Sunday, February 8, 2015

What Kepler Hasn't Told Us

Figure 1. Kepler planet candidates (N = 3697) identified in twelve quarters (three years) of transit data, graphed by radius and orbital period. Most Kepler planets have radii between 1 and 4 times Earth (1-4 Rea) and periods shorter than 200 days. The red box marks the parameter space for Earth-size planets (0.8-1.4 Rea) orbiting Sun-like stars (spectral types G to mid K). This figure is based on the upper panel of Figure 4 of Rowe et al. 2015, with the red box added.
Observations by the Kepler Telescope in fulfillment of its original mission ended in May 2013. Both before and after that date, battalions of astronomers have deployed their talents to analyze the voluminous data collected over 47 months. This work still continues. A new publication (Silburt et al. 2015) and two new preprints (Rowe et al. 2015, Mullally et al. 2015) represent the latest attempts to summarize Kepler’s implications for our understanding of extrasolar worlds.

an abundance of puffy planets
The stated goal of Ari Silburt and colleagues is to “reconstruct the intrinsic occurrence” of low-mass planets, defined as objects between one and four Earth radii (1-4 Rea), around “Solar type” stars, defined as stars between 80% and 120% of the Sun’s radius (0.8-1.2 Rsol). The latter criterion corresponds to an approximate range of 0.75 to 1.25 Solar masses (0.75-1.25 Msol), ruling out a large fraction of confirmed Kepler host stars. They further limit their sample to planet candidates with periods between 20 and 200 days. The lower limit is intended to screen out objects that have been sculpted by the intense stellar flux typical of short-period orbits; many such planets have evidently suffered partial or total loss of atmosphere. The upper limit responds to the dearth of robust data on the parameter space beyond 200 days. Even with the full 16 quarters of observations in hand, the authors note “Kepler’s low efficiency at detecting long-period planets.”

Within their carefully limited sample, they find that the occurrence rate for planets peaks at radii between 2 and 2.8 Rea. (Including objects at shorter periods would have shifted that peak to the smaller radii resulting from atmospheric ablation.) Virtually all planets in this range have bulk compositions that are a few percent gaseous hydrogen and helium (H/He). Most of them probably have masses in the range of 3-10 Mea and surface conditions dominated by powerful greenhouse effects. I’ve been calling them “gas dwarfs” for the past few years, and I notice that the term seems to be catching on, though many authors still prefer “mini-Neptunes.”

Silburt and colleagues draw an interesting comparison between this abundance of extrasolar gas dwarfs and the inner Solar System, which contains only “bare cores” without H/He envelopes:

“Our terrestrial planets are thought to have formed in a gas-free environment by conglomeration of solid materials. The relative shortage of bare-core planets may suggest that the observed Kepler planets may have followed different formation path.”

Clearly the authors are exercising caution in making this generalization. At the moment, though, there seems little doubt that Kepler’s compact systems of puffy planets coagulated rapidly in the presence of a gaseous protoplanetary nebula. The terrestrial planets in our own system, on the other hand, assembled after the Solar nebula dissipated. They appear to be the outcome of a game of galactic pinball played with Moon- and Mars-size embryos over tens of millions of years. This divergence in formation pathways motivates an interesting question: do the Earth-size objects observed in the company of puffy planets truly resemble Earth and Venus, or has their early formation led to very different conditions, despite small radii and thin atmospheres? Natalie Batalha, one of the most visible members of the Kepler team, has already suggested an answer: “There may not be a simple evolutionary pathway that lands an exoplanet inside of a well-defined HZ.”

a shortage of planets like earth
Jason Rowe and colleagues summarize a slightly shorter span of Kepler data, limiting their overview to the first twelve quarters, which represent three years of observations. They report a new total of 3697 planet candidates over the lifetime of the main mission, of which 1013 have been formally confirmed. Several diagrams encapsulate their description. One is the basis of Figure 1, above, which illustrates Kepler’s limited reach in the parameter space occupied by Earth.

A highlight of the article is its section on potentially rocky planets in the habitable zone. These are listed in a table of 13 Kepler Objects of Interest (KOIs), selected on the basis of radius and insolation. Since we’re reading a preprint, it’s uncertain whether the published article will feature revised parameters for any of these objects, or even a different selection altogether. Until then, we can have fun assessing what’s there.

Approximately half the objects in Rowe’s list overlap with the sample presented by Torres et al. last month. These include Kepler-186f and Kepler-438b. Another familiar name on the list is our old friend Kepler-62f. A notable omission is Kepler-442b, reported by Torres’ group but not Rowe’s. After discarding the objects already shown to have larger radii than the ones provided by Rowe et al. (3255.01, 4087.01, 2626.01, 1422.04, 1422.05), as well as an interesting Mars-size planet orbiting a very dim M dwarf (3138.01), the net yield of their selection is four new Earth-like candidates. One of them was recently confirmed as Kepler-395c, the outer of two Earth-size planets orbiting an M dwarf. The other three still have the status of KOIs (2124.01, 2418.01, 4427.01). Accordingly, here is the current best-guess line-up of potentially Earthlike exoplanets, listed in order of increasing radius:

Table 1. Five Potentially Earthlike Extrasolar Planets 
Column 1 presents the host star’s name; column 2 the stellar effective temperature in Kelvin; column 3 the stellar mass in Solar units; column 4 the stellar metallicity; column 5 the stellar age in billions of years; column 6 the distance to the system in parsecs; column 7 the planet name; column 8 the KOI number; column 9 the planet radius in Earth units; column 10 the orbital semimajor axis in astronomical units (Earth’s orbit = 1); column 11 the planet equilibrium temperature in Kelvin; and column 12 the orbital period in days. Data on equilibrium temperatures, and all data on Kepler-62 and Kepler-395, derive from the Kepler Discoveries Table. Other data follow Torres et al. 2015.
Kepler-395c blends smoothly into the growing list of temperate transiting terrestrials with official validation by Kepler scientists. Kepler-62f, however, looks a bit like an outlier. All the other planets in Table 1 orbit M dwarfs on periods shorter than 200 days, and all have smaller estimated radii.

Table 2. Three Potentially Earthlike Kepler Objects of Interest (KOIs)

Column 1 presents the host star’s name; column 2 the stellar effective temperature in Kelvin; column 3 the stellar radius in Solar units; column 4 the KOI number of the planet candidate; column 5 the planet radius in Earth units; column 6 the orbital semimajor axis in astronomical units (Earth’s orbit = 1); column 7 the planet equilibrium temperature in Kelvin; and column 8 the orbital period in days. Data follow the NASA Exoplanet Archive.

The three KOIs identified by Rowe and colleagues also orbit M dwarfs on periods shorter than 200 days, though one of them (KOI-4427.01) is a bit larger than Kepler-62f. Notably, Rowe’s group reports that the parent star of KOI-2418.01 exhibits spots and flaring, the sort of behavior that gives M dwarfs a bad reputation these days.

And so – even in this expanded sample of potentially Earthlike planets, not a single G-type star appears. Kepler-62 remains the only K-type star, and its fifth planet retains the record for the smallest confirmed planet at the longest orbital period.

eta earth revisited
In their opening paragraph, Rowe and colleagues remind us that “The primary objective of the Kepler Mission is to determine the frequency of Earth-like planets around Solar-like stars.” So far, alas, the frequency seems to be one per galaxy.

As Silburt and colleagues observe, all calculations of “Eta Earth” – the fraction of Sun-like stars with Earth-like planets in their habitable zones – are based on extrapolations, since no Earth-like planets have been reported around any Sun-like star except our own. Notwithstanding, they conclude their study by estimating Eta Earth at 6.4%. They add a caveat, however, explaining that they do so “more out of respect for tradition than with any conviction that there is additional accuracy to be assigned to our calculation.” Notably, their estimate is less than one-third of the 22% calculated in 2013 by Erik Petigura and colleagues.

In an article published in September 2014, Natalie Batalha stated that substantial Kepler data still awaited analysis. Her outlook at the time was optimistic: “Hundreds of new discoveries are expected, including the first small planet candidates in the HZ of G-type stars.” Given all the new candidates summarized by Rowe et al., without a single small planet in the green zone of a G star, that optimism will surely be tested over the remainder of 2015. 

postscript on February 16, 2015

Last week, hot on the heels of the preprint by Rowe & colleagues summarizing 36 months of Kepler data (hereafter Rowe 2015), another team led by Fergal Mullally (and including most collaborators on Rowe 2015) released another preprint based on the full 47 months of data. 

Like its very recent predecessor, this article (hereafter Mullally 2015) devotes most of its attention to a description of vetting procedures for transit crossing events. It does not attempt to characterize the full Kepler population in any detail. Nevertheless, it does address the question of Earth-like planets orbiting Sun-like stars. We are shown a “Table of Small HZ Candidates” (Table 2, Mullally 2015), which is described as listing “our strongest candidates for rocky HZ planets.” The table provides select data on six candidates, all KOIs rather than confirmed planets. Readers are referred to the NASA Exoplanet Archive for more information.

Having consulted the archive, I’m struck by the oddness of this selection. Unlike Rowe 2015 and Torres et al. 2015 (see Tables 1 and 2 in the present post and in Much Ado About Earth 2), Mullally 2015 takes 2 Rea instead of 1.5 Rea as the upper limit for Earth-like planets. The authors explain their choice by referring to an unpublished manuscript by Leslie Rogers (2014). However, they omit mention of the manuscript’s title, which is actually “Most 1.6 Earth-Radius Planets Are Not Rocky.” 

The good news about their table is that at least four of the six candidates appear to orbit G-type stars. The bad news is that only one or two of the six are likely to have radii smaller than 1.5 Rea. The authors provide extremely wide error margins for planet radius and equilibrium temperature, noting that the principal source of error for planet radius is uncertainty about host star radius. Their preferred values are near the low end of the range in each case. Within errors, four of their candidates might actually be larger than 2 Rea, and one of them might be almost 3 Rea. Such radii are associated with atmospheres containing H/He, which are generally considered inimical to surface water.

Table 3. Small KOIs in the Habitable Zones of Sun-like Stars
Column 1 presents the host star’s name; column 2 the stellar effective temperature in Kelvin; column 3 the stellar radius in Solar units; column 4 the KOI number of the planet candidate; column 5 the planet radius in Earth units with error margins; column 6 the orbital semimajor axis in astronomical units (Earth’s orbit = 1); column 7 the planet equilibrium temperature in Kelvin; and column 8 the orbital period in days. Data follow the NASA Exoplanet Archive.

So let’s take a look at their most promising candidates. Table 3 shows the three smallest KOIs that they propose. KOI-2194 is actually Kepler-371, an early G-type star with two confirmed Super Earths: Kepler-371b, with a period of 34.76 days, and Kepler-371c, with a period of 67.96 days. Thus KOI-2194.03 arrives in good company, and may well be real. However, the NASA Exoplanet Archive disagrees with the Kepler Discoveries Table regarding the radius of Kepler-371, and thus the radii of its two confirmed companions. The latter source provides a stellar radius of 0.990 instead of 0.922 Rsol. Depending on which value we use, the radius of Kepler-371b jumps from 1.69 to 1.89 Rea, and of Kepler-371c from 1.54 to 1.78 Rea. A corresponding boost in the radius of KOI-2194.03 would put it in the no-no zone defined by Rogers 2014.

In the case of KOI-5737.01, ignorance might be bliss. The preferred radius in the NASA Exoplanet Archive is 1.32 Rea, corresponding to at least two possible compositions: an iron/silicate planet with the same composition as Earth and a mass of about 2.5 Mea, or a less massive planet with an Earth-like core and a mantle of high-pressure ice accounting for 2% to 50% of its bulk composition. The latter option would correspond to masses ranging from about 2.3 down to 1.3 Mea, but such icy environments are probably unfriendly to life. 

KOI-5068 is the oddball in this group, since its effective temperature appears discordant with its radius. The value provided, 6440 K, is more typical of a mid-F star than a G star. By comparison, the effective temperature of our Sun (spectral type G2) is only 5777 K, while the nearby host star Upsilon Andromedae A, with a radius of 1.5 Rsol, has an effective temperature of 6014 K and a spectral type of F8. Even at the stellar and planetary radii endorsed by Mullally 2015, an Earth-like composition for KOI-5068.o1 would yield a mass of about 5 Mea. A significant increase in stellar radius would push the planet into the gas dwarf range, with a puffy atmosphere but not necessarily a higher mass.

And so – our first glimpse of small candidates for G-type habitable zones has proven anticlimactic. At the moment KOI-5737.01 seems the most promising choice, so I look forward to future analyses. Meanwhile, among the combined sample of host stars detailed in Tables 1 through 3 above, I note a strange gap in the range of effective temperatures between 4950 and 5900 K. The habitable zones of such stars correspond to periods between about 150 and 450 days. The lower half of this range, between 150 and 300 days, seems within reach of the 47-month Kepler dataset. A planet orbiting in 200 days would transit at least 7 times over this time frame; a planet orbiting in 300 days would transit at least 4 times. Yet among the eleven planets characterized on this page, only one has a period between 150 and 300 days: our old friend Kepler-62f.

Batalha N. (2014) Exploring exoplanet populations with NASA’s Kepler Mission. Publications of the National Academy of Sciences 111, 12647–12654.
Dressing C, Charbonneau D, Dumusque X, Gettel S, Pepe F, Collier Cameron A, and 29 others. (2014) The mass of Kepler-93b and the composition of terrestrial planets. In press. Abstract: 2014arXiv1412.8687D
Mullally F, Coughlin JL, Thompson SE, Rowe J, Burke C, Latham DW, and 54 others. (2015) Planetary Candidates Observed by Kepler VI: Planet Sample from Q1-Q16 (47 Months). In press. Abstract: 2015arXiv150202038M
Petigura E, Howard AW, Marcy GW. (2013) Prevalence of Earth-size planets orbiting Sun-like stars. Publications of the National Academy of Sciences 110, 19273-19278.
Rogers L. (2014) Most 1.6 Earth-radius planets are not rocky. Unpublished manuscript. Abstract: 2014arXiv1407.4457R
Rowe J, Coughlin JL, Antoci V, Barclay T, Batalha NM, Borucki WJ, and 41 others. (2015) Planetary Candidates Observed by Kepler V: Planet Sample from Q1-Q12 (36 Months). In press. Abstract:
Silburt A, Gaidos E, Wu Y. (2015) A statistical reconstruction of the planet population around Kepler Solar-type stars. Astrophysical Journal 799, 180. doi:10.1088/0004-637X/799/2/180


  1. I'm reserving judgment until we can reliably find planets with smaller-than-Earth radius around sun-like stars at decent orbital distances (like the asteroid belt distance), assuming we ever have the capabilities to find them. If we've got that and it turns out that the planet distribution peaks in the "gas dwarf" category, then I guess we'll have a pretty good answer. Not a happy one if you're hoping for life - although even 1 Earth-like planet in a sample of 145,000 gives you a couple million of them in the Milky Way - but an answer.

  2. Sorry, ". . . and it turns out that the planet distribution still peaks in the "gas dwarf" category".

  3. I somewhat doubt the accuracy of these eta-Earth calculations which are based on completeness assumptions. I suspect the transit detection probability for that red box is so low that the effect of a few fluke detections (or non-detections) is vastly amplified in the eta-Earth calculation ...

  4. Admirable skepticism all around :) I just updated this post with details from an even more recent preprint by the Kepler team.