The Stars Kepler Missed: Investigating the Kepler Target Selection Function Using Gaia DR2 Linnea Wolniewicza, Travis Bergerb, Daniel Huberb aUniversity of Colorado, Boulder, Libby Dr, Boulder, CO 80302, USA bInstitute for Astronomy, University of Hawai`i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Abstract A critical piece of information to exploit Kepler data is the biases of the Kepler selection function. The Kepler Space Telescope selected nearly 200,000 targets for observation from a sample of over a million stars positioned over the Kepler CCDs with minimal information of their evolutionary state, binarity, or proper motions. Planetary occurrence rates have assumed Kepler's selection of the stars in its field of view to be complete and unbiased with respect to stellar multiplicity and kinematics. We identify the stars positioned on the Kepler CCDs that were not chosen for observation. We use Gaia DR2 to identify stellar parameters for both the observed and non-observed samples. We compare this non-observed sample to the observed sample and identify biases in the Kepler target selection function. We find that the selection is complete for main sequence stars, including solar analogs, with Kp < 14 mag but drops to 80% at Kp = 15 mag and 60% at Kp = 16 mag. We use the Gaia Re-normalized Unit Weight Error (RUWE) to show that Kepler was biased against stellar multiplicity. We furthermore use the Gaia proper motions to show that the Kepler selection function was unbiased with respect to kinematics. Keywords: Gaia DR2, Kepler Input Catalog 1. Introduction influence of a binary companion. Dressing and Charbon- neau (2013) found that for the M dwarf stars in the Kepler The discovery of life on other planets is a pursuit that sample, the Earth-sized (0.5 R⊕ - 1.4 R⊕) planetary oc- has long inspired many astronomers, and is fueled by the currence rate is 0.51, all with orbital periods less than 50 search for Earth-like planets. Today, the complex detec- days. All of these analyses have caused the Kepler stars tion of planets around stars is known as extra-solar planet to become one of best-characterized star samples (Berger (exoplanet) science. Exoplanet scientists are constantly et al., 2020). detecting and investigating planets beyond our solar sys- A critical piece of information to exploit Kepler data is tem and categorizing them by size and composition. This the process with which targets were selected. For exam- important science would not be possible without the use of ple, planet occurrence rates studies have so far assumed high-resolution telescopes. For this very purpose of discov- that the Kepler target selection function is unbiased with ering Earth-like planets, NASA launched the Kepler space respect to stellar multiplicity and galacto-centric stellar telescope in March of 2009 - the original exoplanet hunter. velocities (Kraus et al., 2016; McTier and Kipping, 2019). The Kepler mission (Borucki et al., 2010), officially re- Yet Kepler was forced to select targets, as only 200,000 tired in 2018, has left behind a legacy dataset for stellar stars could be observed over the course of the mission. astrophysics and exoplanet science. Most planets observed Many of the underlying assumptions and biases of the Ke- around Kepler host-stars have been found to have sizes be- pler selection function remains unexplored despite its pro- tween Earth and Neptune, a distribution absent in our own lific use in astrophysics research today. solar system (Howard et al., 2012). The uniquely-sized The Kepler Input Catalog (KIC) contains physical and planets found by Howard et al. (2012) have orbital peri- photometric data for sources in the Kepler field of view ods less than 50 days. Kraus et al. (2016) found that there (Brown et al., 2011). The goal of the KIC was to distin- was a deficit in the number of expected binary compan- guish cool dwarf stars from red giants, to which they found ions among planet host stars from the Kepler data, leading themselves to be 98% effective (Brown et al., 2011). Ke- to the conclusion that a fifth of all solar-type stars in the pler selected the optimal targets for observation using the Milky Way are disallowed from hosting planets due to the KIC, with a goal of selecting solar type stars that could host terrestrial-sized planets. The KIC used broadband photometry to infer T values for 85% of their stars. Few Email address: [email protected] (Linnea Wolniewicz) eff Preprint submitted to Icarus August 3, 2020 log(g) values were known, as broadband photometry is in- As a first step, we cross-matched the KIC with Gaia DR2 sensitive to log(g). The highest priority stars were those to obtain Gaia information for each star in the KIC. To where it would be possible to detect an Earth-sized planet do this, we used the Centre de Donn´eesastronomiques de in the habitable zone (HZ), and for which high precision Strasbourg (CDS) cross-match 1. This service is provided radial velocities could be determined (1 - 3 m s−1). The by the Universit´ede Strasbourg and joins any VizieR data, next criterion of the selection process was to include stars in this case Gaia DR2, with a private data table based on that were brighter than the 14th magnitude in the Kepler the right ascension (RA) and declination (Dec) of the stars. passband (Kp). The following highest priority targets were This cross-match created duplicates of Kepler ID's where the brightest stars where terrestrial-sized planets would be multiple stars were located at the same RA and Dec. We detectable in the HZ, even if they were as faint as 15 or 16 removed duplicates by selecting only the Kepler and Gaia magnitudes. Finally, the criterion for detectable planets ID's associated with the most similar magnitudes in the in the HZ was relaxed, allowing stars that would benefit Kepler passband Kp and Gaia passband (G) for analysis. from additional S/N by observing more transits to be ob- This was done with use of the pandas library in Python served. This created a list of 261,363 stars brighter than (pandas development team, 2020; Wes McKinney, 2010). 16th magnitude in the Kepler passband, which was re- duced to less than 200,000 stars due to mission constraints We then queried our data with the Gaia Re-normalized (Batalha et al., 2010). unit weight error (RUWE) values through TOPCAT, as RUWE values can be used to make determinations of The recent Gaia second data release (DR2) provides a stellar multiplicity in Gaia sources. The unit weight er- unique opportunity to look back at the Kepler data and ror (UWE) values are a representation of the normalized better understand its selection function (Gaia Collabora- chi-squared values resulting from the fitting of Gaia DR2 tion et al., 2018). Gaia DR2 has provided astrometry, vari- sources to single-star point spread functions (PSFs). The able star classifications, and astrophysical parameter esti- RUWE value corresponds to a PSF fitting corrected for mates for a total of 1,692,919,135 sources (Lindegren et al., color-dependent biases. RUWE values center around 1.0, 2018). Gaia DR2 is a much expanded and improved astro- but can be large if the fit is not good or there is more metric and photometric data set compared to its predeces- noise than expected. A large RUWE value, such as 1.2 or sor, Gaia DR1, and has been shown to be near complete higher, indicates a multi-stellar system where the presence for G magnitudes between 7 and 20 (Boubert and Everall, of stellar companions increases the noise. 2020). The sources analyzed in Gaia were pulled from 52 billion detections, and reduced to 1.7 billion to reduce spu- rious sources as well as to analyze only those sources with 2.2. Filtering the Data a minimum of 5 detections by the Gaia spacecraft (Linde- gren et al., 2018). With the use of this powerful tool, it 52.5 is possible to look back at the stars chosen by Kepler and garner an understanding of their biases, or lack thereof. 50.0 The goal of this paper is to use the comprehensive Gaia 47.5 DR2 (Gaia Collaboration et al., 2018) to look back at the 45.0 stars the Kepler mission observed, or intended to, and un- derstand the biases of the data and its selection. Many 42.5 conclusions drawn from the Kepler mission data assume Declination (Dec) 40.0 Kepler was unbiased to parameters such as stellar multi- plicity (Kraus et al., 2016). Thus, characterizing the biases 37.5 behind the stars that the Kepler mission chose to observe is important. 300 295 290 285 280 Right Ascension (RA) Figure 1: Spatial extent of the Kepler field. Turquoise points are stars whose light did not fall on the CCDs, while red points are 2. Methodology stars whose light did fall on the CCDs for all four seasons and are 8 arcseconds away from the CCD edges. 2.1. Catalog Cross-matching In this paper we analyze only the stars that fall on the Kepler CCDs that could have been observed. The KIC This paper analyzes the Kepler Input Catalog dataset for contained stars in the Kepler field of view, only a fraction all sources close to the Kepler field of view from the Mikul- of which were located on the Kepler CCDs. Figure 1 shows ski Archive for Space Telescopes (MAST). We analyze only the spatial extent of the Kepler field for stars brighter than the Kepler stars brighter than Kp = 16 mag, as nearly all Kepler targets were below this threshold (Batalha et al., 2010).