TESS Eclipsing Binary Stars. I. Short-cadence Observations of 4584 Eclipsing Binaries in Sectors 1–26

The Quasiperiodic Automated Transit Search (QATS) is a pipeline originally developed to find planets with transit timing variations in the Kepler data (Carter & Agol 2013). It was subsequently updated and revised to be a more general planet and eclipsing binary search tool, as first applied to K2 by Kruse et al. (2019). The implementation used here is identical to that of Kruse et al. (2019), so we refer the reader there for full details. In brief, QATS models a transit at every cadence in a light curve and compares that model's χ² fit to a pure polynomial continuum. It then runs a period-folding search over that sequence of Δχ² to identify periodic signals where the transit fit is better than the continuum. Once it has identified a candidate periodic signal, it runs a more thorough transit fit to accurately measure the transit or eclipse parameters.

ECLIPSR (Eclipse Candidates in Light curves and Inference of Period at a Speedy Rate; IJspeert et al. 2021) is an algorithm that operates in two main stages: finding eclipses in the light curve and subsequently determining the periodicity in those eclipses. Finding (individual) eclipses in the light curve is achieved by looking for peaks in its time derivatives. This enables the successful identification of eclipses in light curves that show strong additional (intrinsic) variability compared to the eclipse signal. This process is fully automated and produces a score at the end for each light curve that can be used to separate light curves that show eclipses from those that do not contain an eclipse signal. Here, we start off from a list of pre-determined EB candidates and use the ECLIPSR algorithm mainly for its ability to determine ephemerides.

The final algorithm employed a traditional and well-tested approach to searching for transit-like signals: the box least squares (BLS) periodogram (Kovács et al. 2002). In the BLS periodogram, a sliding box-like signal is passed over the light curve for a range of orbital periods and the likelihood of the model is recorded at each orbital period. The resulting periodogram is expected to peak at integer multiples of any box-like periodic signals in the light curve, thus it is well-suited to the detection of eclipses. We used the BLS implementation in Astropy (Astropy Collaboration et al. 2013) with the lightkurve package (Barentsen et al. 2019) to normalize and prepare the light curves. No further pre-processing was applied to the light curve beyond a simple normalization of flux. Although straightforward to implement and run, the BLS algorithm relies on strictly periodic signals and thus cannot identify single eclipse events. The orbital periods searched by BLS ranged from 0.1 days to half the timespan of the light curve, with an oversampling factor of 20.

All candidate targets were vetted manually by at least one of the authors through a custom web application. For each TIC entry, phased plots were shown at the period, as well as half period and double period, for each of the automated ephemeris algorithms discussed above.

The triage user would then choose which period (if any) correctly represented the signal and classify whether the signal was that of an eclipsing binary or some other variable source. Subcategories were available to flag eclipsing binaries where the period was ambiguous (whether there are two nearly identical primary and secondary eclipses or no visible secondary eclipse) and whether there was an insufficient number of eclipses in the data to accurately determine the orbital period.

Ephemerides for a single TIC target with periods (or period multiples) within 1% were automatically flagged as representing the same underlying signal. All other multiple ephemerides classified as eclipsing binary signals were then treated independently as either blended EBs or true hierarchical systems.

A total of 27,496 candidate ephemerides (from 10,477 unique TICs) and their half- and double-period counterparts were triaged. Of those, 4592 ephemerides (from 4584 unique TICs) were manually classified as likely being caused by an eclipsing binary signal (see Figure 1) and were passed on to the ephemeris refinement algorithm described below. Additionally, 520 input ephemerides (from 457 unique TICs) were classified as likely eclipsing binaries but with an insufficient number of eclipses to determine an orbital period. We flagged 1872 input ephemerides (from 1725 unique TICs) as requiring further follow-up to determine whether they were eclipsing binaries or pulsating stars (due to sinusoidal signals), 9434 input ephemerides (from 6029 unique TICs) were classified as having no eclipsing binary signal, and 11,078 input ephemerides were marked as duplicates of another ephemeris entry for the same TIC. Figure 2 depicts several examplary EB light curves from the TESS catalog.

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To further refine the ephemerides determined from triage, we fit analytical models to the phase-folded light curves and sample the posteriors of the period used for phase-folding and the model parameters. The two analytical models used are two-Gaussian (Mowlavi et al. 2017) and polyfit (Prša et al. 2008).

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The two-Gaussian models fit a phased light curve by using one or two Gaussian functions and/or a cosine function with its maximum coinciding with one of the eclipses. The Gaussians are supposed to fit eclipses and the cosine function is supposed to fit symmetric ellipsoidal variability. The light curve is fit by all combinations of functions and it finds the solution that minimizes the degrees of freedom while retaining a satisfactory fit. The model with the highest Bayesian information criterion (BIC) is chosen as the best fit and used in the subsequent analysis. The left panels in Figure 3 depict an example of a two-Gaussian fit.

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The polyfit analytical model relies on fitting a piecewise-connected chain of polynomials to the phased light curve. The constraints imposed on the chain are that it should be connected and smoothly wrapped in phase space. There is no requirement that the chain be differentiable in the knots, which allows it to easily fit the discrete breaks caused by eclipses. As such, the knots are typically positioned at the ingress and egress of the eclipses. We use four quadratic polynomials connected at four knots. The right panels in Figure 3 depict an example of a polyfit.

The light-curve geometries induced by the eclipses, ellipsoidal variability, spots, and other potentially present signals are in reality more complex than those that can be modeled with these analytical functions. However, they are sufficient for this preliminary analysis which focuses on period refinement and simple geometrical parameter estimates.

To estimate the initial distributions for the model parameters, we first fit the model to the phase-folded data. For the two-Gaussian model, the best-fitting combination of eclipses and a cosine term are chosen and their corresponding parameters passed on to a Markov Chain Monte Carlo (MCMC) search with walkers initialized in a tight ball around the fitted parameter values. If there are no eclipses or ellipsoidal variability detected by two Gaussians (which results in a constant function fit), the light curve is not passed on to MCMC and flagged as "failed two-Gaussian." Similarly, we fit an initial polyfit to the phase-folded light curve, and if successful, we initialize a sample around the fitted knot positions and polynomial coefficients. A failed polyfit is rare, but if the algorithm raises any errors that do not result in a fit, we flag that system as a "failed polyfit."

We run MCMC with emcee (Foreman-Mackey et al. 2019) on each candidate EB light curve with 96 walkers for 2000 iterations. The burn-in typically takes under 100 iterations, but we discard the first 1000 iterations for the mean and standard deviation computation of the parameter posteriors. We also check for potential multiple "branches" of walkers at different log probabilities and only use the one with the lowest log probability of the posteriors. Out of the 4584 EB candidates, 98.08% were successfully fitted with a two-Gaussian model and 99.85% with polyfit. Out of the fitted two Gaussians, 99.24% within 1% of the triage period, and 98.89% of the fitted polyfits are within 1% of the triage period. Additionally, 98.93% of fitted two Gaussians are within 1% of the polyfit periods.

As depicted in Figure 3, two-Gaussian and polyfit have their deficiencies which hinder their application to all systems. Fortunately, they tend to complement each other (unlike two-Gaussian, polyfit can fit a wide range of out-of-eclipse signals, including highly asymmetric ones; while two-Gaussians will tend to fit eclipses even in noisy data, where polyfit underperforms). We also run additional checks to ensure that a fitted Gaussian or polyfit truly fits an eclipse and not some other feature of the light curve:

• 1.  
  overlapping eclipses check—ensures that a single eclipse is not fitted by two Gaussians or two polynomials;
• 2.  
  noise check—ensures that a Gaussian is not fitted to the data noise;
• 3.  
  ELV check—ensures that a Gaussian is not fitted to ellipsoidal variations (ELVs) or another out-of-eclipse variability;
• 4.  
  polyfit only: check that the eclipse coincides with a polynomial minimum and not a knot position. If a knot exists with a lower flux value than the polynomial minimum, the eclipse is discarded.

Where any one of these checks fails, the eclipse parameters are not reported, even if a two-Gaussian or polyfit model solution exists.

To fully utilize the information returned from both models and their period and parameter distribution, we compute combined ephemerides, which are ultimately reported in the catalog. The combined ephemerides are computed by sampling both the two-Gaussian and polyfit distributions, under the constraint that the number of samples drawn from each distribution is inversely proportional to the reduced χ² value (chi² _r ) of the mean fit (Figure 4). The mean and standard deviation of the new combined distribution are then chosen as the final ephemerides. We perform an additional check to ensure that the models whose distributions we sample are reasonable. If a model reports uncertainty of the time of superior conjunction larger than half the fitted period, the time of superior conjunction for that model is discarded. This happens more often in the case of polyfit, as the eclipse model has more degrees of freedom.

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For morphological classification of the light curves, we rely on the morphology parameter as defined in Matijevič et al. (2012). The morphology parameter is defined as a continuous variable in the range [0,1], where 0 corresponds to the widest detached systems and 1 to ellipsoidal variables. We use the Kepler EBs data set to train a neural-network (NN) model on the light-curve geometry and output a value of the morphology parameter. The Kepler and TESS EBs data sets are both preprocessed in the same way: phase-folded with the final catalog ephemerides and binned in 1000 phase bins over the range [−0.5, 0.5]. The NN architecture consists of an input layer of size 1000, corresponding to the phased light curves; three dense layers of size 300, 100, and 30, respectively; and an output layer of size 1, corresponding to the morphology parameter. The NN is trained on 60% of the Kepler data set and tested on the remaining 40%, yielding a mean squared error loss of 0.0035.

Figure 5 demonstrates the relationship between the morphology, periods, and primary eclipse widths in the catalog. Long-period systems have morphology parameters close to zero, signaling wide detached binaries, while the shortest period systems tend toward a morphology of 1, which corresponds to contact binaries and ellipsoidal variables. The primary eclipse widths, as determined by the two-Gaussian model, are encoded in the color map, further confirming that the morphology parameter captures the expected variability in eclipse widths: narrow eclipses in systems with a morphology close to 0 and wider eclipses going toward a morphology of 1.

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The sample of EBs presented in this paper is inherently nonuniform: mission targets are selected to maximize the exoplanet detection yield and guest investigator targets are selected through proposal competition across a great many science goals. It is thus impossible to use these data to get statistically representative distributions of parameters; we defer that goal until the time when we have a sample of detected and characterized EBs from full-frame images. Thus, when we say "catalog completeness," we mean the overall EB detection success in the data set of 2 minute cadence target observations. Quantifying completeness properly thus remains beyond the scope of this paper, but we provide qualitative estimates here.

To estimate completeness qualitatively, we start with combined differential photometric precision (CDPP; Gilliland et al. 2011). CDPP is a measure of light-curve variation—the rms noise of the result of filtering the time series with a high-pass Savitzky–Golay filter and then applying a moving average of 0.5 hr. The top panel in Figure 12 shows CDPP as a function of magnitude for Sector 1 observations. The CDPP values are inherent to aperture light, so they are not corrected for crowding. The second panel in Figure 12 provides a statistical estimate of per-target crowding, i.e., the fraction of light in the aperture coming from the target itself. Thus, a value of 1 means that all light is due to the observed target, while a value of, say, 0.6, means that 60% of the light comes from the target and 40% of the light comes from background sources. Thus, to account for dilution, we correct the CDPP for crowding by dividing it by the crowding factor. This implicitly assumes that the extraneous source of light in the aperture is constant, and that all variability comes from the target itself, which may or may not be true, but overall it plays a small role in correction because crowding is "top-heavy": 90% of the targets have crowding factors larger than 0.95. The corrected CDPP is depicted in the third panel of Figure 12. We then fit the bottom envelope by sigma-clipping and divide the corrected CDPP by the envelope in order to flatten out the dependence on magnitude (bottom panel). This way, we can assess the distribution of amplitudes for EBs and its qualitative resemblance to the expected geometric distribution (i.e., the probability of eclipses as a function of orbital elements). We emphasize the word "qualitative" here because, in order to calculate the true geometric distribution, we would need to be able to simulate target list selection, generate a synthetic sample of EBs and, from there, calculate the corresponding CDPP values; this, unfortunately, is not tractable because of the non-prescriptive target selection. The top panel in Figure 13 shows this distribution; we observe a monotonically decreasing trend, in line with expectations. For validation purposes, we check the trend of all targets observed in Sector 1; as we see no systematic features in the flattened CDPP, we conclude that the number distribution is a fair reflection of the true CDPP distribution for the observed EBs.

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While not statistically significant, we took a closer look at the slight dip in the fourth bin of the EB distribution; there are 19 EBs out of 299 targets in that bin that were found. We manually went through the entire list of 299 targets again but have failed to find any additional EBs.

Finally, we perform one last check: we test whether the magnitude distribution of EB targets is representative of the overall magnitude distribution; any detected bias might raise completeness questions. Figure 14 demonstrates qualitative equivalence, noting of course that there are no EBs brighter than T = 2.5, and the diminishing signal-to-noise ratio suppresses eclipse detection on the faint end.

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At some level eclipses will blend into the noise background and we will no longer be able to (reliably) detect them; to estimate that level, we take the distribution of primary eclipse depths (see Figure 9) and choose the bin size that yields equal occurrence rates for the first two bins. Phenomenologically that implies that the monotonic increase toward lower S/N stops and that we can no longer reliably detect eclipses. That occurs at S/N ∼ 13. We take that to be our limit. We conclude that the catalog is largely complete to S/N ∼ 13.

In this first part of the series of papers we presented the sample of 4584 EBs observed by TESS in sectors 1–26. The main science goals that the entire series aims to achieve are as follows:

• Study gold-standard EBs. These are known, bright, detached, double-lined binaries with deep eclipses (Torres et al. 2010; Southworth 2015). These are posited to have had minimal interaction histories and have evolved largely independently as single stars. Such systems are considered "gold standards" because they hold promise for the most accurate fundamental parameters. These EBs have spectroscopic data already available and TESS provides us with an improvement in the photometric light-curve quality and temporal coverage.
• Estimate photometric elements for all TESS EBs. Eclipsing binary light curves hold a wealth of information about a system and its stellar components. Using PHOEBE and its framework for inverse problem solvers (Conroy et al. 2020), we can estimate photometric parameters of all TESS EBs with minimal manual intervention. Using the ephemerides and geometrical estimates from the catalog as a starting point, we can determine the sum and ratio of fractional radii; temperature ratio of the components; the inclination, eccentricity, and argument of periastron of the orbit; and passband luminosities and potential third-light contribution. In addition, for closed systems, the mass ratio and semimajor axis can be constrained from light curves alone (Wilson 1994; Terrell & Wilson 2005). A full Bayesian analysis with MCMC also yields posterior distributions for second-order effects, like the effective temperature of the primary, gravity-darkening coefficients, and albedoes, which, given the photometric precision of TESS, can be used to refine the current empirical laws.The main perceived impact of this study will be the period–eccentricity distribution of the TESS EBs sample, which is crucial in studies of binary star populations. In addition, interesting and benchmark systems will be identified for radial-velocity follow-up and more advanced analysis.
• Extend the temporal coverage with archival photometry. TESS observations last about 27 days for each sector. Roughly 70% of the sky was observed during the prime mission (Guerrero et al. 2021) and of the 232,705 stars observed at 2 minute cadence, 152,993 (∼66%) were observed for just one sector, while the rest were observed in multiple sectors, and 3874 (∼1.7%) were observed for 13 consecutive sectors over 351 days. While the observations are not fully continuous, with gaps between orbits and some time lost for engineering or safe modes, in general, a given time baseline of observations means that it is possible to detect EBs with orbital periods up to half the time baseline of observations.At the long end of that detectability time frame, ambiguities exist in the characterization of the EBs. In some cases, it is not clear whether two distinct eclipses are seen. In others, spot modulation or other variability can interfere with the identification or measurement of an eclipse. For EBs with orbital periods greater than half the observing time baseline, only a single eclipse may be detected, yielding a likely identification of an EB without a reliable period measurement. See examples in Figure 17. For all these reasons, the set of TESS-detected EBs can benefit from cross-identification with other photometric surveys.A number of such surveys have been conducted and can be combined with TESS observations. Many surveys were carried out to search for transiting exoplanets, including WASP (Pollacco et al. 2006), HAT (Bakos et al. 2004, 2013), KELT (Pepper et al. 2007, 2012), and others ⁴⁶ Other surveys have been conducted to search for stellar variability, such as ASAS (Pojmanski 1997), ASAS-SN (Shappee et al. 2014), ATLAS (Tonry et al. 2018), and ZTF (Bellm et al. 2019). While none of these surveys have the photometric precision or cadence of TESS, they all have greater observing time baselines over large fractions of the sky. EBs identified in TESS data with ambiguous ephemerides can be matched to the archival photometric observations to identify eclipses and refine the ephemerides. Such an effort will typically only recover EBs with deep eclipses, but that still represents a large fraction of the EB population. The archival photometry can determine or refine the ephemerides of the EBs and can be used to search for eclipse time variations (ETVs; Conroy et al. 2014) or apsidal motion [REF](Orosz 2015; Borkovits et al. 2016a; Kirk et al. 2016b). Further development of the TESS EB catalog will incorporate such analysis.In addition to the use of archival photometry, individual systems of interest can be followed up for astrophysical investigation with modest observing facilities. While broader scientific themes are outlined below, small-telescope observatories are well equipped to observe the bright EBs identified in this catalog. An example of that kind of investigation is multiband photometric follow-up of the O'Connell effect (Milone 1968), in which light curves show unequal maxima before and after the primary eclipse. Follow-up observations in different bandpasses are necessary to understand the underlying cause of this phenomenon. Furthermore, while archival photometry can recover the orbital period for some long-period EBs, as described above, follow-up photometry can readily refine the orbital parameters more precisely.
• Study asteroseismic components in EBs. The exquisite precision, cadence, and duty cycle of TESS observations have revealed resolved pulsations in stars across all spectral types and evolutionary phases (Antoci et al. 2019; Pedersen et al. 2019; Córsico et al. 2021). Given the ubiquity of both stellar pulsations and stellar multiplicity, binary systems with at least one pulsating component are commonly found. The complementary nature of asteroseismic (interior) and binary (bulk) information enables highly detailed evolutionary modeling. Such synergistic combined modeling approaches have led to detailed inference on the structure of stars from solar-like oscillators to massive β-Cep pulsators to evolved stars that have undergone mass transfer (De Cat et al. 2004; Guo et al. 2016; Schmid & Aerts 2016; Guo et al. 2017; White et al. 2017; Beck et al. 2018; Streamer et al. 2018; Johnston et al. 2019, 2021). Furthermore, detailed studies have demonstrated tension between the asteroseismic and binary results for both main sequence and evolved stars, indicating that evolutionary models still have room for improvement (Gaulme et al. 2016; Themeßl et al. 2018; Benbakoura et al. 2021; Sekaran et al. 2021). The large data set provided by TESS will enable synergistic asteroseismic and binary modeling across a much larger parameter range than was previously possible with the more limited samples, allowing investigation into the relationship between pulsational properties and orbital properties (Liakos & Niarchos 2017; Gaulme & Guzik 2019; Sekaran et al. 2020).Ground-based radial-velocity follow-up of binary systems is time-consuming, resource-intensive, and simply expensive. Due to their stability over long time bases, heat-driven pulsations act as regular clocks, whose phase (and frequency) is modulated due to the light-travel-time effect from the orbital motion. By measuring the observed phases of pulsations across the orbit, one can reliably derive the radial-velocity curve of the pulsating component from the photometry alone (Shibahashi & Kurtz 2012; Murphy et al. 2014; Hey et al. 2020). The application of this method to this database (where appropriate, given the ratio of pulsation period to orbital period) can produce a wealth of radial-velocity curves without needing to apply for costly ground-based telescope time.
• Explore the impact of dynamical tides. Kepler discovered 172 heartbeat stars (HBs), and about one fifth show tidally excited oscillations (Kirk et al. 2016a; Guo et al. 2020), i.e., the direct manifestation of dynamical tides. A handful of them have been studied in detail (Welsh et al. 2011; Hambleton et al. 2013, 2016, 2018; Shporer et al. 2016; Fuller et al. 2017; Guo et al. 2017, 2019). Recently, Guo (2021) reviewed the current status of heartbeat binaries with tidally excited oscillations. Most Kepler HBs are of A–F types due to selection biases. TESS is destined to discover more massive O–B type heartbeat binaries. Systems already published include Jayasinghe et al. (2019, 2021) and Kołaczek-Szymański et al. (2021). To date, we have identified 25 HB systems in the 2 minute TESS data up to Sector 26, and over 200 systems in the 2 minute and FFI data combined. Given that 5% of the binary stars in the Kepler catalog with periods less than 27.3 days (the length of a TESS sector) were classified as heartbeat stars, we anticipate that the number we have identified is a lower limit.The advent of the TESS mission has also revealed a new class of pulsating stars in binaries, wherein the pulsation axis is "tidally tilted," producing a characteristic amplitude and phase modulation (Fuller et al. 2020; Handler et al. 2020; Kurtz et al. 2020; Rappaport et al. 2021). Additionally, a few studies have reported the detection of so-called "tidally perturbed" pulsations, where a series of pulsations that are nearly equidistantly spaced by the orbital frequency were detected (Bowman et al. 2019; Southworth et al. 2020; Steindl et al. 2021). Such systems cannot currently be explained by the same model as the "tidally tilted" pulsators, and seem to have a separate connection to the interplay between tides and pulsations. While only a handful of these objects have been identified to date, they signify a unique contribution of TESS to the progress of tidal asteroseismology. The compilation of this database serves to streamline the detection of even more systems.
• Stellar multiples and circumbinary planets. A large number of eclipsing binaries have third-body companions that are detected via eclipse timing variations (ETVs), either light-travel-time effects (LTTE, the most common) or dynamical effect delays. A fraction of these exhibit tertiary eclipses as well. For example, Borkovits et al. (2016b) found good evidence for third bodies in 222 eclipsing binaries out of 2600 studied using Kepler data. In most cases, the ETV signal becomes significant on timescales similar to or longer than the period of the outer orbit, which is typically a few to several hundred days for the systems found by Borkovits et al. (2016b).Rather than being a star, in some cases, the third body is a planet—a so-called circumbinary planet. Kepler revealed 13 such planets that transited their host stars (e.g., see Doyle et al. (2011), Welsh et al. (2012), Orosz et al. (2019)). While few in number, these systems provide a great deal of information, e.g., extremely accurate (not just precise) stellar parameters and planetary radii. But with only a handful of systems, we cannot understand the characteristics of the population of circumbinary planets. TESS's all-sky survey could remedy this small sample-size problem, but for most of the sky, only ∼27 days of near-continuous coverage per two years is available and this window is much shorter than the typical circumbinary planet orbital period. Fortunately, the duty cycle at the ecliptic poles is much better and the first TESS circumbinary planet, TOI-1338 (Kostov et al. 2020a), was detected in observation from TESS's continuous viewing zone (CVZ) at the southern ecliptic cap. In addition to the long-duration observations at the CVZ, we can search for circumbinary planets by taking advantage of the extra information provided when the planet transits both stars in the binary. Unlike a planet orbiting a single star, a circumbinary planet can produce two, and possibly more, transits during one conjunction's pass. This "1–2 punch" technique (Jenkins et al. 1996; Kostov et al. 2020b) was used to detect the second TESS circumbinary planet, TIC 172900988 (Kostov et al. 2021a). Roughly 140±110 new circumbinary planets may potentially be found via this technique, in addition to the 40 ± 32 expected in the two CVZs (Kostov et al. 2020b). Thus TESS should be able to boost the number of circumbinary planets by an order of magnitude, allowing a much more robust estimate of the occurrence rate, population statistics, and searches for correlation with various binary star parameters (e.g., metallicity, eccentricity, mass ratio, etc.).
• Gaia data overlap. Of the 4584 EBs in the catalog, a total of 4550 have entries in the early third data release of the Gaia catalog (Gaia EDR3; Gaia Collaboration et al. 2021). The top three panels in Figure 18 show histograms of the G-band magnitudes and the G_BP − G_RP colors for the combined light of each binary and of their distances, where the latter are derived here simply as the reciprocal of the trigonometric parallax (see Bailer-Jones et al. 2021). The distribution of magnitudes up to about G = 12 largely reflects the content of the TIC candidate target list, while the fainter stars are special interest targets that come from the Guest Investigator Program. The typical color index is very near solar. As expected from their brightness, most of these objects are relatively nearby, with the peak of the distribution located at ∼150 pc, and a long tail toward larger distances (truncated in the figure).The bottom panel displays the distribution of the renormalized unit weight error (RUWE) from Gaia, which is regarded as a useful measure of the quality and reliability of the astrometric solution ⁴⁷ . RUWE values for well-behaved solutions cluster around 1.0, whereas values larger than about 1.4 typically indicate unmodeled excess scatter in the astrometric observations that can be caused, e.g., by binarity of the source or perhaps other effects. Gaia does not spatially resolve any of the EBs in this catalog; it only measures the center of light. In many cases, the binary motion will cause the flux centroid to wobble enough to be detected by Gaia, perturbing the astrometric solution.Stassun & Torres (2021) have shown that even in the 1.0–1.4 range the RUWE values tend to correlate with the semimajor axis of the photocentric motion. For the binaries in the catalog, we do not have sufficient information to estimate the semimajor axis of the photocenter. However, we can place the EB sample into the broader context of typical RUWE values for Gaia stars across the HR diagram. This is shown in Figure 19, where the left panel represents the RUWE in grayscale for the ∼1 million Gaia EDR3 stars within 400 pc having 5 < G < 19 and ∣ b∣ > 60°, and the right panel overlays in green the EB sample. In both panels, a piecewise linear fit is shown over the "spine" of the single-star main sequence, for which the RUWE values are at a minimum (dark gray). Various populations with relatively high binary star fractions appear above and below the single-star main sequence (lighter shades of gray), as described in detail by Belokurov et al. (2020).Relative to the single-star main sequence, the EBs identified in this paper are in almost all cases displaced upward/redward, as expected for the combined light of pairs of stars having various relative luminosities and colors. And relative to the minimal RUWE values typical of the single-star main sequence, the EBs occupy regions that are characterized by higher RUWE values on average.We can also use the recent work of Belokurov et al. (2020) to assess the likely nature and evolutionary states of the EBs. In Figure 20, we represent the EB sample in the color–magnitude diagram with theoretical evolutionary tracks overlaid to provide a sense of the mass range of the systems, as well as boxes with annotations indicating EBs in evolutionary states that may be of particular interest for various astrophysical applications (see, for example, the work on extreme horizontal branch stars by Sahoo et al. 2020 and Baran et al. 2021).Finally, it is now well established that short-period binary stars are very frequently found in hierarchical triple systems, with a tertiary companion on a much larger orbit around the tight binary (see, e.g., Tokovinin et al. 2006; Laos et al. 2020, and references therein). We cross matched our EB sample with the catalog of wide binaries in Gaia EDR3 from El-Badry et al. (2021), to assess if any of the EBs are in fact members of hierarchical triples.We cross-matched our EB sample with the catalog of wide binaries in Gaia EDR3 from El-Badry et al. (2021), to assess if any of the EBs are in fact members of hierarchical triples. This yielded 711 wide binary candidates in which at least one component is in our TESS EB sample. Of these, 665 have greater than 90% probability of being gravitationally bound (R_chance < 0.1). The TESS EB is the brighter (fainter) component in 632 (64) of the high-probability binaries. Thirty-one high-probability binaries have both components in our TESS EB sample. We defer further analysis of this sample to future work.
• Use calibrated 2 minute cadence targets for FFI extraction. There are several community-led projects that focus on light-curve extraction from TESS FFIs. The tools and the data products stemming from those projects have been released to the public; we base our extractions on an adapted version of eleanor (Feinstein et al. 2019). We use the EBs observed with the 2 minute cadence as the training set for the back-propagating neural network that will sift through all FFI light curves and find those that resemble EBs. The amount of cyan in Figure 1 clearly showcases why manual vetting is not tractable and why we must resort to automated techniques. We will extract FFI light curves for each of the 2 minute cadence EBs, formulate a fidelity metric based on the comparison between FFI-extracted and 2 minutes cadence light curves that can be inspected manually, train a classifying, back-propagating neural network on the FFI-extracted light curves of the 2 minute cadence EBs, and deploy the network on all FFI light curves to automatically detect EBs lurking in the images.
• Analyze contents of a catalog of EBs extracted from the FFIs. Several of our co-authors have constructed all light curves from TESS FFIs up to 15th magnitude, resulting in more than 72 million light curves from sectors 1–26. The authors constructed a one-dimensional convolutional neural network, first described in Powell et al. (2021), to extract candidate EBs from these light curves, resulting in a catalog of over 460,000 sources, of which we expect 250,000 to be true sources (i.e., not due to light-curve contamination). The coordinates of these candidates are shown in Figure 21. Among these candidates were found several interesting multiple-star systems (Kostov et al. 2021b; Powell et al. 2021), with many others currently being researched. The greatest value of this effort, however, may indeed lie in the use of the full catalog of candidates. Cross matching with other catalogs could identify higher-order multiples or binaries containing particular stellar types. Statistical analysis of the catalog could also provide tremendous insight into the growing field of EB research.

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The catalog of EBs observed by TESS in short cadence is thus only the first step in the exploration of the physical, dynamical, and statistical properties of EBs across the entire sky. The catalog will continue to be updated with new sectors of data as they become available and it will be broadened to include all EB sources detected in the TESS full-frame images. For the latest version of the catalog, please refer to http://tessEBs.villanova.edu.