Exoplanets: The Hunt for Circular Orbits

by Paul Gilster on May 19, 2015

If you’re looking for planets that may be habitable, eccentric orbits are a problem. Vary the orbit enough and the surface goes through extreme swings in temperature. In our own Solar System, planets tend to follow circular orbits. In fact, Mercury is the planet with the highest degree of eccentricity, while the other seven planets show a modest value of 0.04 (on a scale where 0 is a completely circular orbit — Mercury’s value is 0.21). But much of our work on exoplanets has revealed gas giant planets with a wide range of eccentricities, and we’ve even found one (HD 80606b) with an eccentricity of 0.927. As far as I know, this is the current record holder.

These values have been measured using radial velocity techniques that most readily detect large planets close to their stars, although there is some evidence for high orbital eccentricities for smaller worlds. Get down into the range of Earth and ‘super-Earth’ planets, however, and the RV signal is tiny. But a new paper from Vincent Van Eylen (Aarhus University) and Simon Albrecht (MIT) goes to work on planetary transits. It’s possible to work with Transit Timing Variations to make inferences about eccentricity, but these appear only in a subset of transiting systems.

Instead, van Eylen and Albrecht look at transit duration. The length of a transit can vary depending on the eccentricity and orientation of the orbit. By measuring how long a planetary transit lasts, and weighing the result against what is known about the properties of the star, the eccentricities of the transiting planets can be measured, as explained in the paper:

Here we determine orbital eccentricities of planets making use of Kepler’s second law, which states that eccentric planets vary their velocity throughout their orbit. This results in a different duration for their transits relative to the circular case: transits can last longer or shorter depending on the orientation of the orbit in its own plane, the argument of periastron (ω)… Transit durations for circular orbits are governed by the mean stellar density (Seager & Mallen-Ornelas 2003). Therefore if the stellar density is known from an independent source then a comparison between these two values constrains the orbital eccentricity of a transiting planet independently of its mass…

Using these methods, the researchers have measured the eccentricity of 74 small extrasolar planets orbiting 28 stars, discovering that most of their orbits are close to circular. The systems under study were chosen carefully to avoid false positives — the team primarily used confirmed multi-transiting planet systems around bright host stars, and pulled in asteroseismological data — information on stellar pulsations — to help determine stellar parameters. Asteroseismology can refine our estimates of a star’s mass, radius and density. The stars in the team’s sample have all been characterized in previous asteroseismology studies.

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Image: Researchers measuring the orbital eccentricity of 74 small extrasolar planets have found their orbits to be close to circular, similar to the planets in the Solar System. This is in contrast to previous measurements of more massive exoplanets where highly eccentric orbits are commonly found. Credit: Van Eylen and Albrecht / Aarhus University.

No Earth-class planets appear in the team’s dataset, but the findings cover planets with an average radius of 2.8 Earth radii, while orbital periods range from 0.8 to 180 days. Van Eylen and Albrecht conclude that it is plausible that low eccentricity orbits would be common in solar systems like ours, a finding that would have ramifications for habitability and the location of the habitable zone.

Interestingly, when weighed against parameters like the host star’s temperature and age, no trend emerges. But in systems with multiple transiting planets on circular orbits, Van Eylen and Albrecht believe that the density of the host star can be reliably estimated from transit observations. This information can help to rule out false positives, a technique they use to validate candidate worlds in several systems — KOI-270, now Kepler-449, and KOI-279, now Kepler-450, as well as KOI-285.03, now Kepler-92d, in a system with previously known planets.

The work has helpful implications for upcoming space missions that will generate the data needed for putting these methods to further use:

We anticipate that the methods used here will be useful in the context of the future photometry missions TESS and PLATO, both of which will allow for asteroseismic studies of a large number of targets. Transit durations will be useful to confirm the validity of transit signals in compact multi-planet systems, in particular for the smallest and most interest[ing] candidates that are hardest to confirm using other methods. For systems where independent stellar density measurements exist the method will also provide further information on orbital eccentricities.

The TESS mission (Transiting Exoplanet Survey Satellite) is planned for launch in 2017, and is expected to find more than 5000 exoplanet candidates, including 50 Earth-sized planets around relatively nearby stars. PLATO (PLAnetary Transits and Oscillations of stars) will likewise monitor up to a million stars looking for transit signatures, with launch planned by 2024.

The paper is Van Eylen and Albrecht, “Eccentricity from transit photometry: small planets in Kepler multi-planet systems have low eccentricities,” accepted for publication at The Astrophysical Journal (preprint). An Aarhus University news release is available.

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Andrew LePage May 19, 2015 at 14:03

These findings on orbit eccentricity seem to mesh nicely with other recent work on the architecture of extrasolar planetary systems based on an analysis of Kepler data. Kepler data seem to indicate that about half of planetary systems have a single, usually large planet in an eccentric orbit. The other half are multiplanet systems with the orbits being roughly coplanar – very similar to our solar system. This new work implies these latter systems would also tend to have low eccentricity orbits. A review of recent work for red dwarf systems by Sarah Ballard and John Asher Johnson can be found here:

http://www.drewexmachina.com/2014/10/24/architecture-of-m-dwarf-planetary-systems/

Lionel May 19, 2015 at 14:28

Great as always.

Wanted to note that while the article says “the other seven [solar system] planets show an eccentricity of 0.04”, Mars actually orbits with eccentricity 0.0934. It’s aphelion and perihelion are respectively 1.6660 and 1.3814 AU, and, to demonstrate the impact of this somewhat modest eccentricities have on planets, this causes Mars to receive 45% more solar energy at perihelion than aphelion

Andrew LePage May 20, 2015 at 7:56

@Lionel May 19, 2015 at 14:28

While what you say about the eccentricity of the orbit of Mars is certainly correct, I believe that the 0.04 figure refers to the average eccentricity of the seven planets other than Mercury.

Also, the effects of the eccentricity on the orbit of Mars on its solar flux are true as well. But to put this into context it should be noted that the tilt of Earth’s rotational axis can cause the average daily solar flux to vary by a factor of three over the course of the seasons at mid-latitudes (ignoring the effects of seasonal changes in cloud cover and atmospheric transmission) due to the changes in the incidence angle of the Sun’s rays and changes in the length of the day. This is over twice as much as the variation caused by the eccentricity of Mars’ orbit alone. And these seasonal variations are even more pronounced at higher latitudes.

Harry R Ray May 20, 2015 at 9:31

Andrew Le Page: The above method used by the above authors is somewhat inhibited by TTV’s (in fact, in their paper, the authors found a couple of systems thought not to have TTV’, to ACTUALLY have them), but, there is a new method called the “Photoeccentric Effect” that can do what these authors did in systems with EXTREME TTV’s. The advantage HERE is that not only can you pin down the eccentricities of the planets, but there MASSES as well. Case-in-point, Chthonian planet CANDIDATES Kepler 52b, Kepler 52c, and Kepler 57b could have their Chthonian nature CONFIRMED if their orbits were found to be either perfectly circular, or near-perfectly circular. Up until now, this method could only be used fore Jupiter and Super-Jupiter sized planets, but a recent article indicates that the method has been REFINED so tha it can be used for planets in the same size range as the above mentioned ones. Are you familiar with this method, and specifically, how does it DIFFER from the transit duration method?

Mark Zambelli May 21, 2015 at 11:20

@ Andrew LePage

Spot-on Drew. I used the values here http://www.astronomynotes.com/tables/tablesb.htm to get an average of 0.0393 for the remaining seven planets’ eccentricities.
Venus…… 0.0068
Earth……. 0.0167
Mars…….. 0.0934
Jupiter…. 0.0484
Saturn….. 0.0542
Uranus…. 0.0472
Neptune.. 0.0086

Mark Zambelli May 21, 2015 at 11:31

Our solar system behaves very nicely when considering Ceres and Vesta (0.0789 and 0.0895 respectively). These are more circular than Mars. Is there a resonance with Jupiter at play on these two massive asteroids to explain their eccentricities? Or does ‘circular system’ apply down to lower mass scales like sub-earths and therefore should be unsuprising in such circular systems as our own?

Lionel Ward May 21, 2015 at 15:39

@Andrew LePage

Thanks for those points which put what I wrote into context. Certainly the effect of Earth’s axial tilt causes greater variation in local solar flux. Since we have a thick atomosphere and weather system here to spread out incoming solar energy into other areas, seasonal local variations in solar flux are felt far less on Earth than it otherwise would be. Of course without an atmosphere we would see extreme local variation such those permanently shadowed icy craters on Mercury, as cold as 100 degrees Kelvin. I suppose that when I wrote my original comment I was forgetting that Mars has an incredibly tenuous atmosphere! (possibly because this week I’m doing final exams for my master’s degree so am very sleep deprived ;) ).

James Ray June 7, 2015 at 14:40

Since small planets are currently more likely to be found closer to their stars, and most giant planets with circular orbits are “hot Jupiters” close to their stars, it seems an alternative but equally valid hypothesis is that planets farther away from their stars tend to have orbits of higher eccentricity, regardless of their size. I wonder if the study referenced above supports this hypothesis, i.e. if the planets found to have circular orbits were also relatively close to their stars.

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