An Important Clue for Earth-sized Planets- A Plateau in the Exoplanet Size Distribution

by Dr. Tahir Yaqoob on April 16, 2013

Robust, observational, empirical results are highly desirable and sought-after because they have the potential to make or break theoretical scenarios and thereby provide a significant step forward in understanding. However, such diagnostics are relative rare in exoplanet science, especially with respect to population and demographic properties. One of the holy grails is to understand the planet formation and migration mechanisms. A recent paper posted on in April 2013 (submitted but not yet refereed) reports on a result which may become a cornerstone in the endeavor to tackle the question of the occurrence rate of Earth-sized or near-Earth-sized planets, how they form, and how that formation mechanism fits in with planet formation scenarios in general. Yet the result is a bit too technical to make it to mainstream headlines, although eventually further work will attempt to address the occurrence rate of Earth-sized planets that could support life, at which point it will become more widely appreciated. However, this blog caters to readers who want a bit more depth than is given in the mainstream media, and here you can get in “on the ground floor” so to speak. I think it is quite an exciting result, even though it is not yet clear what it means. What I mean by this can be conveyed by the analogy of the discovery of photographic plates being fogged-up by X-rays. We had no idea what X-rays were but it quickly became clear that the observational result of the fogging-up of the plates was a clue to something quite important.

The paper is entitled, A Plateau in the Planet Population Below Twice the Size of Earth, by Petigura, Marcy, and Howard. Those of you who have been following the story of exoplanets will know that G. Marcy is by now a household name in exoplanet science. The goal of the paper, and in similar studies, can be summarized as an attempt to measure the true fractions of sun-like stars that harbor planets in given size intervals. As mentioned in previous posts, this cannot be done simply by counting discovered exoplanets or exoplanet candidates because corrections have to be applied for complex biases that make some portion of the true exoplanet population invisible. This is quantified by a measure referred to as “completeness,” which in this study is given as a function of intervals of exoplanet period and exoplanet size. (A completeness of 100% means that no exoplanets have been missed, either due to observational bias, or due to biases in the detection algorithms that pull a signal clear of the noise.) This is a very difficult task, especially for small planets in the regime of Earth size because the transit signals (light variations as the planet passes across the host star) are weak because of the small fraction of the star’s area that is occulted. In the authors’ own words: “For the smallest planets, uncertainty in the occurrence distribution stems largely from pipeline incompleteness due to the low signal-to-noise ratio (SNR) of an Earth-size transit.” Here and hereafter, pipeline refers to the set of computational and analysis procedures that are applied to the data to arrive at the final results. The authors succinctly summarize the importance of quantifying completeness: “When measuring the distribution of planets as a function of orbital period and planet size, understanding the number of missed planets is as important as finding planets themselves.”

To avoid any confusion in what exoplanet sample we are talking about, the exoplanets that the study refers to are neither the confirmed exoplanets (as reported, for example, in the Extrasolar Planets Encyclopedia), nor the Kepler mission exoplanet candidates derived by the Kepler team. The study does make use of the same Kepler field data, but independently comes up with a new subsample of small exoplanets (small with respect to Neptune-sized and Jupiter-sized planets). So what is different? The authors have devised their own pipeline, a new set of algorithms and procedures, which they have named “TERRA.” It focuses specifically on small planets with orbital periods in the range 5 to 50 (Earth) days, and sizes in the range of a half to 16 times the size of Earth. The authors claim to calculate a better completeness function than that by the Kepler team, mainly attributable to extensive simulations in which fake data are created and run through the same pipeline as the real data in order to quantify completeness robustly. (The simulations are referred to as “recovery experiments,” since the procedure attempts to evaluate the fractions of the fake exoplanets that are recovered by the pipeline.) It may be somewhat surprising that the analysis of the Kepler data so far reported in the literature has not yet achieved the desired completeness corrections. In the authors’ words:

“While the Kepler Project has initiated a completeness study of the official pipeline (Christiansen et al. 2012), TERRA is the only pipeline for Kepler photometry whose detection completeness has been calibrated by injection and recovery tests.”

The authors go on to clarify that prior to their innovation (TERRA), completeness was either assumed (down to some arbitrarily signal-to-noise ratio level), or completeness was estimated without the end-to-end empirical testing of the performance of the algorithms in the pipeline.

Rewinding a bit, a precursor study in 2012 (Howard et al. 2012) which involved two of the authors of the paper reported on here, tentatively found that planets with radii smaller than Neptune’s radius become more and more common but that this increase in occurrence rate stops at some “critical” radius, after which the occurrence rate levels off (becomes flat). The reason why this is so important is that it implies that there is some aspect of planet formation and/or migration which is not scale-free. In other words, there is something special about a radius between 1 to 3 Earth radii. What that “something” is has yet to be discovered and it is this that makes the result profound and exciting. The present paper by Petigura et al (2013) confirms the result much more robustly than the earlier tentative result. At the end of the paper the possible implications are discussed but nothing is settled, the main conclusion being that the result presents problems for all current planet formation and migration scenarios. In general, when direct empirical observational results conflict with the theories de jour, it is usually a good indicator that things are about to shift dramatically — a precursor for significant advances in understanding. Adapting an old saying, it is easy to flog a dead horse if nobody can prove that the horse is dead.

The bulk of the Petigura et al (2013) paper describes the detailed selection criteria, methodology and pipeline that the authors have developed, along with the simulations used to rigorously derive the completeness estimates. The authors base their analysis on 12,000 of the Kepler sun-like stars that have the highest quality data, and (rather unimaginatively), they call their sample, Best12k. I will not go into the details of the methodology here. However, an important point is that the authors describe how their method does have the shortfall that it is blind to multiplanet systems. So their definition of occurrence rate refers to the frequency of occurrence of sun-like stars with one or more planets (of given period and size), rather than the more usual average number of planets per star system.

Finally, as you may be wondering, the authors do compare their results to the pipeline results of the official Kepler team analysis, and they do find important differences. They find a total of 129 planets in their sample (but they do not use 10 that were marked as false positives by the Kepler team.) The authors find that 82 planets overlap with the official Kepler exoplanet candidates. That leaves 47 that are not in the official sample (i.e. new exoplanet candidates). Conversely, 33 candidates that are not in the official sample, are not found by TERRA. All but 5 of these can be attributed to blindness to multiplanet systems. The authors claim that when these 5 missed planets are included, their main result (a flattening of the occurrence rate below about 2.8 Earth radii) is not impacted. It is important to remind the reader here that in this entire work we are only ever talking about candidates, not confirmed exoplanets. However, the authors point out that the all the data and tools that they used are public and anyone is welcome to analyze the data and argue for any discrepancies that they might find in a re-analysis.

Finally, the paper offers some key statements that look to the future. Here is one of them:

“These low noise stars offer the best chance for the detection of small, Earth-size planets in the Kepler field and will one day be among the stars from which the fraction of sun-like stars bearing Earth-size planets in habitable zone orbits-is estimated.”

In other words, these stars and exoplanet candidates that the authors have identified will become (not might become) part of the calculation that offers an overall estimate of occurrence rate of habitable Earth-like planets in our Galaxy. The authors point out that their result is based on 3 years of data, and 5 more years with the extended Kepler mission will enable the measurements for habitable-zone orbits. Here’s another key statement:

“Close-in, small planets are now the most abundant planets detected by current transit and Doppler searches, yet they are absent from the solar system.”

One more that succinctly summarizes the result of finding a plateau in the exoplanet size distribution:

“The onset of the plateau at 2.8 Earth radii suggests that there is a preferred size scale for the formation of close-in planets.”

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