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Thanks to missions like Kepler and TESS, we now have access to tens of thousands of high precision, fast cadence, and long baseline stellar photometric observations. In principle, these light curves encode a vast amount of information about stellar variability and, in particular, about the distribution of starspots and other features on their surfaces. Unfortunately, the problem of inferring stellar surface properties from a rotational light curve is famously ill-posed, as it often does not admit a unique solution. Inference about the number, size, contrast, and location of spots can therefore depend very strongly on the assumptions of the model, the regularization scheme, or the prior. The goal of this paper is twofold: (1) to explore the various degeneracies affecting the stellar light curve "inversion" problem and their effect on what can and cannot be learned from a stellar surface given unresolved photometric measurements; and (2) to motivate ensemble analyses of the light curves of many stars at once as a powerful data-driven alternative to common priors adopted in the literature. We further derive novel results on the dependence of the null space on stellar inclination and limb darkening and show that single-band photometric measurements cannot uniquely constrain quantities like the total spot coverage without the use of strong priors. This is the first in a series of papers devoted to the development of novel algorithms and tools for the analysis of stellar light curves and spectral time series, with the explicit goal of enabling statistically robust inference about their surface properties., 33 pages, 12 figures. To be submitted to AAS Journals. Updated references

Kepler, K2, and Transiting Exoplanet Survey Satellite (TESS) have demonstrated the power of high-precision uninterrupted photometry. Combining data sets from these two observatories can extend the baseline of high precision photometry on a target. In addition, for some investigations, the differing passbands of the two telescopes may provide additional information about the causes of the observed variability. In order to facilitate studies combining these unique data sets, we present a list of all the 55,641 targets observed by K2 which fell within the TESS field of view during its first three years of observations.

We report the delivery to the Mikulski Archive for Space Telescopes of target pixel and light curve files for up to 160,000 targets selected from full-frame images (FFI) for each TESS Northern hemisphere observing sector. The data include calibrated target pixels, simple aperture photometry flux time series, and presearch data conditioning corrected flux time series. These data provide TESS users with high quality, uniform pipeline products for a selection of FFI targets, that would otherwise not be readily available. Additionally, we deliver cotrending basis vectors derived from the FFI targets to allow users to perform their own systematic error corrections. The selected targets include all 2-minute targets and additional targets selected from the TESS Input Catalog with a maximum of 10,000 targets per sector on each of the sixteen TESS CCDs. The data products are in the same format as the project-delivered files for the TESS 2-minute targets. All of the TESS-SPOC data products are available at the MAST as a High Level Science Product via https://doi.org/10.17909/t9-wpz1-8s54., Submitted to RNAAS, Data are public at MAST as High Level Science Products

Although the Transiting Exoplanet Survey Satellite (TESS) primary mission observed the northern and southern ecliptic hemispheres, generally avoiding the ecliptic, and the Kepler space telescope during the K2 mission could only observe near the ecliptic, many of the K2 fields extend far enough from the ecliptic plane that sections overlap with TESS fields. Using photometric observations from both K2 and TESS, combined with archival spectroscopic observations, we globally modeled four known planetary systems discovered by K2 that were observed in the first year of the primary TESS mission. Specifically, we provide updated ephemerides and system parameters for K2-114 b, K2-167 b, K2-237 b, and K2-261 b. These were some of the first K2 planets to be observed by TESS in the first year and include three Jovian sized planets and a sub-Neptune with orbital periods less than 12 days. In each case, the updated ephemeris significantly reduces the uncertainty in prediction of future times of transit, which is valuable for planning observations with the James Webb Space Telescope and other future facilities. The TESS extended mission is expected to observe about half of the K2 fields, providing the opportunity to perform this type of analysis on a larger number of systems., Comment: 14 pages, 6 figures, 5 tables, published in AJ

The Kepler, K2, and Transiting Exoplanet Survey Satellite (TESS) missions have provided a wealth of confirmed exoplanets, benefiting from a huge effort from the planet-hunting and follow-up community. With careful systematics mitigation, these missions provide precise photometric time series, which enable detection of transiting exoplanet signals. However, exoplanet hunting can be confounded by several factors, including instrumental noise, search biases, and host star variability. In this Letter, we discuss strategies to overcome these challenges using newly emerging techniques and tools. We demonstrate the power of new, fast open-source community tools (e.g., lightkurve, starry, celerite, exoplanet), and discuss four high signal-to-noise ratio (S/N) exoplanets that showcase specific challenges present in planet detection: K2-43c, K2-168c, K2-198c, and K2-198d. These planets have been undetected in several large K2 planet searches, despite having transit signals with S/N > 10. Two of the planets discussed here are new discoveries. In this work we confirm all four as true planets. Alongside these planet systems, we discuss three key challenges in finding small transiting exoplanets. The aim of this Letter is to help new researchers understand where planet detection efficiency gains can be made, and to encourage the continued use of K2 archive data. The considerations presented in this Letter are equally applicable to Kepler, K2, and TESS, and the tools discussed here are available for the community to apply to improve exoplanet discovery and fitting., 10 pages, 4 Figures, 1 Table

Over the past nine years, the Kepler and K2 Missions have carried out high precision photometric monitoring of more than half a million stars. Among these targets are 29 clusters and associations, with ages from 1 Myr to over 11 Gyr. We have generated a catalog of Kepler/K2 clusters, including basic information about the observations as well as the degree of scientific attention paid to them thus far. We present the catalog and a discussion of current and future cluster science endeavors as a way to motivate the astronomical community to continue mining these exquisite datasets.