Extrasolar planets

Secrets that only tides will tell

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Evidence that the most recently discovered extrasolar planet is virtually at the end of its life is a surprise. The odds of that are very low — similar to drawing two consecutive red aces from a well-shuffled deck of cards.

When it was first discovered in 1995, the planet 51 Pegasi b astounded scientists with its 4.3-day orbital period. This placed the Jupiter-sized planet at around 5% of the Earth–Sun distance from its host star (0.05 AU), a sweltering location where no planet had been expected to exist. But now with almost 375 extrasolar planets discovered to date, and nearly 20% of them located within 0.05 AU of their parent stars, a discovery of another 'hot Jupiter' is no longer as exciting as it once was. On page 1098 of this issue, however, Hellier et al.1 report the discovery of WASP-18b, a hot Jupiter (Fig. 1) that is sure to generate some buzz: the predicted remaining lifetime of the planet is less than a thousandth of the age of its host star, far shorter than that for any other known planet.

Figure 1: The ultimate in global warming.


This artist's impression depicts an exoplanet similar to the newly discovered1 WASP-18b. As seen from the planet, the host star spans an angle of more than 30° and hovers menacingly at a fixed position in the sky. WASP-18b completes an orbit in 0.94 days, buzzing just 2.5 stellar radii above the star's surface. That distance may be shrinking surprisingly rapidly.

WASP-18b, the eighteenth planet discovered by Britain's Wide Angle Search for Planets project2, is only the second planet found with an orbital period of less than a day. Proximity to the host star, as well as the planet's large mass (10.3 times that of Jupiter), lead to strong tidal interactions between the two bodies, which elongate both of them along the line joining their centres. If the bodies spin as well, the tidal bulges can misalign, causing torques that couple their spins to their orbital angular momentum.

For a planet orbiting a star, the tides raised on the smaller object act swiftly to reduce its spin until one face is locked towards the star. The planet's initially elongated orbit also rapidly becomes circularized by these tides. By contrast, tides raised on the star usually act more slowly, and can either pull the planetary orbit inward (if the planet orbits faster than the star spins) or push it outward (if the stellar spin is faster). WASP-18b should be spiralling inward towards the star, and it is so close and so massive that the infall timescale is predicted to be well under a million years.

That stings. Planets and stars form together, and Hellier and colleagues1 find the star to be about a billion years old. So it seems that WASP-18b has lived a billion years and has just a million years left before its fiery demise. The odds of finding a planet so close to the end of its life are low — only about 1 in 1,000. Did Hellier et al. really draw the two red aces from the deck? How can this be?

There are a number of possibilities, but none of them is entirely satisfactory. First, 1-in-1,000 odds may not be so bad, considering the roughly 320 planetary systems discovered to date3; effectively, astronomers have had multiple tries at drawing two red aces. Formally, the likelihood of getting a positive result in 320 chances is a respectable 27%. But have we really had 320 chances? The hidden assumption here is that all 320 systems once had a massive planet that was lost to its star. When corrected for the fact that most systems may not have had such a planet, the odds go down considerably. Even more problematic is the fact that there are only three other known planets located within 0.06 AU of their host stars with masses as large as that of WASP-18b. We would probably expect to see many more such objects if this interpretation were correct.

Second, as suggested by Hellier et al., the star may be particularly poor at dissipating tidal energy, which would dramatically increase the planet's lifetime. The tidal-dissipation rate may be loosely parametrized by Q, the quality factor, which depends on properties of the stellar interior. More properly, the dissipation rate is proportional to Q/k2, where k2 is a measure of the star's response to a tidal perturbation. The quantity Q/k2 is often assumed to be about 106 for stars, but is relatively well determined only for colder balls of gas: for example, the values for Uranus4 (Q/k2 = 2 × 105) and Neptune5 (Q/k2 = 4.5 × 104) are uncertain by about a factor of 2. For Jupiter6, the nominal value of Q/k2 is 8 × 105, although it could be up to six times higher or lower. Hellier et al. show that a Q/k2 value as high as 109 would be required to increase the planet's remaining lifetime towards a billion years; longer-lived planets are much easier to find. If the star's Q/k2 really is thousands of times above what is measured for either gaseous planets or binary stars, it would be a spectacular finding.

Third, perhaps we are forced to abandon the assumption that the planet has been tidally evolving throughout the billion-year age of its host star. Hot Jupiters are thought to have formed much farther from their stars than where they are found today. A more distant origin gives a planet a far greater supply of raw materials early in its lifetime, allowing growth to Jupiter mass and beyond. After reaching its full size, however, another process, such as interactions with a second planet, must place one planet close to the star, where tidal forces take over. Perhaps such an event occurred recently in the WASP-18 system. It is impossible to rule this out, and extremely difficult to assess the odds.

Finally, maybe something is holding the planet up against the inward drag of tides. Some poorly understood aspect of stellar convection? An unappreciated subtlety of tides? Another planet? Although these may seem unlikely possibilities, given the existence of the unusual WASP-18 system they should be examined more closely. It is useful here to draw an analogy with the similar situation faced by Mars's largest moon Phobos. Like WASP-18b, Phobos is close to its host, skimming just 1.73 Mars radii above the surface, and its orbit is predicted to decay inward in about 30 million years, a timescale more than 150 times shorter than the age of the Solar System. The past history of Phobos, like that of WASP-18b, is not understood, and possibilities similar to those discussed above are equally unpalatable. Perhaps we really are missing some key bit of physics.

Relief, however, is on the way. Hellier et al.1 emphasize that if the orbit of WASP-18b is really decaying inward rapidly, the effects will become visible within a decade. Continuous monitoring of this system — as well as others that are predicted to undergo slower, albeit still rapid, tidal evolution7 — would be well worth the effort. Only then will tides begin to reveal the secrets of these unusual systems.


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    Hellier, C. et al. Nature 460, 1098–1100 (2009).

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    Tittemore, W. C. & Wisdom, J. Icarus 78, 63–89 (1989).

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    Zhang, K. & Hamilton, D. P. Icarus 193, 267–282 (2008).

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    Yoder, C. F. & Peale, S. J. Icarus 47, 1–35 (1981).

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    Sasselov, D. D. et al. Astrophys. J. 596, 1327–1331 (2003).

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Hamilton, D. Secrets that only tides will tell. Nature 460, 1086–1087 (2009) doi:10.1038/4601086a

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