fact there’s no particular reason to assume that the terrestrial planets in our solar system are particularly representative of terrestrial planet formation elsewhere. For example the low masses of Mars and Mercury suggest that the initial distribution of material in the inner solar system was rather odd, which may have led to a different growth history than in solar systems that grew from a less truncated initial condition.’

Although statistically the number of planets are too low to draw absolute conclusions about atmospheric masses, I am statistically in favour of greater atmospheric masses around increasingly massive planets. I believe the Earths atmospheric mass is lower on average than other Earth massed planets due to the type of impact that it had early on in it’s history as they are quite rare. So we are at a religious opposition, I believe I am right and you believe you are right, now I say let science reveal the truth before all.

In other words we will have to agree to disagree until the matter is settled with better optical systems.

They may have to refine their model as Venus is showing signs of slowing down and it is quite fast

16 minutes over 16 years, that is a lot! Compare this to the Earths slow down of

1.2 second over the same time period, that is a whopping

sorry Paul that should have been 6.5 minutes over 16 years, which is still quite a lot!

## Results

Fig. 1A shows AOGCM simulation results of sea-ice fraction and wind velocity at the lowest model layer for 355 ppmv of CO2. This level of CO2 roughly equals the present-day CO2 concentration in the Earth atmosphere. In the presence of a dynamic ocean, the open-ocean area (blue) is not like the round iris of an “eye” such as that in AGCM simulations coupled with a slab ocean (Fig. S1A also figure 3 in ref. 4). Instead, the spatial pattern of the open-ocean region is more like a “lobster,” showing two “claws” symmetric to the equator and a long tail along the equator. The tail of open water extends eastward to the nightside. At the western side of the substellar point, sea ice is drifted eastward from the nightside toward the substellar point. The open-ocean region remains even for 3.6 ppmv of CO2 and shows the similar lobster-like spatial pattern. For very high-level CO2 (200,000 ppmv), sea ice is completely melted (Fig. 1B). By contrast, the nightside and a large part of the dayside remain frozen for the same level of CO2 in the AGCM simulation (Fig. S1B), and the open-ocean region is only slightly expanded compared with that in Fig. S1A.

Spatial distributions of sea-ice fraction and surface air temperature. (Left) Sea-ice fraction (unit, %) (Right) surface air temperature (unit, °C) (Upper) 355 ppmv CO2 and (Lower) 200,000 ppmv CO2. In A and B, arrows indicate wind velocity at the lowest level of the atmospheric model (990 hPa), with a length scale of 15 m s −1 . In C and D, arrows indicate ocean surface current velocity, with a length scale of 3 m s −1 . Note that the color scale for surface air temperature is not linear. The substellar point is at the equator and 180° in longtitude.

Spatial distributions of surface air temperatures (Ts) (color shading) and surface ocean velocity (arrows) are illustrated in Fig. 1 C and D. For 355 ppmv CO2, the highest Ts is not located at the substellar point but has two centers at each side of the equator with values of about 5–6 °C. This is because the eastward equatorial ocean current transports cold water from the dark side to the dayside. The lowest Ts is not located at either pole or the antistellar point but at subpolar regions of the nightside with values of about −60 °C. The lowest Ts is well above the condensation temperature of CO2 (−78.5 °C at 1 bar of CO2 partial pressure and much lower at lower partial pressures), so there is no risk of CO2 being trapped in the cold regions. As CO2 concentration is increased to 200,000 ppmv (Fig. 1D), the highest Ts on the dayside does not rise very much, only about 2 or 3 °C. However, nightside and polar surface temperatures increase drastically and are all above the freezing point of ocean water. Thus, temperature contrasts between the dayside and nightside and between the tropics and poles are largely reduced. Comparison between Fig. 1D and Fig. S1D reveals that as CO2 concentration is sufficiently high, ocean heat transport is very efficient in warming the nightside and causing sea-ice melting there.

The flow pattern in Fig. 1 is the well-known Gill-type solution responding to a stationary equatorial heating source (24). The two cyclones at each side of the equator are the tropical Rossby-wave modes, and the eastward long tail along the equator is the tropical Kelvin wave. Similar flow patterns have been seen in atmospheric flows in previous simulation studies for tidally locked terrestrial exoplanets and hot Jupiters (e.g., 5 ⇓ –7, 10, 25, 26). Both the simulations for 355 and 200,000 ppmv CO2 show a strong westerly equatorial ocean current on the order of a few meters per second. The equatorial westerly ocean current is mainly driven by westerly winds as demonstrated in ref. 27, although the tropical Kelvin and Rossby waves also contribute to the formation of the ocean current. This is different from the equatorial westerly atmospheric flow of tidal-locking exoplanets, which is driven by equatorward convergence of Rossby-wave momentum fluxes (10, 25, 26). The reason why the equatorial ocean current is so strong is because there are no meridional continental barriers and the wind-driven ocean current can be very strong (28, 29). The equatorial current here is just like the strong Antarctic Circumpolar Current in the Southern Ocean of Earth. Ocean currents, especially the equatorial jet stream, become stronger with increasing CO2 (Fig. 1D). This is because the open-ocean area becomes broader with increasing CO2, so that wind stresses can force on the broader open-ocean surface and generate stronger zonal ocean currents.

Thermal structures and motions of deep-ocean layers also play important roles in ocean heat transports. Fig. 2 illustrates depth–latitude cross-sections of zonal-mean ocean potential temperatures and zonal velocities for 355 and 200,000 ppmv CO2, respectively. For 355 ppmv CO2, the relatively warm layer (higher than −1.8 °C) is limited in the tropics and above 400 m in depth (Fig. 2A), whereas all other parts of the ocean show rather homogeneous temperature distribution. For 200,000 ppmv CO2, the ocean temperatures increase greatly, especially in the tropics where the warm ocean layer, which has potential temperature higher than 0 °C, extends to below 2,000 m near the equator (Fig. 2B). The highest temperature is up to 8 °C, much higher than that of the 355-ppmv case. The increase in ocean temperatures is not only because of much stronger greenhouse effect but also the broader open-ocean area that absorbs more stellar radiation at much lower surface albedo than that of sea ice and snow. Zonal-mean zonal ocean velocities are shown in Fig. 2 C and D. Both demonstrate equatorial jet streams. As CO2 increases from 355 to 200,000 ppmv, the equatorial jet stream becomes stronger and expands both downward and poleward. As shown below, the increases in both ocean temperatures and zonal velocities with increasing CO2 cause more ocean heat transport from the dayside to the nightside. Fig. 2 B and D display a slight asymmetry between the two hemispheres, which is probably introduced by the time interval (100 Earth years) for averaging, which is not long enough.

Depth–latitude cross-sections of zonal-mean ocean potential temperatures and zonal-mean zonal velocity. (Left) Ocean potential temperature (unit, °C) (Right) ocean zonal velocity (unit, m s −1 ) (Upper) 355 ppmv CO2 and (Lower) 200,000 ppmv CO2. In C and D, yellow-red colors indicate westerly flows, blue colors indicate easterly flows, and contours are the mean meridional mass streamfunction. Solid contours indicate clockwise streamlines, and dashed contours are anticlockwise streamlines. Contour interval is 100 Sv.

Contours overlapped in Fig. 2 C and D are the mean meridional mass streamfunction of ocean, which represents zonal-mean ocean meridional overturning circulations (MOC). In both plots, streamlines display two layers of circulation cells with opposite directions. The cells in the upper layer (above 300 m) are driven by wind stress. Westerly winds produce an equatorward Ekman drift and therefore descending motion at the equator, and equatorward wind stress drives cold surface water from high latitudes toward the equator for compensation. Equatorial warm water at depth moves poleward and eventually upward at high latitudes in both hemispheres, forming enclosed ocean meridional circulations. The cells in the lower layer, with maximum values of about 1,000 Sv, are the so-called thermohaline circulations that are driven by meridional density contrast due to temperature and salinity differences. Sea-ice formation generates salty water in the cold ice-covered region, while sea-ice melting in the warm open-ocean region freshens ocean water there. Denser water at high latitudes descends and moves equatorward, while lighter water in the tropics rises and moves poleward, forming the thermohaline circulations. These meridional ocean circulations lead to exchanges between warm tropical water and cold high-latitude water and generate net poleward heat transport. In addition to the mean MOCs, eddy-induced MOCs also transport heat poleward, as shown in Fig. S2 A and B. However, eddy-induced MOCs are about one order weaker than the mean MOCs. As CO2 is increased, both mean and eddy-induced MOCs become stronger and thus transport more heat from the tropics to high latitudes.

Atmospheric and ocean zonal heat transports from the dayside to the nightside are quantified and compared in Fig. 3. Both atmospheric and ocean zonal heat transports have maximum values at the equator and decrease with latitudes (Fig. 3 A and C). This is consistent with the fact that both atmospheric and oceanic flows have maximum velocities at the equator. For 3.6 ppmv CO2, the maximum zonal heat transport by the atmosphere is nearly twice greater than that by the ocean, i.e., 1.2 versus 0.7 PW. In general, atmospheric heat transport decreases with increasing CO2. In contrast, ocean heat transport increases with increasing CO2. For 200,000 ppmv CO2, the maximum ocean heat transport is about twice greater than that by the atmosphere, i.e., 2.0 versus 0.9 PW. The decrease in atmospheric heat transport with increasing CO2 is because of largely reduced thermal contrast between the dayside and nightside (Fig. 1 C and D). The increase in ocean heat transports with increasing CO2 is because of increases in ocean temperatures and zonal velocities as well as downward expansion of ocean layers with warm temperatures and strong zonal velocities, as shown in Fig. 2. Atmospheric and ocean meridional heat transports are plotted in Fig. 3 B and D, respectively. The maximum values of atmospheric meridional heat transports, located between 30 and 40° in latitude in both hemispheres, range from about 4.5 to about 6.5 PW, which are comparable to that of the Earth’s atmosphere [about 3.0 PW (30)]. The maximum ocean meridional heat transports are close to that of Earth oceans [about 2.0 PW (30)] for lower CO2 levels. For much higher CO2 levels (e.g., 100,000 and 200,000 ppmv), ocean meridional heat transports are rapidly increased to 6.0–7.0 PW.

Vertically integrated zonal and meridional heat transports by the atmosphere and by the ocean from the dayside to the nightside for various CO2 levels. (Left) Atmospheric heat transports (Right) ocean heat transports (Upper) zonal heat transports and (Lower) meridional heat transports. Unit is PW. Zonal energy fluxes here are calculated using the method in ref. 31 We first calculate the net upward energy flux through the ocean surface. Second, we use the net surface energy flux to calculate the vertically integrated divergent ocean heat flux. Then, we use the net downward energy fluxes at both the top of the atmosphere and the surface to calculate the divergent atmospheric energy transport. Zonal energy transport from the dayside to the nightside is the sum of energy fluxes across vertical cross-sections at both vertical cross-sections of both 90° and 270° in longitude.

Our simulations show that sea-ice thickness is generally thin (Fig. S3). Sea-ice thickness is about 5 m in the coldest regions, less than 3 m on most parts of the dayside, and less than 2 m near the equator. Sea-ice thickness in the coldest regions is less than 10 m even for 3.6 ppmv of CO2. This largely contrasts with the simulation results without a dynamic ocean, in which sea-ice thickness can grow up to several thousands of meters on the nightside, and the global-mean sea-ice thickness is greater than 500 m (32). Our simulations showed that sea-ice dynamics plays an important role in keeping sea ice thin at the nightside and high latitudes, in addition to ocean heat transports. Such thin sea ice would allow existence of life in not only the open-ocean region but also ice-covered regions on the dayside because stellar radiation can penetrate such thin sea ice and photosynthesis can occur under sea ice.

To further demonstrate how ocean heat transport influences the climate and habitability of tidally locked exoplanets around M stars, we perform AOGCM and AGCM simulations with different stellar radiation fluxes, but with a fixed CO2 concentration of 355 ppmv. The results are shown in Fig. 4. As stellar radiation is decreased to 700 W m −2 , sea-ice coverage reaches 100% in AOGCM (Fig. 4A) that is, the exoplanet enters a Snowball state. By contrast, ocean remains open in AGCM until stellar radiation is lowered to 550 W m −2 . These results suggest that a dynamic ocean tends to draw the outer edge of the HZ inward. On the other hand, as stellar radiation is increased (the exoplanet is moved closer the star), sea ice retreats much faster in AOGCM than in AGCM (Fig. 4A). For 1,400 W m −2 of stellar flux, sea ice is completely melted in AOGCM, whereas about 70% sea-ice coverage still remains in AGCM. This is similar to the situation of increasing CO2. Ocean heat transport can efficiently cause global deglaciation as stellar flux is sufficiently high.

Comparison of sea-ice coverage and surface air temperatures as a function of stellar radiation fluxes between AOGCM (red) and AGCM (blue). (A) Sea-ice coverage (B) global-mean Ts (C) the maximum Ts and (D) the minimum Ts. In both types of simulations, the CO2 concentration is fixed at 355 ppmv.

Ts changes with increasing stellar radiation are illustrated in Fig. 4 BD. The global-mean and minimum surface air temperatures are higher and increase faster with increasing stellar radiation in AOGCM than in AGCM, whereas the maximum Ts is generally lower until stellar radiation reaches 1,400 W m −2 . The difference between the global-mean as well as the minimum Ts and the maximum Ts is because zonal ocean heat transport always tends to cool the dayside and warm the nightside. As stellar radiation is sufficiently strong, however, sea ice is completely melted and global surface temperatures become nearly uniform, similar to that in Fig. 1D, and the maximum Ts thus becomes higher in AOGCM than in AGCM (Fig. 4C). Consistent with Ts differences between the two types of models, atmospheric water-vapor concentration and the tropopause height are all higher in AOGCM than that in AGCM for sufficiently strong stellar radiation. Cloud albedo has significant effects on causing Ts differences between the two types of simulations, as pointed out in ref. 9. It is found that cloud albedo is lower in AOGCM than in AGCM. This is because ocean heat transport reduces day–night temperature contrast in AOGCM, which consequently leads to weaker convections on the dayside and thus lower cloud albedo. The lower cloud albedo causes higher Ts in AOGCM. Because the ocean module becomes numerically unstable, no AOGCM simulations were carried out for stellar radiation stronger than 1,400 W m −2 . Nevertheless, it is expected that water-vapor concentration and the tropopause height would be higher in AOGCM than in AGCM for stellar radiation stronger than 1,400 W m −2 . These results suggest that as a dynamic ocean is considered, an exoplanet would more readily enter the runaway greenhouse state if the exoplanet is close enough to the inner HZ edge and that ocean heat transport likely pushes the inner HZ edge outward.

## Tidal Interactions Between Planets and Host Stars

Hundreds of planets are already known to have orbits only a few times wider than the stars that host them. The tidal interaction between a planet and its host star is one of the main agents shaping the observed distributions of properties of these systems. Tidal dissipation in the planet tends make the orbit circular, as well as synchronizing and aligning the planet’s spin with the orbit, and can significantly heat the planet, potentially affecting its size and structure. Dissipation in the star typically leads to inward orbital migration of the planet, accelerating the star’s rotation, and in some cases destroying the planet.

Some essential features of tidal evolution can be understood from the basic principles that angular momentum and energy are exchanged between spin and orbit by means of a gravitational field and that energy is dissipated. For example, most short-period exoplanetary systems have too little angular momentum to reach a tidal equilibrium state.

Theoretical studies aim to explain tidal dissipation quantitatively by solving the equations of fluid and solid mechanics in stars and planets undergoing periodic tidal forcing. The equilibrium tide is a nearly hydrostatic bulge that is carried around the body by a large-scale flow, which can be damped by convection or hydrodynamic instability, or by viscoelastic dissipation in solid regions of planets. The dynamical tide is an additional component that generally takes the form of internal waves restored by Coriolis and buoyancy forces in a rotating and stratified fluid body. It can lead to significant dissipation if the waves are amplified by resonance, are efficiently damped when they attain a very short wavelength, or break because they exceed a critical amplitude.

Thermal tides are excited in a planetary atmosphere by the variable heating by the star’s radiation. They can oppose gravitational tides and prevent tidal locking, with consequences for the climate and habitability of the planet.

Ongoing observations of transiting exoplanets provide information on the orbital periods and eccentricities as well as the obliquity (spin–orbit misalignment) of the star and the size of the planet. These data reveal several tidal processes at work and provide constraints on the efficiency of tidal dissipation in a variety of stars and planets.

### Subjects

• Extrasolar Planets and Systems
• Solar System Dynamics and Orbital Structure
• Theoretical Techniques
• Planet Formation

### Introduction

Tides raised in the Earth’s seas and oceans by the gravitational attraction of the Moon and the Sun have been studied for centuries (Cartwright, 1999 Deparis, Legros, & Souchay, 2013). Among the key contributors to the theoretical understanding of tides were Sir Isaac Newton ( 17th century ), Pierre-Simon, Marquis de Laplace ( 18th century ), and Sir George Darwin ( 19th century ).

The most important astronomical consequences of the tidal interaction between the Moon and the Earth are that angular momentum is being transferred from the spin of the Earth to the orbit of the Moon, causing both the day and the month to lengthen as the Earth slows and the Moon retreats, and that the orbit is becoming increasingly elliptical. The current rates of increase of the orbital semimajor axis and eccentricity, determined by lunar laser ranging (Williams & Boggs, 2016), are a ˙ = 3.8 cm yr − 1 and e ˙ = 1.5 × 10 − 11 yr − 1 , the source of energy for both these processes being the Earth’s rotation. In addition, as a consequence of tides raised by the Earth on the Moon, the spin of the Moon has been synchronized with its orbital motion, so that it presents the same familiar face towards the Earth this is known as tidal locking.

Further afield in the solar system, tidal theory has been applied to explain many properties of the moons of the other planets (e.g., Peale, 1999). In most cases, like the Earth’s Moon, the satellite is tidally locked and its orbit expands as it receives angular momentum from the rotating planet. This process could be the origin of the remarkable resonant configurations seen around Jupiter and Saturn, such as the 1:2:4 ratio of orbital periods between Io, Europa, and Ganymede (Goldreich, 1965). Most moons have nearly circular orbits, because dissipation in the moon outweighs the tendency of the rotating planet to increase the orbital eccentricity. In cases where a significant eccentricity is maintained by an orbital resonance, intense heating from ongoing tidal dissipation occurs this is thought to explain the dramatic volcanic activity on Jupiter’s moon Io (Peale, Cassen, & Reynolds, 1979) and Saturn’s moon Enceladus (Porco et al., 2006), discovered by the Voyager and Cassini space missions.

Beyond the solar system, tidal theory has been applied to explain observational properties of close binary stars (Zahn, 1977). A spectroscopic binary star is one in which the orbital period and eccentricity can be measured by observing the periodic Doppler shifting of the spectral lines of at least one of the two stars. Within a cluster of stars, binaries of shorter period tend to have circular orbits, while those of longer period have widely spread eccentricities this is interpreted as evidence that tidal dissipation has circularized the orbits of the closer, more strongly interacting binaries. The transitional period is longer in older clusters, providing information about the evolution of the circularization process (Meibom & Mathieu, 2005).

The first exoplanet to be discovered around a main-sequence star, 51 Peg b (Mayor & Queloz, 1995), is an example of a hot Jupiter. With a mass about half that of Jupiter, it orbits every 4.2 days around a star slightly more massive than the Sun, and of similar age, in a circular orbit whose radius is about nine times that of the star. Soon after its discovery, it was proposed that 51 Peg b was formed in a circumstellar disk at a similar orbital radius to Jupiter, and that its inward migration through disk torques could have been halted by a tidal torque from the star, when the star was younger, larger, and more rapidly rotating (Lin, Bodenheimer, & Richardson, 1996). Since 1995 , hundreds of other exoplanets with orbital periods of a few days or less have been discovered by the radial-velocity and transit methods. Evidence for tidal interaction between these planets and their host stars can be seen both in individual systems and in the statistical properties of the population.

### Tidal Theory for Exoplanetary Systems

#### Tidal Forces

A key result of Newtonian dynamics is that two point masses, subject only to their mutual gravitational attraction, move in Keplerian orbits about their center of mass. The orbit is a circle or an ellipse if it is bound a parabola or a hyperbola if it is unbound. The behavior of extended, deformable bodies such as planets and stars differs from this simple picture and involves an interplay between the external dynamics (orbital motion of the centers of masses of the two bodies) and the internal dynamics (fluid or solid mechanics within each body).

Tidal effects result from the spatial variation, over an extended body, of the gravitational field due to an orbital companion. If the gravitational field at the center of the first body provides just the right acceleration required for its orbital motion, then the variation of the field produces a tidal acceleration that tends to deform the body from its natural shape.

Consider the interaction of a planet of mass M p and radius R p with a star of mass M s and radius R s . A simple estimate of the magnitude of the tidal deformation of the star by the planet is provided by the dimensionless tidal amplitude parameter ϵ s = ( M p / M s ) ( R s / r ) 3 , where r is the orbital separation. This can be understood as the tidal potential due to the planet at the point on the stellar surface closest to it, divided by the star’s own gravitational potential at this point. A similar estimate of the deformation of the planet, neglecting any rigidity, is ϵ p = ( M s / M p ) ( R p / r ) 3 . Tidal effects are very sensitive to the orbital separation and are most significant for systems of short orbital period. Values of ϵ s up to 1.8 × 10 − 4 are found for stars with massive hot Jupiters such as WASP-18. Values of ϵ p up to 0.06 , implying significant tidal deformation, are found for hot Jupiters such as WASP-12 b and WASP-19 b.

#### Tidal Deformation and Disruption

The main effect of tidal gravity is to deform each body into a spheroidal shape, elongated along an axis that points towards (and away from) its companion. This is in addition to the flattening of each body due to its rotation. If a planet orbits too close to its host star, the tidal deformation will be so great that the planet will be disrupted.

Consider a planet of mass M p and volumetric radius R p (defined as the radius of a sphere with the same volume as the planet) in a circular orbit of radius a around a star of much greater mass M s . For a fluid planet in synchronous, aligned rotation, two classical models bracket the expected behavior:

In the case of a homogeneous planet of uniform density, the planet can find an equilibrium in the form of a Roche ellipsoid , which is elongated by tidal forces and flattened by rotation, provided that a exceeds a critical value known as the Roche limit , which can be expressed as 2.46 ( M s / M p ) 1 / 3 R p . If a is less than the Roche limit, the planet is disrupted by being drawn out into a needle-like configuration.

In the opposite extreme of a centrally condensed planet whose mass is concentrated in a single point, the planet can find a hydrostatic equilibrium in the Roche potential , which combines the gravity of the two bodies with the centrifugal potential due to the uniform rotation (Figure 1). The same formula for the Roche limit applies but with the coefficient 2.46 replaced by 2.03. For values of a greater than this critical value, the surface of the planet follows a contour of the Roche potential, whereas for smaller a the planetary envelope overflows the Roche lobe and material is lost. A related concept is the Hill radius R H = ( M p / 3 M s ) 1 / 3 a , which gives the distances of the Lagrangian points L 1 and L 2 from the center of the planet in the limit that the planet is much less massive than the star. The volume of the planet’s Roche lobe (also known as the Hill sphere ) in this limit is 1.51 R H 3 (which is considerably less than that of a sphere of radius R H ).

Figure 1. Contours of the Roche potential for a mass ratio of 1/1000, typical of a giant planet similar to Jupiter orbiting a star similar to the Sun. The planet is in a circular orbit in the xy plane around the center of mass of the system, which is located at the origin (far to the left of the plot), close to the center of the star. The unit of length is the orbital separation. The closed part of the red contour is a cut through the Roche lobe (or Hill sphere), which delimits the region in which material co-orbiting with the planet is bound to it, and reaches the inner Lagrangian point L 1 . The blue contour is a slightly higher equipotential that crosses the outer Lagrangian point L 2 .

The coefficient 2.46 in the Roche limit can also be reduced for a solid planet with significant viscosity or material strength (Holsapple & Michel, 2006 Leinhardt, Ogilvie, Latter, & Kokubo, 2012).

The calculation of a hydrostatic tidal (or rotational) bulge of small amplitude in a self-gravitating body is a classical one developed by Clairaut in the 18th century , involving the solution of a linear second-order ordinary differential equation (e.g., Cook, 1980).

#### Tidal Equilibrium

A possible endpoint of tidal evolution is a tidal equilibrium in which the orbit is circular and both the star and the planet are tidally locked. Viewed in a frame of reference that rotates with the common angular velocity Ω , the tidal deformation is then static and no dissipation or tidal evolution occurs.

Given the masses M s and M p of the two bodies and their moments of inertia I s and I p , the total angular momentum of the system in a tidal equilibrium can be evaluated as the sum J = L + S of the orbital angular momentum L = μ G M a and the spin angular momentum S = I Ω , where M = M s + M p is the total mass, μ = M s M p / M is the reduced mass (slightly less than the planet’s mass), I = I s + I p is the sum of the moments of inertia, and a is the radius of the orbit, related to Ω by Kepler’s Third Law, Ω 2 = G M / a 3 . Note that L ∝ a 1 / 2 ∝ Ω − 1 / 3 , whereas S ∝ Ω . Since J = L + S is the sum of a decreasing function of Ω and an increasing function of Ω , it has a minimum value, J c = 4 I Ω c , at a critical angular velocity, Ω c = G M ( μ / 3 I ) 3 / 4 . It is then possible to show the following (Hut, 1980):

If the angular momentum of the system exceeds the critical value J c , then two tidal equilibrium solutions are possible, but only the more slowly rotating one (which has Ω < Ω c and L > 3 S ) minimizes the energy and is stable.

If J < J c , then no tidal equilibrium exists.

Figure 2 shows the stable tidal equilibria and evolutionary tracks of a system consisting of a star and a planet in which the orbit is assumed to be circular and aligned with the stellar spin. The x and y axes represent the orbital angular velocity n and the stellar spin Ω s , both in units of the critical angular velocity Ω c . Each evolutionary track is a curve on which the total angular momentum J = L + S (to which the planetary spin is assumed to make a negligible contribution) is equal to a constant. The direction of evolution, indicated by the arrows, is that in which the total mechanical energy of the system decreases as a result of tidal dissipation. Even though the spin–orbit interaction is frictional in nature, transferring angular momentum from the more rapidly rotating component to the less rapidly rotating one and dissipating energy, this does not always lead to synchronization because of the peculiar property that the orbital angular momentum is a decreasing function of the angular velocity.

Figure 2. Evolutionary tracks for a system consisting of a star, with spin angular velocity Ω s , and a planet in a circular orbit of angular velocity n . On each track the total angular momentum J is conserved, and the direction of evolution is such as to lower the total mechanical energy. J c and Ω c are the critical values defined in the text. Blue dots represent stable tidal equilibria.

Most of the short-period exoplanetary systems for which tidal interactions are important have J < J c , which implies n > Ω s . Both n and Ω s are increasing as a result of tides, and the planet will eventually be consumed. Even for those few short-period systems that have J > J c and may be evolving towards a tidal equilibrium, this equilibrium can only be temporary stars continue to evolve and lose angular momentum through the magnetic torques on outflowing matter as they emit hot, ionized winds along open magnetic field lines.

#### Torque and Dissipation

A deformed body with a spheroidal bulge possesses a gravitational quadrupole moment that causes its external gravitational field to differ from that of a point mass (a gravitational monopole). The quadrupolar component of the field lacks complete rotational symmetry and decays more rapidly with distance than the monopolar component. The tidal interaction between two bodies can be thought of as a coupling of their monopole and quadrupole moments, which allows a torque to be exerted, meaning that angular momentum is exchanged between spin and orbit. If the bulge points towards the companion, which is true of an instantaneous hydrostatic response, as in Figure 1, then this torque vanishes. Misalignment of the bulge can be thought of as resulting from a delay in the response. This requires dissipation and allows a torque to be exerted, leading to an irreversible evolution of spin and orbit it also causes the tidally deformed body in which the dissipation occurs to be heated.

All the relevant information about the tidal interaction is encoded in the gravitational quadrupole moments of the deformed bodies. The Love number k (actually the potential Love number of second degree, k 2 ) is a dimensionless measure of how much a body is deformed hydrostatically by a tidal force. For a fluid body, k is determined from the solution of Clairaut’s equation it is equal to 1.5 for a homogeneous body, but smaller for more centrally condensed bodies such as giant planets and especially for stars. The rigidity of a solid body such as a terrestrial exoplanet also reduces k . (Estimates for Jupiter, the Earth, the Sun, and the Moon are 0.59, 0.30, 0.035, and 0.024, respectively.)

The dissipative aspect of the tidal response can be described in a variety of equivalent ways. Most common are the quality factor Q , the modified quality factor Q ′ , and the time lag τ . These are related by ω τ = 1 / Q (which is the phase lag) and k / Q = 1.5 / Q ′ , where ω is the angular frequency of the tidal forcing in a frame of reference that rotates with the body. There is a long history of describing the damping of waves and oscillations in the Earth in terms of a quality factor Q , which is a dimensionless quantity inversely proportional to the efficiency of dissipation. An advantage of Q ′ is that it combines the parameter Q with the Love number k , which itself may be uncertain, in such a way that they need not be considered separately. Both the tidal torque and the dissipation rate are proportional to k / Q , or to 1 / Q ′ , or to k τ .

It is best not to think of Q , Q ′ , or τ as constant properties of a star or planet. For small-amplitude tides, these parameters are different ways of quantifying the linear response of the body to tidal forcing at a particular frequency, and can depend significantly on that frequency.

### Tidal Force

In the weak friction approximation (Alexander, 1973 Hut, 1981), the phase lag is assumed to be small and proportional to the tidal frequency this means that the tidal deformation is identical to an instantaneous hydrostatic one, but delayed by a constant time lag τ . There is some physical justification for this assumption. In a fluid body of mass M , radius R , and kinematic viscosity ν , the behavior is indeed of this form, with a time lag proportional to ν R / G M , if the tidal frequency is well below the natural frequencies of any relevant normal modes of oscillation.

With this convenient assumption, the tidal acceleration acting on the orbital separation vector r = r r ^ due to dissipation in the star can be written as − γ s ( r ˙ − Ω s × r + 2 r ˙ r ^ ) where γ s = 3 k s τ s ( M p M s ) ( R s r ) 5 G M r 3 is a damping coefficient. Here Ω s is the spin angular velocity of the star, and r ˙ − Ω s × r is the velocity of the planet in a frame of reference moving and rotating with the star. The tidal force therefore tends to damp any asynchronism or misalignment between the orbital and rotational motions (as seen in the first two terms in the expression) and also to damp any radial motion (associated with orbital eccentricity). A similar expression, with subscripts “s” and “p” reversed, gives the acceleration due to dissipation in the planet.

#### Tidal Evolution

Away from a tidal equilibrium, each body experiences a tidal torque that exchanges angular momentum between its spin and the orbit energy is also dissipated, lowering the mechanical energy (spin plus orbit) of the system. This can be conveniently illustrated in the weak friction approximation.

In the simple case of a circular orbit with aligned spins, the following equations determine the evolution of the orbital angular velocity n = G M / a 3 and the two spins:

where, again, μ = M s M p / M is the reduced mass (slightly less than the planet’s mass). The smallness of the moment of inertia of the planet ( I p ≪ I s and I p ≪ μ a 2 ) means that the most rapid tidal process is usually the synchronization (and alignment) of the planetary spin with the orbit. This tidal locking ( Ω p = n ) can have important implications for the atmospheric dynamics and habitability of terrestrial exoplanets.

Once the planetary spin is synchronous, the stellar asynchronism evolves according to

A feature of hot Jupiter systems is that μ a 2 and I s can be comparable, leading to an interesting coupled evolution in which both the stellar spin and the orbital radius change significantly. If, for example, the orbital angular momentum of a Jupiter-mass planet in a three-day orbit around a solar-mass star were transferred to the stellar spin, the star would rotate with a period of about three days. For a system consisting of Jupiter and the Sun, the bracket ( 3 − μ a 2 I s ) is positive for orbits smaller than about 0.07 AU, or shorter than about seven days, and in such cases the angular velocities of the spin and orbit will diverge from each other (despite the frictional nature of the tidal interaction). This corresponds to the condition n > Ω c , that is, to being on the right-hand side of Figure 2.

If a small orbital eccentricity is allowed for, this evolves according to

The eccentricity is damped, leading to circularization of the orbit, provided that neither body spins significantly faster than the orbit. (The precise critical ratio of 18 / 11 suggested by this equation is dependent on the assumptions underlying the weak friction approximation (Darwin, 1880).) The ratio of the rates of circularization due to dissipation in the planet and the star is proportional to

and tends to be dominated by the planet.

If a small misalignment angle i s between the stellar spin and the orbit is also allowed for, this evolves according to

For typical short-period exoplanetary systems, the large bracket is positive and tidal dissipation causes alignment of the spin and orbit.

#### Tidal Encounters

The sensitivity of tides to the orbital separation creates a distinction between situations of small and large orbital eccentricity. In the former case, the tidal interaction involves a small number of Fourier components that vary sinusoidally with time. In the latter case, the interaction is concentrated at the periapsis (where the orbital separation takes its minimum value r = q ) and takes the form of a succession of impulses or tidal encounters. For exoplanets, both situations are relevant a planet set on a highly elliptical orbit by interactions with companions can have its orbit circularized and shrunk through a sequence of dissipative encounters with the star.

It is relatively easy to calculate the effect of a tidal encounter in the weak friction approximation, for illustrative purposes. Assuming that the planetary spin is aligned with the orbit, the angular momentum ( Δ L ) p transferred from spin to orbit due to dissipation in the planet is given by

where, in the limit of a highly eccentric orbit, L = μ 2 G M q is the orbital angular momentum and Ω q = 2 G M / q 3 is the orbital angular velocity at the periapsis (where it is maximal, and where the damping coefficient γ p is to be evaluated). A similar expression applies for the star, with the subscript “p” replaced by “s.” Since the moment of inertia of the planet is relatively small ( I p ≪ I s and I p ≪ μ a 2 ), the planetary spin can be assumed to adjust after relatively few encounters to the pseudosynchronous value 33 40 Ω q (Hut, 1981), which represents a suitably weighted average of the orbital angular velocity close to the periapsis, with little change in the orbit. However, since I s and μ a 2 can be comparable for a hot Jupiter system, adjustment of the stellar spin is strongly coupled to evolution of the orbit. The energy lost from the orbit due to dissipation in the planet causes a change in the orbital eccentricity of

which is negative in the pseudosynchronous state. The corresponding quantity ( Δ e ) s due to the star is also negative in the typical situation that Ω s < Ω q . After many such encounters, the orbit will be circularized.

When dynamical tides are considered, each tidal encounter leads to the impulsive excitation of oscillation modes in the star and planet, with a corresponding transfer of energy and angular momentum from the orbit to the modes (Press & Teukolsky, 1977). Damping of these modes, by linear or nonlinear processes, allows their angular momentum to be deposited, affecting the spin of the body, while energy is dissipated. If the modes are damped within a single orbit, then each successive encounter contributes to the tidal evolution of the system in a qualitatively similar way to that found in the weak friction approximation, albeit with differences of detail. If they are not so efficiently damped, chaotic dynamics can ensue (Vick & Lai, 2018 Wu, 2018, and references therein).

If the periapsis q is too small, the planet will be disrupted as a result of the encounter. For a homogeneous fluid planet, disruption occurs if q < 1.69 ( M s / M p ) 1 / 3 R p , which is smaller than the Roche limit by a factor of 0.69 (Sridhar & Tremaine, 1992). Numerical simulations of tidal disruptions have been carried out with more realistic models of planets (Guillochon, Ramirez-Ruiz, & Lin, 2011).

#### Equilibrium and Dynamical Tides

The dominant response of a star or planet to tidal forcing is usually a spheroidal bulge in which the pressure and density of the body adjust hydrostatically to the modified gravitational potential. Away from a tidal equilibrium, the bulge is time-dependent and a smooth velocity field is required to move it at the appropriate rate around the body. This equilibrium tide (or non-wavelike tide) is not an exact solution of the hydrodynamic equations because the inertial terms in the equation of motion are neglected in estimating it. The dynamical tide (or wavelike tide) is the residual response, which typically takes the form of internal waves.

Internal waves are those restored by buoyancy and Coriolis forces in stratified and rotating fluids. Also known as internal gravity waves, g modes, inertial waves, inertia-gravity waves, and so on, they have been studied extensively in the Earth’s atmosphere and oceans. Their properties are in some ways opposite to those of the more familiar sound waves. First, the frequency of an internal wave is independent of the wavelength and depends only on the direction of propagation it cannot exceed the buoyancy frequency or twice the spin frequency of the fluid (whichever is greater). The buoyancy frequency N is defined by N 2 = g ρ ( d ρ d r | ad − d ρ d r ) , where g is gravity, ρ is density, r is radius, and “ad” refers to the adiabatic gradient that would occur in the case of uniform composition and entropy per unit mass. Second, the motion in an internal wave is approximately incompressible and therefore transverse to the direction in which the phase of the wave varies, which is in turn perpendicular to the direction of propagation.

In most cases of interest for exoplanetary systems, surface-gravity waves and sound waves (also known as f modes and p modes) in stars and planets have frequencies that are too high (with wave periods of less than an hour) to be excited significantly by tidal forcing (with forcing periods of hours or days). Internal waves occupy the low-frequency end of the spectrum of oscillation modes, and are more naturally excited by tidal forcing.

#### Dissipation of the Equilibrium Tide

Any mechanism that provides a frictional or viscous drag on the equilibrium tide will lead to dissipation and a tidal torque. In stars, where the viscosity of the fluid is usually negligible, the main candidate is an effective “eddy viscosity” resulting from turbulent motion. This could be either the convective motion in regions such as the outer part of the Sun, where the star’s luminosity is being carried to the surface predominantly by convection (e.g., Zahn, 1989), or it could be turbulence arising from an instability of the tidal flow itself, such as the elliptical instability (Kerswell, 2002). In planets such as hot Jupiters, convection is less powerful than in stars because of the weaker sources of heat, but instability of the tidal flow is more likely because of the larger tidal amplitudes (e.g., Barker, 2019).

Solid regions of planets are often modeled as viscoelastic materials, which behave like an elastic solid on short timescales but can flow like a viscous fluid on long timescales. The commonly adopted Maxwell model is characterized by a viscosity η and a relaxation time τ , such that the elastic modulus on short timescales is η / τ . In response to periodic strain with angular frequency ω , the effective viscosity of the material is η 1 + ( ω τ ) 2 , which is significantly less than η in the “elastic” regime in which the oscillation period is short compared with the relaxation time. Viscoelastic dissipation of the equilibrium tide is thought to be important for rocky bodies in the solar system and is likely to be so for terrestrial exoplanets (e.g., Correia, Boué, Laskar, & Rodríguez, 2014), although there is considerable uncertainty regarding the viscoelastic parameters.

Interestingly, fluid turbulence also has a viscoelastic character, with the relaxation time being related to the turnover time of the turbulent eddies (Ogilvie, 2019 Ogilvie & Lesur, 2012). The effectiveness of convection in dissipating the equilibrium tide in stars is limited because it is often in the “elastic” regime in which the tidal period is short compared with the turnover time (Goodman & Oh, 1997). The same is true of viscoelastic dissipation in solid regions of planets. This ordering of timescales means that the weak friction approximation is not applicable in detail to either situation.

#### Dissipation of the Dynamical Tide

Different mechanisms apply to the dynamical tide, which usually takes the form of internal waves. If these waves develop a sufficiently short wavelength, then linear dissipative mechanisms, in particular thermal diffusion due to radiative transport, can be relevant. For example, internal gravity waves acquire a short radial wavelength if they propagate into strongly stably stratified regions of a star or planet in which the buoyancy frequency is much greater than the wave frequency. In Zahn’s theory of the dynamical tide in stars more massive than the Sun (e.g., Zahn, 1977), which have convective cores and radiative envelopes, internal gravity waves are excited by tidal forcing near the base of the envelope and propagate towards the stellar surface, where radiative diffusion can be effective. Inertial waves in convective zones can also reach short lengthscales through geometrical focusing as a result of multiple reflections (e.g., Ogilvie & Lin, 2004). In these cases the efficiency of tidal dissipation can be strongly dependent on the tidal frequency, as this determines the detailed behavior of the waves.

Alternatively, if the propagation of internal waves causes them to exceed a critical amplitude, they become unstable and break, dissipating through transmission to waves of smaller scale. This mechanism could apply to stars more massive than the Sun, or to exoplanetary atmospheres. In solar-type stars, internal waves forced by a close planetary companion propagate towards the stellar center, where they break if the planet is sufficiently massive and the star sufficiently evolved (Barker & Ogilvie, 2010). This process could absorb the orbital angular momentum of the planet within a few million years, leading to the consumption of massive hot Jupiters.

For a more detailed and quantitative discussion of mechanisms of tidal dissipation in fluid bodies, the reader is referred to the review articles by Ogilvie (2014) and Mathis (2018).

#### Thermal Tides and Planetary Atmospheres

In addition to gravitational tides, planets experience thermal forcing from their host stars, as some of the radiation from the star that is received by the planet is absorbed and heats the atmosphere. Like gravitational tidal forcing, this effect is strongly dependent on the orbital separation, and results in a periodic disturbance if the planet is not tidally locked.

Stellar heating of the atmosphere creates a thermal bulge, on which the star’s gravity exerts a torque. On the Earth, the thermal bulge can be detected through the periodic variation of the atmospheric pressure at ground level (Haurwitz, 1964), which reflects the changing column density of the overlying atmosphere. The relevant Fourier component of this variation (known as the semidiurnal solar atmospheric tide) has a period of 12 hours and an amplitude exceeding one millibar at the equator, where pressure maxima occur a little before 10 o’clock (am and pm). The temperature variation is out of phase, peaking a little before 4 o’clock, in accord with everyday experience. The fact that a pressure maximum leads the position of the Sun by about two hours means that the solar torque on the thermal bulge accelerates the Earth’s rotation (Thomson, 1882).

Similar effects can be expected in other planets, especially those with a solid surface that can rigidly support the pressure fluctuations of the overlying atmosphere (although thermal tides in hot Jupiters have also been discussed (Arras & Socrates, 2010)). A competition between thermal and gravitational tides can result in a stable equilibrium in which the spin of the planet is significantly asynchronous. This process is thought to explain the rotation of Venus, which is closer to the Sun and has a thicker atmosphere than the Earth (Gold & Soter, 1969 Ingersoll & Dobrovolskis, 1978). It has been proposed that many terrestrial exoplanets in the habitable zone may have asynchronous rotation because of this process (Leconte, Wu, Menou, & Murray, 2015), which may be beneficial for their habitability. Tidal locking may be unfavorable for habitability because of the extreme temperature contrasts between the permanent day and night sides of the planet, which can lead to atmospheric collapse (Kasting, Whitmire, & Reynolds, 1993). General circulation models (GCMs) are now used to compute atmospheric dynamics and thermal tides in exoplanets (Pierrehumbert & Hammond, 2019).

### Application to Observed Exoplanetary Systems

At the time of writing ( August 2019 ), more than 400 exoplanetary systems are known with an orbital semimajor axis less than 10 times the stellar radius, and more than 80 of these have a / R s < 5 . The majority of these short-period exoplanets are transiting systems, which allow measurements of a number of stellar and planetary properties. Little can be said so far about the spins of exoplanets, although the question of whether they are tidally locked may be answered by ongoing developments in atmospheric studies. The main observational data relevant to tidal interactions are the orbital size and eccentricity, the stellar spin and obliquity (spin–orbit misalignment), and possible changes in orbital period. The distributions of these properties will be discussed before selected objects are examined in detail.

### Orbital Circularization

There is a clear trend for exoplanets with the shortest periods to have orbits of lower eccentricity. This can be seen in Figure 3, based on a sample of transiting giant planets studied by Bonomo et al. (2017). Orbital circularization could be explained, in principle, by tidal dissipation in either the planet or the star. O’Connor and Hansen (2018) have obtained estimates of the tidal dissipation constant (related to the time lag of the weak friction approximation) in hot Jupiters by modeling this data.

Figure 3. Orbital eccentricity versus orbital period for the 123 transiting giant planets with well-determined eccentricities tabulated by Bonomo et al. (2017). Blue dots (with error bars) represent planets with eccentricities significantly different from zero, while vertical bars without points represent planets with eccentricities consistent with zero.

#### The Roche Limit

Figure 4 compares the orbital semimajor axes of observed exoplanets with the Roche limit, in cases where this can be determined to reasonable accuracy. As described in the section “Tidal Deformation and Disruption,” the Roche limit for a fluid planet is expected to lie between 2.03 ( M s / M p ) 1 / 3 R p and 2.46 ( M s / M p ) 1 / 3 R p , depending on how centrally condensed it is. It is clear that the observed distribution of a is cut off at, or very close to, the Roche limit as expected theoretically. This suggests that many planets have been destroyed or have lost material as a result of strong tidal forces from their host stars.

Figure 4. Comparison of the orbital semimajor axes of exoplanets with the Roche limit, for systems where this can be determined with reasonable accuracy. The Roche limit for a fluid planet on a circular orbit lies between the two vertical red lines, depending on the internal density profile. The vertical axis shows the planetary mass in Jovian units. Data obtained from the Extrasolar Planets Encyclopaedia.

There is some evidence for an edge in the distribution close to twice the Roche limit, which could be explained if these short-period planets initially had highly elliptical orbits that were circularized while approximately conserving the orbital angular momentum, because the periapsis is doubled during this process (Ford & Rasio, 2006).

#### Orbital Migration and Stellar Spin-Up

If a planet’s orbit decays as a result of tidal dissipation in the host star, its orbital period should gradually decrease. This can be detected through accurate measurements of transit-timing variations if the effect is strong enough and the observational baseline long enough. The best case to date is WASP-12 b, discussed in the section “Selected Case Studies,” but other candidates exist (Bouma et al., 2019 Maciejewski et al., 2018) and the observational constraints are likely to improve in the coming years.

The hosts of several hot Jupiters have been found to be rotating significantly faster than expected for single stars of their mass and age (Brown et al., 2011 Husnoo et al., 2012 Kovács et al., 2014), suggesting that they have gained angular momentum from their planetary companions via tidal torques. This implies in turn that the orbits of these planets have decayed. Penev, Bouma, Winn, and Hartman (2018) have modeled the spin evolution of the hosts of hot Jupiters, finding evidence of a strong dependence of the stellar modified quality factor Q ′ on the tidal forcing frequency. Collier-Cameron and Jardine (2018) have modeled the orbital decay of hot Jupiters, finding evidence for enhanced dissipation in situations where the star spins sufficiently fast that the planet can excite inertial waves in it, but pointing also to important selection effects.

#### Stellar Obliquity

The misalignment of the stellar spin and the orbit of a transiting exoplanet, projected onto the plane of the sky, has been measured in a number of systems using the Rossiter–McLaughlin effect (Triaud, 2018). Observations show that significant misalignments are uncommon for cooler, less massive stars but common for hotter, more massive stars, with the transition occurring roughly where the star changes from having a radiative core and convective envelope (like the Sun) to having a convective core and a radiative envelope (Albrecht et al., 2012). The differing efficiencies of tidal dissipation in the two types of star may contribute to this dichotomy. Theories of dynamical tides involving inertial waves can explain how a misalignment can be damped on a timescale shorter than that for the orbit to decay (Lai, 2012 Lin & Ogilvie, 2017).

#### Tidal Heating

A long-standing observational puzzle is that many hot Jupiters are found to have larger radii than expected for their mass and age, even if they are composed purely of hydrogen and helium, which suggests the existence of an internal source of heat. The radius anomaly is correlated with the equilibrium temperature of the planet as a result of stellar irradiation, and is largest for planets of about the mass of Jupiter (e.g., Thorngren & Fortney, 2018). Tidal dissipation could contribute to the heating required for planetary inflation (Bodenheimer, Lin, & Mardling, 2001), but needs to be sustained and connected with the irradiation of the planet (Jermyn, Tout, & Ogilvie, 2017 Socrates, 2013).

#### Selected Case Studies

Here are listed a number of systems of special interest, some of which are illustrated, to scale, in Figure 5. The subscripts ⊙ , J , and E refer to the Sun, Jupiter, and the Earth, and AU is the astronomical unit (the mean distance between the Earth and the Sun).

Figure 5a. Scale representation of selected exoplanetary systems. Blue: HD 80606 b. Green: WASP-19 b. Red: WASP-18b. Magenta: KOI 1843.03.

Figure 5b. Scale representation of the TRAPPIST-1 multi-planetary system.

WASP-19 b. Currently one of the shortest-period giant planets known, this is a hot Jupiter ( M p ≈ 1.1 M J , R p ≈ 1.4 R J ) in a very short-period (19 hour, a ≈ 0.016 AU ≈ 3.4 R s ) orbit around a G8V star ( M s ≈ 0.9 M ⊙ , R s ≈ 1.0 R ⊙ ) (Hebb et al., 2010 Mancini et al., 2013 Tregloan-Reed, Southworth, & Tappert, 2013). Observations are consistent with the orbit being circular and in the star’s equatorial plane. The star is thought to have been spun up tidally by the planet (Brown et al., 2011), so this is a promising system in which to look for orbital decay, although this has not been detected (Petrucci et al., 2020).

WASP-18 b. This is a very massive hot Jupiter ( M p ≈ 10 M J , R p ≈ 1.2 R J ) in a very short-period (23 hour, a ≈ 0.02 AU ≈ 3.6 R s ), slightly eccentric ( e ≈ 0.008 ) orbit around an F6V star ( M s ≈ 1.3 M ⊙ , R s ≈ 1.3 R ⊙ ) (Hellier et al., 2009 Triaud et al., 2010). Given the relatively large tidal amplitude in the star, dissipation in the star must be relatively inefficient to avoid observable orbital decay.

WASP-12 b. This is a hot Jupiter ( M p ≈ 1.5 M J , R p ≈ 1.9 R J ) in a short-period (26 hour, a ≈ 3.0 R s ) circular orbit around a late F-type star ( M s ≈ 1.3 M ⊙ , R s ≈ 1.5 R ⊙ ) (Hebb et al., 2009 Maciejewski et al., 2018 Weinberg, Sun, Arras, & Essick, 2017). Transit-timing variations indicate that the orbital period is decreasing at a rate of P ˙ = − ( 29 ± 2 ) ms yr − 1 , corresponding to a timescale of − P / P ˙ = 3.25 Myr (Yee et al., 2020). This observation provides the best evidence to date of the orbital decay, or inward migration, of an exoplanet due to tidal dissipation in the host star. The planet is also thought to be overflowing its Roche lobe, predominantly through the inner Lagrangian point L 1 (Figure 1), into a gas ring around the star (Lai, Helling, & van den Heuvel, 2010 Li, Miller, Lin, & Fortney, 2010) this loss contributes to outward migration of the planet, which is more than compensated for by tidal dissipation in the host star.

KOI 1843.03. Currently the shortest-period planet known around a main-sequence star, this is a terrestrial planet in an extremely short-period (4.2 hour) orbit around an M3V star ( M s ≈ 0.4 − 0.5 M ⊙ , R s ≈ 0.4 − 0.5 R ⊙ ) (Rappaport, Sanchis-Ojeda, Rogers, Levine, & Winn, 2013). The star is slowly rotating (34 days) and expected to be fully convective. The tidal period (more than two hours) is still not short enough to resonate with the quadrupolar surface gravity mode (f mode) of the star. The planet’s mass is estimated to lie in the range 0.32 − 1.06 M E , and its mean density must exceed 7 g cm − 1 (implying a composition of at least 70% iron) to avoid disruption. Extreme proximity to the star ( a / R s is estimated to lie between 1.4 and 2.2) implies a molten surface. A very similar object, with an orbital period only four minutes longer, is K2-137 b (Smith et al., 2018). These are the most extreme examples currently known of ultra-short period planets (USPs) (Winn, Sanchis-Ojeda, & Rappaport, 2018), a population of planets with periods less than one day and radii less than twice that of the Earth. Their tidal deformation has been modeled by Price and Rogers (2020), who find that they should have aspect ratios of between 1.3 and 1.8.

HD 80606 b. A prime candidate for high-eccentricity migration, this is a massive planet ( M p ≈ 4 M J , R p ≈ 1.0 R J ) in a highly eccentric ( e ≈ 0.93 ) orbit around a G5V star ( M s ≈ 1.0 M ⊙ , R s ≈ 1.0 R ⊙ ) (Hébrard et al., 2010 Naef et al., 2001). The remarkable 111-day orbit has a minimum separation of 0.030 AU (about 6.6 R s ) and a maximum separation of 0.88 AU . The projected stellar spin–orbit misalignment is significant, at 42 ± 8 ° . By analyzing the Spitzer phase curve, de Wit et al. (2016) deduced a stellar rotation period of 93 hours (with a large error), significantly longer than the standard pseudosynchronous value. The star has a binary companion, HD 80607, with a projected separation of about 1000 AU. This system led Wu and Murray (2003) to propose “Kozai migration,” in which the planet gains a large orbital eccentricity from a binary companion on a highly inclined orbit the orbit is then circularized progressively through a succession of tidal encounters with the star, eventually producing a hot Jupiter on a compact, circular orbit (see also Fabrycky & Tremaine, 2007 Naoz, Farr, Lithwick, Rasio, & Teyssandier, 2013). High-eccentricity migration can also occur if the planet gains eccentricity through dynamical or secular interactions with other planets (Dawson & Johnson, 2018).

TRAPPIST-1. This is a very compact system of at least seven Earth-sized planets around an M8V star (Gillon et al., 2017). The inner six planets are in a chain of orbital resonances. Combining the resonant dynamics with tidal dissipation in each planet, which tends to circularize the orbits, Papaloizou, Szuszkiewicz, and Terquem (2018) have placed constraints on the tidal quality factors of the planets. This is also a system in which planet–planet tidal interactions may be relevant (Hay & Matsuyama, 2019).

### Conclusions

The tidal interaction of two bodies on a close Keplerian orbit is one of the classical problems of planetary science and theoretical astrophysics. Developed originally for the Earth–Moon system and other solar-system bodies, the theory has found a new lease of life in application to exoplanets that interact with their host stars. While the celestial mechanics of tidally interacting systems is fairly well understood, much remains to be learned about the efficiency of tidal dissipation in stars and planets. Significant progress has already been made in identifying a number of relevant mechanisms, many of which involve complicated fluid dynamical processes, often in a nonlinear regime. More work, including advanced linear calculations and nonlinear numerical simulations, is required in order to enable a reliable evaluation of the tidal dissipation rate in realistic applications and so to predict the rates of tidal evolution. Further improvements in the understanding of the interior structure and properties of planets may also be required.

Observations of transiting exoplanets have supplied a wide range of valuable data that provide evidence of a number of tidal processes having occurred, including tidal disruption, orbital circularization, orbital decay, stellar spin-up, spin–orbit alignment, and tidal heating. As this remarkable dataset continues to expand through the work of new and existing facilities, the observational constraints will tighten and more will certainly be learned about tidal interactions in exoplanetary systems.

So far, attempts to model the observational data have, for good reasons, used simple empirical models of tidal dissipation to obtain useful constraints on its efficiency in stars and planets. It is to be hoped that, in the years to come, advances in theory, simulations, and observations will allow a convergence towards a quantitative understanding of tidal evolution with predictive power.

### Acknowledgements

This article was prepared with the use of NASA’s Astrophysics Data System and the Extrasolar Planets Encyclopaedia.

## Red Dwarf Planets and Habitability

The question of habitability on planets around M-dwarfs is compelling, and has been a preoccupation of mine ever since I began working on Centauri Dreams. After all, these dim red stars make up perhaps 75 percent of the stars in the galaxy (percentages vary, but the preponderance of M-dwarfs is clear). The problems of tidal lock, keeping one side of a planet always facing its star, and the potentially extreme radiation environment around young, flaring M-dwarfs have fueled an active debate about whether life could ever emerge here.

At Northwestern University, a team led by Howard Chen, in collaboration with researchers at the University of Colorado Boulder, NASA’s Virtual Planet Laboratory and the Massachusetts Institute of Technology, is tackling the problem by combining 3D climate modeling with atmospheric chemistry. The paper on this work, in press at the Astrophysical Journal, examines how general circulation models (GCM) have been able to simulate the large-scale circulation and climate system feedbacks on planets around red dwarfs, but these models have not accounted for atmospheric chemistry-driven interactions that the authors believe are critical for habitability. Thus so-called coupled chemistry-climate models (CCM) are needed to factor in how an atmosphere responds to the star’s radiation.

The study takes both ultraviolet radiation (UV) from the star and the rotation of the planet into consideration, noting how UV affects gases like water vapor and ozone. Says Chen:

“3D photochemistry plays a huge role because it provides heating or cooling, which can affect the thermodynamics and perhaps the atmospheric composition of a planetary system. These kinds of models have not really been used at all in the exoplanet literature studying rocky planets because they are so computationally expensive. Other photochemical models studying much larger planets, such as gas giants and hot Jupiters, already show that one cannot neglect chemistry when investigating climate.”

Image: An artist’s conception shows a hypothetical planet with two moons orbiting within the habitable zone of a red dwarf star. Credit: NASA/Harvard-Smithsonian Center for Astrophysics/D. Aguilar.

The researchers simulate the atmospheres of synchronously-rotating planets (i.e., with one side always facing the star) at the inner edge of the habitable zones of both K- and M-class stars. using numerical simulations of climate coupled with photochemistry and atmospheric chemistry through their 3D CCM. They find that the thin ozone layers produced on planets around active stars can render an otherwise habitable planet (in terms of surface temperatures) hazardous for complex life, as there is insufficient ozone to block UV radiation from reaching the surface.

Active photochemistry is a crucial issue, for according to Chen and team, planets can also lose significant amounts of water due to vaporization. Added to the ozone issue, we find boundaries beyond which a planet habitable in terms of liquid water on the surface is rendered lifeless. Understanding stellar activity becomes a predictive tool for gauging which M-dwarfs are most likely to merit precious telescope time for future missions looking for biosignatures. More active M-dwarfs appear far less likely to host life-bearing planets. From the paper:

…we find that only climates around active M-dwarfs enter the classical moist greenhouse regime, wherein hydrogen mixing ratios are sufficiently high such that water loss could evaporate the surface ocean within 5 Gyrs. For those around quiescent M-dwarfs, hydrogen mixing ratios do not exceed that of water vapor. As a consequence, we find that planets orbiting quiescent stars have much longer ocean survival timescales than those around active M-dwarfs. Thus, our results suggest that improved constraints on the UV activity of low-mass stars will be critical in understanding the long-term habitability of future discovered exoplanets (e.g., in the TESS sample…)

The effects of stellar UV radiation become a useful predictive tool as we narrow the target list. Vertical and horizontal winds in the upper atmosphere are strengthened as UV flux goes up. Moreover, the global distribution of ozone and hydrogen depends upon all these processes, which can affect the contrast between the dayside and nightside conditions under varying UV flux. The authors believe that only by bringing atmospheric chemistry into the picture of 3D modeling can we gauge whether a planet can attain true habitability and maintain it. Usefully, using their results, they show that both water vapor and ozone features could be detectable by instruments aboard the James Webb Space Telescope if we choose our targets carefully.

The paper is Chen et al., “Habitability and Spectroscopic Observability of Warm M-dwarf Exoplanets Evaluated with a 3D Chemistry-Climate Model,” in press at the Astrophysical JournaL (preprint).

Comments on this entry are closed.

I was imagining a tidally locked world losing its water due to vaporization. I’d think most of the water would freeze on the dark side and build up. Could it build up so much the planet became unbalanced, and flip hemispheres facing their sun? It would be an amusing event if it could happen.

I hope red dwarfs do have habitable zones. There is something romantic about a red sun and a civilization that could live, thrive, and evolve over a time frame of perhaps 30 trillion on a planet orbiting a small red dwarf. Since most stars are red dwarfs, establishing habitability around red dwarfs could be interesting.

Andrew Lepage has a very interesting post on the two recently planets orbiting Wolf 359. The bad news is that neither one is habitable. The good news is that there is still room for a potentially habitable planet orbiting in between them. I posted a comment on his Drew Ex Machina website asking him if either Carmines or SPIRu has the sensitivity to detect a 1 Earth mass planet in Wolf 359’s habitable zone . No reply as of yet. Check his post out. It is an excellent read.

I thought I felt my ears burning -) Here is the link to my latest piece on Wolf 359. While neither of the pair of planet candidates found in this system are potentially habitable, an Earth-size exoplanet orbiting in the HZ would have escaped detection and could still lurk in this system:

Sorry about the delayed response but I checked into your question about the ability of CARMENES and SPIRou to make useful radial velocity measurements of Wolf 359. I found that with the J mag of 7.1 for Wolf 359, CARMENES is capable of a radial velocity accuracy of 1 m/s with an integration time of

350 second. CARMENES easily can measure radial velocities with sufficient accuracy to detect Earth-size exoplanets in the HZ. I have yet to find the needed details on SPIRou but it appears it will also be capable of making useful observations of Wolf 359 as well. Of course the ultimate detection limits will depend on the magnitude and nature of the star’s jitter. Hope that answers the question!

Great! Now. based on the assumption that Carmines has been observing Wolf 359 for an extended period of time, two possible scenarios emerge. One is obvious: no evidence for an Earth mass planet in the HZ. However, that leads to the question: Why haven’t they published a paper confirming or refuting Toumi et al’s planets, with the above possible non-detection mentioned in the paper? Because of this I favor the second scenario: There IS evidence for a small planet in the HZ, but, because it is in RESONANCE with one of the above mentioned planets, it is extremely hard to tease out strong enough evidence as of now to publish and more observations will be needed.

I think it is dangerous to attempt to infer anything meaningful about the lack of any published CARMENES results on Wolf 359. While it MIGHT mean there are no Earth-size exoplanets in the HZ, they have yet to publish anything about Wolf 359c either which would be readily detectable by them. Having only been up and running for three years (compared to 13 years for the HARPS/HIRES data set), the CARMENES team might not have sufficient data yet to publish any results or maybe noise created from jitter is causing some issues (not unexpected given the youth of Wolf 359) or any number of other plausible issues one could contrive. I learned quite some time ago not to read too much into the lack of published, peer-reviewed results.

Space Telescope Live tweeted this 22 hours ago:” I am looking at the star WOLF 359 with Space Telescope Imaging Spectrograph for Dr Christopher Michael Johns-Krull.” Dr Johns-Krull’s field of expertise is T Tauri stars, so I have absolutely no idea why he would target Wolf 359 with STIS. Any ideas?

UV emissions and near red frequencies are the least problematic of the issues with M class stars. Even if the photochemistry works out, any atmosphere is going to escape dude to proton flux while any macromolecules are going to be disassociated by xrays.

The real problem with M class stars is their inherent magnetic instability, and not planetary tidal locking in orbits where the water phase diagram looks familiar under earth like pressure and temperature conditions.

It depends on the thickness or amount of atmosphere. If the exoplanet has one Earth atmosphere, then the night side would be much colder. We would have one large Hadley cell with a tidally locked planet and no rotation with the winds blowing from the night side into the lower pressure, daylight side. If the atmosphere was two or several bars or Earth atmospheres, then a greenhouse effect, then the night side might be warmer.

The problem with all tidally locked planets is that the Hill radius prevents it from having any moons and without a moon, there can be no magnetic field since the liquid iron core’s charged particles have to move in circles from a fast rotation to generate a magnetic field like Earth’s rotation does. There is still hope that maybe life might develop near the terminator between day and night were the radiation from the star is less intense and then the life might live near the terminator, but this is asking a lot from life. It might have to adapt in some way or live underground if it needed to leave that area.

If we seeded one of those tidally locked planets with life it would survive, but if there is any native life and it was restricted it might be hard to detect biosignature gases unless life somehow adapted to the dark side of the planet and the atmosphere would reflect the large scale release of biogases. I still don’t think there is any life on such exoplanets, and a lack of biosignature gases in the atmospheric spectra would support a too hostile environment for life, but the only way to completely rule it out would be to go there and land on the planet and look for it with probes or human exploration.

It is possible to have a magnetic field without a moon or even in a tidally locked slowly rotating planet. As long as you have a liquid outer iron:nickel core which is convective. Key to this in turn is a convective mantle which helps transport heat away from the core keeping it partially liquid. Also offering plate tectonics , vulcanism and secondary atmosphere outgassing to boot.

By way of comparison Venus doesn’t have a significant magnetic moment. This is because it’s mantle is locked in by a ‘stagnant lid’ crust with no tectonics and no mantle convention – likely due to its runaway greenhouse past history giving rise to total desiccation. No water, no lubricated mantle and no convection. Mantle or core, despite the latter being similar in size and nature to
Earth’s. See ‘Characterising Exoplanet Habitability’ , Kopparapu et al, 14th Nov 2019 Astro-ph. Great read all round.

It is also possible for tidally locked planets to have moons though generally gas giants given the Hill radius gravitational sphere of influence you refer too ( as well as the Roche limit ). See ‘Exomoons in the habitable zones of M dwarfs’ – Martinez-Rodriguez et al ,26th Oct 2019 Astro-ph

Wondering why Venus still had an atmosphere without a magnetosphere, I’d read that friction between solar wind and a robust ionosphere can create a magnetic field, no convection or tectonics required.

But that might not be a protective magnetic field. Runaway greenhouse conditions could just replenish atmosphere through non-tectonic volcanism.

Venus-like might be a better exoplanet norm anyway. Easier to reform a hot rocky planet with too much atmosphere, than a cold one with not enough?

“without a moon, there can be no magnetic field ”

I think that is not right: the magnetic field of the earth is generated by electric currents, in turn caused by the convective motion (convection currents) of molten iron in the Earth’s outer core, and these convection currents are caused by internal heat (geo-dynamo). The internal heat is caused both by residual heat from the Earth’s formation and, probably more important, from radioactive decay, foremost Uranium and Thorium.

The moon seems to become less and less important anyway, over the years: formerly it was often suggested that the moon was particularly important to stabilize the axial tilt of the Earth and in fact this is still often quoted.
However, even this has been seriously questioned in recent years, e.g. by Lissauer, Barnes and Chambers (Obliquity variations of a moonless Earth 2011), quote: “We find that (…) the obliquity remains within a constrained range, typically 20–25 in extent,
for timescales of hundreds of millions of years. (…) A large moon
thus does not seem to be needed to stabilize the obliquity of an Earth-like planet on timescales relevant to the development of advanced life.”.

I still think they’d all be Venus-style planets because of the long Pre-Main Sequence Phase with heightened luminosity, but maybe the water can come after that from comets, etc.

Or from the planet’s core where it can have been sequestered since formation from a volatile rich accretion disk .

A normative overabundance of exposed, cold, dry, Andean mummy-planets, everywhere we look. It’s demoralizing — at least, to hopes of encountering other conversationally intelligent species.

But I’m coming to appreciate what that could mean in terms of ethically unencumbered real estate. Native terrestrial magnetospheres may be rare, but for a spacefacing technological species magnetospheres will just be a school of architecture:

We’re actually on a pretty tight clock here, circling this late middle-aged star. Even our magnificent natural magnetosphere won’t save us forever. And if we don’t thrive I doubt there’ll be time for Earth to raise another species like ours from scratch.

Experience with Mars could equip Homo sapiens to breathe first life into a wealth of mummy planets comfortably situated around longer-lived stars. In what appears to be an otherwise depressingly sterile universe, that’s a silver lining I could live with.

You have to see this paper for what it is . A pragmatic approach to identifying and then targeting those planets orbiting in the habitable zones of less active ( at this current time and presumably for some billions of years before ) M dwarfs. Then using this to allocate available resource.

Observing time on JWST is going to be at an absolute premium and whilst finding out that a planet has had its atmosphere stripped is scientifically useful it’s rather a dull outcome and WOULD NOT be able to be extrapolated to all M dwarf planets. The ELTs too, even with their huge capabilities and much longer lives . The kind of cross correlation high dispersion spectroscopy / high contrast imaging techniques they would employ to look for biosignatures will be both hugely labour intensive and expensive ON TOP of observing time on the scope.

What this article does not do is rule out potentially habitable planets around M dwarfs . Even those orbiting active, atmosphere stripping stars , can keep a large volatile content sequestered in their mantles to replenish vulcanism driven secondary atmospheres in more favourable times. Or undergo volatile injection via late cometary bombardment . Or migrate in late from beyond the ice line as appears to have been the case with the Trappist-1 planets. Many of which have already been shown by Hubble spectrophotometry to have maintained a substantial volatile fraction ( which is of course not necessarily indicative of having atmospheres on its own – hence the prioritisation for JWST ) . Trappist-1, though much less active now, being a fully convective late M dwarf must have had an extended pre and most main sequence period of high activity. If some or any of its seven planets have significant atmospheres despite this, such results WOULD be 1/ hugely interesting 2/ highly indicative and 3/ able to be extrapolated .

Keep a thick primordial or secondary atmosphere – perhaps with an ocean too – volatiles anyway – and you have two very efficient ways of transferring heat from star facing to non facing hemispheres . More than capable of preventing atmospheric collapse on the “cold” side even in a fully synchronised planet. Bearing in mind too that gravitational interactions with other planets , especially if closely packed as with the Trappist-1 system, might induce 3:2 or 2:1 resonances even in tidally locked planets. Gravitational tides induced by thick atmospheres have also been shown by Leconte et al ( 2015) to help M dwarf planets resist synchronicity over Giga years.

I have to say that it is exciting to see 3-D atmospheric modelling coming into its own . Not just in screening potential targets , it represents a big step forward in describing various exoplanetary atmospheres . This will be central to the interpretation of the ground based high dispersion spectroscopy utilised to characterise exoplanet atmospheres by the ELTs.

Related interesting paper about planets with multiple host stars, a survey:
https://www.uni-jena.de/en/191113_Mehrfachsternsysteme_en.html

What is the definition of, or criteria for ‘active’ M dwarf?
Aren’t most M dwarfs active, in UV output and flaring?

This seems like another confirmation (plus flaring and tidal locking), that M dwarfs are not the most suitable class of stars for planets with (complex) life.

Gee, how quickly the tide changes! Oh, as I said before in the last article on Ariel these planets in the compact M-dwarfs are constantly being bombarded by comets at a much higher rate then any thing in our solar system. Short orbit period – in close to the red dwarf makes for many more comet encounters, think about it!
Now, just to make it more confusing, the M-dwarfs on the low end M5-M9 are fully convective but have a mass 80 or more times Jupiter’s mass but are close to the same size as Jupiter. This means their density is also much higher, but they are also having many more large impacts from comets and asteroids. Remember the impacts on Jupiter in 1994 from a huge comet?
These stars are a different beast compared to our Sun and the dynamics and flaring work differently then ours. One of the unusual aspects of low end red dwarfs is the carbon based molecules like Methane in their atmosphere. Plus Titanium-oxide compounds, with other metals that would fuel magneto-hydrodynamic (MHD) processes in flares in the powerful magnetic fields around and in M-dwarfs. Remember the ink black impact spots from when the chain of comets crashed into Jupiter?
Well take a guess, the comets and asteroids are seeding the red dwarfs and causing the active flaring rates. So as these system age there is less and less comets and asteroids impacts just as in our solar system. So the older stars have more or less stopped flaring. Like I said these late red stars are a different beast. O’ don’t forget that brown dwarfs also give out huge UV flares, so go figure!

“The depletion of the Ozone layer from UV flaring around active M-dwarfs may not be as bad as indicated in the article, though. Recently an article mentions the higher impact rates from comets around these tightly wound M-dwarf planetary systems. The early active period of M-dwarfs may be countered in later life by the addition of large quantities of water from the much higher cometary impact rates. This would resupply the Ozone layer along with the surface based water supply. It will not be long till we find out if this question is so, the JWT should show if the Ozone layers are present around the numerous nearby M-dwarfs planets.

Cometary impactors on the TRAPPIST-1 planets can destroy all planetary atmospheres and rebuild secondary atmospheres on planets f, g, h.
“The TRAPPIST-1 system is unique in that it has a chain of seven terrestrial Earth-like planets located close to or in its habitable zone. In this paper, we study the effect of potential cometary impacts on the TRAPPIST-1 planets and how they would affect the primordial atmospheres of these planets. We consider both atmospheric mass loss and volatile delivery with a view to assessing whether any sort of life has a chance to develop. We ran N-body simulations to investigate the orbital evolution of potential impacting comets, to determine which planets are more likely to be impacted and the distributions of impact velocities. We consider three scenarios that could potentially throw comets into the inner region (i.e within 0.1au where the seven planets are located) from an (as yet undetected) outer belt similar to the Kuiper belt or an Oort cloud: Planet scattering, the Kozai-Lidov mechanism and Galactic tides. For the different scenarios, we quantify, for each planet, how much atmospheric mass is lost and what mass of volatiles can be delivered over the age of the system depending on the mass scattered out of the outer belt. We find that the resulting high velocity impacts can easily destroy the primordial atmospheres of all seven planets, even if the mass scattered from the outer belt is as low as that of the Kuiper belt. However, we find that the atmospheres of the outermost planets f, g and h can also easily be replenished with cometary volatiles (e.g. ∼ an Earth ocean mass of water could be delivered). These scenarios would thus imply that the atmospheres of these outermost planets could be more massive than those of the innermost planets, and have volatiles-enriched composition.”
https://arxiv.org/abs/1802.05034

Susceptibility of planetary atmospheres to mass loss and growth by planetesimal impacts: the impact shoreline.
“This paper considers how planetesimal impacts affect planetary atmospheres. Atmosphere evolution depends on the ratio of gain from volatiles to loss from atmosphere stripping f_v for constant bombardment, atmospheres with f_v1. An impact outcome prescription is used to characterise how f_v depends on planetesimal impact velocities, size distribution and composition. Planets that are low mass and/or close to the star have atmospheres that deplete in impacts, while high mass and/or distant planets grow secondary atmospheres. Dividing these outcomes is an fv=1 impact shoreline analogous to Zahnle & Catling’s cosmic shoreline. The impact shoreline’s location depends on assumed impacting planetesimal properties, so conclusions for the atmospheric evolution of a planet like Earth with f_v

1 are only as strong as those assumptions. Application to the exoplanet population shows the gap in the planet radius distribution at

1.5R_earth is coincident with the impact shoreline, which has a similar dependence on orbital period and stellar mass to the observed gap. Given sufficient bombardment, planets below the gap would be expected to lose their atmospheres, while those above could have atmospheres enhanced in volatiles. The level of atmosphere alteration depends on the total bombardment a planet experiences, and so on the system’s (usually unknown) other planets and planetesimals, though massive distant planets would have low accretion efficiency. Habitable zone planets around lower luminosity stars are more susceptible to atmosphere stripping, disfavouring M stars as hosts of life-bearing planets if Earth-like bombardment is conducive to the development of life.”
https://arxiv.org/abs/1910.10731

The question is whether the super-Earths and sub-Neptunes would have a thick organic goo covering it. Trappist 1c may be an example of this, with the hydrogen atmosphere depleted. The other factor that would be effecting all planets in the M-dwarf family would be a much faster moving Lithosphere similar to our oceanic crust. The higher impact rates from comets and asteroid would cause higher mixing rates for the Asthenosphere and upper Mantle with a higher content of water.
This could indeed make for a completely different type of crust with much higher concentration of carbon and organic matter. The late impacts could also give rise to seamounts and volcanic eruptions, see this https://www.gns.cri.nz/Home/News-and-Events/Media-Releases/largest-caldera

While the possibility for *native* ETI in red dwarf systems may be problematic, there is nothing saying that non-native species with interstellar capabilities could not be inhabiting such systems for settlement, resources, etc. Especially since they may otherwise be unoccupied. I wish these astronomers would seriously consider that possibility.

Most M dwarf exoplanets might have considerable atmospheres, but their surfaces also might be sterile due to the continual EUV and X rays. A magnetic field could block or deflect some solar wind, but a tidally locked exoplanet will never have a magnetic field since there is no rotation to spin the liquid core and make charged particles move in circles. Tidal forces could certainly help with volcanism and replenish an atmosphere. If there are not any biosignature gases like oxygen and methane I won’t be surprised. We still have to study their spectra and also we are only scratching the surface of how many potential exoplanets are out there.

Maybe with the extremely large telescope and other missions like JWST we could look at only G class stars or design a search to look at them and locate a good portion of those stars if we can’t find any biosignature gases. In other words keep long term watch of only G class star systems instead of just looking for what we can see in short term.

## Modeling an Astrospheric Current Sheet

Kay’s team modeled the effects of theoretical CMEs on the red dwarf V374 Pegasi, using a tool Kay developed for CME modeling called ForeCAT. They found that the strong magnetic fields of the star produce CMEs that can reach the so-called Astrospheric Current Sheet, where the background magnetic field is at its minimum. The same effect occurs with our Sun, when solar CMEs are deflected by magnetic forces toward the minimum magnetic energy.

At the Sun, the Heliospheric Current Sheet — the local analog to a different star’s Astrospheric Current Sheet — is a field that extends along the Sun’s equatorial plane in the heliosphere and is shaped by the effect of the Sun’s rotating magnetic field on the plasma in the solar wind. The HCS separates regions of the solar wind where the magnetic field points toward or away from the Sun.

Let’s dwell on that for a moment. Here’s what a NASA fact sheet has to say about the Heliospheric Current Sheet:

The sun’s magnetic field permeates the entire solar system called the heliosphere. All nine planets orbit inside it. But the biggest thing in the heliosphere is not a planet, or even the sun. It’s the current sheet — a sprawling surface where the polarity of the sun’s magnetic field changes from plus (north) to minus (south). A small electrical current flows within the sheet, about 10 −10 A/m². The thickness of the current sheet is about 10,000 km near the orbit of the Earth. Due to the tilt of the magnetic axis in relation to the axis of rotation of the sun, the heliospheric current sheet flaps like a flag in the wind. The flapping current sheet separates regions of oppositely pointing magnetic field, called sectors.

Image: The Heliospheric Current Sheet results from the influence of the Sun’s rotating magnetic field on the plasma in the interplanetary medium (solar wind). The wavy spiral shape has been likened to a ballerina’s skirt. The new work uses a software modeling package called ForeCAT to study interactions between CMEs and the Astrospheric Current Sheet around the red dwarf V374 Pegasi. Credit: NASA GSFC.

Kay and team have modeled the Astrospheric Current Sheet expected to be found around M-dwarfs like V374 Pegasi. The authors find that upon reaching the ACS, CMEs become ‘trapped’ along it. Planets can dip into and out of the ACS as they orbit. A CME moving out into the Astrospheric Current Sheet around an M-dwarf can cancel out a habitable zone planet’s local magnetic field, opening the world to devastating flare effects. The upshot:

We expect that rocky exoplanets cannot generate sufficient magnetic field to shield their atmosphere from mid-type M dwarf CMEs… We expect that the minimum magnetic field strength will change with M dwarf spectral type as the amount of stellar activity and stellar magnetic field strength change, and that early-type M dwarfs would be more likely to retain an atmosphere than mid or late-type M dwarfs.

The authors calculate that a mid-type M-dwarf planet would need a minimum planetary magnetic field between tens to hundreds of Gauss to retain an atmosphere, values that are far higher than Earth’s (0.25 to 0.65 gauss). CME impacts as numerous as five per day could occur for planets near the star’s Astrospheric Current Sheet. The only mitigating factor is that the rate decreases for planets in inclined orbits. The paper notes:

The sensitivity to the inclination is much greater for the mid-type M dwarf exoplanets due to the extreme deflections to the Astrospheric Current Sheet. For low inclinations we find a probability of 10% whereas the probability decreases to 1% for high inclinations. From our estimation of 50 CMEs per day, we expect habitable mid-type M dwarf exoplanets to be impacted 0.5 to 5 times per day, 2 to 20 times the average at Earth during solar maximum. The frequency of CME impacts may have significant implications for exoplanet habitability if the impacts compress the planetary magnetosphere leading to atmospheric erosion.

So we have much to learn about M-dwarfs. In particular, how accurate is the ForeCAT model in developing the CME scenario around such stars? As we examine such modeling, we have to keep in mind that magnetic field strength will change with the type of M-dwarf we are dealing with. Based on this research, only early M-dwarfs are likely to maintain an atmosphere.

The paper is Kay, Opher and Kornbleuth, “Probability of CME Impact on Exoplanets Orbiting M Dwarfs and Solar-Like Stars,” accepted at the Astrophysical Journal (preprint).

Comments on this entry are closed.

The ebb and flow of M dwarf star suitability for habitability. First one way then the other. This paper even acknowledges that for the same mid M dwarf star should a “hab zone” planet have even a small inclination to the equatorial plane of the star ( where the CME concentration is worst ) then the CME rate could drop from five plus per day to less than one every other day. Regardless of magnetic field interaction. With M dwarfs age for a start is critical too in terms of CME activity dropping off , particularly for earlier M dwarfs at around 1 billion years . CME activity peaks for M6 dwarfs , but even stars of this class like Barnard’s star display markedly reduced activity at around 5 billion years . With expected main sequence lifetimes of a trillions of years or so . Even the biggest most quiescent M dwarfs ( which are not fully convective and thus lose their potent and chaotic magnetic fields much sooner than the star cited here, and with greater luminosity can push that hab zone out as far as 0.4 AU ) lasting ten times as long as the Sun.

Although as we all know, M dwarfs have an extended active pre main sequence period too, from work done on the TRAPPIST-1 planets it also looks as if these are formed beyond the “ice line ” before migrating in from distance much later , thus avoiding the worst of the stellar activity prior to entering the proximal “habitable zone” . Given Kepler has shown that M dwarfs have a preference for forming Earth sized terrestrial planets almost independent of stellar “metallicity ” ( and thus age ) , and that these stars represent 70 % of all stars , I think it likely that at least some will harbour life of some sort. It may be easy to put forwards obstacles to this , but it is equally easy to envisage plenty of circumstances in which these could be bypassed .

Role on TESS, PLATO,JWST and the ELTs!

excellent study, since it confirms my own thoughts about little red suns with a few scorched rocks whizzing around them in 9-day “years”. If we want to find interesting life forms, we’ll find them on habitable zone planets moving around yellow suns in a dignified manner, say, 250-500 day years. Sara Seager is wasting her life. So sad.

‘Sara Seager is wasting her life. So sad.’

The seeking of knowledge is not wasted time, what is sad is seeking time to waste.

There is at least one planet (f) around TRAPPIST-1 (a M-dwarf) that has all the characteristic of an ocean planet with a rocky core and a dense atmosphere. This counter-example contradicts all the theories – including the one presented in this article – saying that the frequent flares from M stars should completely erode the atmosphere of any tidally-locked planet to the point where no life can ever exist on its surface.

Therefore it’s too early to rule out completely all M-dwarves in our search for extraterrestrial life.

Scientists used to think life could not exist at the bottom of Earth’s oceans or in boiling hot acidic springs, but guess what? And certain microbes were found swimming in the reactor pools of nuclear power plants that were able to handle radiation levels that were over three thousand times beyond what a human could tolerate before being fried into bacon.

So maybe life cannot exist on worlds circling red dwarf suns, but as I noted above we have been surprised before. And oh yeah, it was quite recent that astronomers realized exoplanets can have stable orbits around binary stars – just another example.

The accretion theory of planetary production itself has only gained precedence in the last thirty years or so. Before that many plausibly believed that the solar system had been created by a “passing star” ( something that still has traction in numerous other theories ) dragging out mass from the Sun that then condensed into planets . Hot Jupiters more recently defied all planetary formation simulations as have Super Earths and mini Neltunes more recently still . I think it’s fair to say that once there is detailed spectroscopic characterisation of temperate terrestrial planets , even around M dwarfs , then we are in for yet more surprises .

Omniscient are you? How lucky for you.

Certainly not, but hopefully lucky enough to see some interesting exoplanetary atmospheric spectroscopy within the next decade .

On the one hand we have M-dwarf star’s CMEs potentially eroding a planets atmosphere.

On the other hand we have evidence for heaps of mini Neptune / large super Earths whose atmospheres are thought to be too thick to be habitable.

I’m beginning to think that the most likely “habitable” planet around M-dwarfs is going to be a large super Earth whose previously thick atmosphere has been stripped down to something more life friendly.

My worry with this scenario would be that the heat of the ‘evaporation’ process would create conditions that would destroy organic molecules before they could form complex life.

On the plus side there will be plenty of room for intelligent beings to occupy.

The heat of the evaporation process just shifts the habitable zone out a little.

Nice to know that, while the necessary field to protect against the CME’s is higher than plausible for a natural field, it’s quite feasible to supply technologically. So if we did find a suitable planet, we could keep it that way.

If say we had an Earth mass and solar irradiance equivalent at the start of the contraction phase by the end of it a billion years later the planet would be in the deep freezer. It will most likely keep a magnetic field due to lower chance of tidal locking and could have life under the ice, this life could emerge much, much later as the star goes through its main sequence and gets hotter.

Now if say we had a large planet that ‘evaporates’ to an Earth mass and solar irradiance one it would most likely have no magnetic field due to tidal locking and no organics required for life due to thermal/chemical destruction.

Red Dwarfs are looking more and more like life producing stellar dead zones at least for complex life.

Put a substantial terrestrial class moon in orbit around a Neptune of Mini Neptune planet ( both of which have shown to be relatively frequent around M dwarfs ) and it tidally locks to the planet not the star . It may thus rotate quickly enough to stir up an atleast partially protective magnetic field from its outer convective core ( which could create a reasonable field in its own right if the mantle is suitably convective too) .

Given the high absorption of M dwarf near infrared radiation by even 0.5 bar CO2 atmospheres , there is also potential to reduce the required instellation below even 25 % Earth thus pushing the habitable zone further out perhaps even beyond 0.4 AU for an M0 star . ( further still for a hydrogen rich “habitable evaporated core ” planet ) Thus bringing in the inverse square law to offer additional mitigation of CMEs etc. Stretch into late K class and it could even go beyond 0.5 AU and out if tidal locking territory , or not for billions of years anyway . ( Leconte et al (2015 ) have also shown that substantial CO2 atmospheres can resist orbital synchronisation in their own right also )

Put all these together and we have a good deal of protection against anything nasty coming from the host star without even considering any mitigation provided by the nature of said star itself. ( larger mass, greater age / lower rotation and consequent magnetic field etc )

‘Put a substantial terrestrial class moon in orbit around a Neptune of Mini Neptune planet…’

Unfortunately a moon around these close in planets would be unstable as the star facing LaGrange point is quite close to the planet.

Not necessarily , especially not for any hab zone planet/moon sitting in the outer hab zone of larger M dwarfs ( and smaller K dwarfs thinking of the wider definition of ” red dwarf “) . Where the gravitational zone of influence of any planet orbiting a larger star , the Hill radius , r , = a x cube root (m/3M ) with a= the planetary semi major axis , m= planetary mass and M = stellar mass . Even the hot Super Earth CoRoT-7b orbiting at just 0.017 AU from a 0.91 Msun star has a Hill radius of 61000 Kms , six times the planetary radius . Gravitational tidal heating provided from a larger planet might even help extend the hab zone for an erstwhile moon even further .

Here is a neat quick hill radius calculator, from it we can see there is not a lot of room between the Hill and the Roche limit for some stable moon systems.

Nice find. Thanks . Ever the optimist I still think there is latitude for stable terrestrial moon around the Mini-“maxi “Neptunes in the outer hab zones of early M and late K “red dwarfs ” at the least .

Ironically when exomoons are finally discovered it’s likely to be around red dwarfs ,via transit photometry as its sensitivity increases most likely up to and during an extended PLATO mission. TESS hab zone planets will likely be too close in to hold onto a moon as per Hill/Roche as you point out , though if they’re there it should be easier to tease their signatures out of the deeper transits associated with larger TESS planets .

We’re currently at that twixt and between stage were theory and simulation is running ahead of practical observation sensitivity .

So why do the Trappist1 planets in the habitable zone have low densities?

They formed from volatile rich accretion disk outside of the “ice line” before migrating inwards at a much later time . Thus avoiding a lot of the worst pre and post main sequence stellar activity of what is likely to have been lively star even by M dwarf standards.

It must be frustrating to discover that the exoplanets that are the easiest for us to find, are the ones that are the least likely to harbor life. I wouldn’t advise giving up, however.

There’s a hell of a lot of them though , with many not nearly as active as the example star cited here either through age or mass or both. With a propensity for forming Earth sized terrestrial planets too. If you count “late” K class stars as “red dwarfs” as well ( as is often done ) then things improve further still, with potentially up to 80% of all stars falling in this class.

And we still keep assuming that the types of ETI we have the best chance of detecting are still living on dirty old planets.

Just like the rich humans on this planet, the really advanced aliens are off somewhere in the really nice sections of the galaxy, probably living in structures of their own making and not very big on advertising their existence. Or perhaps they ARE the structures they built.

We need to think outside the box even if it leads us to more dead ends. SETI still keeps focusing on ideas going back to Project Ozma from 1960, namely that aliens not too different from us are sitting on Earthlike planets circling yellow dwarf suns broadcasting away because they want to make contact because that is what an altruistic scientist would do.

Well if such beings do exist and they are conducting such METI projects, they certainly are not being very obvious to us. Then again look at the history of human SETI and you will see that it probably would take someone doing some massive, constant transmitting right at our Sol system to get our attention.

No, we keep assuming that we will find ETI everywhere that we look.

Ashley Baldwin I wouldn’t assume the theory that the TRAPPIST-1 planets had to form outside the snowline and migrate inward is a general principle of the smaller red dwarf stars. It is highly speculative since it says that the planets had to form sequentially, but not all at the same time like planetary accretion theory.

I like the idea of the migrating millimeter and centimeter sized particles, but since the force of gravity is stronger than thermal emission, these sized particles would not have to migrate to the ice line to come together to form a planetesimal. It sounds like the theory says that these sized particles have to be cleared out by thermal emission from the life belt and closer to the star than the life belt, the water vapor line where the temperature is high enough for water to only be in a vapor. It’s not a bad idea if that is what is meant.

With planetary accretion theory, the planetesimals and the star form at the same time so by the time the star is born, there already are planetesimals the size of our Moon. I am not an expert on planetary accretion theory, but I don’t think that thermal emission plays a significant role in the formation of planetesimals before the star is born or even after. I could be wrong of course but there still is the problem of ultra violet light It sounds like the TRAPPIST-1 migration theory says that the millimeter and centimeter particles could only accumulate inside the snow line where water is frozen. They wouldn’t need thermal emission to move the particles out of the life belt, the liquid water line, or water vapor line where it is too hot and close to the star for water to exist as a liquid.

Accretion theory suggests that planets could just as well form very close to a red dwarf. I could be wrong, and maybe things are different with smaller stars. It seems logical with a smaller star and less gravity, planets would form nearer to it. There still is the problem of the space weather though, the x-rays, ultra violet, and CME’s, and cosmic rays.

Technological limitations of both transit photometry and Doppler spectroscopy have so far favoured discovery of close in planets around smaller M dwarfs with small related “hab zones ” like Proxima b and the TRAPPIST planets . It will interesting when , as seems likely , terrestrial planets are discovered in the hab zones of larger M dwarfs extending out towards 0.5 AU . Debra Fischer’s 100 Earths project is due to start later this year when the EXPRES high res spectroscope becomes operational on the Discovery telescope . Given its chromospheric activity reducing software it is optimised for discovering just such planets . TESS should push the hab zone discovery field out a bit and PLATO will take it to its maximum.

What would be the optimal design for a large space station that could comfortably play host to terrestrial life but be in orbit around a burping red dwarf star? It seems like these things are orbited by lots of good construction material. It might not generate its own lifeforms, but I bet we could make a cozy home there.

I assume that silicon solar cells would degrade pretty fast, but the station would need some robust and hopefully efficient method of generating power. Could coronal mass ejections themselves be harvested by giant antennas and capacitors?

Stellar Chemical Clues As To The Rarity of Exoplanetary Tectonics

Press Release – Source: astro-ph.EP

Posted July 5, 2017 1:58 PM

Earth’s tectonic processes regulate the formation of continental crust, control its unique deep water and carbon cycles, and are vital to its surface habitability.

A major driver of steady-state plate tectonics on Earth is the sinking of the cold subducting plate into the underlying mantle. This sinking is the result of the combined effects of the thermal contraction of the lithosphere and of metamorphic transitions within the basaltic oceanic crust and lithospheric mantle. The latter of these effects is dependent on the bulk composition of the planet, e.g., the major, terrestrial planet-building elements Mg, Si, Fe, Ca, Al, and Na, which vary in abundance across the Galaxy.

We present thermodynamic phase-equilibria calculations of planetary differentiation to calculate both melt composition and mantle mineralogy, and show that a planet’s refractory and moderately-volatile elemental abundances control a terrestrial planet’s likelihood to produce mantle-derived, melt-extracted crusts that sink. Those planets forming with a higher concentration of Si and Na abundances are less likely to undergo sustained tectonics compared to the Earth.

We find only 1/3 of the range of stellar compositions observed in the Galaxy is likely to host planets able to sustain density-driven tectonics compared to the Sun/Earth. Systems outside of this compositional range are less likely to produce planets able to tectonically regulate their climate and may be inhabitable to life as we know it.

Cayman T. Unterborn, Scott D. Hull, Lars P. Stixrude, Johanna K. Teske, Jennifer A. Johnson, Wendy R. Panero

Comments: Submitted. 18 pages, 7 figures, 1 Table

Subjects: Earth and Planetary Astrophysics (astro-ph.EP)

Cite as: arXiv:1706.10282 [astro-ph.EP] (or arXiv:1706.10282v1 [astro-ph.EP] for this version)

[v1] Fri, 30 Jun 2017 17:31:51 GMT (1111kb,D)

Press Release – Source: astro-ph.EP

Posted July 10, 2017 8:19 PM

The discovery of exoplanets has both focused and expanded the search for extraterrestrial intelligence.

The consideration of Earth as an exoplanet, the knowledge of the orbital parameters of individual exoplanets, and our new understanding of the prevalence of exoplanets throughout the galaxy have all altered the search strategies of communication SETI efforts, by inspiring new “Schelling points” (i.e. optimal search strategies for beacons).

Future efforts to characterize individual planets photometrically and spectroscopically, with imaging and via transit, will also allow for searches for a variety of technosignatures on their surfaces, in their atmospheres, and in orbit around them. Even in the near-term, searches for new planetary systems might even turn up free-floating megastructures.

Comments: 9 page invited review

Subjects: Earth and Planetary Astrophysics (astro-ph.EP)

Cite as: arXiv:1707.02175 [astro-ph.EP] (or arXiv:1707.02175v1 [astro-ph.EP] for this version)

[v1] Fri, 7 Jul 2017 13:55:03 GMT (13kb,D)

Radio Exploration of Planetary Habitability: Conference Summary

Press Release – Source: astro-ph.EP

Posted July 10, 2017 8:18 PM

Radio Exploration of Planetary Habitability was the fifth in the series of American Astronomical Society’s Topical Conference Series.

Notable aspects of the conference included the interdisciplinary nature of both the topics and the intellectual breadth of the participants, the diversity of approaches to studying this topic presented by recent discoveries and of the participants themselves, the expanding meaning of the topic of “star-planet interactions,” and the expectation of an increasingly statistical approach to the topic.

Potential areas of future research include the actual extent to which planetary magnetic fields shield planetary atmospheres the planetary dynamo process itself, particularly once multiple extrasolar planetary magnetic fields are confirmed and “planet-star interactions.”

A major major topic of the conference concerned observational opportunities, highlighted by a number of new or upcoming, specialized observatories to observe exoplanets especially at radio wavelengths. This article summarizes these main points of the conference and expands briefly upon these potential avenues for future investigation. A future meeting on this topic, given the variety of data sets being generated over the next few years, is warranted.

T. Joseph W. Lazio (JPL, CIT), A. Wolszczan (Penn. State Univ.), M. Güdel (Univ. Vienna), Rachel A. Osten (STScI), Jan Forbrich (Univ. Vienna), M. M. Jardine (Univ. St. Andrews), P. K. G. Williams (CfA)

Comments: Five pages conference Web site: this http URL

Subjects: Earth and Planetary Astrophysics (astro-ph.EP) Instrumentation and Methods for Astrophysics (astro-ph.IM) Solar and Stellar Astrophysics (astro-ph.SR)

Cite as: arXiv:1707.02107 [astro-ph.EP] (or arXiv:1707.02107v1 [astro-ph.EP] for this version)

[v1] Fri, 7 Jul 2017 10:17:07 GMT (134kb)

Seemingly strange radio signals from a red dwarf star spark interest at Arecibo

## Contents

Red dwarf stars Ζ] are the smallest, coolest, and most common type of star. Estimates of their abundance range from 70% of stars in spiral galaxies to more than 90% of all stars in elliptical galaxies, Η] ⎖] an often quoted median figure being 73% of the stars in the Milky Way (known since the 1990s from radio telescopic observation to be a barred spiral). ⎗] Red dwarfs are either late K or M spectral type. ⎘] Given their low energy output, red dwarfs are never visible by the unaided eye from Earth neither the closest red dwarf to the Sun when viewed individually, Proxima Centauri (which is also the closest star to the Sun), nor the closest solitary red dwarf, Barnard's star, is anywhere near visual magnitude.

## Haikus on Thursday

### Rapidly-Rotating Lithium-Rich Giants Observed by Kepler

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Benjamin T. Montet
University of New South Wales

Several mechanisms to produce lithium-rich red giants have been proposed, including interactions between the red giant and a binary companions as the star reaches the tip of the red giant branch. One consequence of this model would be tidal spin-up of the red giant to the few km/s level. This level of rotation could in principle be detected in photometry from missions like Kepler and TESS, but signals longer than $sim 50$ days are typically overwhelmed by instrumental systematics and removed by the processing pipeline. Here, I will describe our data-driven reanalysis of Kepler pixel-level data that more accurately preserves slower signals in the data and our measurements of rotation periods of the lithium-rich giants in the Kepler field compared to lithium-normal giants and the implications for the formation of lithium-rich giants, as well as the potential to apply this method to other cool stars with up to $sim 100$-day rotation periods.

### Measuring the Solar Wind Angular Momentum Flux and Examining its Astrophysical Implications

science theme: The Sun and the Heliosphere
schedule: Thu, 13:00 (haiku)

(1) University of Exeter, UK (2) CEA Paris-Saclay, France

The rate at which the solar wind extracts angular momentum from the Sun has been predicted by theoretical models for many decades, and yet we lack a conclusive measurement from in-situ spacecraft. Complementary information can be gained by studying other Sun-like stars, as it is known that the rotation rates of Sun-like stars follow a tight relationship with age. This allows us to evaluate their angular momentum-loss rates, without any knowledge of stellar wind physics, and produce an independent prediction of the current solar angular momentum-loss rate to compare with numerical models and in-situ observations of the solar wind. I will discuss recent measurements of the solar wind angular momentum flux from Parker Solar Probe, in context with previous observations and model predictions. I aim to show that by better understanding the current solar angular momentum-loss rate we can further constrain rotation-evolution models of low-mass stars, which will subsequently influence how magnetic activity evolves during the late main sequence. It is thought that in future, a combination of observations from Parker Solar Probe and Solar Orbiter may lead to a better evaluation the solar wind angular momentum-loss rate.

### Determining the luminosity of the third dredge-up: The promise of Gaia

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Shreeya Shetye (1) Sophie Van Eck (1) Alain Jorissen (1) Stephane Goriely (1) Lionel Siess (1)
(1) Institute of Astronomy and Astrophysics, Universite libre de Bruxelles

Asymptotic Giant Branch (AGB) stars are low- to intermediate-mass stars in the late stages of stellar evolution. Due to their huge mass-loss and sheer number, these stars are major contributors of heavy (s-process) elements in the interstellar medium. AGB stars are ideal testbeds for understanding the mixing processes that take place in the stellar interiors. Despite its importance, the AGB is one of the least understood phases of stellar evolution, owing to the complex atmospheres and molecule-rich spectra of AGB stars. In this talk, I will present a novel method to determine the intricate atmospheric parameters of AGB stars. This method combines the recently released Gaia parallaxes and the high-resolution visible spectra with the state-of-the-art AGB models to derive the stellar parameters and abundances. With this method, we have been able to obtain observational constraints on the most crucial mixing process on the AGB namely, the third dredge-up. Furthermore, our investigation led to the discovery of low-mass AGB (initial mass

1 Msun) stars. This is an evidence for third dredge-up occurrence at low-mass and solar metallicity which was not accounted for by most AGB models. Finally, I will discuss how the derived AGB s-process abundances provide crucial constraints to the galactic chemical evolution models.

### Nonlinear models of fundamental mode pulsation in AGB stars

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Michele Trabucchi (1,2) Peter R. Wood (3) Nami Mowlavi (1) Giada Pastorelli (2,4) Paola Marigo (2) Leo Girardi (5) Thomas Lebzelter (6)
(1) Department of Astronomy, University of Geneva, Ch. des Maillettes 51, CH-1290 Versoix, Switzerland (2) Dipartimento di Fisica e Astronomia, Università di Padova, Vicolo dell’Osservatorio 2, I-35122 Padova, Italy (3) 3Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia (4) STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA (5) Osservatorio Astronomico di Padova – INAF, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy (6) Department of Astrophysics, University of Vienna, Tuerkenschanzstrasse 17, A-1180 Vienna, Austria

I present the results of the first systematic analysis of nonlinear pulsation as a function of stellar mass, luminosity and temperature in 1D hydrodynamic models of the envelopes of O-rich Asymptotic Giant Branch stars. It is found that large-amplitude fundamental mode pulsation induces a structural readjustment of the oscillating resulting in a shorter variability period with respect to linear predictions, leading to a substantial improvement in the agreement with observations. The grid of nonlinear pulsation models presented here is the first to allow for an accurate description of the fundamental mode period of Miras and related variable stars, and of their period-luminosity relation. I will also discuss the dependence of pulsational stability on physical and model parameters, and present exploratory analysis of the effects of varying chemical composition.

### TESSting Subgiant Physics

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Jamie Tayar the TESS-Subgiant collaboration
(1) Institute for Astronomy, University of Hawaii (2) various

There are still significant uncertainties in our understand of convection and rotation in evolved low-mass stars. To address this, we have spectroscopically, photometrically, and asteroseismically characterized a set of subgiant and lower red giant stars in the TESS southern continuous viewing zone, and combined them with previous samples from Kepler. I will show that when quantitatively compared, these stars can identify inaccuracies in the temperature and gravity evolution of currently used grids of models. They also show a coherent evolution of the internal rotation rate from the main sequence to the red giant branch and a significant contrast between the core and envelope rotation rates that is incompatible with several proposed theories of angular momentum transport in stellar interiors. Finally, I will end with a discussion of how we can continue to improve our understanding and what these changes mean for future studies of stellar evolution.

### The curious case of Betelgeuse

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Thomas Granzer (1) Klaus G. Strassmeier (1) Michael Weber (1) Andrea Dupree (2)
(1) Leibniz Institute for Astrophysics, Potsdam (2) Harvard–Smithsonian Center for Astrophysics

Since more than a decade, the AIP is monitoring $alpha$ Ori with its robotic spectroscopic facility STELLA/SES in Teide observatory, Tenerife along with its automated photoelectric telescope T7 in Fairborn observatory, Az. Additionally, we were awarded with exclusive two-band photometric data on Betelgeuse from the BRITE satellite consortium, covering the last seven seasons. In late 2019, Betelgeuse showed a rapid brightness decline, reaching an all-time low in Feb. 2020, followed by a quick re-brightening.

In this talk, I want to investigate the question whether this recent dip can be traced back to semi-periodic variability behavior or if it has been an outstanding event. In particular, I will show that periods and cycles found in the radial velocity data have a close match to Betelgeuse's photometric cycles.

### Probing Physics of Evolved Stars and their Short Period Planetary Companions with TESS

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Samuel Grunblatt
(1) American Museum of Natural History (2) Center for Computational Astrophysics, Simons Foundation

Despite the discovery of thousands of planets orbiting various stars thoughout our Galaxy, star-planet interaction remain poorly understood. In particular, late-stage star-planet interaction has remained particularly elusive, largely due to the difficulties in detecting planets around evolved stars. However, the Full Frame Image data from the TESS mission has provided 30-min cadence light curves of hundreds of thousands of evolved stars across the sky. Here I will introduce the newest planet discoveries around these evolved stars, including the shortest-period planet ever discovered around a red giant star. These particularly short period systems have been predicted to decay quickly, but the timescale of orbital decay is strongly dependent on the stellar structure in these subgiant and low-luminosity red giant stars, which has not yet been accurately modeled. We introduce new constraints on tidally driven period decay in these systems, tidal qualities of the evolved host stars studied here and provide updated boundaries between convective and radiative cores in subgiant and red giant stars. Finally, we consider additional constraints on star and planet structure and evolution that can be deduced from the larger population of planet candidates around evolved stars observed by TESS.

### First radio evidence for ubiquitous impulsive heating in the quiet solar corona

science theme: The Sun and the Heliosphere
schedule: Thu, 13:00 (haiku)

Surajit Mondal (1) Divya Oberoi (1) Ayan Biswas (1) Shabbir Bawaji (2) Ujjaini Alam (2) Arpit Behera (1) Devojyoti Kansabanik (1) Federico Fraschetti (3) Kathy Reeves(4)
(1) National Centre for Radio Astrophysics, Tata Institute of Fundamental Research (2) ThoughtWorks (3) University of Arizona (4) Smithsonian Astrophysical Observatory

It has a long standing problem as to how the solar corona can maintain its million K temperature, while the photosphere, which is the lowest layer of the solar atmosphere, is only at a temperature of 5800 K. A very promising theory to explain this is the “nanoflare” hypothesis. However, detecting these nanoflares directly is challenging with the current instrumentation as they are hypothesised to occur at very small spatial, temporal and energy scales. These nanoflares are expected to produce nonthermal electrons, which is expected to emit in the radio band. Due to its importance a lot of searches for these nonthermal emissions has been done, but they were only limited to active regions. The quiet corona is also hot, and so it is equally important to understand the physical processes which maintain this medium at MK temperatures. This presentation will describe the results from our effort to use the data from the Murchison Widefield Array (MWA) to search for impulsive radio emissions in the quiet solar corona. We have uncovered ubiquitous very impulsive nonthermal emissions from the quiet sun. We now refer to these emissions as Weak Impulsive Narrowband Quiet Sun Emissions (WINQSEs). We have done independent observations spanning very different solar conditions and proved that WINQSEs are present throughout the quiet corona at all times. Their occurrence rate lies in the range of many hundreds to a $sim$thousand per minute, implying that on average $sim$10 WINQSEs in every 0.5 s MWA image. Preliminary estimates suggest that WINQSEs have a bandwidth of $sim$2 MHz. Due to the importance of WINQSEs and their possible connection to the hypothesised “nanoflares”, we are pursuing several projects to characterise their spectro-temporal structure and their energetics. In this talk, I will present these results.

### Understanding the magnetic activity of red-giant stars

science theme: Post main sequence cool stars
schedule: Thu, 13:00 (haiku)

Patrick Gaulme (1,2) Federico Spada (1) Jason Jackiewicz (2)
(1) Max Planck Institute for Solar System Research, Goettingen, Germany (2) Department of Astronomy, New Mexico State University, Las Cruces, NM, USA

According to dynamo theory, stars with convective envelopes efficiently generate surface magnetic fields (which manifest as magnetic activity: starspots, faculae, flares) when their rotation period is shorter than their convective turnover time. Most red giants (RG), having undergone significant spin down while expanding, have slow rotation and no spots. However, Gaulme et al. (2020) showed that out of a sample of 4500 RGs observed by the NASA Kepler space telescope, about 8% display spots. They also detected solar-like oscillations in 99.3% of the sample, and determined the evolutionary stage (hydrogen-shell or helium-core burning) of 76% of them. From complementary high-resolution spectroscopic observations of 85 targets, the active RGs can be categorized as: 1) RGs in close binary systems spun up by tidal forces 2) solar-mass RGs that gained angular momentum by engulfing stellar or substellar companions 3) intermediate-mass RGs that were fast rotators in the late main sequence before entering the red giant phase. In this presentation, we report new insights on the active RGs that may have engulfed a companion based on spectroscopic observations of the entire active solar-mass RGs identified by Gaulme et al. (2020).

Gaulme et al. (2020) A&A 639, A63

### A distinct supernova enrichment history as the source of the non-solar odd-even effect in the solar twin HIP 11915

science theme: The Sun among stars
schedule: Thu, 13:00 (haiku)

Jorge Meléndez Jhon Yana Galarza
Departamento de Astronomia, IAG-USP

The abundance patterns observed in the Sun and in metal-poor stars show a clear odd-even effect. An important question is whether the odd-even effect in solar-metallicity stars is similar to the Sun, or if there are variations that can tell us about different chemical enrichment histories. We report for the first time observational evidence of a differential odd-even effect in the solar twin HIP 11915, relative to the solar odd-even abundance pattern. We analysed high resolving power (R = 140 000) and high S/N ratio (∼400) VLT/ESPRESSO spectra, obtaining precise chemical abundances (∼0.01 dex). The differential abundances relative to the Sun, show a non-solar odd-even effect even after performing Galactic Chemical Evolution corrections. This suggest a supernova enrichment history different to the Sun's.

### Helium observations of exoplanet atmospheres are connected to stellar coronal abundances

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

Katja Poppenhaeger
(1) Leibniz Institute for Astrophysics Potsdam (2) University of Potsdam, Institute for Physics and Astronomy

Transit observations in the helium lines near 10830 Angstrom are a new successful tool to study exoplanetary atmospheres and their mass loss. Forming those lines requires ionization and recombination of helium in the exoplanetary atmosphere. This ionization is caused by stellar photons in the extreme UV (EUV) however, no currently active telescopes can observe this part of the stellar spectrum. The stellar spectrum close to the helium ionization threshold consists of individual emission lines, many of which are formed by iron at coronal temperatures. Coronal elemental abundances exhibit distinct patterns related to the first ionization potential (FIP) of those elements, with elements like iron being strongly depleted for high-activity low-mass stars. I show that stars with high versus low coronal iron abundances follow different scaling laws that tie together their X-ray emission and the EUV flux close to the helium ionization threshold. I also show that the currently observed large scatter in the relationship of EUV irradiation with exoplanetary helium transit depths can be reduced by taking coronal iron abundances into account, allowing us to target exoplanets with well-observable helium signatures with much higher confidence.

### Radio exoplanets and stars at low-frequencies

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

J. R. Callingham (1,2) H. Vedantham (2,3) T. Shimwell (2,1) B. J. S. Pope (4) and LoTSS team
(1) Leiden University (2) ASTRON, Netherlands Institute for Radio Astronomy (3) Groningen University (4) Sagan Fellow, New York University

For more than thirty years, radio astronomers have searched for auroral emission from exoplanets. With the Dutch radio telescope LOFAR we have recently detected strong, highly circularly polarised low-frequency (144 MHz) radio emission associated with a M-dwarf - the expected signpost of such radiation. The star itself is quiescent, with a 130-day rotation period and low X-ray luminosity. In this talk, I will detail how the radio properties of the detection imply that such emission is generated by the presence of an exoplanet in a short period orbit around the star. I will also discuss how our LOFAR observations represents the most comprehensive survey of stellar systems at low frequencies, and the implications of this new population we have detected in understanding the magnetosphere of M dwarfs and exoplanetary magnetic fields.

### Characterizing Differential Rotation with Tides in Eclipsing Binaries

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

Adam S Jermyn (1) Jamie Tayar (2,3) Jim Fuller (4)
(1) Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA (2) Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA (3) Hubble Fellow (4) TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA

Over time, tides synchronize the rotation periods of stars in a binary system to the orbital period. However, if the star exhibits differential rotation then only a portion of it can rotate at the orbital period, so the rotation period at the surface may not match the orbital period. The difference between the rotation and orbital periods can therefore be used to infer the extent of the differential rotation. We use a simple parameterization of differential rotation in stars with convective envelopes in circular orbits to predict the difference between the surface rotation period and the orbital period. Comparing this parameterization to observed eclipsing binary systems, we find that in the surface convection zones of solar-like stars in short-period binaries there is very little radial differential rotation, with $|rpartial_r ln Omega| < 0.02$. This holds even for longer orbital periods, though it is harder to say which systems are synchronized at long periods, and larger differential rotation is degenerate with asynchronous rotation.

### Stellar Flares and Habitable(?) Worlds from the TESS Primary Mission

science theme: Stellar flares and activity
schedule: Thu, 15:00 (haiku)

Maximilian N. Günther
Massachusetts Institute of Technology (MIT)

On our search for habitable worlds, we have to account for explosive stellar flaring and coronal mass ejections (CMEs) impacting exoplanets’ surface (or cloud) habitability. These stellar outbursts are a double-edged sword. On the one hand, flares and CMEs are capable of stripping off atmospheres and extinguishing existing biology. On the other hand, flares might be the (only) means to deliver the trigger energy for prebiotic chemistry and initiate life. In this talk, I will highlight our TESS study of all stellar flares from Years 1 & 2 of the mission, driven by the "stella" convolutional neural network. Where manual vetting would have taken a lifetime, and conventional outlier detection would have missed the smallest flares, state-of-the-art machine learning approaches allow us a fast, efficient, and probabilistic characterization of flares. I will also discuss flaring as a function of stellar type, age, rotation, spot coverage, and other factors. Finally, I will link our findings to prebiotic chemistry and ozone sterilization, identifying which worlds might lie just in the right regime between too much and too little flaring. With the TESS extended mission and increased cadences (20s, 2min and 10min), stellar flare studies and new exoplanet discoveries will ultimately aid in defining criteria for exoplanet habitability.

### Lithium abundance dispersion in metal-poor stars

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

M. Deal (1) O. Richard (2) S. Vauclair (3)
(1) Instituto de Astrofísica e Ciências do Espaço (IA), Porto, Portugal (2) LUPM, Montpellier, France (3) IRAP, Toulouse, France

The formation and evolution of light elements in the Universe act as important cosmological constraints. The oldest stars of the Galaxy have long been assumed to display in their outer layers the primordial lithium abundance, although all studies of stellar physics proved that this abundance must have decreased with time. The primordial Li abundance deduced from the observations of the Cosmological Background is indeed larger than the maximum one observed in these stars. Recent observations gave evidence of a large Li abundance dispersion in very metal poor stars.

During this presentation, we address the general question of the lithium abundance dispersion obtained from observations of metal-poor stars, and how the interplay of atomic diffusion and accretion of matter modifies the element abundances in these metal-poor stars. In particular, we focus on the hydrodynamic processes that could take place after accretion. We consider initial metallicities from [Fe/H]=-2.31 down to [Fe/H]=-5.45.

We show that the observations of lithium dispersion, associated or not with carbon enrichment, are well accounted for in terms of accretion onto the metal-poor stars, with accreted masses smaller than a few Jupiter masses, when using a lithium initial abundance in accordance with the primordial lithium abundance obtained from latest BBN results.

### Exploring the M-dwarf Radius Inflation Problem

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

Sam Morrell Tim Naylor
University of Exeter

There has been growing evidence in the literature that M-dwarf stars suffer radius inflation compared to theoretical models, suggesting that models are missing some key physics required to completely describe stars at effective temperatures less than about 4000K. We presented evidence at the previous Cool Stars meeting that this problem is evident in pre-main sequence populations within stellar clusters. With the advent of Gaia DR2, we have been able to generalise our novel SED fitting methodology, which relies only upon multiband photometry and geometric distances, to measure the radii of >15,000 nearby main-sequence field M-dwarf stars, and show that radius inflation persists onto the main sequence.

From this sample, we have determined that M-dwarfs show an inflation of 3 - 7 per cent from the purely theoretical models, with no more than 1 - 2 per cent intrinsic spread in the inflated sequence. We show that this measurement technique is able to measure M-dwarf radii to an accuracy of 2.4 per cent, however we determined that this is limited by the precision of metallicity measurements which contribute 1.7 per cent to measurement uncertainty. We also present evidence that stellar magnetism is currently unable to explain the radius inflation in M-dwarfs.

### Using new asteroseismic rotation to study the evolution of rotation in main sequence stars

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

Oliver J. Hall (1,2,3) Guy R. Davies (2,3) Jennifer van Saders (4) Martin B. Nielsen (2,3) Mikkel N. Lund (3) William J. Chaplin (2,3) Rafael A. Garcia (5,6) Louis Amard (7) Angela A. Breimann (7) Saniya Khan (2,3) Victor See (7) Jamie Tayar (4,8)
(1) European Space Agency (ESA), European Space Research and (2) Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The (3) Netherlands (4) School of Physics and Astronomy, University of (5) Birmingham, Edgbaston, Birmingham, B15 2TT, UK (6) Stellar (7) Astrophysics Centre, Department of Physics and Astronomy, Aarhus (8) University, Ny Munkegade 120, 8000 Aarhus C, Denmark (9) Institute (10) for Astronomy, University of Hawai'i, Honolulu, HI 96822 (11) IRFU, (12) CEA, Universite Paris-Saclay, F-91191 Gif-sur-Yvette, France (13) AIM, CEA, CNRS, Universite Paris-Saclay, Universite Paris Diderot, (14) Sorbonne Paris Cite, F-91191 Gif-sur-Yvette, France (15) University (16) of Exeter Department of Physics and Astronomy, Stocker Road, Devon, (17) Exeter, EX4 4QL, UK (18) Hubble Fellow

Studies using asteroseismic ages and rotation rates from star-spot rotation have indicated that standard age-rotation relations may break down roughly half-way through the main sequence lifetime, a phenomenon referred to as weakened magnetic braking. While rotation rates from spots can be difficult to determine for older, less active stars, rotational splitting of asteroseismic oscillation frequencies can provide rotation rates for both active and quiescent stars, and so can confirm whether this effect really takes place on the main sequence.

In this talk, I’ll show how we obtained asteroseismic rotation rates of 91 main sequence stars showing high signal-to-noise modes of oscillation. Using these new rotation rates, along with effective temperatures, metallicities and seismic masses and ages, we built a hierarchical Bayesian mixture model that showed that our new ensemble more closely agreed with weakened magnetic braking, over a standard rotational evolution scenario.

### Far beyond the Sun: Simultaneous observations of the young Sun Iota-Horologii

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

E. M. Amazo-Gómez (1) J. D. Alvarado-Gómez (1) G. A. J. Hussain (2) K. Poppenhäger (1) P. C. König (3) J. F. Donati (4) B. E. Wood (5) J. J. Drake (6) J. Do Nascimento (6) F. Del Sordo (7) M. Damasso (7) Jorge Sanz-Forcada (8) Beate Stelzer (9)
(1) Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany (2) European Spatial Agency, Keplerlaan 1, 2201 AZ Noordwijk, Netherlands (3) European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany (4) CNRS-IRAP, 14, avenue Edouard Belin, F-31400 Toulouse, France (5) Naval Research Laboratory, Space Sciences Division, Washington, DC 20375, USA (6) Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge MA 02138, USA (7) Osservatorio di Torino, INAF, Via Osservatorio, 20, 10025 Pino Torinese TO, Italy (8) Centro de Astrobiología (CSIC-INTA), ESAC Campus, Camino Bajo del Castillo, E-28692 Villanueva de la Cañada, Madrid, Spain (9) Eberhard Karls Universität, Institut für Astronomie und Astrophysik, Sand 1, 72076 Tübingen, Germany

A simultaneous and revealing stellar analysis has been performed on the young Sun-like star iota-Horologii. The star has one the shortest reported magnetic cycle, of about 1.4 years. That short period, in comparison with the 22 years solar magnetic cycle, allowed a faster activity analysis of a young Sun. We compiled a long-term spectropolarimetric follow-up under the "Far beyond the Sun" campaign of about 6 observational semesters. During the last semester of observation, we combined simultaneous observations of the star by TESS and HST satellites. Those observations let us compare the stellar activity for different atmospheric stratifications. By using the GPS method combined, for the first time, with Zeeman Doppler Imaging (ZDI) mapping technique we constrained the faculae to spot driver ratio. Such combined information helps us to better interpret the stellar surface. We found that the stellar surface is spot dominated, with a facular to spot ratio $(S_/S_)$ of about 0.74. For reference, the Sun displays a roughly constant $(S_/S_)$ about 3, faculae dominated surface along its activity cycle. We retrieved diagnostics of the coronal transition region, derived from the $O_< m iv>$ and $S_< m iv>$ inter-combination lines observed by HST. We describe and place our results in the context of the correlations between the different observables, which improves the magnetic activity characterization for the different atmospheric layers.

### Stellar Rotation in the Gaia Era: Revised Open Clusters Sequences

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

Diego Godoy-Rivera (1) Marc H. Pinsonneault (1) Luisa M. Rebull (2)
(1) The Ohio State University (2) Infrared Science Archive (IRSA), IPAC

The period versus mass diagrams (i.e., rotational sequences) of open clusters provide crucial constraints for angular momentum evolution studies. However, their memberships are often heavily contaminated by field stars, which could potentially bias the interpretations. In this work, we use data from Gaia DR2 to re-assess the memberships of seven open clusters with rotational data, and present an updated view of stellar rotation as a function of mass and age. We use the Gaia astrometry to identify the cluster members in phase-space, and applying our membership analysis to the rotational sequences reveals that: 1) the contamination in clusters observed from the ground can reach up to $sim$ 35\% 2) the overall fraction of rotational outliers decreases substantially when the field contaminants are removed, but some outliers still persist 3) there is a sharp upper edge in the rotation periods at young ages 4) stars in the 1.0–0.6 $M_$ range inhabit a global maximum in terms of rotation periods, potentially providing an optimal window for habitable planets. Additionally, we see clear evidence for a strongly mass-dependent spin-down process. In the regime where rapid rotators are leaving the saturated domain, the rotational distributions broaden (in contradiction with popular models), which we interpret as evidence that the torque must be lower for rapid rotators than for intermediate ones. The cleaned rotational sequences from ground-based observations can be as constraining as those obtained from space.

### Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (Mega- MUSCLES)

science theme: Cool Stars on the main sequence
schedule: Thu, 15:00 (haiku)

David Wilson Mega-MUSCLES Collaboration
UT Austin

M dwarf stars have emerged as ideal targets for exoplanet observations. Their small radii aids planetary discovery, their close-in habitable zones allow short observing campaigns, and their red spectra provide opportunities for transit spectroscopy with JWST. The potential of M dwarfs has been underlined by remarkable systems such as the seven Earth-sized planets orbiting TRAPPIST-1 and the habitable-zone planet around Proxima Centauri.

Assessing the characteristics of such planets requires a firm understanding of how M dwarfs differ from the Sun, beyond just their smaller size and mass. Of particular importance are the time-variable, high-energy ultraviolet and x-ray regions of the M dwarf spectral energy distribution (SED), which can influence the chemistry and lifetime of exoplanet atmospheres, as well as their surface radiation environments. Unfortunately, those wavebands are extremely faint for most M dwarfs, requiring too large an investment of telescope time to obtain data at most stars.

The Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (Mega-MUSCLES) Treasury project, together with the precursor MUSCLES project, will produce full SEDs of a representative sample of M dwarfs, covering a wide range of stellar mass, age, and planetary system architecture. We have obtained x-ray and ultraviolet data for 12 stars using the Hubble, Chandra and XMM space telescopes, along with state-of-the-art DEM modelling to fill in the unobservable extreme ultraviolet regions. Our completed SEDs will be available as a community resource, with the aim that a close MUSCLES analogue should exist for most M dwarfs of interest.

In this presentation I will overview the Mega-MUSCLES project, describing our choice of targets, observation strategy and SED production methodology. I will also discuss notable targets such as the TRAPPIST-1 host star, comparing our observations with previous data and model predictions.