Revised Radii of Kepler Stars and Planets Using Gaia Data Release 2

[    [    Eric Gaidos    [

A critical bottleneck for stellar astrophysics and exoplanet science using data from the Kepler mission has been the lack of precise radii and evolutionary states of the observed target stars. Here we present revised radii of 186,813 Kepler stars derived by combining parallaxes from Gaia Data Release 2 with the DR25 Kepler Stellar Properties Catalog. The median radius precision is  8 %, a factor 4-5 improvement over previous estimates for typical Kepler stars. We find that % ( 128,000) of all Kepler targets are main-sequence stars, % ( 40,600) are subgiants, and % ( 23,000) are red giants, demonstrating that subgiant contamination is less severe than previously thought and that the Kepler parent population mostly consists of unevolved main-sequence stars. Using the revised stellar radii, we recalculate the radii for 2218 confirmed and 1958 candidate exoplanets. Our results confirm the presence of a gap in the radius distribution of small, close-in planets, but yield evidence that the gap is mostly limited to incident fluxes 200  and may be located closer to 2 . We furthermore find several confirmed exoplanets which occupy the “hot super-Earth desert”, detect direct evidence for a correlation of gas-giant planet inflation with increasing incident flux, and establish a bona-fide sample of 8 confirmed planets and 34 planet candidates with 2  in the habitable zone. The results presented here demonstrate the enormous potential for the precise characterization of stellar and exoplanet populations using the transformational dataset provided by Gaia.

stars: fundamental parameters — techniques: photometric — catalogs — planetary systems
Corresponding author: Travis

0000-0002-2580-3614]Travis A. Berger \move@AU\move@AF\@affiliationInstitute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA

0000-0001-8832-4488]Daniel Huber \move@AU\move@AF\@affiliationInstitute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA \move@AU\move@AF\@affiliationSydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia \move@AU\move@AF\@affiliationSETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043, USA \move@AU\move@AF\@affiliationStellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark


Department of Geology & Geophysics, University of Hawaii at Manoa, Honolulu, HI 96822, USA

0000-0002-4284-8638]Jennifer L. van Saders \move@AU\move@AF\@affiliationInstitute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA

1 Introduction

Nearly 95% of all known exoplanets have been discovered using indirect methods such as radial velocities or transits. As a result, the bulk properties of planets such as radius, mass, and density critically depend on the characterization of the host stars. In addition to determining precise planet radii and masses, stellar classifications are also critical to study orbital dynamics through the inference of eccentricities (sliski14; vaneylen15) and to derive accurate planet occurrence rates (e.g Howard2012; burke15).

Traditional methods used to classify stellar populations targeted in exoplanet surveys include broadband colors and proper motions, which efficiently separate dwarfs from giants but have limited sensitivity to intermediate evolutionary states, with typical uncertainties of 0.3–0.4 dex in  (brown11; huber16). High-resolution spectroscopy delivers typical precisions of 0.15 dex in  (torres12) for solar-type stars, while methods calibrated to benchmark stars can achieve precisions down to 0.07 dex (brewer15; petigura15b). Finally, time-domain variability of stars offers the current benchmark for field stars, for example by measuring amplitudes or timescales of stellar granulation (0.1 dex bastien13 bastien13; 0.03 dex kallinger16 kallinger16) or stellar oscillations (0.01 dex huber13).

Despite this progress, most methods are only applicable to a subset of the large samples of stars that are typically observed in exoplanet transit surveys (190,000 stars for Kepler, 200,000 stars for K2, 500,000 stars for TESS). Improved stellar radii of Kepler hosts have recently led to several important results for our understanding of exoplanets, such as the discovery of a gap in the distribution of small planets by the California-Kepler Survey (CKS Fulton2017; Petigura2017; Johnson2017) and evidence for a dearth of hot super-Earths (Lundkvist2016). Both results have been tied to processes such as photoevaporation (Lopez2012; Owen2017), but are biased subsamples consisting of less than half of planet candidates. Furthermore, 70% of the overall Kepler population in the latest version of the Kepler Stellar Properties Catalog (KSPC DR25, Mathur2017) still have  values determined from photometry, translating into 30-40% uncertainties in stellar radii that are severely limiting our understanding of the stellar and planet population probed by Kepler.

The bottleneck caused by imprecise stellar radii of Kepler stars can now be relieved thanks to the transformational data provided by Gaia Data Release 2 (DR2), which provides highly precise parallaxes for over one billion stars in the galaxy (Brown2018; Lindegren2018). In this paper we re-derive radii for 186,813 Kepler stars using Gaia DR2 parallaxes, and investigate the stellar and exoplanet radius distributions of Kepler targets.

2 Methodology

2.1 Kepler-Gaia DR2 Crossmatching

First, we crossmatched the positions of all stars from the KSPC DR25 (Mathur2017) by utilizing the CDS X-match service. This provided a table of DR2 source matches within three arcseconds of each Kepler star. To determine bona-fide Kepler- source matches, we first cut all matches with distances greater than 1.5 arcseconds from the Kepler-determined position. We chose 1.5 arcseconds because the distribution of separations displayed a minimum there, and the increase of matches at greater angular separations indicates the inclusion of spurious background sources.

Next, we used a variety of magnitude cuts, depending on the available photometry, to ensure our Kepler- matches were similar. Unfortunately, not all Kepler stars had similar quality photometry to compare to the measured -band magnitudes, so we had to utilize AAVSO Photometric All-Sky Survey (APASS) , , and/or photometry for instances where KSPC stars did not have -, -, or - band photometry through the Kepler Input Catalog (KIC, brown11). For stars that were still missing any , , or photometry, we used Kepler magnitudes () for comparisons with magnitudes.

To compute our predicted magnitudes, we utilized the , , and color-color polynomial fits in Table 7 of jordi10. After inspecting the distribution of , we chose to remove all stars with absolute differences greater than two magnitudes. For the remaining sample of stars with only  magnitudes, we compared  and again removed all stars with absolute differences greater than two magnitudes.

For the remaining stars with multiple matches, we decided to keep those with the smallest angular separations. Of the 197,104 stars present in the KSPC, we identify 195,713 DR2 source matches. Some of these stars have poorly determined parallaxes/distances ( 0.2), low effective temperatures (  3000 K), extremely low  ( 0.1), and/or missing , , and photometry and/or errors. Excluding these stars reduces our final sample to 186,813 Kepler stars.

2.2 Stellar Radii Determination


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefHistogram of the fractional radius uncertainty for 185,580 Kepler stars derived in this work. A sample of 1233 stars have higher fractional radius uncertainties – these are some of the most distant stars in the field. The typical radius uncertainty pre- DR2 was  30%. The peak at 4.5% errors corresponds to stars that have spectroscopic constraints on , while the peak at 8% corresponds to stars with photometric .


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefRadius versus effective temperature for  186,000 Kepler stars with reclassified radii based on Gaia DR2 parallaxes presented in this work. A sample of 255 stars falling off the plot limits shown here includes hot stars (  10000 K) and white dwarfs. Color-coding represents logarithmic number density. Note that the discontinuity in  near 4000 K is an artifact due to systematic shifts in  scales in the DR25 Kepler Stellar Properties Catalog.

To calculate stellar radii we used the stellar classification code isoclassify (huber17) in its “direct method”, using as input the Gaia DR2 parallax (Lindegren2018), 2MASS K-band magnitude, and , ,  values from the DR25 KSPC (Mathur2017). We replaced the input values given in the KSPC for two samples: stars in the California- Survey (CKS), for which we adopted spectroscopic parameters from Petigura2017, and stars with  K with  provenances from the KIC, for which we adopted revised  values from Gaidos2016.

For each star, we first converted parallaxes into distances using an exponentially decreasing volume density prior with a length scale of 1.35 kpc (bailer15; astraatmadja16), while adding the systematic parallax offset of 0.03 mas (Lindegren2018). We then combined the 2MASS -band magnitude with extinctions from the 3D reddening map by green15, as implemented in the mwdust package by bovy16, to calculate absolute magnitudes and derived bolometric corrections by linearly interpolating , ,  and in the MIST/C3K grid (Conroy et al., in prep333˙grids.html) to calculate luminosities. Finally, we combined the derived luminosities with  from Mathur2017 to calculate stellar radii. The procedure is implemented as a Monte-Carlo sampling scheme, and the resulting distributions were used to calculate the mode and 1 confidence interval for the radius of each star. Table 5 lists our revised radii for all 186,813 Kepler stars analyzed here.

Figure 2.2 shows a histogram of fractional radius uncertainties for 185,580 of 186,813 Kepler stars with radii derived in this work. The remaining 1233 stars have higher fractional radius uncertainties, and are likely some of the most distant stars in the Kepler field. The typical uncertainty is  8%, a factor of 4-5 improvement over the KSPC. The radius uncertainty is dominated by , which for a typical Kepler target is  3.5% based on broadband photometry (huber14). The tail towards lower uncertainties corresponds to stars with spectroscopic temperatures, for which the KSPC assumes uncertainties of 2% in . Our error budget also includes uncertainties of 0.02 mag in and 0.02 mag in bolometric corrections, which are typical values for the Kepler field (huber17). We emphasize that the above routine uses  from the KSPC only to determine bolometric corrections, which are only mildly dependent on  and hence the derived radii are mostly insensitive to inaccurate  values.

We note that 3.5% and 2% uncertainties in (200 K and 115 K at solar ) are conservative, but large enough to encompass systematic differences between  scales and covariances between extinction and color- relations (pinsonneault11). Future revisions of the  scale for Kepler stars, taking into account revised reddening maps based on Gaia DR2, can be expected to improve the typical radius precision to  5% or better.

The Collaboration released radii and effective temperatures for 178,706 of our 186,813 Kepler targets based on Gaia photometry and parallaxes (Brown2018; Lindegren2018; Andrae2018). However, these parameters are optimized for 160 million stars across the sky. In contrast, the Kepler field is one of the most well-studied samples of stars due to its relevance to exoplanet science, and the KSPC includes information from the vast amount of photometric, spectroscopic and asteroseismic analyses that have been performed over the past ten years. Therefore, we expect the stellar radii derived in this work are preferable over those reported by the Collaboration.

3 Revised Radii of Kepler stars

3.1 The Gaia H-R Diagram of Kepler Stars

Figure 2.2 shows stellar radius versus effective temperature for the entire Kepler sample using the revised radii presented in this work. This diagram is the first nearly model-independent H-R diagram of the Kepler field. We see a clear main sequence, from M dwarfs at  = 3000 K at , up through A stars at   9000 K and . The main sequence turnoff at   6000 K and is visible, along with the giant branch. We identify the “red clump” as the over-density of stars surrounding   K and . As expected, the Kepler targets are heavily dominated by FG-type stars as a result of the target selection focusing on solar-type stars to detect transiting exoplanets (batalha10).

A few regions in Figure 2.2 display artifacts, most prominently the gap in the main sequence around 4000 K. This gap is the result of the combination of two photometric  scales in the KSPC (Mathur2017), namely  values from pinsonneault11 for FGK stars and the classification of M dwarfs by dressing13. An accurate re-calibration of the  scale for all Kepler targets is beyond the scope of this paper, but we emphasize the use of the DR25 overall ensures the use of the best possible values for  and  on a star-by-star basis. Furthermore, we identify a number of stars below the main sequence, representing a population of white dwarfs ( = 6500–10000 K and ) and subdwarfs (solar  and 0.6 ) observed by Kepler. We caution that some of the stars in extreme parameter regimes in Table 5 may also be affected by catalog mismatches or erroneous  values in the KSPC.

A remarkable intrinsic feature of Figure 2.2 is an apparent second sequence above main sequence for dwarfs with  K. Because K stars are less massive than their hotter main sequence counterparts, we do not expect these stars to have evolved significantly over a Hubble time, and intrinsic spread in metallicity is not expected to be asymmetric enough to produce this feature. Thus, this additional sequence is likely the result from contamination of binaries, enhancing the apparent magnitude and leading to overestimated radii based on the Gaia parallax. This indicates that DR2 parallaxes can be used to efficiently identify cool main-sequence binaries in the Kepler sample.

3.2 Comparison to the DR25 Kepler Stellar Properties Catalog


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefComparison of radii in the DR25 Kepler Stellar Properties Catalog (Mathur2017) and the radii derived in this paper. The colors represent the density of points. The red dashed line is the 1:1 comparison between DR25 radii and our derived radii. The bottom panel shows the ratio between DR25 stellar radii and our stellar radii.

Figure 3.2 shows a comparison of stellar radii in the DR25 stellar properties catalog (Mathur2017) to those derived in this paper. The distribution approximately tracks the 1:1 line, but there is large scatter and strong systematic offsets caused by large uncertainties in the DR25 radii, which were mostly based on photometric  values from the KIC. We measure an overall median offset and scatter in the /DR25 residuals of 11% and 35% for all stars, 13% and 33% for unevolved stars (), and 8% and 35% for red giants () between the DR25 and DR2 radii. The residuals clearly demonstrate that a substantial fraction of Kepler stars are more evolved than implied in the KSPC.

We also identify 978 giants which were misclassified as dwarfs and 590 dwarfs which were misclassified as giants (bottom right and top left areas in the top panel of Figure 3.2, respectively). The revised classifications presented here will thus aid in increasing cool dwarf samples for studies of stellar rotation and activity (e.g. McQuillan2014; angus15; davenport16) and red giants for asteroseismology (e.g. hekker11; mosser11c; stello13; yu18). The large differences in Figure 3.2 highlight the transformational impact of Gaia DR2 on our understanding of Kepler targets.

3.3 Evolutionary States of Kepler Stars


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefEvolutionary state classifications of all Kepler targets based on physically motivated boundaries for evolutionary states (see text). We find that % (123,500) of all Kepler targets are main-sequence stars (black), % (44,500) are subgiants (green), and % (23,300) are red giants (red). Approximately 4000 cool main-sequence stars are affected by binarity (blue).

Since the initial Kepler target selection (batalha10), there has been growing evidence that the number of subgiants in the Kepler Input Catalog (KIC, brown11) and subsequent KSPC revisions (huber14; Mathur2017) have been significantly underestimated due to Malmquist bias (e.g. gaidos13) and the insensitivity of broadband photometry to determine surface gravities. For example, verner11 showed that radii in the KIC are underestimated by up to 50% for a sample of subgiants with asteroseismic detections. everett13 used medium resolution spectroscopy to arrive at a similar conclusion for faint Kepler exoplanet host stars, while surface gravities derived from granulation indicated that nearly 50% of all bright exoplanet host stars are subgiants (bastien14).

The revised radii using Gaia DR2 parallaxes presented in this work allows the first definite classification of the evolutionary states of all Kepler targets. To do this, we used solar-metallicity Parsec evolutionary tracks (bressan12) to define the terminal age main sequence and base of the red-giant branch (RGB) in the temperature-radius plane, as shown in Figure 3.3. Assuming solar metallicity means that the classifications will be only statistically accurate, but spectroscopic surveys of the Kepler field such as LAMOST (decat15) have confirmed that Kepler target have on average solar metallicities (dong14).

To classify cool main sequence stars affected by binarity, we combined a 15 Gyr isochrone with = 0.5 dex with an empirical cut-off determined from a fiducial main sequence. The latter was determined by fitting Gaussians to radius distributions at fixed bins and fitting a fourth order polynomial, yielding:


where . Based on the observed bi-modality at a given temperature we choose a cut-off of to define candidate cool main-sequence binaries (blue points in Figure 3.3).

Based on the classifications shown in Figure 3.3, we find that % (123,500) of all Kepler targets are main-sequence stars, % (44,500) are subgiants, and % (23,300) are red giants. Approximately 4000 Kepler targets are cool main-sequence binary candidates (blue). Restricting the sample to  K yields a subgiant fraction of 31%, and we confirmed that this fraction is relatively insensitive to apparent magnitude. While this confirms that a substantial fraction of Kepler stars are more evolved than previously thought (see also Figure 3.2), it also demonstrates that earlier findings of large subgiant contaminations in the KIC and KSPC were likely overestimated, and that Kepler did mostly target main-sequence stars. Indeed, the subgiant fractions stated above are upper limits since some stars will be affected by binarity similar to the cool main-sequence stars. The new classifications provided here will provide valuable input for planet occurrence studies, which rely on accurate stellar parameters of the parent sample (e.g. burke15).

4 Revised Properties of Kepler Exoplanets


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefHertzprung-Russell diagram displaying 1541 Kepler confirmed planet hosts (in red) and 1618 Kepler candidate planet host stars (in black).

4.1 The Gaia H-R Diagram of Kepler Planet Host Stars

Figure 4 displays the stellar radii and  distribution of the Kepler planet host stars, which mostly tracks the overall Kepler population in Figure 2.2. We note that while there are a similar number of confirmed (1541, red) and candidate (1618, black) planet hosts, a larger proportion of the candidate hosts stars are more evolved. This is consistent with the expected larger number of false-positives around more evolved stars, which display larger correlated noise due to granulation (sliski14; barclay14). We also note that several confirmed and candidate host stars fall below the main sequence, and hence may be metal-poor subdwarfs.

4.2 Comparison to Previous Planet Radii


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefPlanet radii calculated from stellar radii derived in this work compared to those based on stellar radii in the Kepler DR25 Stellar Properties Catalog (Mathur2017). The red points are confirmed planets, while the black points are planet candidates. The black dashed line is the 1:1 comparison between DR25 planet radii and our derived planet radii. The bottom panel shows the ratio between DR25 radii and our radii.

From the stellar radii derived above, we compute updated planet radii by utilizing the planet-star radius ratio reported in the cumulative Kepler Object of Interest (KOI) table of the NASA Exoplanet Archive (akeson13; Thompson2018) and then multiplying this ratio by our computed stellar radius. Our revised planet radii and uncertainties are given in Table 5. In an attempt to quantify how much the pre- stellar radii affect planet radii, we compare planet radii calculated using the stellar radii in KSPC DR25 and in this work in Figure 4.2. We can see from the top panel that some planets were highly discrepant before DR2. The bottom panel reveals a slight systematic offset from 1–5 , with our revised planet radii being larger. We expect this discrepancy arises because most of these planets orbit subgiant stars that were previously misclassified as dwarfs.


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefDistribution of Kepler exoplanet radii computed in this work. Panel (a): The red, gray, and black histograms contain the confirmed (2218 planets), candidate (1958 planets), and combined samples of 4176 total Kepler planets, respectively. Panel (b): Same as Panel (a) but after performing the clean sample cuts detailed in Fulton2017. 515 planets comprise the red confirmed planet histogram and 279 comprise the gray planet candidate histogram. Panel (c): Combined histogram is the same as that in Panel (b), and the blue dashed-line histogram contains the CKS-derived planet radii instead of those derived in this paper. Both the blue and the black histograms contain 664 planets.

In Figure 4.2 we plot histograms of planet radii, separating candidate (gray) from confirmed (red) planets where instructive. Figure 4.2a includes the entire sample of 4176 planets with computed radii 30 Earth radii. Even from this (likely contaminated) sample, we observe a gap at 2 . This is not the first observation of a gap in the distribution of small planets. Utilizing the precise radii of the California-Kepler Survey (CKS Petigura2017), Fulton2017 confirmed an under-density of planets at 1.8 . Interestingly, we notice that our gap appears to occur at slightly larger planet radii, and that the intrinsic width of the gap is not visibly reduced by the more precise planet radii made possible by DR2.

Next, we implemented the same filters as in Fulton2017 to eliminate potential sources of contamination. Figure 4.2b, which includes 515 confirmed and 279 candidate planets, shows our “clean” sample after making the cuts of Fulton2017: mag, 4700   6500 K, , days, remove all giants and subgiants, and ignore all false positive planets. We see a significantly deeper gap in the confirmed sample, and it appears to occur at the same location as the combined sample displayed in Figure 4.2a. Figure 4.2b also reveals a population of small candidate planets (), although we expect at least some of these planet candidates will be flagged as false positives in the future.


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefPlanet radius versus incident flux for Kepler exoplanets. Red and black dots are confirmed and candidate exoplanets, respectively. We also plot our asymmetric error bars in transparent gray. The dashed line box represents the extension of the super-Earth desert identified in Lundkvist2016, while the green bar indicates the approximate optimistic habitable zone for FGK stars as detailed in Kane2016.

Figure 4.2c provides a comparison of planet radii for only the CKS sample as derived in this work (black histogram) and those computed by the CKS team (Petigura2017; Johnson2017, blue dashed histogram) after applying the Fulton2017 filters for a total of 664 planets. The histograms are similar, but our gap is shifted to slightly larger radii than the gap revealed in Fulton2017. Nevertheless, this difference is within the reported errors.

We emphasize that the subgiant filter significantly affects the comparisons between our revised radii and those provided by the CKS. After plotting the combined sample (black histogram) of Figure 4.2a for only the CKS stars/planets and comparing it to the CKS-derived radii, we observe a larger shift of the center of the gap (and the surrounding bins) to larger planetary radii than what we see in Figure 4.2c. A 1:1 comparison of CKS stellar radii to our stellar radii reveals a slight systematic underestimation of stellar radii for subgiants. Because the CKS stellar radii are underestimated, so are the planet radii, resulting in a slight shift of the gap. This emphasizes that the choice of cuts in stellar parameters can affect the apparent location of the planet radius gap.

4.3 Distributions of Planets with Radius and Stellar Irradiation

Figure 4.2 plots planet radii versus incident stellar irradiation in Earth units, using the revised host star parameters and assuming the semi-major axes reported in the NASA Exoplanet Archive, and near-circular orbits. We do not account for possible changes in host star mass as those effects will be much smaller than the change in luminosity and would require isochrone fitting. Several features in this diagram that have been previously described in the literature become more distinct with the improved precision in stellar and planet properties enabled by Gaia.


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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefSame as Figure 4.2, but with orbital period in place of incident flux as the x-axis.

4.3.1 The Small Planet Radius Gap

As shown in both Figs. 4.2 and 4.2, our revised parameters confirm the bi-modal distribution of planet radii, with a gap or “evaporation valley” between. This gap appears to depend on stellar irradiance, with a clear gap just above 2 for , the absence of an obvious gap at 30–200, and a less distinct deficit of planets in this size range at . The gap in the high-irradiance regime appears to be at a larger planet radius than the value reported in Fulton2017. We identify a small systematic offset in stellar radii between the CKS and Gaia as the source of this difference.

The gap is predicted by models in which photo-evaporation due to high stellar irradiance removes the light molecular weight envelopes of planets, and the relationship between planet mass, surface gravity, and loss rate means that the envelopes of intermediate-size planets are efficiently stripped, producing distinct populations of rocky planets and more massive planets that retain their envelopes (Owen2017; Jin2018). This process is more efficient at high irradiance, which explains the prominence of the gap in that regime. Also according to models, the location of the gap constrains the composition of the residual planet “cores”. A gap at a larger radius would mean a greater contribution by lower density ices. For example, Jin2018 finds that an “evaporation valley” at 1.6 corresponds to an Earth-like composition of silicates and metals, so a valley at a larger radius implies a significant ice component.

4.3.2 Hot Super-Earth “Desert”

Our revised radius and irradiance values confirm the existence of a deficit or “desert” of super-Earth to Neptune-size planets at high irradiance (owen13), i.e. with and (Lundkvist2016). This desert could be a consequence of photo-evaporation of the hydrogen-helium envelopes of sub-Neptune-size planets at stellar irradiance levels more extreme than that which produced the gap (owen16; Lehmer2017), but see ionov18. Alternatively, the desert could be explained if only rocky planets, not mini-Neptunes form close to stars because he inner disk is depleted in gas and volatiles(lopez16). For these two mechanisms, the underlying important variable is the irradiation by the host star and the orbital period/semi-major axis, respectively. These variables are weakly related at the population level because of the wide range of luminosities (five orders of magnitude) of the host stars in the Kepler sample. In a plot of radius vs. orbital period (Figure 4.3) the boundaries of the desert as well as the gap are much less distinct, indicating that irradiance is the more important underlying variable and supporting photo-evaporation as the primary mechanism of desertification.

Additionally, we find that the “hot” desert is not so empty after all. Forty-five confirmed and 28 candidate planets fall within this range. About half are close to the 650 boundary, and our refined parameters suggest that a distinct edge exists at , but 12 confirmed and 2 candidate planets are more than 2 interior to all the edges of the desert. The host stars of these desert dwellers are almost exclusively subgiant stars more massive than the Sun that are evolving towards or at the red giant branch. This is in contrast with the smaller planets in this irradiance range, which orbit both evolved and main sequence stars, and larger (sub-Jovian and Jovian) hot planets, which are found around subgiants with a range of masses. Transit detection bias can explain the large numbers of smaller hot planets around dwarf stars, but not the absence of mini-Neptunes. If the hot mini-Neptunes were the transient remnant of a depleted population we would expect their host stars to be younger than average, but their evolutionary state suggests that they are older.

Lopez2017 finds that the absence of sub-Neptunes in the “desert” can be explained if planets of this size have hydrogen-helium envelopes, but not substantial envelopes of high molecular weight volatiles (e.g. HO) which would be retained. The exceptions here suggest that at least some of these objects do have high molecular weight envelopes, and/or that they have evolved from a different planet population. One explanation for these interlopers is that they are the product of evaporation of still larger objects, i.e. sub-Jovian or even Jupiter-size planets that have lost much of their envelopes. dong18 find that the metallicities of host stars of hot Neptunes are distributed similarly to that of the host stars of hot Jupiters, suggesting a relationship between the two populations. One long-standing idea is that hot Neptunes are the product of massive photo-evaporation of a giant planet’s envelope (baraffe05).

4.3.3 Inflated Hot Jupiters

Another feature revealed by Figure 4.2 is the well-known trend of increasing giant planet radius with increasing stellar irradiance (e.g., Burrows2000; Demory2011; Laughlin2011). Confirmed planets with inflated () radii are numerous at , consistent with previous work and planet inflation theory (Lopez2016). These include giant planets orbiting subgiants and low-luminosity red giants hosts, including previously discovered examples (Grunblatt2016; Grunblatt2017). Giant planet inflation by irradiation could arise from different mechanisms of transport of heat to the planet interior, or suppression of cooling (Lopez2016). We identified four confirmed inflated giant planets at low (150 ) irradiation: Kepler-447b, Kepler-470b, Kepler-706b, and Kepler-950b, but of these only Kepler-470b satisfy the “cool” inflated planet at more than two sigma significance. Despite the disposition listed in DR25, Kepler-470b was identified by Santerne16 to be an eclipsing binary based on radial velocities.

4.3.4 Habitable Zone Planet Candidates

Finally, we address candidate and confirmed planets within the circumstellar “habitable zone” where surface temperatures on an Earth-size planet with an Earth-like composition, geology, and geochemistry would permit liquid water. Following Kane2016, we adopt the “optimistic” definition and illustrate this as the green bar in Figure 4.2. In this habitable zone we identify 35 confirmed planets and 115 candidate planets. Of these, 34 planet candidates and 8 confirmed planets have   2: Kepler-62e, Kepler-62f, Kepler-186f, Kepler-440b, Kepler-441b, Kepler-442b, Kepler-452b (but see also Mullally18), and Kepler-1544b. These candidate planets should be priority targets for follow-up observations to vet the planets and better characterize the host stars, so as to better establish the occurrence of potential Earth-like planets .

5 Summary and Conclusions

We presented a re-classification of stellar radii for 186,813 observed by the Kepler Mission by combining Gaia DR2 parallaxes with the DR25 Kepler Stellar Properties Catalog (KSPC, huber14; Mathur2017). The typical precision of stellar radii is 8%, a factor of 4-5 better than previous estimates in the KSPC. Based on the revised stellar radii, we have furthermore re-derived radii for 2218 confirmed planets 1958 planet candidates discovered by Kepler. Our main conclusions are as follows:

  • We find that 65% (123,500) of all Kepler targets are main-sequence stars, 23% (44,500) are subgiants, and 12% (23,300) are red giants. While many radii are revised to larger values, this demonstrates that previous findings of large subgiant contaminations in the Kepler Input Catalog (KIC) and KSPC were likely overestimated, and that the Kepler parent population indeed consists mostly of main-sequence stars.

  • We find evidence for binarity in 4400 cool main-sequence stars ( 2% of the overall sample) based on their inflated radii in the H-R diagram. This demonstrates that Gaia parallaxes can be used to efficiently identify binary stars, and we encourage follow-up observations of the binary candidates identified in our work (see Table 5).

  • We confirm the gap in the radius distribution of small Kepler planets (Fulton2017), but find that its location is shifted to slightly larger radii. The planet radius–incident flux plot reveals the gap at 2.0  over a wide range of incident fluxes, with the largest gap occurring at 200 . The location of the gap has important implications for planet formation and evolution theory, as it can constrain planetary core compositions, in addition to revealing dynamic effects on exoplanet populations.

  • The hot super-Earth desert is no longer unpopulated. We identify 73 stars hosting 45 confirmed planets and 28 planet candidates that receive 650  and have radii between 2.2 and 3.8 . However, we confirm that there is a clear paucity of super-Earths in the desert regime, especially at incident fluxes 1000 .

  • We observe a clear inflation trend for hot Jupiters, where inflated planets become numerous at an irradiation level . We identify a few confirmed planets that may be inflated Jupiters at incident fluxes  (Kepler-447b, Kepler-470b, Kepler-706b, and Kepler-950b), but find that the most promising case (Kepler-470b) was previously reported as an eclipsing binary.

  • We identify 35 confirmed planets and 115 planet candidates within the habitable zone. Of these planets, 34 planet candidates and 8 confirmed planets have   2: Kepler-62e, Kepler-62f, Kepler-186f, Kepler-440b, Kepler-441b, Kepler-442b, Kepler-452b (but see also Mullally18), and Kepler-1544b. These systems in particular represent a high priority sample for ground-based follow-up.

We have applied DR2 measurements to Kepler stars and their planets and identified several patterns in the distribution of both stars and planet properties that suggest avenues of future investigation. In this work, we have restricted our refinement of stellar properties to their radii and luminosities, but future work will exploit precise Gaia parallaxes by applying stellar evolution models to infer surface gravities, densities, masses and ages. Planet populations are expected to evolve with time as a result of cooling and contraction of envelopes, photo-evaporation of atmospheres, and mutual dynamical scattering. It may also be possible to observe this evolution with sufficiently well-selected and characterized samples of old and young stars and planetary systems, (e.g., Mann2017; Berger2018). The unprecedented parallaxes provided by will continue to reveal new and interesting information about stars and their companions, and more in-depth analyses of singular systems will inevitably lead to some unpredicted discoveries.

\H@refstepcounter table \hyper@makecurrenttable\hb@xt@ Table 1. \Hy@raisedlink\hyper@@anchor\@currentHrefRevised Parameters of Kepler Stars

KIC ID DR2 ID  [K] [K] Distance [pc] [pc] [pc] [] [] [] [mag] Evol. Flag 757076 2050233807328471424 5164 181 657.77 20.68 20.68 3.96 0.31 0.27 0.29 1 757099 2050233601176543104 5521 193 369.17 3.76 3.76 1.04 0.09 0.07 0.18 0 757137 2050230543159814656 4751 166 570.16 8.58 8.12 13.36 1.04 0.91 0.26 2 757280 2050230611879323904 6543 229 824.12 15.23 15.23 2.66 0.20 0.20 0.30 0 757450 2050231848829944320 5306 106 834.13 19.36 17.08 0.96 0.04 0.04 0.30 0 891901 2050246795316077952 6325 221 1199.94 214.76 153.40 2.26 0.44 0.33 0.59 1 892010 2050234975566082176 4834 169 1850.36 90.21 78.93 15.16 1.37 1.37 0.60 2 892107 2050234696381511808 5086 178 940.64 20.15 20.15 4.32 0.35 0.31 0.32 2 892195 2050234735047928320 5521 193 480.53 4.01 4.01 0.98 0.08 0.07 0.23 0 892203 2050236521754360832 5945 208 554.78 4.87 4.87 1.02 0.08 0.07 0.26 0

Note—KIC ID, DR2 ID, , distance, stellar radii, reddening, and evolutionary flag (and errors, where reported) for our sample of 186,813 Kepler stars. The evolutionary flags are as follows: 0 = main sequence dwarf, 1 = subgiant or main-sequence (MS) binaries, 2 = red giant, and 3 = cool MS binary candidate, according to the cuts made in Figure 3.3. A slice of our derived parameters is provided here to illustrate the form and format. The full table, in machine-readable format, can be found online.


\H@refstepcounter table \hyper@makecurrenttable\hb@xt@ Table 2. \Hy@raisedlink\hyper@@anchor\@currentHrefRevised Parameters of Kepler Exoplanets

KIC ID KOI ID  [] [] [] [] [] [] 10797460 K00752.02 2.90 0.96 0.22 10.23 1.44 1.44 10854555 K00755.01 2.25 0.41 0.22 619.41 148.18 125.07 10872983 K00756.01 4.63 0.71 0.37 124.46 18.58 20.84 10872983 K00756.02 3.29 0.32 0.35 463.60 69.21 77.61 10872983 K00756.03 1.89 0.51 0.23 875.64 130.72 146.59 10910878 K00757.01 4.87 0.28 0.27 21.60 2.96 2.96 10910878 K00757.02 3.27 0.20 0.19 6.15 0.84 0.84 10910878 K00757.03 2.24 0.15 0.13 76.07 10.41 10.41 11446443 K00001.01 14.13 0.59 0.59 896.85 104.12 104.12

Note—KIC ID, KOI ID, planetary radii, and incident fluxes (and errors where reported) of a our sample of 4176 Kepler confirmed/candidate planets. A slice of our derived parameters is provided here to illustrate the form and format. The full table, in machine-readable format, can be found online.


We gratefully acknowledge everyone involved in the Gaia and Kepler missions for their tireless efforts which have made this paper possible. T.A.B. and D.H. thank Savita Mathur for providing supplementary material for the DR25 stellar properties catalog. D.H. thanks Erik Petigura and BJ Fulton for discussions on Gaia DR2 day zero. T.A.B. and D.H. acknowledge support by the National Science Foundation (AST-1717000) and the National Aeronautics and Space Administration under Grants NNX14AB92G issued through the Kepler Participating Scientist Program. This work has made use of data from the European Space Agency (ESA) mission Gaia (, processed by the Gaia Data Processing and Analysis Consortium (DPAC, Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS), funded by the Robert Martin Ayers Sciences Fund. This research made use of the cross-match service provided by CDS, Strasbourg. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

Software: astropy (astropy), isoclassify (huber17), Matplotlib (Matplotlib), mwdust (bovy16), Pandas (Pandas), SciPy (Scipy)



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