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Resonance and Probability Around Kepler-18

Three planets recently discovered through Kepler data provide an interesting take on how we look at smaller planets. Not that the planets around the star designated Kepler-18 are all that small — two of them are Neptune-class and one is a super-Earth. But what is becoming clear is that given the state of our current technology, we’ll have to get used to a process different from planet verification as we move to ever smaller worlds. The technique is being referred to as planet validation — it helps us determine the probability that the detected object could be something other than a planet.

Image: The orbits of the three known planets orbiting Kepler-18 as compared to Mercury’s orbit around the Sun. Credit: Tim Jones/McDonald Obs./UT-Austin.

The new system shows how this works. Kepler-18 is a star similar to ours, about 10 percent larger than the Sun and with 97 percent of the Sun’s mass. Around it we have Kepler-18 c and d, which turn up through transits. Planet c has a mass of about 17 Earths and is thought to be some 5.5 times the size of Earth. Its orbit takes it around Kepler-18 in 7.6 days. Kepler-18 d is 16 times as massive as the Earth, 7 times Earth’s size, and orbits its primary in 14.9 days. These two Neptune-class worlds are, interestingly enough, in a 2:1 resonance: Planet c orbits the star twice for every single orbit of planet d. The demonstrable resonance is ample proof that these are planets in the same system and not something else mimicking a planetary signature.

But the super-Earth, Kepler-18 b, is something else again. A team led by Bill Cochran (University of Texas at Austin) went to work with the 5-meter Hale Telescope at Palomar, aided by adaptive optics, to examine Kepler-18 to see whether the transit signal they thought to be a super-Earth was genuine. Finding no background objects that could have influenced the finding, they were able to calculate the odds that Kepler-18 b is not a planet at 700 to 1. Cochran thinks this process of planet validation is going to become much more significant as Kepler brings in new data:

“We’re trying to prepare the astronomical community and the public for the concept of validation. The goal of Kepler is to find an Earth-sized planet in the habitable zone [where life could arise], with a one-year orbit. Proving that such an object really is a planet is very difficult [with current technology]. When we find what looks to be a habitable Earth, we’ll have to use a validation process, rather than a confirmation process. We’re going to have to make statistical arguments.”

So we can with a high degree of probability rule out any of the objects — stars, background galaxies — that might in any way compromise the transit data. The planetary signature of the super-Earth seems real enough, though established in a different way than Kepler-18 c and d, whose gravitational interactions can be readily demonstrated. The planet is thought to be 6.9 times Earth mass and twice Earth’s size. All three worlds orbit much closer to their parent star than Mercury does to the Sun, the super-Earth Kepler-18 b being the closest, with a 3.5 day period.

We can also deduce an interesting possibility about Kepler-18 b, as noted in the paper:

The inner, 3.5-day period planet Kepler-18b, is a super-Earth that requires a dominant mixture of water ice and rock, and no hydrogen/helium envelope. While the latter cannot be excluded simply on the basis of the planet’s mass and radius, the evaporation timescale for a primordial H/He envelope for a hot planet such as Kepler-18b is much shorter than the old age derived for the Kepler-18 system, and such a H/He envelope should not be present. Thus, despite its lower equilibrium temperature, Kepler-18b resembles 55 Cnc e and CoRoT-7b… Kepler-18b, together with 55 Cnc e… are likely our best known cases yet of water planets with substantial steam atmospheres (given their high surface temperatures).

The discovery was announced at a joint meeting of the American Astronomical Society’s Division of Planetary Science and the European Planetary Science Conference in Nantes, France. More on the Kepler-18 results in this news release from the University of Texas at Austin. Look for these results in an upcoming issue of the Astrophysical Journal Supplement Series devoted to Kepler, which will appear in November. The paper is Cochran et al., “Kepler 18-b, c, and d: A System Of Three Planets Confirmed by Transit Timing Variations, Lightcurve Validation, Spitzer Photometry and Radial Velocity Measurements” (preprint).


Comments on this entry are closed.

  • Alex Tolley October 5, 2011, 9:27

    “…calculate the odds that Kepler-18 b is a planet at 700 to 1. ”

    That is very long odds. I think you mean “NOT a planet” or “700 to 1 against”.

  • Paul Gilster October 5, 2011, 9:56

    Thanks, Alex. I fixed the goof.

  • Michael October 5, 2011, 15:42

    I think with the closeness of the planet to the star and the stars U.V the steam would break down leaving the hydrogen to escape, the oxygen would combine with something else or simply enriching the atmosphere.

  • coolstar October 5, 2011, 18:47

    A lot of very careful work by a large group of authors but really, once
    a) the 2:1 resonance was established for the more massive planets
    b) Spitzer observations of their secondary eclipses were observed and
    c) TTVs were well established
    the odds of planet b being a false positive were already very low. The same is almost certainly true if you pick only two of the above. Systems as interesting as this one (or more so) are turning out to be abundant in the Kepler data. In a year, or less, we’ll probably be forced by the sheer glut of data not to pay a lot of attention to individual systems like this. I’m just about there now, as I had only read the abstract before Paul wrote this post.
    This is a very good thing for the field, of course.

  • spaceman October 5, 2011, 21:23

    I like the puzzle-solving aspect of “planet validation.” It is true scientific detective work to show beyond a reasonable doubt that individual systems are probably planets as opposed to other astrophysical objects.

    Paul, I was wondering if you knew of any teams of astronomers who may be combing the Kepler data set to look for Alpha Centauri A and B analogues and then testing to see if there are any transiting planets in them. This would at least give us an early hint that planets can exist in the intermediate separation binary systems before the radial velocity searches weigh in. I am fascinated by the rate of progress: we now know, thanks to the Kepler mission, that planets can exist around those sci-fi very close eclipsing binaries! But what about the intermediate cases, the ones like those in this site’s title, what can Kepler tell about these cases?

  • Paul Gilster October 5, 2011, 21:25

    spaceman, I haven’t heard of any specific work on Alpha Centauri A and B analogues through the Kepler data, but perhaps some of our resident astronomers have and will weigh in.

  • Scott G. October 5, 2011, 23:39

    I haven’t read this paper, but I’m guessing that Kepler-18 b, with a 3.5 day orbital period, is tidally locked to its parent star.

    If that’s true and the authors are also correct in hypothesizing that “Kepler-18b, together with 55 Cnc e… are likely our best known cases yet of water planets with substantial steam atmospheres”, could it be possible that there exists a small region on the far side of the planet (whether it be at the ocean surface or on the ocean floor) where the temperature is cool enough to support life as we know it?

    My thought was that if the planet is twice Earth’s size, then it seems plausible that with half the planet in perpetual dark, there may be enough heat lost to space that the temperature may not be so extreme in some places.

  • henk October 6, 2011, 3:14


    It does not really matter if they found those kind of planets. It will make the chance higher that Alpha Centauri A and B have a planet, but if they do not find any does not mean that alpha centauri can not have planets. It is hard to find planets around systems like that. So kepler will also have a problem with it. They already found planets around close binary stars only they were gas giants and they were not as close

  • Enzo October 6, 2011, 16:44

    @ SCott,

    I doubt it very much. The very same argument that may allow life in planets tidally locked around red stars (thick atmosphere that redistributes the heat) here works against this. In a thick atmosphere, strong winds would redistribute the heat very efficiently, probably leading to fairly uniform temperatures, a bit like Venus (but higher here).
    These planets are much closer than Mercury and around a sun like star : they are very very hot.
    Unless they have further off, unseen planets, such “compact” systems are a complete “waste” of a good G star :-)

  • Ronald October 7, 2011, 10:32

    Enzo: “Unless they have further off, unseen planets, such “compact” systems are a complete “waste” of a good G star :-)”

    I fully agree, with slight amusement.

    What this universe needs is a few good stars :-)

  • spaceman October 7, 2011, 21:02

    Actually, one of the stated goals of the Kepler mission is to determine the frequency of planets around stars of a variety of spectral types and around single AND multiple star systems. The existence of this stated goal leads me to believe that although difficult, it is not impossible to find planets in these systems with an observatory like Kepler. The reason why I think combing the Kepler data for close binary planets is worth-while is the same reason why Kepler was devised in the first place: to give us a broad brush statistical picture of planetary systems in our galaxy. Excluding close binaries from the search, given their reasonably high prevalence, would limit the amount of information in the census. Additionally, finding out what percentage of close binaries have planets would help us constrain planet formation models and give us a much better idea of what is the probability of finding planets around Alpha Centauri A and B perhaps before the RV searches weigh in.

  • coolstar October 8, 2011, 1:57

    @spaceman Transits around an Alpha Cen analog at the average distance of the stars in the Kepler field would be tough. Alpha Cen A & B have about a factor of 3 luminosity difference in the Kepler passband so that would dilute transits around either star such that transits of terrestrial sized planets would probably be unobservable (at least around the cool star). The analysis of transits deep enough to be detected would give pretty grossly wrong radii for the planets for the same reason unless the luminosity ratio was known. This might not be possible since the fact that the system is a binary might go undetected. The orbital period of around 80 years is such that the change in velocity is low and the maximum separation in rv for the two components is on the order of 5- 10 km/sec. Two spectra might be noticed with high resolution spectroscopy, but that would depend on where the stars were in their orbits. The stars would be faint enough that it would be hard to acquire spectra with high enough s/n to make this a certainty. If BOTH stars had planets that were seen to transit that might help some. Chances for the stars themselves to be caught in eclipse would of course be very low and their separation and distance from earth would make them unresolvable in images (and they’d be too faint for ground based interferometry).