The Role of Core Mass in Controlling Evaporation: the Kepler Radius Distribution and the Kepler-36 Density Dichotomy
TL;DR: In this article, the authors use models of coupled thermal evolution and photo-evaporative mass loss to understand the formation and evolution of the Kepler-36 system and find that the large contrast in mean planetary density observed by Carter et al. (2012) can be explained as a natural consequence of photoevaporation from planets that formed with similar initial compositions.
Abstract: We use models of coupled thermal evolution and photo-evaporative mass loss to understand the formation and evolution of the Kepler-36 system. We show that the large contrast in mean planetary density observed by Carter et al. (2012) can be explained as a natural consequence of photo-evaporation from planets that formed with similar initial compositions. However, rather than being due to differences in XUV irradiation between the planets, we find that this contrast is due to the difference in the masses of the planets' rock/iron cores and the impact that this has on mass loss evolution. We explore in detail how our coupled models depend on irradiation, mass, age, composition, and the efficiency of mass loss. Based on fits to large numbers of coupled evolution and mass loss runs, we provide analytic fits to understand threshold XUV fluxes for significant atmospheric loss, as a function of core mass and mass loss efficiency. Finally we discuss these results in the context of recent studies of the radius distribution of Kepler candidates. Using our parameter study, we make testable predictions for the frequency of sub-Neptune sized planets. We show that 1.8-4.0 R_earth planets should become significantly less common on orbits within 10 days and discuss the possibility of a narrow "occurrence valley" in the radius-flux distribution. Moreover, we describe how photo-evaporation provides a natural explanation for the recent observations of Ciardi et al. (2013) that inner planets are preferentially smaller within the systems.
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TL;DR: The size of a planet is an observable property directly connected to the physics of its formation and evolution as discussed by the authors, and the size of close-in (P < 100 days) small planets can be divided into two size regimes: R_p < 1.5 R⊕ or smaller with varying amounts of low-density gas that determine their total sizes.
Abstract: The size of a planet is an observable property directly connected to the physics of its formation and evolution. We used precise radius measurements from the California-Kepler Survey to study the size distribution of 2025 Kepler planets in fine detail. We detect a factor of ≥2 deficit in the occurrence rate distribution at 1.5–2.0 R⊕. This gap splits the population of close-in (P < 100 days) small planets into two size regimes: R_p < 1.5 R⊕ and R_p = 2.0-3.0 R⊕, with few planets in between. Planets in these two regimes have nearly the same intrinsic frequency based on occurrence measurements that account for planet detection efficiencies. The paucity of planets between 1.5 and 2.0 R⊕ supports the emerging picture that close-in planets smaller than Neptune are composed of rocky cores measuring 1.5 R⊕ or smaller with varying amounts of low-density gas that determine their total sizes.
1,100 citations
TL;DR: In this article, the authors show that the envelope erosion is the longest for those planets with hydrogen/helium-rich envelopes that, while only a few percent in weight, double its radius.
Abstract: A new piece of evidence supporting the photoevaporation-driven evolution model for low-mass, close-in exoplanets was recently presented by the California-Kepler-Survey. The radius distribution of the Kepler planets is shown to be bimodal, with a ``valley' separating two peaks at 1.3 and 2.6 Rearth. Such an ``evaporation-valley' had been predicted by numerical models previously. Here, we develop a minimal model to demonstrate that this valley results from the following fact: the timescale for envelope erosion is the longest for those planets with hydrogen/helium-rich envelopes that, while only a few percent in weight, double its radius. The timescale falls for envelopes lighter than this because the planet's radius remains largely constant for tenuous envelopes. The timescale also drops for heavier envelopes because the planet swells up faster than the addition of envelope mass. Photoevaporation, therefore, herds planets into either bare cores ~1.3 Rearth, or those with double the core's radius (~2.6 Rearth). This process mostly occurs during the first 100 Myrs when the stars' high energy flux are high and nearly constant. The observed radius distribution further requires that the Kepler planets are clustered around 3 Mearth in mass, are born with H/He envelopes more than a few percent in mass, and that their cores are similar to the Earth in composition. Such envelopes must have been accreted before the dispersal of the gas disks, while the core composition indicates formation inside the ice-line. Lastly, the photoevaporation model fails to account for bare planets beyond ~30-60 days, if these planets are abundant, they may point to a significant second channel for planet formation, resembling the Solar-System terrestrial planets.
640 citations
TL;DR: In this article, the authors apply a hierarchical Bayesian statistical approach to the sample of Kepler transiting sub-Neptune planets with Keck RV follow-up, constrain the fraction of close-in planets (with orbital periods less than ~50 days) that are sufficiently dense to be rocky, as a function of planet radius.
Abstract: The Kepler Mission, combined with ground based radial velocity (RV) follow-up and dynamical analyses of transit timing variations, has revolutionized the observational constraints on sub-Neptune-size planet compositions. The results of an extensive Kepler follow-up program including multiple Doppler measurements for 22 planet-hosting stars more than doubles the population of sub-Neptune-sized transiting planets that have RV mass constraints. This unprecedentedly large and homogeneous sample of planets with both mass and radius constraints opens the possibility of a statistical study of the underlying population of planet compositions. We focus on the intriguing transition between rocky exoplanets (comprised of iron and silicates) and planets with voluminous layers of volatiles (H/He and astrophysical ices). Applying a hierarchical Bayesian statistical approach to the sample of Kepler transiting sub-Neptune planets with Keck RV follow-up, we constrain the fraction of close-in planets (with orbital periods less than ~50 days) that are sufficiently dense to be rocky, as a function of planet radius. We show that the majority of 1.6 Earth-radius planets are too low density to be comprised of Fe and silicates alone. At larger radii, the constraints on the fraction of rocky planets are even more stringent. These insights into the size demographics of rocky and volatile-rich planets offer empirical constraints to planet formation theories, and guide the range of planet radii to be considered in studies of the occurrence rate of "Earth-like" planets, $\eta_{Earth}$.
492 citations
Additional excerpts
...1 Myr) (Rogers et al. 2011; Lopez & Fortney 2013)....
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TL;DR: In this paper, the authors investigate the presence, location, and shape of a radius valley using a small sample with highly accurate stellar parameters determined from asteroseismology, which includes 117 planets with a median uncertainty on the radius of 3.3 per cent.
Abstract: Various theoretical models treating the effect of stellar irradiation on planetary envelopes predict the presence of a radius valley, i.e. a bimodal distribution of planet radii, with super-Earths and sub-Neptune planets separated by a valley at around ≈2R⊕. Such a valley has been observed recently, owing to an improvement in the precision of stellar and therefore planetary radii. Here, we investigate the presence, location, and shape of such a valley using a small sample with highly accurate stellar parameters determined from asteroseismology, which includes 117 planets with a median uncertainty on the radius of 3.3 per cent. We detect a clear bimodal distribution, with super-Earths (≈1.5R⊕) and sub-Neptunes (≈2.5 R⊕) separated by a deficiency around 2R⊕. We furthermore characterize the slope of the valley as a power law R∝Pγ with
γ=−0.09^(+0.02)_(−0.04). A negative slope is consistent with models of photoevaporation, but not with the late formation of rocky planets in a gas-poor environment, which would lead to a slope of opposite sign. The exact location of the gap further points to planet cores consisting of a significant fraction of rocky material.
396 citations
Cites background from "The Role of Core Mass in Controllin..."
...Similarly, Lopez & Fortney (2013) predict an occurrence valley with a width of roughly 0.5 R⊕, occurring at larger radii for closer-in planets....
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...Indeed, if sub-Neptune planets formed beyond the snowline, they would have large amounts of water and volatile ices (Rogers et al. 2011), which may completely eliminate the presence of any radius gap (Lopez & Fortney 2013)....
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...…a “photoevaporation desert”, i.e. an absence of sub-Neptunesize planets (1.8 − 4.0 R⊕) and an increase in rocky planets (R<1.8 R⊕) has been predicted (Lopez & Fortney 2013) and observed with increasing clarity as the precision of stellar parameters increased (Borucki et al. 2011; Lundkvist et…...
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Aarhus University1, University of Birmingham2, Yale University3, University of Paris4, Centre national de la recherche scientifique5, Space Science Institute6, University of Sydney7, Australian National University8, Search for extraterrestrial intelligence9, Spanish National Research Council10, Pennsylvania State University11, Max Planck Society12, Iowa State University13
TL;DR: In this article, the authors present a study of 33 planet-candidate host stars for which asteroseismic observations have sufficiently high signal-to-noise ratio to allow extraction of individual pulsation frequencies.
Abstract: We present a study of 33 {\it Kepler} planet-candidate host stars for which asteroseismic observations have sufficiently high signal-to-noise ratio to allow extraction of individual pulsation frequencies. We implement a new Bayesian scheme that is flexible in its input to process individual oscillation frequencies, combinations of them, and average asteroseismic parameters, and derive robust fundamental properties for these targets. Applying this scheme to grids of evolutionary models yields stellar properties with median statistical uncertainties of 1.2\% (radius), 1.7\% (density), 3.3\% (mass), 4.4\% (distance), and 14\% (age), making this the exoplanet host-star sample with the most precise and uniformly determined fundamental parameters to date. We assess the systematics from changes in the solar abundances and mixing-length parameter, showing that they are smaller than the statistical errors. We also determine the stellar properties with three other fitting algorithms and explore the systematics arising from using different evolution and pulsation codes, resulting in 1\% in density and radius, and 2\% and 7\% in mass and age, respectively. We confirm previous findings of the initial helium abundance being a source of systematics comparable to our statistical uncertainties, and discuss future prospects for constraining this parameter by combining asteroseismology and data from space missions. Finally we compare our derived properties with those obtained using the global average asteroseismic observables along with effective temperature and metallicity, finding an excellent level of agreement. Owing to selection effects, our results show that the majority of the high signal-to-noise ratio asteroseismic {\it Kepler} host stars are older than the Sun.
393 citations
Cites background from "The Role of Core Mass in Controllin..."
...…surprising given that evolutionary effects which are expected to affect planet radii or orbital periods such as photoevaporation and orbital migration are expected to occur within <1 Gyr (Lin, Bodenheimer & Richardson 1996; Lopez & Fortney 2013), and our sample does not contain such young stars....
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References
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TL;DR: The detection of atomic hydrogen absorption in the stellar Lyman α line during three transits of HD209458b is reported, showing that this absorption should take place beyond the Roche limit and therefore can be understood in terms of escaping hydrogen atoms.
Abstract: The planet in the system HD209458 is the first one for which repeated transits across the stellar disk have been observed1,2. Together with radial velocity measurements3, this has led to a determination of the planet's radius and mass, confirming it to be a gas giant. But despite numerous searches for an atmospheric signature4,5,6, only the dense lower atmosphere of HD209458b has been observed, through the detection of neutral sodium absorption7. Here we report the detection of atomic hydrogen absorption in the stellar Lyman α line during three transits of HD209458b. An absorption of 15 ± 4% (1σ) is observed. Comparison with models shows that this absorption should take place beyond the Roche limit and therefore can be understood in terms of escaping hydrogen atoms.
1,218 citations
University of California, Berkeley1, Ames Research Center2, San Jose State University3, Lowell Observatory4, Jet Propulsion Laboratory5, University of Texas at Austin6, Harvard University7, Las Cumbres Observatory Global Telescope Network8, Space Telescope Science Institute9, Niels Bohr Institute10, National Center for Atmospheric Research11, Aarhus University12, NASA Exoplanet Science Institute13, Massachusetts Institute of Technology14, Fermilab15, University of California, Santa Cruz16, Yale University17, University of Florida18, California Institute of Technology19, University of California, Santa Barbara20, University of Hertfordshire21, San Diego State University22, Carnegie Institution for Science23, Lawrence Hall of Science24, Villanova University25
TL;DR: In this paper, the authors report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around solar-type (GK) stars.
Abstract: We report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around solar-type (GK) stars. These results are based on the 1235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 R_⊕. For each of the 156,000 target stars, we assess the detectability of planets as a function of planet radius, R_p, and orbital period, P, using a measure of the detection efficiency for each star. We also correct for the geometric probability of transit, R_*/a. We consider first Kepler target stars within the "solar subset" having T_eff = 4100-6100 K, log g = 4.0-4.9, and Kepler magnitude K_p 2 R_⊕ we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50 days, we measure occurrence of 0.130 ± 0.008, 0.023 ± 0.003, and 0.013 ± 0.002 planets per star for planets with radii 2-4, 4-8, and 8-32 R_⊕, in agreement with Doppler surveys. We fit occurrence as a function of P to a power-law model with an exponential cutoff below a critical period P_0. For smaller planets, P_0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over a broader stellar T_eff range of 3600-7100 K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R_⊕ planets in the Kepler field increases with decreasing T_eff, with these small planets being seven times more abundant around cool stars (3600-4100 K) than the hottest stars in our sample (6600-7100 K).
1,159 citations
1,157 citations
TL;DR: In this article, the authors report the distribution of planets as a function of planet radius (R_p), orbital period (P), and stellar effective temperature (Teff) for P < 50 day orbits around GK stars.
Abstract: We report the distribution of planets as a function of planet radius (R_p), orbital period (P), and stellar effective temperature (Teff) for P < 50 day orbits around GK stars. These results are based on the 1,235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 Earth radii (Re). For each of the 156,000 target stars we assess the detectability of planets as a function of R_p and P. We also correct for the geometric probability of transit, R*/a. We consider first stars within the "solar subset" having Teff = 4100-6100 K, logg = 4.0-4.9, and Kepler magnitude Kp < 15 mag. We include only those stars having noise low enough to permit detection of planets down to 2 Re. We count planets in small domains of R_p and P and divide by the included target stars to calculate planet occurrence in each domain. Occurrence of planets varies by more than three orders of magnitude and increases substantially down to the smallest radius (2 Re) and out to the longest orbital period (50 days, ~0.25 AU) in our study. For P < 50 days, the radius distribution is given by a power law, df/dlogR= k R^\alpha. This rapid increase in planet occurrence with decreasing planet size agrees with core-accretion, but disagrees with population synthesis models. We fit occurrence as a function of P to a power law model with an exponential cutoff below a critical period P_0. For smaller planets, P_0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over Teff = 3600-7100 K, spanning M0 to F2 dwarfs. The occurrence of 2-4 Re planets in the Kepler field increases with decreasing Teff, making these small planets seven times more abundant around cool stars than the hottest stars in our sample. [abridged]
1,134 citations