Searching the Entirety of Kepler Data. I. 17 New Planet Candidates Including One Habitable Zone World

So far, independent Kepler searches have focused on only a subset of light curves (e.g., Kunimoto et al. 2018; Shallue & Vanderburg 2018) or a more limited range of orbital periods than examined by the Kepler team (e.g., Wang et al. 2015; Caceres et al. 2019). In this paper, we present an independent systematic search of the entirety of Kepler data (∼200,000 stars) for planets, using the same three-transit minimum detection criteria as the Kepler team.

We describe our planet detection and vetting pipelines in Sections 2 and 3, which we make available for public use on Github⁵ under the BSD 3-Clause License and version 1.0 is archived in Zenodo (Kunimoto et al. 2020). The main difference between our search and Kepler's is our use of a Box-Least Squares (BLS) algorithm (Kovács et al. 2002) and the associated effective BLS signal-to-noise ratio (S/N) for measuring the significance of a detection, instead of a wavelet-based algorithm (Jenkins et al. 2010) and the associated Multiple Event Statistic (MES). Furthermore, while our vetting is largely inspired by the automated DR25 Robovetter (Thompson et al. 2018), we introduce different tests and follow our automated vetting with a final manual vetting stage, similar to Petigura et al. (2013).

Our ability to differentiate between planets and noise-like false positives (FPs) is discussed in Section 4. We compare our results to the findings across all Kepler catalogs in Section 5, and detail 17 new PCs in Section 6. These candidates are processed through further analysis, including centroid vetting, adaptive optics (AO) imaging follow-up, and astrophysical FP calculation to increase confidence in their planet status.

Q1–Q17 DR25 long-cadence light-curve files were downloaded from MAST. This photometry includes systematic corrections for instrumental trends and estimates of dilution due to other stars that may contaminate the photometric aperture (Stumpe et al. 2014). To initially set up the data, we used the kfitsread routine from the Kepler Transit Model Codebase (Rowe 2016), which includes code previously used by the Kepler team for transit detection and characterization. kfitsread reads in each FITS file, removes data flagged as low quality, stitches all quarters of data together to create one continuous light curve, and subtracts the median flux from each data point.

We then detrended each light curve to filter out astrophysical and instrumental signatures using the detrend5 routine. Each observation is corrected by fitting a cubic polynomial to a segment W days wide centered on the time of measurement. A good choice of W is longer than the duration of a typical transit (several hours) to prevent significant transit shape distortion, while short enough to adequately filter out astrophysical signatures (several days). The ideal choice of W is star-dependent, as stars having varying levels of noise and intrinsic stellar variability. In an effort to reflect this, we detrended each light curve using W = 1, 1.5, and 2 days, and measured the corresponding standard deviations σ₁, σ_1.5, and σ₂. We used W = 1 if σ₁/σ_1.5 < 0.8 or σ₁/σ₂ < 0.8, W = 1.5 if σ_1.5/σ₂ < 0.8, and W = 2 otherwise, similar to the process used by Dressing & Charbonneau (2015) to flag stars with greater levels of noise. In other words, a more aggressive detrend would only be favored if it resulted in a significant decrease in overall light-curve variability.

We then 5σ-clipped outliers in the data. Only outliers in the positive flux direction were removed so as to leave any deep transits untouched. Lastly, we searched for data gaps within the detrended light curves. Data gaps are frequently accompanied by sharp increases or decreases in flux that can interfere with the search for planets. For example, the Kepler telescope would execute a 90° roll every 90 days to reorient its solar panels, resulting in a break in observations of approximately one day. We defined a data gap as 0.75 or more days of missing photometry. Gaps are often accompanied by sharp increases or decreases in flux, which can interfere with the search for transits. Thus, we removed all data points within one day of the start and end of each gap.

We searched the light curves using a box-fitting least squares (BLS) routine, based on the original algorithm by Kovács et al. (2002) which was designed to identify periodic transit signals in time-series photometry. In the Kepler Transit Model Codebase, this is available as transitfind2.

Once a possible transit was identified, its period P, epoch T₀, depth T_dep, and duration T_dur were estimated. We calculated the S/N of an event to be the ratio of the mean transit depth integrated over the transit duration relative to the standard deviation of out-of-transit observations σ_OT,

$$\begin{eqnarray}&&{\rm{S}}/{\rm{N}}=\displaystyle \frac{\sqrt{N}}{{\sigma }_{\mathrm{OT}}}{T}_{\mathrm{dep}},\end{eqnarray} \tag{ 1 }$$

where N is the number of in-transit data points. To be more robust to outliers, σ_OT was calculated using the Median Absolute deviation (MAD) with σ_OT = 1.48MAD (Hoaglin et al. 1983). Equation (1) is comparable to the "effective" S/N mentioned in Kovács et al. (2002), and assumes that the depth of the transit is uniform. While this is a good approximation for small Earth-sized planets with central transits, relatively large planet-to-star radius ratios and/or large impact parameters can have significant ingress and egress durations. In these cases, the S/N will be overestimated, but this is expected to have minimal impact on the full assessment of PC events (Rowe et al. 2014).

For each light curve, we searched for transit signals with S/N > 6. After identifying a transit signal, we removed its associated events from the data and searched the residuals. This enabled sensitivity to multiplanet systems. We capped this multipassthrough search at five consecutive searches and set aside light curves that reached this maximum for manual inspection. Usually this meant a particularly noisy light curve was causing the BLS algorithm to return many obviously poor signals. If this was not the case, we would continue searching until no more S/N > 6 signals were detected.

2.2.1. Choice of S/N Threshold

A total of 130,312 signals with S/N > 6 were detected around the 198,640 stars searched. An overwhelming number of these are false alarms due to instrumental or astrophysical systematics in the time series. This is a weakness of using S/N as the only detection criterion. Thus, before following up each signal with the full suite of candidacy tests, we ran a first stage of vetting to discard likely false alarms. Signals that passed these tests were designated TCs.

Since the detrending process is destructive to the shape of a planetary transit and often results in a loss in S/N, we produced a re-detrended version of each light curve before running the tests. We masked out each transit by excluding all observations within one transit duration of the central time of each transit. Then, we ran the detrending algorithm to determine the cubic polynomial fit to each segment of data as before, essentially only fitting to all out-of-transit observations. Finally, we unmasked the transit in the light curve and used an extrapolation of the fit to estimate corrections during transit. These re-detrended light curves are used for the remainder of the analysis in this paper unless otherwise specified.

2.3.1. S/N Recalculation Test

2.3.2. Robust Statistic Test

2.3.3. S/N Consistency Test

This test examines the S/Ns of each transit individually and compares them to what is expected based off the full transit S/N. Since the depths of individual transits of PCs should be equal to each other, the ith transit comprised of n_i observations has an expected S/N of

$$\begin{eqnarray}&&\langle {\rm{S}}/{{\rm{N}}}_{i}\rangle =\displaystyle \frac{\sqrt{{n}_{i}}}{{\sigma }_{\mathrm{OT}}}{T}_{\mathrm{dep}}.\end{eqnarray} \tag{ 2 }$$

This is compared to the actual S/N of the ith transit, S/N_i, using a χ² statistic with N_T degrees of freedom

$$\begin{eqnarray}&&{\chi }^{2}=\sum _{i=1}^{{N}_{T}}{\left({\rm{S}}/{{\rm{N}}}_{i}-\langle {\rm{S}}/{{\rm{N}}}_{i}\rangle \right)}^{2}\end{eqnarray} \tag{ 3 }$$

where N_T is the number of transits. We define

$$\begin{eqnarray}&&\mathrm{CHI}={\rm{S}}/{\rm{N}}{\left(\displaystyle \frac{{\chi }^{2}}{{N}_{T}}\right)}^{-1/2}\end{eqnarray} \tag{ 4 }$$

for use as the false alarm discriminator, requiring a candidate to pass with CHI > 6 in both the original and re-detrended light curves.

2.3.4. Number of Transits

We used a Mandel & Agol (2002) quadratic limb darkening transit model assuming circular orbits,⁶ fit to each transit with least-squares. Limb darkening parameters were taken from Claret & Bloeman (2011) based on the known T_eff, log g, and [Fe/H] from the Mathur et al. (2017) stellar properties catalog. To speed up the fit process, data more than two transit durations from the center of each transit were ignored.

3.1.1. Fitted Parameters

The model is parameterized by orbital period, transit epoch, ratio of planet and star radii (R_p/R_s), distance between planet and star at midtransit in units of stellar radius (a/R_s), impact parameter (b), and zero-point flux (z).

For initial guesses, P and T₀ were taken from the BLS search results. ${R}_{p}/{R}_{s}$ was estimated as the square root of the BLS transit depth,

$$\begin{eqnarray}&&\displaystyle \frac{{R}_{p}}{{R}_{s}}=\sqrt{{T}_{\mathrm{dep}}},\end{eqnarray} \tag{ 5 }$$

while the initial guess for z was 0. a/R_s was estimated using Equation (8) in Seager & Mallen-Ornelas (2002):

$$\begin{eqnarray}&&\displaystyle \frac{a}{{R}_{s}}={\left[\displaystyle \frac{{\left(1+\sqrt{{T}_{\mathrm{dep}}}\right)}^{2}-{b}^{2}\left(1-{\sin }^{2}\tfrac{\pi {T}_{\mathrm{dur}}}{P}\right)}{{\sin }^{2}\tfrac{\pi {T}_{\mathrm{dur}}}{P}}\right]}^{1/2}\end{eqnarray} \tag{ 6 }$$

with b set to its initial guess and transit duration ${T}_{\mathrm{dur}}$ set to the BLS estimate. Since the model is sensitive to b, the fit was run once for each b = 0, 0.1, 0.2, ..., 0.9. The fit with reduced χ² closest to 1 was chosen to determine the best-fit parameters.

In case the transit model fit would fail to converge, a trapezoid fit parameterized by T₀, R_p/R_s, z, width of the flat part of transit, and slope of the sides of the trapezoid was used instead. P was set fixed to the BLS-detected value.

The first candidacy tests aim to identify non-transit-like (NTL) FPs—signals that do not resemble transiting or eclipsing objects. Frequently, candidates with low S/N and/or few transits are simply due to noise or instrumental artifacts. Candidates may also be due to quasi-sinusoidal signals such as pulsating stars or star spots.

3.2.1. Transit Model Fit Test

The transit model should fit the data better than a straight line, parameterized by the zero-point flux z. We compare each model fit's reduced chi-squared values

$$\begin{eqnarray}&&{\chi }_{\mathrm{red}}^{2}=\displaystyle \frac{1}{\nu }\sum _{i=1}^{N}\displaystyle \frac{{({y}_{i}-{m}_{i})}^{2}}{{\sigma }_{i}^{2}}\end{eqnarray} \tag{ 7 }$$

where y_i, m_i, and σ_i represent the flux, modeled flux, and error of the ith data point, and ν are the total degrees of freedom. Given N points fitted, the transit model with 6 parameters will have N − 6 degrees of freedom while the straight line model with 1 parameter has N − 1. A signal passes this test if the reduced chi-squared of the transit model is less than the reduced chi-squared of the straight line model.

3.2.2. Transit Model S/N Test

3.2.3. Depth Mean-to-median Ratio Test

3.2.4. Chases Test

3.2.5. Uniqueness Tests

For a transit to be considered "unique," there should not be any other transit-like events in the folded light curve with a depth, duration, and period similar to the primary signal, in either the positive or negative flux directions.

Two uniqueness statistics are calculated for each TC:

$$\begin{eqnarray}&&{\sigma }_{{\rm{U}}1}=\displaystyle \frac{| {d}_{\mathrm{pri}}-{d}_{\sec }| }{\sqrt{{\sigma }_{\mathrm{pri}}^{2}+{\sigma }_{\sec }^{2}}}\end{eqnarray} \tag{ 8 }$$

and

$$\begin{eqnarray}&&{\sigma }_{{\rm{U}}2}=\displaystyle \frac{| {d}_{\mathrm{pri}}-{d}_{\mathrm{ter}}| }{\sqrt{{\sigma }_{\mathrm{pri}}^{2}+{\sigma }_{\mathrm{ter}}^{2}}}\end{eqnarray} \tag{ 9 }$$

where d_pri, d_sec, and d_ter are the depths of the TC event, second-largest event, and third-largest event, respectively, and σ_pri, σ_sec, and σ_ter are their uncertainties. Secondary and tertiary events may be in either the positive or negative flux direction. A TC must have both ${\sigma }_{{\rm{U}}1}\gt 3.0$ and ${\sigma }_{{\rm{U}}2}\gt 3.0$ (i.e., at least 3σ significance).

Running this analysis on the re-detrended light curve is a good choice when the transit is due to a planet, as it ensures the planet transit is not distorted by detrending and the test correctly indicates strong uniqueness. However, a noise TC is essentially the only noise in the light curve that is not detrended in this version of the light curve, making an indication of uniqueness against the rest of the noise misleading. Thus, we also perform this analysis on the original light curve, requiring a slightly lower 2σ significance to pass.

The Kepler team also developed their own "model-shift uniqueness test," which is publicly available on GitHub⁷ (Coughlin 2017a) and described in Appendix A.3.4 of KDR25. While the statistics described above take into account the uniqueness of the TC in the form of a square pulse, this test takes into account the full transit shape as follows. After removing outliers, the best-fit model of the primary transit is used to measure the best-fit depth at all other phases. The two deepest events aside from the primary event (called the secondary and tertiary events) and the most positive flux event are all identified. The significances of these events (σ_pri, σ_sec, σ_ter, and σ_pos) are computed by dividing their depths by the standard deviation of the light curve residuals outside of the primary and secondary events, assuming white noise. The amount of systematic red noise in the light curve on the timescale of the transit is also computed, as the standard deviation of the best-fit depths at phases outside of the primary and secondary events. Taking the ratio of the red noise to the white noise gives the value F_red. F_red = 1 means there is no red noise in the light curve.

The threshold at which an event is considered statistically significant is given by

$$\begin{eqnarray}&&{{FA}}_{1}=\sqrt{2}\mathrm{erfcinv}\left(\displaystyle \frac{{T}_{\mathrm{dur}}}{P\cdot {N}_{\mathrm{TCs}}}\right).\end{eqnarray} \tag{ 10 }$$

Here N_TCs is the number of transit candidates examined, the quantity P/T_dur represents the number of independent statistical tests for a single target, and erfcinv is the inverse complementary error function. Similarly, the threshold at which the difference in significance between two events is considered to be significant is given by

$$\begin{eqnarray}&&{{FA}}_{2}=\sqrt{2}\ \mathrm{erfcinv}\left(\displaystyle \frac{{T}_{\mathrm{dur}}}{P}\right).\end{eqnarray} \tag{ 11 }$$

The following quantities are used as decision metrics:

$$\begin{eqnarray}&&{{MS}}_{1}={{FA}}_{1}-{\sigma }_{\mathrm{pri}}/{F}_{\mathrm{red}},\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&{{MS}}_{2}={{FA}}_{2}-({\sigma }_{\mathrm{pri}}-{\sigma }_{\mathrm{ter}}),\end{eqnarray} \tag{ 13 }$$

and

$$\begin{eqnarray}&&{{MS}}_{3}={{FA}}_{2}-({\sigma }_{\mathrm{pri}}-{\sigma }_{\mathrm{pos}}).\end{eqnarray} \tag{ 14 }$$

A candidate fails the test if ${{MS}}_{1}\gt -3$, ${{MS}}_{2}\gt 1$, or ${{MS}}_{3}\gt 1$. These criteria ensure that the primary event is statistically significant when compared to the systematic noise level of the light curve, the tertiary event, and the positive event, respectively.

3.2.6. Transit Shape Test

The transit shape test determines if the measured depth deviates from the mean value more in the positive flux direction, negative flux direction, or are symmetrically distributed in both directions. The SHP metric, provided alongside the model-shift uniqueness test from Coughlin (2017a), is defined by

$$\begin{eqnarray}&&\mathrm{SHP}=\displaystyle \frac{{F}_{\max }}{{F}_{\max }-{F}_{\min }}\end{eqnarray} \tag{ 15 }$$

where F_max and F_min are the maximum and minimum measured flux amplitudes, respectively. Since the light curve is normalized, F_max is always a positive value and F_min is always negative. SHP lies between 0 and 1, where 0 indicates the light curve only decreases in flux, consistent with a planet transit, and a value near 1 indicates the light curve only increases in flux, such as for a lensing event or systematic outlier. A candidate passes with SHP < 0.5.

3.2.7. Single Event Domination Test

Assuming all individual transits have equal S/Ns, S/N_I, the full transit S/N given in Equation (1) can be rewritten as

$$\begin{eqnarray}&&{\rm{S}}/{\rm{N}}=\sqrt{{N}_{T}}{\rm{S}}/{{\rm{N}}}_{{\rm{I}}}\end{eqnarray} \tag{ 16 }$$

where N_T is the number of individual events. It follows that if the largest individual transit's S/N value, S/N${}_{i,\max }$, divided by the S/N is much larger than $\sqrt{{N}_{T}}$, the calculation of the candidate's S/N is likely dominated by one of the individual events.

A candidate fails this test if S/N${}_{i,\max }$/S/N > 0.8, as in the Kepler team's own signal event domination test (Appendix A.3.5 of KDR25). Only candidates with P > 90 days are tested, as short-period candidates often have a large number of individual transit events, increasing the chance of one event coinciding with a large systematic feature.

3.2.8. Individual Transit Metrics

TCs that pass the previous tests are designated transit-like. However, some may still be nonplanetary in origin. One of the most common types of astrophysical FPs are eclipsing binary stars (EBs), which could just graze the target star enough for the eclipse depth to be consistent with a planet transit.

Transit-like FPs may also be due to off-target signals, such as background eclipsing binaries or planet transit signals coming from off-target sources. These scenarios can typically be indicated by identifying significant centroid offsets. Our vetting pipeline does not currently incorporate automated tests to identify these FPs. However, we later perform centroid analysis as part of a more in-depth analysis of new PCs.

3.3.1. Significant Secondary Test

A secondary eclipse could manifest as the secondary event in the phased light curve. This test follows the same procedure as the uniqueness test, but assesses the uniqueness of the secondary event rather than the primary using a new set of metrics (see Appendix A.4.1.2 of KDR25):

$$\begin{eqnarray}&&{{MS}}_{4}={{FA}}_{1}-{\sigma }_{\sec }/{F}_{\mathrm{red}},\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&{{MS}}_{5}={{FA}}_{2}-({\sigma }_{\sec }-{\sigma }_{\mathrm{ter}}),\end{eqnarray} \tag{ 18 }$$

and

$$\begin{eqnarray}&&{{MS}}_{6}={{FA}}_{2}-({\sigma }_{\sec }-{\sigma }_{\mathrm{pos}}).\end{eqnarray} \tag{ 19 }$$

If ${{MS}}_{4}\gt 2$, ${{MS}}_{5}\gt 1$, or ${{MS}}_{6}\gt 1$, the candidate fails due to having a significant secondary event.

3.3.2. Planet Candidates with Significant Secondaries

3.3.3. Odd–Even Depth Tests

Secondary eclipses could also be erroneously marked as half of the primary events if the eclipsing binary is detected at half its actual period and its eclipses would otherwise occur at phase 0.5. These eclipsing binaries can be identified as candidates with significantly different odd and even transit depths. As with the S/N Consistency Test, the Odd–Even Depth Tests are only used for candidates with $P\lt 90$ days.

An odd–even depth statistic is calculated for each TC:

$$\begin{eqnarray}&&{\sigma }_{\mathrm{OE}1}=\displaystyle \frac{| {d}_{\mathrm{odd}}-{d}_{\mathrm{even}}| }{\sqrt{{\sigma }_{\mathrm{odd}}^{2}+{\sigma }_{\mathrm{even}}^{2}}}\end{eqnarray} \tag{ 20 }$$

where d_odd and d_even are the median of all points within 30 minutes of the center of odd and even transits, respectively, and σ_odd and σ_even are the standard deviations of those points. For the case of trapezoidal model fits, all points making up the flat part in transit are also included. A TC fails if ${\sigma }_{\mathrm{OE}1}\gt 1.0$.

A second odd–even depth statistic is also calculated as part of the model-shift uniqueness test. This method takes into account the full transit shape as well as the noise level of the full light curve. However, it is more susceptible to outliers and systematics compared to the first statistic. Thus, we use a lenient requirement of ${\sigma }_{\mathrm{OE}}-{{FA}}_{1}\lt 10$.

3.3.4. V-shape Test

The final round of vetting involves a visual inspection of each of the TCs that passed the automated vetting stage. We look at the full light curve, the light curve phase-folded to the transit's period, a close-up of the transit in the phase diagram, and a side-by-side comparison of odd and even transits. The latter two images include the data averaged into 30 minute bins as well as the model fit to the light curve to assess the fit. While the previous tests are able to remove the majority of FPs and attempt to mimic decisions made by human vetters, manual inspection still serves as an important "reality check" that each passing TC is convincing enough to be promoted to PC.

A total of 5608 of the 33,322 TCs survived the automated vetting stage. Of those, 3972 passed manual vetting to become PCs.

We injected 120,642 planet transits into the light curves and prepared, searched, and vetted the data using the same process as for the actual observed data. The only exception was that we tested the manual component on a small subset of the injected detections. The overall process is consistent with injection and recovery tests performed for completeness measurements of other independent pipelines in the literature (e.g., Petigura et al. 2013; Dressing & Charbonneau 2015). We injected signals log-uniformly distributed over the ranges 0.5 < P < 500 days and 0.5 < R_p < 16.0 R_⊕. Each transit was created using a quadratic limb darkening Mandel & Agol (2002) model, with impact parameters uniformly distributed between 0 and 1 and assuming circular orbits.

For testing against noise FPs, the simulated data should allow realistic signals with noise properties similar to the real data, while ensuring no possibility of detecting true exoplanets still in the light curve. To achieve this, we took the 198,640 light curves originally searched and inverted them. Essentially, this recreated the Inverted (INV) set of simulations described in Christiansen (2017) for their own vetting tests. Any "transit" would actually be a positive flux increase in the observed data, and thus not a planet.

The Kepler team also created a Scrambled (SCR) data set for testing against noise FPs, corresponding to reordering of the Kepler quarters by yearly chunks. Three orders were created, as described in Coughlin (2017b). We tested our pipeline on Scrambled Group 1 (SCR1).

Of the 48,610 simulated TCs detected by our search pipeline, 45,676 (94.0%) passed the automated candidacy tests. More usefully, completeness is binned over period and S/N in Figure 1. As expected, completeness decreases with lower S/N and larger period, where most noise TCs would be expected to lie.

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The vetting process also involves a manual component in the form of the final visual inspection. Performing a full completeness measurement that takes this into account is difficult due to the presence of human bias. Additionally, it is infeasible to manually review each of the simulated TCs that passed the automated tests. Thus, we chose a random subset of 1000 of the passing TCs to review. In an attempt to remove human bias, we combined these TCs with all passing TCs from the simulated FP set, and removed any labeling that would indicate the origin set of each TC. We failed 15 of the 1000 planet TCs (1.5%). Overall, we expect the manual vetting to reduce our overall vetting completeness by 1%–2% from the 94% success rate of the automated component.

Our pipeline identified 15,283 TCs in the inverted set, and 12,103 in SCR set. The automated tests failed 14,494 (94.8%) and 11,222 (92.7%) of these, respectively. We then manually reviewed all surviving TCs, combined with the simulated planet TCs as described above. We found that the majority of the FP TCs were high-S/N events that had obviously asymmetric transits, making them easy to distinguish from bona fide planets. Overall, we failed all but 8 TCs in the inverse set and 28 TCs in the SCR set, giving a total success rate of 99.8%.

The fraction of FPs successfully classified as FPs is also known as the effectiveness of the pipeline. This can be combined with the final vetting results to estimate the reliability. Letting E denote the effectiveness, KDR25 define reliability R as

$$\begin{eqnarray}&&R=1-\displaystyle \frac{{N}_{\mathrm{FP}}}{{N}_{\mathrm{PC}}}\left(\displaystyle \frac{1-E}{E}\right),\end{eqnarray} \tag{ 21 }$$

where N_PC and N_FP are the numbers of observed PCs and FPs identified by the vetting pipeline, respectively.

Considering we identified 3971 PCs and 29,348 FPs out of all TCs, our effectiveness of 99.8% gives an overall reliability of 98.3%. However, plotting reliability as in Figure 2 reveals areas in period-S/N space where the pipeline is particularly unreliable, namely S/N < 10 and P > 200 days. While our effectiveness in this regime was 99.6%, we only identified 10 PCs compared to 1214 FPs.

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We successfully detected and passed 2268 of the 2295 (98.8%) planets confirmed by Kepler, defined as having an Exoplanet Archive Disposition of CONFIRMED and a Disposition Using Kepler Data of CANDIDATE on the NASA Exoplanet Archive.

Another 20 were marked as TCs, but failed our candidacy tests. Upon manual inspection, it appears that significant Transit Timing Variations were to blame for the failing of five confirmed planets (KOI-142.01, 227.01, 377.01, 377.02, and 884.02). The other 15 planets were either very close to passing or only failed a single test (KOI-46.02, 172.02, 701.04, 1236.03, 1574.02, 2038.03, 2298.02, 2365.02, 2533.01, 3458.01, 4034.01, 4384.01, 5416.01, 5706.01, and 7016.01). We found that these planets often had much lower calculated S/N than what was listed on the NASA Exoplanet Archive (for example, KOI-4384.01 had an S/N of only 6.3 according to our pipeline, but 12.2 from Kepler). Thus, it is likely that the lack of whitening in our search pipeline can explain these discrepancies, rather than these signals being intrinsically poor candidates.

Six were detected but failed to meet the requirements to be a TC (KOI-179.02, 245.03, 490.02, 1274.01, 1718.02, and 3234.01). KOI-179.02, KOI-490.02, and KOI-1274.01 had only one or two detected transits, lower than the required three. KOI-1718.02 had a barely failing RS (5.8), KOI-3234.01 had too low of a CHI value (4.6), and KOI-245.03 failed both. Only a single confirmed planet, KOI-4846.01, was missed entirely.

We successfully detected and passed 1447 of the 2421 (59.8%) known Kepler PCs, defined as having both dispositions listed as CANDIDATE.

The lower rate of recovery among PCs is to be expected given that confirmed planets typically have higher S/N and transit shapes more clearly consistent with a planetary origin. Furthermore, we note that 576 (around 60%) of the 974 candidates missed or failed by our pipeline were also not detected by Kepler's DR25 pipeline.

Of our PCs, 193 have both dispositions listed as FALSE POSITIVE. Of these 109 were flagged by Kepler as FPs solely due to having a significant centroid offset, while another 71 had an ephemeris match indicating contamination. Given that we did not incorporate centroid tests or ephemeris matching between KOIs into our vetting pipeline, it is unsurprising that we would pass these as candidates. However, we address both of these issues for our new candidates.

Six of our PCs have a Disposition Using Kepler Data of FALSE POSITIVE, but an Exoplanet Archive Disposition of CONFIRMED (KOI-125.01, 129.01, 631.01, 1416.01, 1450.01, and 3032.01). Furthermore, one of our PCs is the sole KOI on the NASA Exoplanet Archive with a Disposition Using Kepler Data of CANDIDATE, but an Exoplanet Archive Disposition of FALSE POSITIVE (KOI-242.01).

Light that contributes to the target's light curve may not necessarily originate from the target. If this contamination is caused by a star with a variable signal, then the same signal will be observed in the target with reduced amplitude due to dilution. Thus, if two signals have the same ephemeris, then at least one of them is an FP due to contamination.

We compared the periods and epochs of each new PC to all KOIs, searching for cases where

$$\begin{eqnarray}&&| P-{P}_{\mathrm{match}}| \leqslant \min (2\ \mathrm{hr},0.001P)\end{eqnarray} \tag{ 22 }$$

and

$$\begin{eqnarray}&&| {T}_{0}-{T}_{0,\mathrm{match}}| \leqslant \min (4\ \mathrm{hr},0.001P)\end{eqnarray} \tag{ 23 }$$

as in Dressing & Charbonneau (2015). We did not find any matches.

False positives may also be due to stellar variability that was not fully removed during the detrending process. In particular, failing to remove the rotation signal of the star can create a periodic, transit-like signal in the light curve. Finding a match between the orbital period of the PC and the rotation period of the host star would indicate an FP due to stellar variability.

We ran each un-detrended light curve through the Lomb–Scargle periodogram in Astropy (Astropy Collaboration et al. 2013, 2018) and searched for cases where the rotation period (or a multiple thereof) matched the detected orbital period of the PC. We determined rotation periods from the period corresponding to the highest peak in the periodogram. Fourteen of our host stars also had rotation periods listed in McQuillan et al. (2014). Furthermore, we manually inspected each periodogram to search for smaller peaks or excess noise at the orbital periods, which could confound the search for planets. For periods that corresponded to a peak, we determined its false alarm probability (the probability of measuring a given peak height under the assumption that the noise is Gaussian with no periodic component), and flagged cases where the power had a probability less than 0.05. Following this analysis, we identified 30 of our 52 PCs as likely FPs due to stellar variability.

We also investigated whether or not transits would change or disappear depending on different stellar variability removal methods. We used the biweight time-windowed slider implemented in the ${\rm{W}}\overline{{\rm{o}}}$ tan Python package,⁹ which was identified by Hippke et al. (2019) as the ideal method for recovering transits from light-curve data based on comprehensive comparison of common detrending routines. Using window lengths of 0.5, 1, and 2 days, we detrended each raw light curve, examined the data phased at the planet period, and calculated the S/N by measuring the depth of the transit and assuming the same duration, period, and epoch as the PC. The only exception was that we did not use a 0.5 day width for transits with durations greater than 0.2 days, so as to avoid significantly distorting the transit itself. Four of the PCs had either S/N < 6 (KIC-6937870 b) or the transit itself was inconsistent in shape and duration with the original PC (KIC-2985262 b, KIC-6380164 b, and KIC-10419787 b) using one of these alternate detrends. Then, we re-detrended the remaining 18 light curves after masking out the transits, re-examined the phase diagram, recalculated the S/N, and fit a least-squares transit model. We found that regardless of window length used, the S/N remained above 6 for all 18 PCs, and the model best-fit parameters were within 1σ of the results using our original detrending algorithm, giving further confidence that these signals were not an artifact of stellar variability.

We used the difference imaging method described in Bryson et al. (2013) to identify background FPs for the remaining 18 PCs, which is summarized here. We downloaded all necessary target pixel files from MAST. For each quarter, we combined all in-transit cadences to produce an average in-transit pixel image. We took an equal number of cadences on either side of the transit to produce an average out-of-transit pixel image. Subtracting the in-transit from the out-of-transit image gives the difference image. We fit the Kepler Pixel Response Function (PRF) to each of the out-of-transit and difference images. The PRF is defined as the composite of Kepler's optical point-spread function, integrated spacecraft pointing jitter during a nominal cadence, and other systematic effects, and is represented as a piece-wise continuous polynomial on a subpixel mesh (Bryson et al. 2010). We used PyKE (Still & Barclay 2012), which provides fitting of the Kepler PRF as a function of flux, center positions, width, and rotation angle to a given target pixel file. Respectively, the center positions of the out-of-transit and difference images give the location of the target star and transit source, providing a direct measurement of the centroid offset for that quarter.

Bryson et al. (2013) discuss that the difference images for low-S/N transits are typically noise dominated. The difference image can appear significantly different from the out-of-transit image in one quarter, and may show the transit at other locations or on the target star in others. Thus, we attain a more reliable estimate of the centroid offset and its uncertainty by robustly averaging all quarterly offsets. We also use the bootstrapping technique described in Bryson et al. (2013) to estimate the uncertainty in the result, taking the larger of the two values. Given the Q measured offsets (where Q is the number of quarters analyzed), we produce Q² different sets, randomly selecting from the list of offsets to fill each set. We then find the average of each set. The standard deviation of the Q² averages provides the bootstrap uncertainty estimate.

Following Bryson et al. (2013), we classify candidates as FPs if they have a 3σ significant offset larger than 2'', or 4σ offset larger than 1''. One of our PCs (KIC-3336146 b) met these thresholds and was reclassified as an FP. We complete the rest of our analysis with the remaining 17 new PCs.

We obtained AO follow-up imaging for six of our host stars, prioritizing our potentially rocky candidates. The uses of AO data are twofold: first, nearby stars dilute the observed transit depth, resulting in an underestimated planet radius. This is especially of concern for small, rocky planets due to their relative rarity, and those just under the proposed 1.6R_⊕ "rocky limit," past which most planets are not rocky (Rogers 2015). Second, a contaminant star could be the source of an FP signal, whether as a background or foreground eclipsing binary. Contrast curves derived from the AO images serve as effective constraints for unseen companions in our FPP calculations. We found that our AO images reduced FP probabilities by a factor of ∼16 on average (see Section 6.5), emphasizing the usefulness of AO follow-up for planet validation.

We collected observations of three stars on the Gemini North 8.1 m telescope in the K_s band with the Natural Guide Star (NGS) AO assisted Near InfraRed Imager and spectrograph (NIRI, Hodapp et al. 2003). Data were taken between 2018 July and 2019 June (Program ID GN-2018B-Q-134). Another three stars were observed with the Laser Guide Star (LGS) AO system and NIRI in 2019 July as part of a Fast Turnaround program (Program ID GN-2019A-FT-213). Total exposure time for each target was between 5 and 6 minutes. We used the f/32 NIRI camera, providing a plate scale of 0022 px⁻¹ and a 22'' × 22'' field of view.

Data were reduced by median-stacking each dark-subtracted and flat-divided image into a single AO image per star. We manually inspected each image for artifacts and potential companions in order to mask them out before computing 5σ contrast curves. To calculate each curve, we used the procedure outlined in Ngo et al. (2015), computing the standard deviation of flux values in a series of annuli with widths equal to twice the FWHM of the central star's point-spread function. Figure 3 shows all 5σ contrast curves along with the median to indicate our typical sensitivity. We provide the data for all contrast curves in Table 1, out to a maximum separation of ∼8'' (typical). We chose our maximum separation on a per-target basis based on the limit at which separations were no longer covered by all median-stacked images, due to the dither pattern used to take our observations.

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Table 1.  Contrast Curve Data for All Six Targets Observed with Gemini NGS-AO and LGS-AO in the K_s Band

KIC	Guide Star	UT Obs. Date	Sep. ('')	${\rm{\Delta }}{K}_{s}$
	System
6126245	NGS-AO	2019 May 31	0.20	0.76265
			0.35	3.80569
			0.51	4.62049
			0.66	5.22778
			⋯	⋯
6224562	LGS-AO	2019 Jun 30	0.20	0.69001
			0.35	3.25464
			0.51	4.47640
			0.66	5.49310
			⋯	⋯

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We manually examined each image for contaminant stars within 4'', the size of a Kepler pixel. We fit a two-Gaussian model to the two targets with detected companions in order to derive the angular separation, position angle (PA), and ΔK_s. Results are shown in Table 2, and the AO images of targets with companions are shown in Figure 4. One of our targets, KIC-7340288, has a potential companion just outside of 4'' (at 42) that is thus excluded from our analysis but indicated in the plots by dotted circles.

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Table 2.  Gemini NIRI and Robo-AO Imaging Searches for Companions within 4'' of Our Target Stars

KIC	Telescope	Filter	UT Obs. Date	Comp?	Sep. ('')	PA (°)	${\rm{\Delta }}m$	Ref.
6126245	Gemini NGS-AO	Ks	2019 May 31	N	⋯	⋯	⋯	This work
6224562	Gemini LGS-AO	Ks	2019 Jun 30	N	⋯	⋯	⋯	This work
6782399	Gemini NGS-AO	Ks	2019 Jun 14	N	⋯	⋯	⋯	This work
7269798	Gemini LGS-AO	Ks	2019 Jun 30	Y	3.006 ± 0.002	13.034 ± 0.001	5.64 ± 0.04	This work
7340288	Gemini LGS-AO	Ks	2019 Jul 1	Y	3.870 ± 0.002	283.380 ± 0.001	5.20 ± 0.03	This work
7747788	Gemini NGS-AO	Ks	2019 Jun 11	N	⋯	⋯	⋯	This work
11350118	Robo-AO	LP600	2014 Sep 01	N	⋯	⋯	⋯	Zie17

Note. Zie17 refers to Ziegler et al. (2017).

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One of our new PCs (KIC-11350118 c) corresponds to a known KOI already observed in the LP600 band as part of the Robo-AO KOI surveys (Law et al. 2014). Robo-AO did not detect any nearby stars.

We observed an additional 56 targets across both programs. However, during the execution of the observation program, the vetting pipeline described in Section 3 and follow-up analysis described earlier in this section was modified and these targets are no longer PCs. We provide contrast curves and companions for these targets in the Appendix. Of note, 32 of our targets are KOIs, 12 of which do not have Robo-AO observations. Our observations can be used in future follow-up analysis of all the confirmed and candidate planets associated with these KOIs.

We tested each of our candidates against astrophysical FP hypotheses using vespa, a Python package built to enable astrophysical FPP analysis of transiting signals (Morton 2012, 2015).

vespa uses stellar posteriors calculated with isochrones, a Python package that provides MCMC fitting of single-, binary-, and triple-star model stellar properties to MIST stellar model grids (Morton 2018), as an input. We provided isochrones with R.A./Decl. coordinates and grizJHK photometry from the KIC, with griz bands corrected to the Sloan Digital Sky Survey according to Pinsonneault et al. (2012). T_eff, log g, and [Fe/H] from Mathur et al. (2017) were used if the provenance of these values is from spectroscopy or asteroseismology. We provided parallaxes from Gaia DR2 (Gaia Collaboration et al. 2016, 2018) when available.

As constraints, we followed the convention of Morton et al. (2016) by setting the allowed "exclusion" radius for a blend scenario as three times the uncertainty in the fitted centroid position, floored at 05. We also set the maximum secondary eclipse depth allowed by the Kepler photometry as

$$\begin{eqnarray}&&{\delta }_{\max }={\delta }_{\sec }+3{\sigma }_{\sec },\end{eqnarray} \tag{ 24 }$$

where δ_sec and σ_sec are the fitted depth and uncertainty of the secondary event in the light curve, as calculated by the model-shift uniqueness test in the vetting pipeline. Lastly, we inputted contrast curves derived from the AO imaging. In vespa, these eliminate the possibility of bound or background stars above a certain brightness at a given projected distance.

Considering all of these inputs, vespa assigns probabilities to different hypotheses that might describe a transiting PC signal: unblended eclipsing binary, hierarchical-triple eclipsing binary, chance-aligned background/foreground eclipsing binary, and transiting planet. We consider candidates with total non-transiting-planet probabilities FPP > 0.9 as FPs. All other candidates, including those that have vespa fail to return an FPP (typically due to a nonconverging MCMC fit), remain PCs. None of our 17 remaining PCs were classified as FPs based on of our vespa results.

Twelve of the candidates have FPP < 0.01 (confidence at the 99% level). vespa has been used to validate over a thousand KOIs (Morton et al. 2016) as confirmed planets using this threshold. However, given that all of these PCs have S/N < 10, a noise or systematic explanation for the signals cannot be ignored. Burke et al. (2019) indicated that statistical validation methods based only on astrophysical scenarios, such as vespa, are insufficient for such a low-S/N regime. Thus, we chose to retain their candidate disposition.

We refit each transit using emcee, a Python implementation of an affine invariant Markov Chain Monte Carlo (MCMC) ensemble sampler (Foreman-Mackey et al. 2013), seeded by the best-fit parameters from the least-squares fit discussed in Section 3.1. We set P and T₀ fixed to their least-squares values. Fit results are shown in Table 3. These fit results are mixed with isochrones stellar parameter posteriors, given in Table 4, to produce derived planet parameters shown in Table 5. The reported values use the median, with uncertainties given by 15.9% and 84.1% percentiles, corresponding to a 68.2% confidence region. Plots of the phase diagrams of each transit with the MCMC fits and residuals are shown in Figure 5.

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Table 3.  MCMC Fit Results for Select Fitted Planet Parameters (${R}_{p}/{R}_{s}$, a/R_s, and b)

KIC	P (days)	T0 (BKJD)	${R}_{p}/{R}_{s}$	a/Rs	b
1570311 b	23.44253108 ± 0.00046135	148.98683 ± 0.01301	${0.017478}_{-0.002075}^{+0.005396}$	${8.487}_{-2.065}^{+4.907}$	${0.977}_{-0.036}^{+0.016}$
2696784 b	82.30223397 ± 0.00196956	130.31551 ± 0.01966	${0.009613}_{-0.000561}^{+0.000652}$	${22.104}_{-6.402}^{+5.043}$	${0.923}_{-0.042}^{+0.038}$
2861140 b	36.87848594 ± 0.00033789	364.07192 ± 0.00612	${0.016318}_{-0.001597}^{+0.00173}$	${63.344}_{-19.783}^{+10.242}$	${0.43}_{-0.296}^{+0.351}$
2985262 b	$13.0351506\pm 5.443\times {10}^{-5}$	140.06886 ± 0.00392	${0.009084}_{-0.000449}^{+0.000517}$	${29.901}_{-6.193}^{+2.269}$	${0.383}_{-0.266}^{+0.3}$
3336146 b	$3.27626622\pm 1.652\times {10}^{-5}$	134.62799 ± 0.00298	${0.007098}_{-0.000508}^{+0.000596}$	${14.447}_{-3.703}^{+1.248}$	${0.41}_{-0.279}^{+0.33}$
3345775 b	$6.22112577\pm 2.924\times {10}^{-5}$	122.33384 ± 0.00401	${0.004294}_{-0.000189}^{+0.000232}$	${13.329}_{-2.986}^{+1.97}$	${0.847}_{-0.055}^{+0.064}$
3347135 b	226.52674578 ± 0.00125028	160.17927 ± 0.0051	${0.017495}_{-0.000459}^{+0.000529}$	${242.158}_{-23.965}^{+8.295}$	${0.271}_{-0.185}^{+0.229}$
3662290 b	288.23951462 ± 0.01314029	322.24425 ± 0.04069	${0.011739}_{-0.000658}^{+0.000882}$	${101.68}_{-29.933}^{+17.014}$	${0.815}_{-0.081}^{+0.101}$
3728762 b	$6.73928932\pm 6.924\times {10}^{-5}$	122.20544 ± 0.00867	${0.007275}_{-0.000501}^{+0.000553}$	${5.557}_{-1.476}^{+1.023}$	${0.914}_{-0.04}^{+0.042}$
3967744 b	57.88535219 ± 0.00040897	143.26298 ± 0.0065	${0.011696}_{-0.000693}^{+0.000888}$	${47.663}_{-15.352}^{+6.252}$	${0.439}_{-0.304}^{+0.358}$
4346258 b	$4.90776291\pm 1.936\times {10}^{-5}$	354.03734 ± 0.00291	${0.013645}_{-0.00114}^{+0.001287}$	${19.513}_{-5.171}^{+1.919}$	${0.418}_{-0.291}^{+0.329}$
4551429 b	35.37625461 ± 0.00023684	147.08621 ± 0.00434	${0.012458}_{-0.000774}^{+0.00096}$	${75.028}_{-17.846}^{+6.129}$	${0.386}_{-0.262}^{+0.325}$
4556565 b	$5.54559321\pm 3.186\times {10}^{-5}$	353.80389 ± 0.004	${0.011497}_{-0.000861}^{+0.001035}$	${16.36}_{-4.241}^{+1.875}$	${0.427}_{-0.289}^{+0.32}$
5095499 b	$4.29501271\pm 1.861\times {10}^{-5}$	134.0872 ± 0.00411	${0.008775}_{-0.000546}^{+0.000575}$	${9.371}_{-1.944}^{+0.698}$	${0.379}_{-0.274}^{+0.305}$
5184017 b	$6.25985244\pm 2.664\times {10}^{-5}$	135.91422 ± 0.00367	${0.006305}_{-0.000386}^{+0.000557}$	${11.235}_{-3.042}^{+1.007}$	${0.409}_{-0.279}^{+0.345}$
5342061 c	$11.49044213\pm 7.721\times {10}^{-5}$	137.65928 ± 0.00558	${0.013311}_{-0.000975}^{+0.001104}$	${23.445}_{-5.977}^{+2.578}$	${0.413}_{-0.29}^{+0.327}$
5628770 b	$11.42952942\pm 6.504\times {10}^{-5}$	132.35509 ± 0.00511	${0.008349}_{-0.000623}^{+0.000662}$	${39.42}_{-8.723}^{+3.527}$	${0.4}_{-0.278}^{+0.303}$
5649129 b	$2.82857392\pm 1.138\times {10}^{-5}$	133.09613 ± 0.00321	${0.007052}_{-0.000446}^{+0.000701}$	${8.999}_{-2.605}^{+1.073}$	${0.469}_{-0.324}^{+0.314}$
5794479 b	$5.92912541\pm 3.014\times {10}^{-5}$	125.34438 ± 0.00419	${0.007263}_{-0.000324}^{+0.000445}$	${14.551}_{-2.751}^{+1.261}$	${0.412}_{-0.277}^{+0.263}$
5893807 b	$7.66465733\pm 5.173\times {10}^{-5}$	133.13869 ± 0.00444	${0.009196}_{-0.000853}^{+0.000885}$	${18.378}_{-4.85}^{+1.785}$	${0.41}_{-0.287}^{+0.338}$
6021193 e	26.48588826 ± 0.0001843	126.89598 ± 0.00597	${0.009068}_{-0.000482}^{+0.000736}$	${27.39}_{-7.436}^{+3.054}$	${0.401}_{-0.275}^{+0.351}$
6126245 b	$3.48546885\pm 1.049\times {10}^{-5}$	134.83373 ± 0.0022	${0.004019}_{-0.000334}^{+0.000346}$	${11.424}_{-2.809}^{+1.283}$	${0.4}_{-0.276}^{+0.332}$
6139884 b	$4.80084532\pm 2.32\times {10}^{-5}$	122.04373 ± 0.00401	${0.005274}_{-0.000372}^{+0.000447}$	${10.93}_{-2.984}^{+1.501}$	${0.611}_{-0.184}^{+0.21}$
6224562 b	$2.32907482\pm 4.46\times {10}^{-6}$	133.31436 ± 0.00164	${0.012356}_{-0.000948}^{+0.001302}$	${18.11}_{-4.558}^{+1.936}$	${0.42}_{-0.287}^{+0.316}$
6347299 b	38.64138416 ± 0.00025459	148.42833 ± 0.006	${0.009747}_{-0.000596}^{+0.000678}$	${43.08}_{-9.797}^{+3.242}$	${0.374}_{-0.26}^{+0.326}$
6380164 d	167.78839179 ± 0.00333756	206.04216 ± 0.01562	${0.014345}_{-0.000478}^{+0.000522}$	${189.128}_{-26.707}^{+9.523}$	${0.326}_{-0.225}^{+0.26}$
6440915 b	365.41156475 ± 0.01311087	317.94313 ± 0.01688	${0.023918}_{-0.001569}^{+0.00191}$	${105.273}_{-30.741}^{+35.13}$	${0.829}_{-0.163}^{+0.087}$
6782399 b	34.20150223 ± 0.00018815	134.63965 ± 0.00479	${0.008004}_{-0.000335}^{+0.000517}$	${43.655}_{-11.713}^{+5.013}$	${0.387}_{-0.274}^{+0.359}$
6837899 b	$8.99702134\pm 5.882\times {10}^{-5}$	137.73126 ± 0.00441	${0.010686}_{-0.000889}^{+0.00098}$	${22.957}_{-5.947}^{+2.935}$	${0.428}_{-0.293}^{+0.32}$
6888194 b	46.04031439 ± 0.00077561	163.79766 ± 0.01181	${0.009233}_{-0.000632}^{+0.000687}$	${96.009}_{-21.171}^{+8.866}$	${0.382}_{-0.267}^{+0.317}$
6929071 b	61.85364904 ± 0.00031287	183.29319 ± 0.00792	${0.012057}_{-0.000935}^{+0.000992}$	${126.476}_{-33.009}^{+13.322}$	${0.433}_{-0.295}^{+0.315}$
6937870 b	27.46007046 ± 0.00027629	140.54046 ± 0.00769	${0.010037}_{-0.000705}^{+0.001033}$	${45.134}_{-12.159}^{+4.254}$	${0.423}_{-0.299}^{+0.33}$
7020834 b	369.4781786 ± 0.01213654	187.4524 ± 0.01568	${0.018399}_{-0.00126}^{+0.003931}$	${43.816}_{-4.313}^{+4.82}$	${0.985}_{-0.006}^{+0.009}$
7119412 b	10.54126725 ± 0.00012629	136.69996 ± 0.01003	${0.011053}_{-0.00088}^{+0.001328}$	${8.323}_{-2.616}^{+1.625}$	${0.919}_{-0.04}^{+0.047}$
7186892 b	$17.23935628\pm 7.05\times {10}^{-5}$	131.71803 ± 0.00421	${0.006875}_{-0.000397}^{+0.000666}$	${38.689}_{-9.623}^{+5.189}$	${0.416}_{-0.284}^{+0.329}$
7187389 b	23.77032399 ± 0.00027154	359.57155 ± 0.00879	${0.01145}_{-0.00086}^{+0.000984}$	${27.557}_{-6.466}^{+2.576}$	${0.411}_{-0.272}^{+0.308}$
7269798 b	21.44308742 ± 0.00011838	152.55136 ± 0.00472	${0.014886}_{-0.001118}^{+0.00144}$	${59.932}_{-16.839}^{+7.183}$	${0.44}_{-0.296}^{+0.326}$
7340288 b	142.53244069 ± 0.00335958	204.71041 ± 0.01799	${0.025258}_{-0.001766}^{+0.00201}$	${156.563}_{-32.38}^{+12.21}$	${0.369}_{-0.255}^{+0.311}$
7747788 b	133.09439782 ± 0.00221722	215.34785 ± 0.01357	${0.00893}_{-0.000531}^{+0.000627}$	${161.086}_{-42.123}^{+15.814}$	${0.409}_{-0.286}^{+0.328}$
7974496 b	$3.96943045\pm 2.652\times {10}^{-5}$	133.95697 ± 0.0056	${0.008433}_{-0.000747}^{+0.000843}$	${8.43}_{-2.343}^{+1.201}$	${0.632}_{-0.188}^{+0.203}$
8172679 b	194.05437841 ± 0.00399057	197.40431 ± 0.00878	${0.017765}_{-0.000449}^{+0.000949}$	${182.339}_{-32.662}^{+11.466}$	${0.359}_{-0.244}^{+0.287}$
9274173 b	$4.43040627\pm 1.401\times {10}^{-5}$	134.02566 ± 0.00261	${0.011594}_{-0.000835}^{+0.000968}$	${17.616}_{-4.748}^{+3.045}$	${0.804}_{-0.089}^{+0.097}$
9716483 b	209.40859648 ± 0.00225065	166.46013 ± 0.00829	${0.012104}_{-0.000497}^{+0.000696}$	${128.227}_{-32.405}^{+10.877}$	${0.4}_{-0.281}^{+0.33}$
9777962 b	367.20909928 ± 0.00969414	359.4191 ± 0.02022	${0.02824}_{-0.00282}^{+0.004365}$	${80.972}_{-19.615}^{+40.269}$	${0.949}_{-0.08}^{+0.027}$
10018357 b	133.78748404 ± 0.00230495	253.99492 ± 0.01191	${0.01555}_{-0.000618}^{+0.001482}$	${97.298}_{-31.568}^{+12.202}$	${0.481}_{-0.341}^{+0.328}$
10083396 b	113.46453674 ± 0.0020158	210.81344 ± 0.01041	${0.006687}_{-0.000304}^{+0.000366}$	${70.969}_{-13.633}^{+4.505}$	${0.347}_{-0.243}^{+0.309}$
10419787 b	122.71394705 ± 0.00096645	208.46146 ± 0.00552	${0.015731}_{-0.001016}^{+0.001187}$	${140.29}_{-34.704}^{+12.715}$	${0.413}_{-0.283}^{+0.319}$
10598829 b	67.52966257 ± 0.00045439	191.28971 ± 0.00578	${0.011558}_{-0.000819}^{+0.000907}$	${76.452}_{-18.646}^{+6.627}$	${0.396}_{-0.275}^{+0.329}$
10879314 b	49.19380825 ± 0.00037771	164.61498 ± 0.0069	${0.014659}_{-0.001153}^{+0.001378}$	${70.276}_{-18.504}^{+9.683}$	${0.418}_{-0.289}^{+0.338}$
11092463 b	$6.87343628\pm 8.866\times {10}^{-5}$	135.83495 ± 0.01066	${0.013895}_{-0.001421}^{+0.002293}$	${7.309}_{-2.8}^{+1.561}$	${0.923}_{-0.043}^{+0.054}$
11139863 b	$7.22517263\pm 3.616\times {10}^{-5}$	120.75217 ± 0.00397	${0.004123}_{-0.000177}^{+0.00029}$	${19.012}_{-5.91}^{+3.395}$	${0.558}_{-0.356}^{+0.264}$
11350118 c	$2.65550668\pm 1.532\times {10}^{-5}$	133.27041 ± 0.00483	${0.009019}_{-0.0007}^{+0.000877}$	${6.396}_{-1.649}^{+0.612}$	${0.419}_{-0.293}^{+0.33}$
11565976 b	24.24399123 ± 0.00016113	143.36071 ± 0.0042	${0.006635}_{-0.00048}^{+0.000506}$	${52.545}_{-12.444}^{+4.43}$	${0.397}_{-0.272}^{+0.318}$
11805835 b	23.52676998 ± 0.00024171	142.63053 ± 0.00886	${0.013617}_{-0.001029}^{+0.001429}$	${46.944}_{-12.626}^{+5.132}$	${0.427}_{-0.296}^{+0.33}$
12023559 b	84.55709677 ± 0.00127186	206.60834 ± 0.01139	${0.016528}_{-0.000877}^{+0.001056}$	${77.011}_{-16.798}^{+6.172}$	${0.39}_{-0.271}^{+0.305}$
12216301 b	116.53116276 ± 0.00220776	160.14551 ± 0.01344	${0.012935}_{-0.000673}^{+0.000896}$	${83.959}_{-23.552}^{+11.893}$	${0.676}_{-0.148}^{+0.173}$
12505309 b	$2.89755848\pm 3.03\times {10}^{-6}$	122.99708 ± 0.00109	${0.003888}_{-0.000306}^{+0.00036}$	${16.478}_{-4.924}^{+2.215}$	${0.447}_{-0.305}^{+0.337}$

Note. P and T₀ were set to their least-squares best-fit values.

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Table 4.  isochrones Fit Results for Select Fitted Stellar Parameters (R_s, M_s, ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, [Fe/H], and Distance d)

KIC	Rs (R⊙)	Ms (M⊙)	Teff (K)	log g (cm s−2)	[Fe/H] (dex)	d (kpc)
1570311	${5.26}_{-0.34}^{+0.26}$	${2.11}_{-0.2}^{+0.27}$	${5062}_{-45}^{+39}$	${3.347}_{-0.072}^{+0.035}$	$-{0.181}_{-0.171}^{+0.086}$	${2.17}_{-0.13}^{+0.11}$
2696784	${1.42}_{-0.03}^{+0.04}$	${1.45}_{-0.06}^{+0.04}$	${7106}_{-291}^{+419}$	${4.292}_{-0.026}^{+0.028}$	$-{0.021}_{-0.126}^{+0.133}$	${0.62}_{-0.01}^{+0.01}$
2861140	${1.28}_{-0.09}^{+0.1}$	${1.2}_{-0.08}^{+0.09}$	${6391}_{-203}^{+221}$	${4.302}_{-0.06}^{+0.053}$	$-{0.026}_{-0.139}^{+0.149}$	${1.78}_{-0.13}^{+0.14}$
2985262	${0.95}_{-0.01}^{+0.01}$	${1.02}_{-0.04}^{+0.03}$	${5902}_{-167}^{+158}$	${4.494}_{-0.017}^{+0.011}$	$-{0.059}_{-0.176}^{+0.153}$	${0.53}_{-0.0}^{+0.0}$
3336146	${1.11}_{-0.02}^{+0.02}$	${1.13}_{-0.05}^{+0.04}$	${6281}_{-195}^{+176}$	${4.407}_{-0.029}^{+0.017}$	$-{0.08}_{-0.157}^{+0.172}$	${0.69}_{-0.01}^{+0.01}$
3345775	${1.87}_{-0.04}^{+0.03}$	${2.58}_{-0.13}^{+0.07}$	${11580}_{-193}^{+214}$	${4.306}_{-0.022}^{+0.018}$	$-{0.215}_{-0.199}^{+0.114}$	${0.28}_{-0.0}^{+0.0}$
3347135	${1.13}_{-0.04}^{+0.05}$	${1.16}_{-0.05}^{+0.05}$	${5932}_{-89}^{+65}$	${4.395}_{-0.029}^{+0.029}$	${0.272}_{-0.095}^{+0.091}$	${0.38}_{-0.02}^{+0.02}$
3662290	${1.56}_{-0.04}^{+0.05}$	${1.48}_{-0.1}^{+0.09}$	${6986}_{-322}^{+265}$	${4.221}_{-0.05}^{+0.039}$	${0.078}_{-0.133}^{+0.132}$	${0.58}_{-0.01}^{+0.01}$
3728762	${1.7}_{-0.07}^{+0.06}$	${1.43}_{-0.07}^{+0.16}$	${6706}_{-234}^{+269}$	${4.129}_{-0.042}^{+0.084}$	${0.111}_{-0.196}^{+0.151}$	${1.02}_{-0.03}^{+0.03}$
3967744	${2.43}_{-0.1}^{+0.12}$	${1.85}_{-0.07}^{+0.08}$	${7004}_{-260}^{+266}$	${3.932}_{-0.039}^{+0.041}$	${0.273}_{-0.121}^{+0.106}$	${1.86}_{-0.08}^{+0.08}$
4346258	${0.8}_{-0.03}^{+0.03}$	${0.86}_{-0.04}^{+0.04}$	${5279}_{-146}^{+163}$	${4.567}_{-0.025}^{+0.021}$	$-{0.038}_{-0.125}^{+0.145}$	${0.97}_{-0.03}^{+0.04}$
4551429	${0.55}_{-0.0}^{+0.0}$	${0.58}_{-0.01}^{+0.01}$	${3786}_{-32}^{+52}$	${4.727}_{-0.01}^{+0.007}$	${0.334}_{-0.115}^{+0.086}$	${0.15}_{-0.0}^{+0.0}$
4556565	${1.37}_{-0.1}^{+0.19}$	${1.29}_{-0.04}^{+0.05}$	${6063}_{-139}^{+120}$	${4.272}_{-0.113}^{+0.078}$	${0.345}_{-0.049}^{+0.096}$	${1.51}_{-0.09}^{+0.19}$
5095499	${1.22}_{-0.04}^{+0.05}$	${1.14}_{-0.06}^{+0.07}$	${6286}_{-185}^{+194}$	${4.323}_{-0.041}^{+0.039}$	$-{0.044}_{-0.167}^{+0.153}$	${1.51}_{-0.05}^{+0.07}$
5184017	${2.61}_{-0.5}^{+0.16}$	${1.73}_{-0.1}^{+0.04}$	${6187}_{-81}^{+293}$	${3.841}_{-0.041}^{+0.159}$	${0.388}_{-0.082}^{+0.05}$	${1.27}_{-0.14}^{+0.05}$
5342061	${1.09}_{-0.04}^{+0.05}$	${1.09}_{-0.08}^{+0.06}$	${6120}_{-193}^{+214}$	${4.395}_{-0.038}^{+0.037}$	$-{0.047}_{-0.154}^{+0.147}$	${1.29}_{-0.05}^{+0.06}$
5628770	${1.2}_{-0.02}^{+0.03}$	${1.22}_{-0.05}^{+0.04}$	${6510}_{-193}^{+195}$	${4.363}_{-0.025}^{+0.017}$	$-{0.057}_{-0.169}^{+0.148}$	${0.84}_{-0.01}^{+0.01}$
5649129	${4.31}_{-0.35}^{+0.19}$	${1.6}_{-0.26}^{+0.26}$	${4839}_{-108}^{+173}$	${3.37}_{-0.058}^{+0.072}$	${0.004}_{-0.438}^{+0.111}$	${1.47}_{-0.08}^{+0.06}$
5794479	${2.56}_{-0.12}^{+0.16}$	${3.65}_{-0.85}^{+0.19}$	${12631}_{-2685}^{+961}$	${4.189}_{-0.14}^{+0.055}$	${0.257}_{-0.174}^{+0.113}$	${1.44}_{-0.06}^{+0.04}$
5893807	${1.71}_{-0.11}^{+0.16}$	${1.51}_{-0.11}^{+0.09}$	${6692}_{-283}^{+260}$	${4.147}_{-0.083}^{+0.076}$	${0.212}_{-0.156}^{+0.119}$	${2.1}_{-0.13}^{+0.16}$
6021193	${1.62}_{-0.02}^{+0.03}$	${1.29}_{-0.03}^{+0.03}$	${5919}_{-85}^{+131}$	${4.128}_{-0.015}^{+0.019}$	${0.302}_{-0.079}^{+0.077}$	${0.78}_{-0.01}^{+0.01}$
6126245	${1.54}_{-0.04}^{+0.04}$	${1.5}_{-0.1}^{+0.07}$	${7190}_{-330}^{+346}$	${4.235}_{-0.044}^{+0.035}$	${0.013}_{-0.172}^{+0.137}$	${0.76}_{-0.02}^{+0.02}$
6139884	${0.89}_{-0.01}^{+0.01}$	${0.96}_{-0.04}^{+0.03}$	${5931}_{-166}^{+194}$	${4.523}_{-0.018}^{+0.012}$	$-{0.263}_{-0.196}^{+0.178}$	${0.37}_{-0.0}^{+0.0}$
6224562	${0.8}_{-0.02}^{+0.03}$	${0.86}_{-0.03}^{+0.04}$	${4977}_{-121}^{+106}$	${4.571}_{-0.024}^{+0.018}$	${0.234}_{-0.125}^{+0.108}$	${0.68}_{-0.03}^{+0.03}$
6347299	${1.01}_{-0.01}^{+0.01}$	${1.07}_{-0.04}^{+0.03}$	${5965}_{-79}^{+80}$	${4.455}_{-0.024}^{+0.014}$	${0.01}_{-0.091}^{+0.085}$	${0.7}_{-0.01}^{+0.01}$
6380164	${2.19}_{-0.13}^{+0.1}$	${1.67}_{-0.06}^{+0.05}$	${6717}_{-120}^{+135}$	${3.977}_{-0.037}^{+0.054}$	${0.21}_{-0.119}^{+0.113}$	${1.03}_{-0.05}^{+0.04}$
6440915	${2.14}_{-0.15}^{+0.13}$	${1.64}_{-0.08}^{+0.07}$	${6577}_{-184}^{+220}$	${3.986}_{-0.05}^{+0.07}$	${0.265}_{-0.145}^{+0.12}$	${1.89}_{-0.11}^{+0.11}$
6782399	${1.89}_{-0.09}^{+0.06}$	${1.51}_{-0.08}^{+0.08}$	${6659}_{-110}^{+101}$	${4.06}_{0.031}^{+0.062}$	${0.133}_{-0.154}^{+0.176}$	${0.84}_{-0.03}^{+0.02}$
6837899	${1.09}_{-0.02}^{+0.03}$	${1.12}_{-0.05}^{+0.04}$	${6228}_{-188}^{+191}$	${4.415}_{-0.031}^{+0.018}$	$-{0.078}_{-0.153}^{+0.168}$	${1.1}_{-0.02}^{+0.02}$
6888194	${2.74}_{-0.35}^{+0.25}$	${1.82}_{-0.07}^{+0.08}$	${6482}_{-149}^{+282}$	${3.812}_{-0.058}^{+0.118}$	${0.33}_{-0.128}^{+0.077}$	${1.36}_{-0.12}^{+0.1}$
6929071	${1.98}_{-0.07}^{+0.08}$	${1.54}_{-0.07}^{+0.09}$	${6633}_{-251}^{+254}$	${4.03}_{-0.035}^{+0.041}$	${0.148}_{-0.153}^{+0.153}$	${1.51}_{-0.04}^{+0.05}$
6937870	${0.6}_{-0.01}^{+0.01}$	${0.62}_{-0.02}^{+0.02}$	${4209}_{-89}^{+89}$	${4.681}_{-0.014}^{+0.008}$	$-{0.089}_{-0.144}^{+0.146}$	${0.21}_{-0.0}^{+0.0}$
7020834	${2.14}_{-0.08}^{+0.09}$	${1.76}_{-0.11}^{+0.17}$	${7166}_{-356}^{+589}$	${4.018}_{-0.049}^{+0.077}$	${0.203}_{-0.164}^{+0.146}$	${0.76}_{-0.02}^{+0.02}$
7119412	${0.74}_{-0.01}^{+0.01}$	${0.79}_{-0.03}^{+0.02}$	${4880}_{-83}^{+102}$	${4.6}_{-0.017}^{+0.011}$	${0.021}_{-0.1}^{+0.094}$	${0.4}_{-0.0}^{+0.0}$
7186892	${0.74}_{-0.02}^{+0.03}$	${0.81}_{-0.03}^{+0.03}$	${4979}_{-72}^{+77}$	${4.603}_{-0.016}^{+0.017}$	$-{0.027}_{-0.095}^{+0.117}$	${0.19}_{-0.01}^{+0.01}$
7187389	${0.88}_{-0.02}^{+0.02}$	${0.95}_{-0.04}^{+0.03}$	${5658}_{-165}^{+176}$	${4.529}_{-0.02}^{+0.015}$	$-{0.044}_{-0.182}^{+0.148}$	${0.86}_{-0.02}^{+0.02}$
7269798	${0.54}_{-0.01}^{+0.01}$	${0.58}_{-0.01}^{+0.01}$	${3758}_{-21}^{+28}$	${4.73}_{-0.008}^{+0.009}$	${0.377}_{-0.075}^{+0.055}$	${0.22}_{-0.0}^{+0.0}$
7340288	${0.55}_{-0.01}^{+0.01}$	${0.57}_{-0.01}^{+0.02}$	${3949}_{-52}^{+79}$	${4.722}_{-0.012}^{+0.008}$	${0.029}_{-0.149}^{+0.114}$	${0.33}_{-0.0}^{+0.0}$
7747788	${1.71}_{-0.05}^{+0.05}$	${1.63}_{-0.1}^{+0.07}$	${7146}_{-314}^{+389}$	${4.186}_{-0.042}^{+0.031}$	${0.174}_{-0.124}^{+0.115}$	${0.75}_{-0.01}^{+0.02}$
7974496	${1.62}_{-0.1}^{+0.09}$	${1.33}_{-0.07}^{+0.08}$	${6448}_{-284}^{+218}$	${4.14}_{-0.043}^{+0.065}$	${0.079}_{-0.126}^{+0.156}$	${1.91}_{-0.1}^{+0.1}$
8172679	${4.89}_{-0.48}^{+0.55}$	${1.7}_{-0.17}^{+0.19}$	${5040}_{-72}^{+64}$	${3.284}_{-0.078}^{+0.084}$	$-{0.452}_{-0.18}^{+0.181}$	${1.37}_{-0.12}^{+0.17}$
9274173	${1.12}_{-0.03}^{+0.04}$	${1.12}_{-0.06}^{+0.05}$	${6006}_{-106}^{+97}$	${4.385}_{-0.038}^{+0.035}$	${0.122}_{-0.112}^{+0.122}$	${1.17}_{-0.03}^{+0.04}$
9716483	${1.57}_{-0.05}^{+0.05}$	${1.54}_{-0.1}^{+0.09}$	${7327}_{-417}^{+410}$	${4.229}_{-0.043}^{+0.041}$	${0.008}_{-0.128}^{+0.143}$	${0.98}_{-0.02}^{+0.02}$
9777962	${2.42}_{-0.15}^{+0.14}$	${1.77}_{-0.08}^{+0.08}$	${6764}_{-241}^{+282}$	${3.916}_{-0.045}^{+0.05}$	${0.24}_{-0.124}^{+0.126}$	${2.6}_{-0.14}^{+0.15}$
10018357	${4.69}_{-1.02}^{+0.14}$	${1.99}_{-0.21}^{+0.78}$	${5251}_{-178}^{+667}$	${3.406}_{-0.056}^{+0.252}$	$-{0.435}_{-0.491}^{+0.382}$	${1.83}_{-0.11}^{+0.04}$
10083396	${1.56}_{-0.03}^{+0.03}$	${1.33}_{-0.06}^{+0.05}$	${6387}_{-137}^{+116}$	${4.176}_{-0.026}^{+0.026}$	${0.109}_{-0.087}^{+0.14}$	${0.46}_{-0.01}^{+0.01}$
10419787	${1.2}_{-0.03}^{+0.03}$	${1.21}_{-0.06}^{+0.05}$	${6361}_{-195}^{+208}$	${4.364}_{-0.032}^{+0.022}$	${0.012}_{-0.163}^{+0.141}$	${1.01}_{-0.02}^{+0.03}$
10598829	${1.55}_{-0.13}^{+0.2}$	${1.47}_{-0.08}^{+0.1}$	${6743}_{-235}^{+166}$	${4.235}_{-0.109}^{+0.054}$	${0.206}_{-0.15}^{+0.137}$	${1.35}_{-0.11}^{+0.17}$
10879314	${2.47}_{-0.3}^{+0.21}$	${1.69}_{-0.08}^{+0.08}$	${6235}_{-120}^{+152}$	${3.877}_{-0.054}^{+0.092}$	${0.378}_{-0.087}^{+0.062}$	${2.18}_{-0.24}^{+0.19}$
11092463	${0.88}_{-0.03}^{+0.03}$	${0.95}_{-0.04}^{+0.03}$	${5601}_{-168}^{+148}$	${4.533}_{-0.024}^{+0.02}$	$-{0.004}_{-0.144}^{+0.154}$	${1.1}_{-0.04}^{+0.04}$
11139863	${1.8}_{-0.06}^{+0.05}$	${1.63}_{-0.13}^{+0.14}$	${7185}_{-353}^{+330}$	${4.14}_{-0.058}^{+0.057}$	${0.119}_{-0.277}^{+0.196}$	${0.26}_{-0.0}^{+0.0}$
11350118	${0.67}_{-0.01}^{+0.01}$	${0.72}_{-0.02}^{+0.02}$	${4751}_{-153}^{+154}$	${4.646}_{-0.014}^{+0.011}$	$-{0.171}_{-0.153}^{+0.15}$	${0.52}_{-0.01}^{+0.01}$
11565976	${1.93}_{-0.05}^{+0.05}$	${1.51}_{-0.07}^{+0.1}$	${6668}_{-211}^{+239}$	${4.044}_{-0.031}^{+0.04}$	${0.102}_{-0.132}^{+0.167}$	${0.81}_{-0.02}^{+0.02}$
11805835	${0.63}_{-0.01}^{+0.01}$	${0.67}_{-0.02}^{+0.02}$	${4723}_{-141}^{+184}$	${4.663}_{-0.014}^{+0.012}$	$-{0.364}_{-0.191}^{+0.151}$	${0.38}_{-0.01}^{+0.0}$
12023559	${1.03}_{-0.02}^{+0.02}$	${1.06}_{-0.05}^{+0.04}$	${6136}_{-201}^{+172}$	${4.438}_{-0.026}^{+0.019}$	$-{0.126}_{-0.175}^{+0.194}$	${1.02}_{-0.02}^{+0.02}$
12216301	${2.57}_{-0.1}^{+0.18}$	${3.54}_{-0.33}^{+0.16}$	${12170}_{-1230}^{+930}$	${4.165}_{-0.087}^{+0.054}$	${0.293}_{-0.159}^{+0.092}$	${1.63}_{-0.04}^{+0.04}$
12505309	${1.63}_{-0.03}^{+0.04}$	${1.52}_{-0.09}^{+0.09}$	${6931}_{-270}^{+289}$	${4.196}_{-0.041}^{+0.034}$	${0.138}_{-0.134}^{+0.13}$	${0.48}_{-0.01}^{+0.01}$

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Table 5.  Summary of Results for All New Candidate Planets (CAND; FPP $\lt 0.9$) and False Positives (FP; Due to Low Reliability, Stellar Variability, Centroid Offset, or FPP > 0.9)

KIC	P (days)	Rp (R⊕)	a (au)	${T}_{\mathrm{eq}}$ (K)	S $({S}_{\oplus })$	S/N	FPP	Status	Notes
1570311 b	23.4	${8.40}_{-1.77}^{+2.49}$	${0.197}_{-0.008}^{+0.005}$	${1033}_{-88}^{+88}$	${270.45}_{-81.37}^{+104.82}$	8.9	⋯	FP	Stellar variability
2696784 b	82.3	${1.50}_{-0.10}^{+0.11}$	${0.418}_{-0.007}^{+0.005}$	${579}_{-25}^{+30}$	${26.68}_{-4.27}^{+6.06}$	7.2	⋯	CAND	vespa failed
2861140 b	36.9	${2.28}_{-0.27}^{+0.32}$	${0.230}_{-0.005}^{+0.006}$	${666}_{-33}^{+37}$	${46.52}_{-8.50}^{+11.15}$	7.2	0.0526	CAND	⋯
2985262 b	13.0	${0.94}_{-0.05}^{+0.06}$	${0.109}_{-0.001}^{+0.001}$	${767}_{-22}^{+23}$	${81.92}_{-9.15}^{+10.26}$	10.7	⋯	FP	Stellar variability
3336146 b	3.3	${0.86}_{-0.07}^{+0.08}$	${0.045}_{-0.001}^{+0.001}$	${1374}_{-44}^{+45}$	${845.59}_{-102.32}^{+115.09}$	9.2	⋯	FP	Centroid offset
3345775 b	6.2	${0.87}_{-0.04}^{+0.05}$	${0.091}_{-0.002}^{+0.001}$	${2320}_{-50}^{+55}$	${6867.32}_{-568.34}^{+678.38}$	7.8	⋯	FP	Stellar variability
3347135 b	226.5	${2.16}_{-0.10}^{+0.12}$	${0.765}_{-0.011}^{+0.010}$	${318}_{-8}^{+8}$	${2.42}_{-0.24}^{+0.27}$	10.0	⋯	FP	Stellar variability
3662290 b	288.2	${2.01}_{-0.13}^{+0.17}$	${0.974}_{-0.023}^{+0.018}$	${391}_{-19}^{+17}$	${5.53}_{-0.99}^{+1.05}$	6.5	⋯	FP	Likely noise
3728762 b	6.7	${1.35}_{-0.11}^{+0.12}$	${0.079}_{-0.001}^{+0.003}$	${1372}_{-59}^{+63}$	${845.85}_{-140.52}^{+159.92}$	8.2	$1.45\times {10}^{-5}$	CAND	⋯
3967744 b	57.9	${3.10}_{-0.25}^{+0.30}$	${0.360}_{-0.004}^{+0.005}$	${801}_{-34}^{+40}$	${97.73}_{-15.76}^{+21.24}$	7.8	⋯	FP	Stellar variability
4346258 b	4.9	${1.19}_{-0.11}^{+0.12}$	${0.054}_{-0.001}^{+0.001}$	${899}_{-29}^{+31}$	${155.10}_{-19.27}^{+22.71}$	8.3	⋯	FP	Stellar variability
4551429 b	35.4	${0.74}_{-0.05}^{+0.06}$	${0.176}_{-0.001}^{+0.001}$	${294}_{-3}^{+4}$	${1.78}_{-0.07}^{+0.10}$	9.0	⋯	FP	Stellar variability
4556565 b	5.5	${1.74}_{-0.20}^{+0.26}$	${0.067}_{-0.001}^{+0.001}$	${1213}_{-54}^{+82}$	${513.70}_{-85.37}^{+153.38}$	9.2	⋯	FP	Stellar variability
5095499 b	4.3	${1.17}_{-0.08}^{+0.09}$	${0.054}_{-0.001}^{+0.001}$	${1317}_{-48}^{+50}$	${714.34}_{-98.96}^{+114.32}$	8.9	⋯	FP	Stellar variability
5184017 b	6.3	${1.72}_{-0.30}^{+0.23}$	${0.080}_{-0.002}^{+0.001}$	${1555}_{-132}^{+93}$	${1387.16}_{-415.38}^{+364.15}$	7.7	⋯	FP	Stellar variability
5342061 c	11.5	${1.59}_{-0.13}^{+0.15}$	${0.103}_{-0.002}^{+0.002}$	${884}_{-34}^{+35}$	${144.89}_{-21.26}^{+24.70}$	7.8	⋯	FP	Stellar variability
5628770 b	11.4	${1.10}_{-0.08}^{+0.09}$	${0.106}_{-0.002}^{+0.001}$	${969}_{-31}^{+32}$	${208.86}_{-25.80}^{+28.60}$	8.1	⋯	FP	Stellar variability
5649129 b	2.8	${3.30}_{-0.32}^{+0.37}$	${0.046}_{-0.003}^{+0.002}$	${2068}_{-106}^{+104}$	${4338.53}_{-824.17}^{+941.03}$	8.2	⋯	FP	Stellar variability
5794479 b	5.9	${2.03}_{-0.14}^{+0.27}$	${0.099}_{-0.006}^{+0.002}$	${2865}_{-511}^{+309}$	${15980.38}_{-8692.91}^{+8086.37}$	9.1	⋯	FP	Stellar variability
5893807 b	7.7	${0.85}_{-0.09}^{+0.12}$	${0.087}_{-0.002}^{+0.002}$	${1309}_{-71}^{+74}$	${695.49}_{-138.60}^{+172.15}$	8.0	$1.70\times {10}^{-6}$	CAND	⋯
6021193 e	26.5	${1.60}_{-0.09}^{+0.14}$	${0.189}_{-0.001}^{+0.002}$	${763}_{-13}^{+19}$	${80.41}_{-5.5}^{+8.14}$	8.3	⋯	FP	Stellar variability
6126245 b	3.5	${0.68}_{-0.06}^{+0.06}$	${0.052}_{-0.001}^{+0.001}$	${1739}_{-86}^{+91}$	${2166.86}_{-398.49}^{+488.70}$	7.3	$6.65\times {10}^{-3}$	CAND	⋯
6139884 b	4.8	${0.51}_{-0.04}^{+0.04}$	${0.055}_{-0.001}^{+0.001}$	${1053}_{-31}^{+36}$	${291.76}_{-33.13}^{+42.43}$	8.7	⋯	FP	Stellar variability
6224562 b	2.3	${1.08}_{-0.09}^{+0.12}$	${0.033}_{-0.001}^{+0.001}$	${1083}_{-32}^{+32}$	${326.34}_{-36.61}^{+40.05}$	9.3	0.110	CAND	⋯
6347299 d	38.6	${1.08}_{-0.07}^{+0.08}$	${0.229}_{-0.003}^{+0.002}$	${444}_{-9}^{+10}$	${22.48}_{-1.37}^{+1.58}$	8.2	⋯	FP	Stellar variability
6380164 b	167.8	${3.42}_{-0.23}^{+0.21}$	${0.707}_{-0.009}^{+0.007}$	${521}_{-19}^{+17}$	${17.51}_{-2.36}^{+2.34}$	9.2	⋯	FP	Stellar variability
6440915 b	365.4	${5.56}_{-0.52}^{+0.60}$	${1.179}_{-0.019}^{+0.017}$	${391}_{-18}^{+18}$	${5.54}_{-0.96}^{+1.11}$	8.8	⋯	FP	Likely noise
6782399 b	34.2	${1.65}_{-0.10}^{+0.12}$	${0.237}_{-0.004}^{+0.004}$	${828}_{-25}^{+21}$	${111.59}_{-12.95}^{+11.86}$	8.2	$1.29\times {10}^{-4}$	CAND	⋯
6837899 b	9.0	${1.27}_{-0.11}^{+0.12}$	${0.088}_{-0.001}^{+0.001}$	${968}_{-33}^{+33}$	${207.91}_{-26.61}^{+29.44}$	7.7	⋯	FP	Stellar variability
6888194 b	46.0	${2.76}_{-0.40}^{+0.33}$	${0.307}_{-0.004}^{+0.004}$	${858}_{-59}^{+50}$	${128.74}_{-32.03}^{+33.07}$	7.4	⋯	FP	Stellar variability
6929071 b	61.9	${2.45}_{-0.21}^{+0.24}$	${0.363}_{-0.006}^{+0.005}$	${692}_{-28}^{+27}$	${54.38}_{-8.25}^{+8.86}$	7.7	⋯	CAND	vespa failed
6937870 b	27.5	${0.65}_{-0.05}^{+0.07}$	${0.152}_{-0.002}^{+0.001}$	${368}_{-8}^{+9}$	${4.33}_{-0.36}^{+0.42}$	7.7	⋯	FP	Stellar variability
7020834 b	369.5	${4.34}_{-0.39}^{+0.92}$	${1.218}_{-0.026}^{+0.039}$	${420}_{-25}^{+35}$	${7.34}_{-1.60}^{+2.80}$	9.6	⋯	FP	Likely noise
7119412 b	10.5	${0.89}_{-0.07}^{+0.10}$	${0.087}_{-0.001}^{+0.001}$	${623}_{-12}^{+14}$	${36.84}_{-2.65}^{+3.34}$	9.3	⋯	FP	Stellar variability
7186892 b	17.2	${0.56}_{-0.04}^{+0.06}$	${0.122}_{-0.002}^{+0.001}$	${543}_{-13}^{+13}$	${20.61}_{-1.88}^{+2.09}$	10.1	⋯	FP	Stellar variability
7187389 b	23.8	${1.10}_{-0.09}^{+0.10}$	${0.159}_{-0.002}^{+0.002}$	${488}_{-20}^{+21}$	${28.28}_{-3.57}^{+4.36}$	6.8	⋯	FP	Stellar variability
7269798 b	21.4	${0.88}_{-0.07}^{+0.09}$	${0.126}_{-0.001}^{+0.001}$	${344}_{-3}^{+4}$	${3.34}_{-0.12}^{+0.14}$	8.2	0.0113	CAND	⋯
7340288 b	142.5	${1.51}_{-0.11}^{+0.13}$	${0.444}_{-0.004}^{+0.004}$	${194}_{-3}^{+4}$	${0.33}_{-0.02}^{+0.03}$	7.4	$7.91\times {10}^{-4}$	CAND	Rocky HZ
7747788 b	133.1	${1.67}_{-0.11}^{+0.13}$	${0.601}_{-0.012}^{+0.009}$	${533}_{-25}^{+29}$	${19.19}_{-3.33}^{+4.61}$	7.6	$4.92\times {10}^{-4}$	CAND	⋯
7974496 b	4.0	${1.48}_{-0.16}^{+0.18}$	${0.054}_{-0.001}^{+0.001}$	${1549}_{-81}^{+75}$	${1364.17}_{-262.54}^{+283.65}$	7.1	⋯	FP	Stellar variability
8172679 b	194.0	${9.61}_{-1.09}^{+1.23}$	${0.784}_{-0.027}^{+0.029}$	${557}_{-33}^{+34}$	${22.80}_{-5.00}^{+6.11}$	10.5	⋯	FP	Stellar variability
9274173 b	4.4	${1.42}_{-0.11}^{+0.13}$	${0.055}_{-0.001}^{+0.001}$	${1199}_{-29}^{+30}$	${490.71}_{-46.03}^{+51.21}$	8.7	⋯	FP	Stellar variability
9716483 b	209.4	${2.08}_{-0.11}^{+0.14}$	${0.797}_{-0.017}^{+0.015}$	${454}_{-26}^{+28}$	${10.10}_{-2.15}^{+2.68}$	8.6	⋯	FP	Likely noise
9777962 b	367.2	${7.46}_{-0.84}^{+1.35}$	${1.215}_{-0.019}^{+0.017}$	${422}_{-21}^{+21}$	${7.51}_{-1.37}^{+1.61}$	8.9	⋯	FP	Likely noise
10018357 b	133.8	${7.87}_{-1.72}^{+0.71}$	${0.644}_{-0.023}^{+0.075}$	${616}_{-74}^{+89}$	${34.05}_{-13.69}^{+24.49}$	9.1	$1.13\times {10}^{-8}$	CAND	⋯
10083396 b	113.5	${1.14}_{-0.06}^{+0.07}$	${0.504}_{-0.007}^{+0.006}$	${495}_{-12}^{+12}$	${14.19}_{-1.28}^{+1.39}$	7.4	$5.86\times {10}^{-5}$	CAND	⋯
10419787 b	122.7	${2.06}_{-0.14}^{+0.17}$	${0.515}_{-0.009}^{+0.007}$	${429}_{-15}^{+15}$	${8.03}_{-1.05}^{+1.19}$	7.6	⋯	FP	Stellar variability
10598829 b	67.5	${1.96}_{-0.22}^{+0.30}$	${0.369}_{-0.007}^{+0.009}$	${607}_{-32}^{+42}$	${32.29}_{-6.37}^{+9.81}$	7.4	$3.59\times {10}^{-3}$	CAND	⋯
10879314 b	49.2	${3.92}_{-0.54}^{+0.57}$	${0.313}_{-0.005}^{+0.005}$	${773}_{-51}^{+43}$	${84.68}_{-20.40}^{+20.52}$	7.2	⋯	FP	Stellar variability
11092463 b	6.9	${1.33}_{-0.14}^{+0.24}$	${0.070}_{-0.001}^{+0.001}$	${877}_{-31}^{+30}$	${140.06}_{-18.65}^{+20.17}$	7.8	⋯	FP	Stellar variability
11139863 b	7.2	${0.81}_{-0.05}^{+0.07}$	${0.086}_{-0.002}^{+0.002}$	${1444}_{-77}^{+87}$	${1031.85}_{-202.39}^{+272.09}$	10.6	⋯	FP	Stellar variability
11350118 c	2.7	${0.66}_{-0.05}^{+0.07}$	${0.034}_{-0.001}^{+0.001}$	${935}_{-31}^{+31}$	${181.58}_{-22.96}^{+25.48}$	8.2	$9.62\times {10}^{-4}$	CAND	KOI-4509.02
11565976 b	24.2	${1.40}_{-0.11}^{+0.12}$	${0.188}_{-0.003}^{+0.004}$	${941}_{-37}^{+39}$	${186.19}_{-27.77}^{+32.67}$	7.4	⋯	FP	Stellar variability
11805835 b	23.5	${0.94}_{-0.07}^{+0.10}$	${0.141}_{-0.001}^{+0.001}$	${442}_{-14}^{+17}$	${9.01}_{-1.08}^{+1.49}$	7.2	$2.30\times {10}^{-3}$	CAND	⋯
12023559 b	84.6	${1.86}_{-0.11}^{+0.13}$	${0.385}_{-0.006}^{+0.005}$	${444}_{-16}^{+14}$	${9.19}_{-1.25}^{+1.24}$	8.1	$4.54\times {10}^{-4}$	CAND	⋯
12216301 b	116.5	${3.66}_{-0.26}^{+0.41}$	${0.712}_{-0.023}^{+0.010}$	${1029}_{-108}^{+104}$	${265.44}_{-95.33}^{+124.64}$	7.6	⋯	FP	Stellar variability
12505309 b	2.9	${1.20}_{-0.08}^{+0.10}$	${0.046}_{-0.002}^{+0.001}$	${1823}_{-62}^{+81}$	${2617.39}_{-336.756}^{+497.97}$	7.4	⋯	FP	Stellar variability

Note. Planetary radii do not take into account dilution; refer to Table 6.

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6.6.1. Derived Parameters from MCMC

The planet radius R_p is determined from the fitted parameter R_p/R_s using

$$\begin{eqnarray}&&{R}_{p}=\left(\displaystyle \frac{{R}_{p}}{{R}_{s}}\right){R}_{s},\end{eqnarray} \tag{ 25 }$$

where R_s is the known stellar radius.

The semimajor axis of the planet's orbit a is determined from the fitted P and known stellar parameters, rather than the fitted $a/{R}_{s}$,

$$\begin{eqnarray}&&a=\displaystyle \frac{{{GM}}_{s}{P}^{2}}{4{\pi }^{2}},\end{eqnarray} \tag{ 26 }$$

where G is the gravitational constant and M_s is the stellar mass.

The planet equilibrium temperature T_eq is calculated assuming thermodynamic equilibrium between the incident stellar flux and the radiated heat from the planet,

$$\begin{eqnarray}&&{T}_{\mathrm{eq}}={T}_{\mathrm{eff}}{\left(1-A\right)}^{1/4}\sqrt{\displaystyle \frac{{R}_{s}}{2a}},\end{eqnarray} \tag{ 27 }$$

where A is the albedo of the planet. We assume Earth's albedo, A = 0.3, for all cases.

The planet's stellar insolation S, defined as the ratio of the flux of the host star at the planet to the solar flux at Earth, is determined by

$$\begin{eqnarray}&&S={\left(\displaystyle \frac{{R}_{s}/{R}_{\odot }}{a}\right)}^{2}{\left(\displaystyle \frac{{T}_{\mathrm{eff}}}{{T}_{\mathrm{eff},\odot }}\right)}^{4}.\end{eqnarray} \tag{ 28 }$$

When a nearby star is resolved in the AO images, we must consider the effects of dilution on the estimated planet radius. We note that we do not take into account changes to the measured values of the primary star's properties due to the presence of a companion. Since most of our targets have properties inferred from photometry only, light from a companion could cause the stellar type to be misidentified. However, this is likely negligible for companions with large contrast ratios.

We consider two cases: that the PC is transiting the brighter primary star (pri), or the fainter companion (sec). Using Equations (3) and (4) in Law et al. (2014), the corresponding radius corrections are

$$\begin{eqnarray}&&{R}_{p,\mathrm{pri}}={R}_{p}\sqrt{\displaystyle \frac{{F}_{\mathrm{tot}}}{{F}_{\mathrm{pri}}}}\end{eqnarray} \tag{ 29 }$$

and

$$\begin{eqnarray}&&{R}_{p,\sec }={R}_{p}\displaystyle \frac{{R}_{\sec }}{{R}_{\mathrm{pri}}}\sqrt{\displaystyle \frac{{F}_{\mathrm{tot}}}{{F}_{\sec }}}\end{eqnarray} \tag{ 30 }$$

where F_i/F_tot is the fraction of total light contributed by star i in the aperture and R_p is the planet radius without dilution corrections. If we assume that the total flux is provided by the two stars, F_tot = F_pri + F_sec, we can rewrite these equations in terms of magnitudes as

$$\begin{eqnarray}&&{R}_{p,\mathrm{pri}}={R}_{p}\sqrt{1+{10}^{-0.4{\rm{\Delta }}m}}\end{eqnarray} \tag{ 31 }$$

and

$$\begin{eqnarray}&&{R}_{p,\sec }={R}_{p}\displaystyle \frac{{R}_{\sec }}{{R}_{\mathrm{pri}}}\sqrt{1+{10}^{0.4{\rm{\Delta }}m}}.\end{eqnarray} \tag{ 32 }$$

Since the ${\rm{\Delta }}m$ values in Equations (31) and (32) are in the Kepler band (Kp), they must be converted from our K_s band AO results. Howell et al. (2012) derived the following conversion between Kp and K_s magnitudes:

$$\begin{eqnarray}\begin{array}{rcl}{Kp}-{K}_{s} & = & -643.05169+246.00603{K}_{s}-37.136501{K}_{s}^{2}\\ & & \qquad +\,2.7802622{K}_{s}^{3}-0.10349091{K}_{s}^{4}\\ & & \qquad +\,0.0015364343{K}_{s}^{5}\end{array}\end{eqnarray} \tag{ 33 }$$

for 10 < K_s < 15.4 mag, and

$$\begin{eqnarray}&&{Kp}-{K}_{s}=-2.7284+0.3311{K}_{s}\end{eqnarray} \tag{ 34 }$$

for K_s > 15.4 mag, allowing us to convert ΔK_s to ΔKp.

Furthermore, for the case that the PC transits the secondary, we require an estimate of the ratio of stellar radii, R_sec/R_pri. If the companion is in the background our single-band photometry is not able to constrain R_sec. However, if we assume the primary and secondary stars are bound, we can use our knowledge of the primary star to estimate the properties of the secondary.

We follow the general strategy outlined in Furlan et al. (2017), which we summarize here. First, we assume that K_p magnitudes are roughly equivalent to R magnitudes. We use the primary star's known T_eff,pri (from our isochrones fit) with a table of colors and effective temperatures¹⁰ (Pecaut & Mamajek 2013) to derive ${(V-R)}_{\mathrm{pri}}$ colors and absolute V magnitudes (${M}_{V,\mathrm{pri}}$). Then, we assume that the bound stars are the same distance to the Sun to let ${M}_{V,\sec }={m}_{V,\sec }\,-{m}_{V,\mathrm{pri}}+{M}_{V,\mathrm{pri}}$, or ${M}_{V,\sec }={K}_{p,\sec }\,+{(V-R)}_{\sec }-{K}_{p,\mathrm{pri}}\,-{(V-R)}_{\mathrm{pri}}+{M}_{V,\mathrm{pri}}$. We find the ${(V-R)}_{\sec }$ color that yields a self-consistent ${M}_{V,\sec }$ value, which in turn gives an estimate of the radius of secondary from the table.

We determined correction factors only for companions which could physically account for the observed transit depth. If the planet needed to fully obscure the companion in order to explain the transit, we ruled out this scenario for the planet host star. For example, a 1% transit depth would rule out any companion fainter than 5 mags or more as a potential planet host.

Table 6 shows the results of each case for the candidates with resolved stars within 4''. For both cases, the secondary was too faint to account for the transit depth or cause significant dilution.

Table 6.  Revised Planetary Radii for the Two Candidates with AO-resolved Stars within 4'', considering whether the Planet Transits the Primary or Secondary

KIC	Rp $({R}_{\oplus })$	${R}_{p,\mathrm{pri}}$ $({R}_{\oplus })$	${R}_{p,\sec }$ $({R}_{\oplus })$
7269798 b	0.88	0.88	⋯
7340288 b	1.51	1.51	⋯

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We highlight select discoveries from our new PC list. One of our candidates, KIC-7340288 b, is both likely rocky and in the Habitable Zone of its star, where the planet's surface temperatures could allow liquid water oceans. Finding Earth-sized planets in the Habitable Zone was one of the original goals of the Kepler mission (Borucki et al. 2010). Furthermore, KIC-11350118 c is a new candidate associated with a known KOI system.

KIC-7340288 b is a $1.51{R}_{\oplus }$ PC orbiting a K dwarf (${T}_{\mathrm{eff}}\,=3959K$, ${R}_{s}=0.547{R}_{\odot }$, and ${M}_{s}=0.574M$) with an orbital period of 142.5 days. This candidate is in the Habitable Zone with an insolation of 0.33S_⊕, and is also likely rocky given its $\lt 1.6{R}_{\oplus }$ radius.

Phase diagrams are plotted in Figure 6, showing the full transit as well as indicating data corresponding to odd and even transits. The odd–even plot shows consistency between their depths and durations, compared to each other as well as to the full transit's best-fit model.

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We also review our results from the stellar variability analysis in Section 6.2. Figure 7 shows the Lomb–Scargle periodogram, with the 142.5 day orbital period indicated by a dotted line. We find a strong rotation period at ∼13.4 days (half the 26.711 ± 0.231 day rotation period reported in McQuillan et al. 2014), but no multiples of this rotation period correspond to the orbital period.

Figure 8 also confirms that the transit remains consistent regardless of the choice of detrending algorithm used to remove the stellar variability. Plotted are phase diagrams of KIC-7340288, created by detrending the raw MAST light curve with our original algorithm as well as the Hippke et al. (2019) time-windowed slider with 1 and 2 day window lengths. In each case, the light curve was folded at the BLS-detected period of the planet (P = 142.5282 days) and centered at the epoch (${T}_{0}=204.7231$ BKJD). Assuming the BLS-detected duration of 0.2355 days, the transits have S/N of 7.4, 7.5, and 7.2, respectively. We also fit least-squares and MCMC transit models to each light curve after masking the transits and re-detrending as in our standard pipeline. The best-fit parameters are given in Table 7, indicating good agreement within 1σ.

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Table 7.  LS + MCMC Fit Results for KIC-7340288 b Using Three Different Detrends

Detrend	P (days)	T0 (BKJD)	${R}_{p}/{R}_{s}$	$a/{R}_{s}$	b
Original	142.5324 ± 0.0034	204.7104 ± 0.0180	${0.02526}_{-0.00177}^{+0.00201}$	${156.56}_{-32.38}^{+12.21}$	${0.369}_{-0.255}^{+0.311}$
Biweight (1 day)	142.5319 ± 0.0039	204.7125 ± 0.0167	${0.02417}_{-0.00198}^{+0.00183}$	${159.98}_{-40.96}^{+13.52}$	${0.385}_{-0.286}^{+0.347}$
Biweight (2 day)	142.5319 ± 0.0039	204.7125 ± 0.0170	${0.02232}_{-0.00206}^{+0.00198}$	${159.58}_{-44.28}^{+15.68}$	${0.402}_{-0.293}^{+0.351}$

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Our AO imaging revealed one stellar companion within 4'', with ${\rm{\Delta }}K=5.20$ and an angular separation of 39. Assuming this planet orbits the primary star, its radius is unchanged by dilution and it remains below the rocky limit. We are also able to rule out the scenario that the planet orbits the companion, since the faintness of the star implies it would need to be fully obscured by the planet to explain the observed 0.06% transit depth. After incorporating our AO results into vespa, we found an astrophysical FPP of $7.91\times {10}^{-4}$.

The KIC-11350118 system, also known as KOI-4509, already has a single known candidate with P = 12.0 days and ${R}_{p}=0.97{R}_{\oplus }$. We detect an additional, smaller candidate with P = 2.7 days and ${R}_{p}=0.66{R}_{\oplus }$. The full transit and odd–even phase diagrams are plotted in Figure 9.

The Robo-AO survey observed the host star and did not detect any companions within 4'' (Ziegler et al. 2017). Furthermore, its membership in a multiplanet system lowers its FPP (Lissauer et al. 2012). For systems containing two planets in the Kepler field, Lissauer et al. (2012) estimated a "multiplicity-boost" factor of 25 to the planet prior probability. After incorporating this into our vespa calculation, we found an astrophysical FPP of $9.62\times {10}^{-4}$.