The Planet Population Plateau


An outline of the paper: A Plateau in the Planet Population below Twice the Size of Earth by Petigura et al.

One of the key scientific objectives of the Kepler mission has been to determine the abundance of terrestrial planets. In fact, with current instrumentation, the Kepler mission has been the only instrument capable of detecting planets in the 1-2RE radius regime. In the pursuit of performing a statistical analysis of the smallest planets detectable, Petigura et al. set out to determine the fraction of stars harbouring transiting planets with sizes 0.5 – 8.0 times that of Earth. In particular they were interested in knowing the distribution of Earth-size planets as a function of orbital period and radius. In Mayor et al. (2011) and Howard et al. (2010) we saw how the radii of planets follow a power-law rise in occurrence with smaller planets being much more abundant than hot-Jupiters. In Howard et al. (2012) we saw how the number of planets per star clearly flattened out beyond a planetary radius of ~2 RE:


Plot from Howard et al. (2012) showing the planet occurrence as a function for planets with a period < 50 days. The hatched region marks the region where the occurrence statistics are incomplete. The error bars represent the statistical uncertainties and do not include the systematic effects which become important in the region where the detection sensitivity drops off (<2RE).

However, in Howard et al. (2012) caution was taken when interpreting the planet occurrence below ~2 RE as no completeness analysis of the Kepler pipeline had been done. This time around Petigura et al. assess the completeness of their sample by the injection of synthetic dimmings into the Kepler data itself to simulate transit events. By seeing how many of the injected transits they recover they assess the sample completeness. Characterising the sample of missed planets is equally important as detecting planets, especially for smaller planets where the statistics hinges on the completeness of the sample.

The dataset consisted of three years worth of Kepler photometry with a carefully selected subsample of the quietest 12,000 solar type (GK-type) stars with photometry good enough to allow for the detections of planets down to 1 RE. The authors independently analyse the Kepler photometry using the transit search algorithm pipeline, TERRA. They detect 129 planet candidates, ranging from 6.83 to 0.48 Rwith a median exoplanet candidate radius of 1.58 RE.  The authors present a number of interesting results such as the occurrence rate of exoplanets as a function of orbital period and planetary radius. What I personally found very interesting was the radius distribution of the smaller planets and how the occurrence rate flattens beyond ~2 RE:


Although the group are not the first to see this effect, they are the first to independently analyse the Kepler data, taking completeness into account and confirming the flat relation for planets in the 1-2.8 RE radius range. Currently this plateau is not well understood theoretically, and there is a lot of debate ongoing on how core accretion happens, i.e. how the material moves or on what timescales.

The large occurrence of sub-Neptune planets (< 4 RE) around sun-like stars on orbits less than 0.25 AU support the in situ core accretion formation scenario, whereby planets form near their current location without migrating. An alternative formation model consists of the planet having formed further out (beyond the water ice snow line at ~2 AU) and subsequently migrated inwards. More on snowlines here. The authors argue the latter model seems less likely  judging by the recent Kepler statistics, as an inward migration beyond ~2 AU ceasing at 0.25 AU without migrating further inwards, requires finely tuned models. This is not to say the in situ formation theory is the solution. In fact, the in situ formation scenario requires a substantial amount of rocky material (~50 – 100 ME) interior to 1 AU (Hansen and Murray, 2012) which is in excess of many protoplanetary disk mass profiles. A way of testing the in situ vs the inward migration hypothesis would we be to conduct spectroscopic measurements to probe the chemical composition of the planet atmospheres. If the in situ model is correct, the planets are expected to be predominantly composed of a rocky core with a thick H/He envelope, whereas the inward migration model is more likely to result in a rocky core with a water-dominated atmosphere. This is one of the reasons why planets such as GJ 1214b (more here and here) are of particular interest.


Further Reading:

Prevalence of Earth-size planets orbiting Sun-like stars by Petigura et al. 2013 (Conference proceeding)

Papers on planet migration:

Toward A Deterministic Model Of Planetary Formation Vi: Dynamical InteractionAnd Coagulation Of Multiple Rocky Embryos And Super-earth Systems AroundSolar Type Stars by Ida & Lin 2010

Extrasolar planet population synthesis by Mordasini et al.

Papers on in situ formation:

Migration then assembly: Formation of Neptune mass planets inside 1 AU by Hansen and Murray

The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths by Chiang and Laughlin


Feature image credit: NASA Ames/JPL-Caltech


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Editor of Observational exoplanet and brown dwarf astronomer studying the atmospheres of exoplanets. Interested in public outreach and conveying my interest in astronomy to others. Follow me on Twitter or Google+. (More)