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Follow-Up and Validation of K2 and TESS Planetary Systems With Keck NIRC2 Adaptive Optics Imaging

High resolution imaging (HRI) is a critical part of the transiting exoplanet follow-up and validation process. HRI allows previously unresolved stellar companions and background blends to be resolved, vetting false positive signals and improving the radii measurements of true planets. Through a multi-semester Keck NIRC2 adaptive optics imaging program, we have pursued HRI of K2 and TESS candidate planet host systems to provide the transiting exoplanet community with necessary data for system validation and characterization. Here we present a summary of our ongoing program that includes an up to date list of targets observed, a description of the observations and data reduction, and a discussion of planetary systems validated by the community using these data. This observing program has been key in NASA's K2 and TESS missions reaching their goals of identifying new exoplanets ideal for continued follow-up observations to measure their masses and investigate their atmospheres. Once processed, all observations presented here are available as calibrated images and resulting contrast curves through the Exoplanet Follow-up Observing Program (ExoFOP) website. We encourage members of the exoplanet community to use these data products in their ongoing planetary system validation and characterization efforts.


INTRODUCTION
The era of high-precision, space-based photometry to discover transiting exoplanets has led to a revolution in our understanding of planets beyond our solar system. NASA's Kepler mission (Borucki et al., 2010), which launched in 2009 and observed targets in a ∼115 sq. deg. part of the sky for nearly 4 years, identified ∼4,000 candidate transiting planets (Thompson et al., 2018). This sample allowed for ground breaking constraints on the statistical distribution and frequency of exoplanets (e.g., Dressing and Charbonneau, 2015;Fulton et al., 2017) and the discovery of many interesting individual systems (Lissauer et al., 2011;Quintana et al., 2014).
After hardware failures, the Kepler mission ended and the observatory was re-purposed as the K2 mission (Howell et al., 2014), a community driven, time domain photometry survey of 19 fields around the ecliptic plane. Compared to Kepler, K2 surveyed an order of magnitude more sky, accessed more diverse stellar populations, and observed a larger numberof bright targets amenable to follow-up observations. The exoplanet community has so far identified more than 1,300 candidate planets in K2 data (e.g., Kruse et al., 2019, and references therein). In this haul, K2 revealed small candidates transiting bright host stars suitable for detailed characterization (Crossfield et al., 2015;Montet et al., 2015) and allowed for additional statistical studies of the exoplanet population . After the space craft expended its fuel in the Fall of 2018, it was no longer able to point precisely enough to perform science observations and the observatory was decommissioned.
The Transiting Exoplanet Survey Satellite (TESS, Ricker et al., 2015) launched in April 2018 and continues the Kepler/K2 transiting planet discovery legacy with a nearly all-sky survey. TESS observes in ∼27 day Sectors and has so far obtained high precision photometric time-series over ≈80% of the sky to search for transiting planets. The mission aims to discover small planets around the closest brightest stars, leading to systems that are ideal for mass measurements and atmospheric characterization. So far, TESS has identified more than 3,000 candidate planets when those identified by the project (Guerrero and TESS Science Office, 2021) and the community 1 are taken into account. The mission is providing some of the most promising small planets for atmosphere characterization with the upcoming James Webb Space Telescope (JWST, e.g., Kostov et al., 2019).
An essential part of the process to confirm and characterize the ever increasing number of transiting exoplanet candidates is large scale, coordinated follow-up observations. Traditional confirmation of planet-like signals relies on precision radial velocity (PRV) spectroscopy to directly measure stellar reflex motion due to planets and derive planet masses. However, RV confirmation requires resource intensive long-term monitoring programs and may not be possible for faint targets and small planets due to signal-to-noise and expected RV amplitudes. In the majority of cases, a more tractable path to convert a candidate to a reliable planet requires follow-up to rule out sources of false positive signals (e.g., bound and background eclipsing binaries) with high statistical significance. Typical follow-up includes spectroscopy to determine the host star properties, lower precision RV screening for massive, short period companions, and imaging to identify bound companions and background sources. Statistical validation and dedicated follow-up has been used to rule out false-positives at high confidence for a large number of the Kepler, K2, and TESS candidates described previously. So far, approximately 2,400 Kepler candidates, more than 400 K2 candidates, and more than 100 TESS candidates have been validated or confirmed.
High spatial resolution imaging (HRI) has been critical to candidate exoplanet validation efforts. HRI has become the standard technique for detecting companion stars and 1 https://exofop.ipac.caltech.edu/tess/view_ctoi.php background eclipsing binaries closer than 1 ′′ and is a vital input for the statistical validation of small planets beyond the reach of RV observations. In addition to validation, HRI is crucial for measuring the true planetary radii and planet sizes by measuring the photometric blending of their hosts with bound and background stars (Ciardi et al., 2015). Here we describe a key program in a large HRI follow-up campaign to characterize K2 and TESS planetary systems. The program uses Keck NIRC2 adaptive optics (AO) imaging to discover and characterize close-in bound and background sources and provide the necessary data to validate high priority K2 and TESS targets, study exoplanet host star multiplicity, correct planetary radii for dilution from newly discovered companions, and place constraints on exoplanet demographics and occurrence rates. In subsequent sections we provide details on the construction of the program, our observations and analyses, and the results. We also discuss future plans with these data and, once processed, make available reduced data products for each observed target through the NASA Exoplanet Archive Exoplanet Follow-up Observing Program (ExoFOP) services for K2 and TESS. We encourage the exoplanet community to use these data in their ongoing analyses.

Overview of the Observing Program
Following the need for HRI observations demonstrated with Kepler candidates and the transition to the community driven K2 mission, our team and collaborators undertook a largescale effort to identify, follow-up, and validate K2 planet candidates (Crossfield et al., 2016Dressing et al., 2017aDressing et al., ,b, 2019Livingston et al., 2018;Mayo et al., 2018;Petigura et al., 2018;Yu et al., 2018). As a key part of the follow-up campaign, we organized a multi-facility HRI program to observe and characterize K2 candidate exoplanet systems. As the K2 mission ended in 2018, the TESS mission began routine science operations and began delivering new exoplanet candidates. With this transition, we expanded our HRI follow-up program to pursue TESS targets through the TESS Follow-up Observers Program (TFOP).
Here we describe a portion of the K2 and TESS HRI program that was competitively pursued through the public NASA Keck time allocation 2 . We provide details on the NASA Keck observing programs allocated for these observations in Table 1. In the following sub-sections we describe our approaches to target selection, observations, data reduction, and analysis.

Target Selection
For the K2 aspect of the HRI program, we selected targets from the list of candidate exoplanet systems identified by this team and collaborators. The majority of these systems were identified in publicly available K2 data by our team using a multi-step process. K2 time-series were corrected for systematic errors introduced by the degraded pointing performance of the observatory using the k2phot software package 3 . Planet candidates were then  (Petigura et al., 2013). Diagnostic plots describing threshold crossing events (TCEs) were then visually vetted by a team of human volunteers to remove the most obvious false positives in the form of eclipsing binaries, stellar variability, and instrumental noise and produce lists of exoplanet candidates for each K2 campaign. Additional, community candidates identified using other systematics correction algorithms and planet search approaches were also considered. These included candidates resulting from the light curve detrending approaches described in Vanderburg and Johnson (2014) . The combined potential targets were prioritized for Keck AO imaging follow-up on the basis of planet radius (planets ≤4 R ⊕ were preferred), host star properties (R * < 1.5 R ⊙ , V 14 mag), and the planet's prospects as a future target for PRV mass measurements and transmission spectroscopy. This led to a total of 174 candidate K2 exoplanet systems being targeted in this program. The observed K2 targets and their observing parameters are provided in Table 2. This table is a portion of the full K2 target table and is provided as an example of the format and content. The full table is available in electronic formation as Supplementary Data Table 1.
The TESS aspect of the HRI program was organized through the TESS Follow-up Observing Program (TFOP) 4 and drew targets from the lists of exoplanet candidates publicly released by the TESS project. Building on the community driven, adhoc approach to follow-up from K2, TFOP was designed to prioritize and perform observations to go from a large sample of planet candidates (thousands) to a small sample of targets for PRV mass measurements (∼100). Once transit-like events are identified in TESS 2-min cadence data by the Science Processing Operations Center (SPOC) mission pipeline (Jenkins et al., 2016) and in 30-min cadence data by the MIT Science Operations Center (SOC) Quick Look Pipeline (QLP), manual vetting of both SPOC and QLP transit events is performed by a dedicated SOC team to provide a list of the most likely planet candidates. These candidates are then disseminated to the TFOP community for follow-up. The TESS observations presented here are part of TFOP Sub-Group 3 (SG3), which targets candidates with HRI to detect nearby sources unresolved by seeing limited observations ( 1 ′′ ). The TESS mission began public releases of exoplanet candidates, called TESS Objects of Interest (TOIs), that fed into TFOP in September of 2018 5 . To select TESS targets for Keck AO imaging, we primarily considered TOI systems with small planets that would be most suitable for PRV follow-up to measure planet masses. This included selection on both the host star properties (R * < 1.5 R ⊙ , V 14 mag) and the candidate planets (R p ≤ 4 R ⊕ ). We also requested additional interesting TESS targets from the broader exoplanet community. This led to a total of 72 candidate TESS systems being targeted so far in this program. The observed TESS targets are detailed in

Observations
The observations described here cover nights in Keck semesters 2017B, 2018A, 2018B, 2019A, and 2020A; spanning the dates UT September 09 2017 to UT May 28 2020. The details of each observing run are provided in Table 1. In each of the observing runs, we used the NIRC2 instrument behind the Natural Guide Star (NGS) AO system (Wizinowich et al., 2000) on the 10 m Keck-II telescope. The observations were obtained in a number of narrow and broad-band filters with central wavelengths near ∼2.2 µm to maximize the sensitivity to faint, low-mass companions. The exact choice of filter was dictated by the target NIR magnitude and the observing conditions (broader filters were used for fainter targets and in degraded conditions). If a potential companion was detected in quick look analyses, the target was also observed with shorter wavelength NIR filters, typically J-band, to facilitate companion color analyses. A full list of the NIRC2 filters used in this program is provided in Table 4. We used the narrow-angle mode of the camera to provide a pixel scale of 9.942 mas pixel −1 and a full field-of-view of 10 ′′ . All of the observations in this program followed the standard dither set-up for NIRC2 observations that avoids the noisier lower-left quadrant of the detector. The observing sequences used a dither pattern with a step-size of 3 ′′ that was repeated three times, with each dither offset 0.5 ′′ from the previous, resulting in 9 frames. Integration times varied from <1 to 60 s per dither, depending on target NIR magnitudes, and typically used 1 coadd. Detailed information on the observations of each target are included in Tables 2, 3.

Data Reduction and Analysis
All of the data in this program was reduced and analyzed using standard imaging approaches. The dithered science frames were dark corrected using calibration observations obtained each night. Sky frames were produced from the median average of the dithered science frames. Flats were produced from the median average of dark subtracted flat-field observations obtained each night. The science frames were then sky-subtracted and flatfielded. The reduced frames where then combined into a single We estimated the sensitivity to these companions in each final, combined image by injecting simulated sources in 45 • azimuthal increments at discrete separations that were integer multiples of the central source's FWHM (following Furlan et al., 2017). To estimate the contrast sensitivity, the flux of each simulated source was increased until aperture photometry yielded a 5σ detection. The final contrast sensitivity as a function of separation was calculated by averaging all of the limits at that separation. Beginning approximately with the first TESS target observations in this program, we introduced contrast sensitivity uncertainties into our standard analyses. Uncertainties were estimated by measuring the RMS dispersion of the 5σ limits in each azimuthal annulus at each discrete separation. This process leads to contrast curves (in mag) for each target observation that represent the 5σ sensitivity limits of the imaging data as a function of separation from the central source. The NIRC2 observations typically yields NIR contrasts 7 mag at 0.5 ′′ separations, and 4 mag at 0.1 ′′ separations, providing access to faint, close-in companions (see e.g., Crossfield et al., 2016, their Figure 5).

RESULTS
After processing, the results of this observing program are made publicly available for community use on the NASA Exoplanet Archive's ExoFOP-K2 6 and ExoFOP-TESS 7 websites. For each observation we include: the reduced, combined images as FITS files, contrast curves as ASCII tables, and publication ready figures showing the contrast curve and final image as an inset.

HRI in Planet Validation
The HRI data resulting from this observing program are key inputs to efforts to statistically validate transiting exoplanet candidates. HRI places deep constraints on the presence of bound and background sources in the vicinity of the presumed host stars that are blended in the much lower resolution images from Kepler/K2 and TESS used to produced light curves. These blended sources along the line of sight can host eclipsing binaries (EBs), that when diluted by the brighter primary source, mimic planet transits in the light curve. HRI is an observationally inexpensive and effective approach to mitigate contamination from blends.
The process of exoplanet validation systematically explores the large parameter space that could contain planet mimicking configurations and statistically constrain the probability. In practice, validation software combines light curve data, stellar properties, and observing constraints (i.e., contrast curves from HRI) with statistical priors on the likelihood of false positives. The aforementioned priors include simulations of the stellar population near the target and common false positive configurations (e.g., bound, background, and hierarchical EBs). The result of the validation analysis is the probability that a given transit signal is caused by one of the false positive scenarios explored or a true planet, the false positive probability (FPP). Validation is a powerful technique to confirm small planets beyond the reach of PRV measurements (like those in the habitable zone) and planets that orbit fainter stars. Several validation software packages have been developed and used by the Kepler, K2, and TESS communities. These include BLENDER (Torres et al., 2011), PASTIS (Díaz et al., 2014), vespa (Morton, 2012(Morton, , 2015, and TRICERATOPS (Giacalone and Dressing, 2020).
The HRI observations presented here, along with other complementary HRI observations from other Keck programs and other imaging facilities, have contributed to the validation of many hundreds of transiting exoplanet systems. For example, these data were key in the validation of many systems from the K2 mission. Some systems of note include K2-233, a young early-K dwarf hosting three small planets ; K2-266, a K dwarf in a wide binary hosting at least four planets with one significantly misaligned (Rodriguez et al., 2018); and K2-288B, an M dwarf in a binary system hosting a small habitable-zone planet discovered by citizen scientists . The HRI observations of TESS targets are also beginning to validate and characterize systems around brighter, closer stars. This includes the TOI-421 system, three planets orbiting a bright G dwarf (Carleo et al., 2020); GJ 3473 (TOI-488), a nearby M dwarf hosting a hot, transiting, Earth-size planet (Kemmer et al., 2020), and TOI-503, a short period brown dwarf transiting an A type star (Šubjak et al., 2020).

DISCUSSION
The Keck HRI program described here and complementary observations with other facilities are ongoing and continue to secure time through the NASA Keck and other TACs. Future observations of high-priority TESS candidate planet hosts through TFOP SG3 will provide further characterizing data and progress the TESS mission toward its scientific goals via continued system validation. The data in hand will be included in forthcoming publications to present the full list of newly discovered companions and their properties, the multiplicity statistics of K2 and TESS planet host stars (e.g., Matson et al., 2018) and the effects of multiplicity on planetary systems (e.g., Kraus et al., 2016;Ziegler et al., 2018Ziegler et al., , 2020. The observations will also be critical in future analyses of K2 and TESS exoplanet demographics and occurrence rates (e.g., Hardegree-Ullman et al., 2020;Zink et al., 2020). The HRI observations allow true planet radii to be included in these analysis. In the absence of HRI observations, planet radii could be underestimated due to dilution from unresolved, nearby sources that cause photometric blending of the transit (Ciardi et al., 2015;Furlan et al., 2017). Planet demographic and occurrence rates studies that do not account for these blends may overestimate the frequency of small planets. The inclusion of HRI data will improve our understanding of the true distributions and frequencies of planets across the Galaxy.
In addition to studies enabled directly by the HRI data, planetary systems validated and characterized in the context of HRI feed into further characterization efforts. This includes Doppler mass measurements and transmission and emission spectroscopy to detect planet atmospheres. These observations place direct constraints on the bulk compositions and chemical constituents of exoplanets. This is particularly true for the bright targets discovered by K2 and TESS that are most amenable to these measurements as we enter the era of extreme PRV observations and the JWST.

CONCLUSIONS
Here we summarized our multi-year campaign to observe K2 and TESS candidate exoplanet host stars using Keck NIRC2 AO imaging through the NASA Keck time allocation. The hundreds of targets we have observed continue to contribute to the validation of key new exoplanet systems and will be the focus of future studies delving into host star multiplicity and exoplanet occurrence rates. The TESS aspect of our program is ongoing through the TFOP consortium and will continue to provide HRI observations of high-priority candidate TESS systems. This includes ideal targets for further characterization to measure planet masses and study exoplanet atmospheres with current and future facilities. We encourage the exoplanet community to explore the calibrated and reduced data products we make available through ExoFOP and use these results in their validation and characterization efforts.

DATA AVAILABILITY STATEMENT
The Keck HRI datasets obtained through the described programs are publicly available from the Keck Observatory Archive (KOA) on a rolling basis following a proprietary period [https://www2. keck.hawaii.edu/koa/public/koa.php]. Once they are processed, the calibrated and reduced data products resulting from the described programs are publicly available from the ExoFOP websites for the K2 and TESS missions [https://exofop.ipac. caltech.edu/k2/ and https://exofop.ipac.caltech.edu/tess/].

AUTHOR CONTRIBUTIONS
JS led the manuscript, produced the tables and figure, performed the observations, and wrote the NASA Keck proposals. EG contributed to the text and tables, performed the observations, and wrote the NASA Keck proposals. DC contributed to the text, tables, and figure, performed the data reduction, produced the publicly available data products, and performed the observations. RP and IC contributed to the text and performed the observations. JC, CD, TB, and AH contributed to the text. All authors contributed to the NASA Keck proposals that led to the described data.

FUNDING
This work was supported by multiple NASA Keck PI Data Awards, administered by the NASA Exoplanet Science Institute. telescope time allocated to the National Aeronautics and Space Administration through the agency's scientific partnership with the California Institute of Technology and the University of California. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors recognize and acknowledge the significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community.
We were most fortunate to conduct observations from this mountain.