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The Virtues of Oddly Shaped Planets

A new paper out of George Mason University tackles the subject of planets deformed by tidal effects in close proximity to their star. It’s a useful study for reasons I’ll explain in a moment, but first a digression: I once had the chance to talk physics with the late Sheridan Simon, who besides being a popular lecturer on astrophysics at Guilford College (Greensboro, NC) also had a cottage industry designing planets for science fiction writers. Simon loved oddly shaped planets and because the Super Bowl was coming up, he had taken it upon himself to design a planet in the shape of a football, just to see what would happen if a place like this actually existed.

“And you know what? It works,” the bearded, exuberant Simon said with a grin. “But when you model what it looks like from space, the atmosphere is a problem. It looks plaid!”

TheFlightOfTheDragonfly

Simon played around with planets of every description, and if you’d like to see him at work on a planetary system around Tau Ceti, check what he developed back in 1992 for James K. Hoffman. I don’t know if he ever worked with Robert Forward, but of course the ultimate deformed planet in science fiction would be Rocheworld, from the novel of the same name (in an early version, Flight of the Dragonfly), where Forward envisions two worlds close enough to each other that they are deformed into egg-shapes and actually share an atmosphere.

Deformed planets in the realm of hot Jupiters have been studied for some time, for some of these worlds are close enough to their star to experience significant distortion in shape. One that Prabal Saxena and his George Mason University team mention in their paper is WASP-12b, which has been shown in earlier studies to have ellipsoidal variations in its transit depth that suggest a 3:2 ratio between the planet’s longest and its shortest axes. It’s an important effect because misunderstanding the distortion in shape caused by rotational and tidal effects can lead to mistakes in calculating the radius of the planet, and thus parameters such as density.

What Saxena and team are interested in is how rocky worlds orbiting red dwarf stars may experience stresses that can change their shape. Saxena comments:

“Imagine taking a planet like the Earth or Mars, placing it near a cool red star and stretching it out. Analysing the new shape alone will tell us a lot about the otherwise impossible to see internal structure of the planet and how it changes over time.”

Sun_planet

Image: An artist’s impression of a stretched rocky planet in orbit around a red dwarf star. So close to the star, there is a difference in the strength of the gravitational field on each side of the planet, stretching it significantly. Credit: Shivam Sikroria.

The paper, which appears in Monthly Notices of the Royal Astronomical Society, goes to work on how to take both tidal and rotational forces into account. The French astronomer Édouard Roche (1820-1883) was the first to calculate the distance within which an orbiting body will disintegrate because of the tidal forces induced by its primary. Inside what we now call the Roche limit, material in orbit will become dispersed into rings, while outside the limit, it can coalesce. The process varies depending on the innate rigidity of the body in question. A more fluid world deforms gradually, a process that compounds the tidal forces that will destroy it, while a more rigid planet may hold its shape until being broken apart by these same forces.

All of this could be useful as we try to learn more about the planet’s characteristics. From the paper:

The variation of rigidity of a planet may produce a small but detectable signal in the cases that were tested as one gets very close to the fluid Roche limit, and again it is important to remember planets have also been detected interior to the fluid Roche limit (the inner distance bound). Merely the constraining of tidal bulge amplitude along with Roche limit considerations may put meaningful limits on interior structure. The ability to directly constrain the shape of a planet would provide clues towards tidal theory, the orbital configuration of the system and bulk properties of the planet.

Not many M-dwarf planetary systems are likely to show the signature of worlds near the Roche limit, but the paper argues that the general physical principles in play here may also help us interpret the signatures of planets in particular orbital resonances or other configurations. Several dozen ‘hot Jupiters’ have been found that should, by virtue of their proximity to the Roche limit, show observable effects. For solid planets, the large transit depth may make red dwarf planets near the Roche limit an excellent realm for further study as we learn to interpret what any planetary deformations can tell us about their internal characteristics.

The paper is Saxena et al., “The observational effects and signatures of tidally distorted solid exoplanets,” published online by Monthly Notices of the Royal Astronomical Society 14 December 2014 (abstract / preprint).

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Comments on this entry are closed.

  • galacsi December 16, 2014, 15:43

    And also : Imagine a rocky planet as massive as Jupiter but rotating so fast that gravity will be one g on the equator and of course much greater when going to the poles.I did some back of the envelope calculations andI think it can work. The planet will be shaped like a pumpkin !

  • Lionel December 16, 2014, 18:40

    @galasci

    Some queries…

    Why would a planet as massive as jupiter be rocky and not a gas giant?
    Wouldn’t such a massive planet always suck up all the gas in the vicinity and become a gas giant?
    Or has it been shown that a Jupiter mass planet extremely close to a star can have all its gas ripped away?

    Thx

  • Andrew Palfreyman December 16, 2014, 18:58

    @ galacsi : That’s Mesklin, from Hal Clement’s Mission of Gravity.

  • Alex Tolley December 16, 2014, 20:40

    @galacsi – isn’t that very similar to Mesklin from Hal Clement’s “Mission of Gravity”? (700g at poles, 3g at equator).

    What would induce a planet to spin so fast that its surface gravity was very different at the poles and the equator? We know asteroid can spin up to the point of tearing themselves apart. But with a terrestrial world, spin would impact all sorts of geologic processes. How far could this go? Even on Earth without a moon, solar tides would slow down the spin due to friction.

  • Brett Bellmore December 17, 2014, 7:26

    Well, if you started out with a large moon *below* synchronous orbit, tidal dissipation would accelerate the spin of the primary, while the moon, dropping into a lower orbit, would also end up going around faster, and gravitational interactions would increase, causing more tidal dissipation.

    At some point, the gravitational attraction of the moon would drag atmosphere up, and it might be lost.

    If things started out just right, you might end up with Mesklin.

  • Harry R Ray December 17, 2014, 10:33

    This study should not be limited to red dwarf stars! When Prabal Saxena states in his paper “…planets have been detected interior to the fluid Roche limit, the planet that IMMEDIATELY comes to mind is Kepler 70b, with a five hour orbital period (also OBVIOUSLY the pulsar “diamond planet, with a two hour orbital period, but the planetary nature of that object is still in debate) around a blue subdwarf star. I am wondering whether enough of these stars have been detected as to be feasible to do a ground based transit search around all of them since their radii are similar to main sequence M star radii, and earth sized planets may be detectable.

  • Ron S December 17, 2014, 12:07

    I think a truly odd-shaped planet would be perfectly spherical. That is, with allowances for local topographic variations which sum to zero. The natural formation of which would a difficult one to explain.

  • ljk December 17, 2014, 13:16

    Life on an aquaplanet

    MIT study finds an exoplanet, tilted on its side, could still be habitable if covered in ocean.

    Jennifer Chu | MIT News Office

    December 17, 2014

    Nearly 2,000 planets beyond our solar system have been identified to date. Whether any of these exoplanets are hospitable to life depends on a number of criteria. Among these, scientists have thought, is a planet’s obliquity — the angle of its axis relative to its orbit around a star.

    Earth, for instance, has a relatively low obliquity, rotating around an axis that is nearly perpendicular to the plane of its orbit around the sun. Scientists suspect, however, that exoplanets may exhibit a host of obliquities, resembling anything from a vertical spinning top to a horizontal rotisserie. The more extreme the tilt, the less habitable a planet may be — or so the thinking has gone.

    Now scientists at MIT have found that even a high-obliquity planet, with a nearly horizontal axis, could potentially support life, so long as the planet were completely covered by an ocean. In fact, even a shallow ocean, about 50 meters deep, would be enough to keep such a planet at relatively comfortable temperatures, averaging around 60 degrees Fahrenheit year-round.

    Full article here:

    http://newsoffice.mit.edu/2014/titled-aquaplanet-exoplanet-habitable-1217

    To quote:

    Darren Williams, a professor of physics and astronomy at Pennsylvania State University, says past climate modeling has shown that a wide range of climate scenarios are possible on extremely tilted planets, depending on the sizes of their oceans and landmasses. Ferreira’s results, he says, reach similar conclusions, but with more detail.

    “There are one or two terrestrial-sized exoplanets out of a thousand that appear to have densities comparable to water, so the probability of an all-water planet is at least 0.1 percent,” Williams says. “The upshot of all this is that exoplanets at high obliquity are not necessarily devoid of life, and are therefore just as interesting and important to the astrobiology community.”

  • Rob Henry December 17, 2014, 16:43

    galacsi’s world above is at lighter that Meskin by greater than the ratio of Mars to Earth. What hit me about Meskin was the orbital velocity from the top of its atmosphere was comparable to the rms of its gasses, and far less than its main breathing gas H2. It is very hard to reach escape velocity on Meskin, but very easy to reach orbital velocity, so it should be circled by a torus of gas that contains a similar amount of H2 to the remainder of the atmosphere. In principle, a unpowered hot hydrogen balloon could float into orbit!

  • galacsi December 17, 2014, 18:58

    @Andrew Palfreyman & Alex Tolley
    Yes the giant planet of Hal Clement ! But less extreme.
    What would induce a planet to spin so fast ? I dunno ,perhaps a magnetic effect could do it ?
    @Lionel
    I think there can be very interesting possibility with planets surviving the red giant phase of their star. A giant planet may be rid of of its gas but survive and end orbiting a white dwarf.
    Planet around white dwarfs ,I don’t know if it has been researched.

  • Marshall Eubanks December 17, 2014, 19:02

    A very fast rotating planet (far from any tidal forces) should be a Jacobi ellipsoid (think of an American football). 136108 Haumea is supposed to have such a shape.

    As there are some very fast rotating brown dwarfs (with periods as short as 2 hours – see http://iopscience.iop.org/0004-637X/684/1/644/ ), it is highly likely that there are also fast rotating super-Jupiters, and these could have a “football” type shape.

  • stephen December 19, 2014, 20:16

    Have any of you read G. David Nordley’s To Climb. a Flat Mountain? It involves a flat planet. He offers equations to support it.

    A spinning fluid has a concave center. Is there any way a rapidly rotating planet can have concave poles? Is there any way it could end up being a ring?

    Perhaps that could happen to a molten body smaller than Pluto or its moons, then it cools down and solidifies?

  • Rob Henry December 20, 2014, 0:00

    I riddle you this about Roche world. Under special circumstances with very dense solid worlds of very similar size, I could place each planet outside the Roche limit of the other, but their atmospheres always extended too far. By my calculations, the atmosphere would have to extend in a ‘smoke ring’ as I n the Integral tree. Now the problem…

    How on earth is the gravitational well of that combined system sufficient to retain such a loosely bound atmosphere?

  • Adam December 20, 2014, 18:26

    Mesklin was 16 Jupiter masses (5000 Earths) of ‘metals’ – mostly various ices – which would seem to pose an impediment to its formation. If the Sun lost most of its hydrogen and all its helium, there’d be about 16 Jupiter masses of other elements left over. Thus forming Mesklin naturally seemed insuperably difficult. However Phil Hopkins has computed that all metal “stars” can form naturally: http://arxiv.org/abs/1406.5509
    Being “all metal” would mean Mesklin could cool much quicker than a hydrogen/helium planet would. Thus Mesklin could exist, just not around Clement’s original locale of 61 Cygni. The super-Jovian that has long been suspected in that system doesn’t seem to exist according to more recent observations.

  • Rob Henry December 21, 2014, 15:40

    Adam, Mesklin’s was highly eccentric so perhaps it was captured (collision with a Jovian??). It was also unique, presenting by far the highest gravitational field that humans could place their scientific instruments in, so its rarity of formation is no problem. Interesting article, thanks.