DETECTION OF POTENTIAL TRANSIT SIGNALS IN 17 QUARTERS OF KEPLER MISSION DATA

The details of Kepler operation and data acquisition have been reported elsewhere (Haas et al. 2010). In brief: the Kepler spacecraft is in an Earth-trailing heliocentric orbit and maintained a boresight pointing centered on $\alpha ={{19}^{{\rm h}}}{{22}^{{\rm m}}}{{40}^{{\rm s}}}$, δ = +445 during the primary mission. The Kepler photometer acquired data on a 115 square degree region of the sky. The data were acquired in 29.4 minute integrations, colloquially known as "long cadence" data. The spacecraft was rotated about its boresight axis by 90° every 93 days in order to keep its solar panels and thermal radiator correctly oriented; the interval which corresponds to a particular rotation state is known colloquially as a "quarter." Because of the quarterly rotation, target stars were observed throughout the year in 4 different locations on the focal plane. Science acquisition was interrupted monthly for data downlink, quarterly for maneuver to a new roll orientation (typically this is combined with a monthly downlink to limit the loss of observation time), once every 3 days for reaction wheel desaturation (one long cadence sample is sacrificed at each desaturation), and at irregular intervals due to spacecraft anomalies. In addition to these interruptions which were required for normal operation, data acquisition was suspended for 11.3 days, from 2013-01-17 19:39Z through 2013-01-29 03:50Z (555 long cadence samples)⁵ during this time, the spacecraft reaction wheels were commanded to halt motion in an effort to mitigate damage which was being observed on reaction wheel 4, and spacecraft operation without use of reaction wheels is not compatible with high-precision photometric data acquisition.

In 2012 July, one of the four reaction wheels used to maintain spacecraft pointing during science acquisition experienced a catastrophic failure. The mission was able to continue using the remaining three wheels to permit three-axis control of the spacecraft, until 2013 May. At that time a second reaction wheel failed, forcing an end to Kepler data acquisition in the nominal Kepler field of view (FOV). As a result, the analysis reported here is the first which incorporates the full volume of data acquired from that FOV.⁶

Kepler science data acquisition of Quarter 1 began at 2009-05-13 00:01:07Z, and acquisition of Quarter 17 data concluded at 2013-05-11 12:16:22Z. This time interval contains 71,427 long cadence intervals. Of these, 5077 were consumed by the interruptions listed above. An additional 1100 long cadence intervals were excluded from use in searches for transiting planets. These samples were excluded due to data anomalies which came to light during processing and inspection of the flight data. This includes a contiguous set of 255 long cadence samples acquired over the 5.2 days which immediately preceded the 11 day downtime described above: the shortness of this dataset combined with the duration of the subsequent gap led to a judgement that the data would not be useful for transiting planet searches (TPS). A total of 65,250 long cadence intervals for each target were dedicated to science data acquisition. This is only 1242 or ∼2% more searchable cadences than available for the analysis of 16 quarters of kepler data in Tenenbaum et al. (2014). This highlights the fact that quarter 17 was only about a month long in duration before the failure of the second reaction wheel.

A total of 198,675 targets observed by Kepler were searched for evidence of transiting planets. This set of targets includes all stellar targets observed by Kepler at any point during the mission, and specifically includes target stars which were not originally observed for purposes of TPS (asteroseismology targets, guest observer targets, etc). The exception to this is a subset of known eclipsing binaries, as described below. Figure 1 shows the distribution of targets according to the number of quarters of observation. A total of 112,014 targets were observed for all 17 quarters. An additional 35,653 targets were observed for 14 quarters: the vast majority of these targets were in regions of the sky which are observed in some quarters by CCD Module 3, which experienced a hardware failure in its readout electronics during Quarter 4 in 2010 January, resulting in a "blind spot" which rotates along with the Kepler spacecraft, gapping 25% of the quarterly observations for affected targets. The balance of 51,008 targets observed for some other number of quarters is largely due to gradual changes in the target selection process over the duration of the mission.

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As described in Tenenbaum et al. (2014), some known eclipsing binaries were excluded from planet searches in the pipeline. For this search over Q1–Q17, a total of 1033 known eclipsing binaries were excluded. This is smaller than the number excluded in the Q1–Q16 analysis due to a change in exclusion criteria. Specifically, we excluded eclipsing binaries from the most recent Kepler catalog of eclipsing binaries (Prša et al. 2011; Slawson et al. 2011) that did not have a morphology <0.6 (Matijevič et al. 2012), i.e., the primary and secondary eclipses must be well separated from one another, and were not in conflict with established planet candidates archived at NExScI. This requirement on the morphology is identical to that of the Q1–Q16 run but all the other criteria have been dropped to exclude fewer targets. Note, however, that the Data Validation (DV; Wu et al. 2010; J. D. Twicken et al. 2015, in preparation) step of the Data Processing Pipeline may still exclude some events based on its own analysis of primary and secondary depths. Thus, the excluded eclipsing binaries are largely contact binaries which produce the most severe misbehavior in the TPS pipeline module (Tenenbaum et al. 2012, 2013), while well-detached, transit-like, eclipsing binaries are now processed in TPS. This was done in order to ensure that no possible transit-like signature was excluded, and also to produce examples of the outcome of processing such targets through both TPS and DV, such that quantitative differences between planet and eclipsing binary detections could be determined and exploited for rejecting other, as-yet-unknown, eclipsing binaries detected by TPS.

The steps in processing Kepler science data have not changed since Tenenbaum et al. (2012), and are briefly summarized below. The pixel data from the spacecraft were first calibrated, in the CAL pipeline module, to remove pixel-level effects such as gain variations, linearity, and bias(Quintana et al. 2010). The calibrated pixel values were then combined, within each target, in the Photometric Analysis pipeline module, to produce a flux time series for that target (Twicken et al. 2010b). In the Pre-search Data Conditioning (PDC) pipeline module the ensemble of target flux time series were then corrected for systematic variations driven by effects such as differential velocity aberration, temperature-driven focus changes, and small instrument pointing excursions(Stumpe et al. 2014). These corrected flux time series became the inputs for the TPS.

The TPS software module analyzed each corrected flux time series individually for evidence of periodic reductions in flux which would indicate a possible transiting planet signature. The search process incorporated a significance threshold against a multiple event statistic (MES)"⁷ and a series of vetoes; the latter were necessary because while the significance threshold was sufficient for rejection of the null hypothesis, it was incapable of discriminating between multiple competing alternate hypotheses which can potentially explain the flux excursions. An ephemeris on a given target which satisfied the significance threshold and passed all vetoes is known as a Threshold Crossing Event (TCE). Each target with a TCE was then searched for additional TCEs, which potentially indicated multiple planets orbiting a single target star.

After the search for TCEs concluded, additional automated tests were performed to assist members of the Science Team in their efforts to reject false positives. A TCE which has been accepted as a valid astrophysical signal (either planetary or an eclipsing binary), based on analysis of these additional tests, is designated as a KOI. The collection of KOIs that pass additional scrutiny are promoted to planet candidate status, while those that do not are dispositioned as false positives. Note that, while the TCEs were determined in a purely algorithmic fashion by the TPS software module, KOIs were selected on the basis of examination and analysis by scientists.

Since the publication of Tenenbaum et al. (2014), there have been considerable improvements to the Kepler Science Processing Pipeline. We describe here only the recent improvements and refer the interested reader to Tenenbaum et al. (2012, 2013, 2014) for a description of past improvements. The pixel-level calibration performed by the CAL module of the Science Processing Pipeline has been improved to include a cadence-by-cadence 2D black correction. In an effort to mitigate the effects of the image artifacts described in Caldwell et al. (2010) on the TPS, CAL also generates rolling band flags (Clarke et al. 2014) that can be used to identify the cadences on a given target that are affected. Improvements to the undershoot correction have also been made in CAL.

The PDC module corrects for both attitude tweaks and Sudden Pixel Sensitivity Dropouts (SPSDs). Previously it was noticed that those corrections can occasionally be very poor for several reasons such as local trends or noise in the data. Improvements were made to fix this problem of poor corrections. Additionally, some improvements were made to the wavelet band-splitting method used by PDC's multi-scale Bayesian Maximum a posteriori algorithm for removing systematic noise from the data (Smith et al. 2012).

In addition to improvements in the science algorithms used to process the data, the data was also improved. A major effort was undertaken by the Kepler Science Operations staff to, for the first time, uniformly reprocess all the data through the newly released codebase. This was aided by the fact that all major modules of the pipeline have been ported over to the NASA Ames supercomputer to allow for reprocessing of multiple quarters in parallel. In all however, processing all the data uniformly from the start to the end of the pipeline takes several months. Each module of the pipeline is necessarily, and painstakingly, configured and managed separately as they are run in sequence.

Pixel-level data as well as light curves from these pre-search processing steps are publicly available at the Mikulski Archive for Space Telescopes⁸ as Data Release 24. Each data release is also accompanied by a Data Release Notes document that describes the data in general.

Owing to the complicated and varied noise sources across the many stellar targets in the Kepler field, the core detection algorithm in TPS is a wavelet-based, adaptive matched filter. The data are transformed to the wavelet domain using Daubechies 12-tap wavelets (Debauchies 1988) in a joint time-frequency overcomplete wavelet decomposition. In the wavelet domain, the noise at each time-frequency scale is estimated and used to whiten both the data and the templates which span the space of physically allowable orbital period, orbital phase (epoch), and transit duration. Although the window sizes used to estimate the noise at the various time-frequency scales are large compared to the transit duration, the whitening process can lower the signal-to-noise ratio (S/N) due to the way that any signal present in the data perturbs the estimates of the noise (or whitening coefficients). The same is true of any detrending of the data that is performed prior to a search. For this reason, we do not detrend the data in any way prior to the search other than to remove edge effects of spacecraft pointing at quarter and monthly boundaries where the spacecraft broke from data acquisition in order to beam the data back to Earth. We also attempt to filter out coherent stellar oscillations by identifying and removing harmonics from each quarterly segment. This does, indeed, suppress such stellar variability, but also reduces the sensitivity of TPS to strong short period planetary signatures (Christiansen et al. 2013). TPS normalizes each quarterly segment by its median and fills the monthly and quarterly gaps using methods that attempt to preserve the correlation structure of the observation noise and permit FFT-based approaches to be used in the subsequent search.

After TPS has found a signal with a MES (Jenkins et al. 2010) above threshold, however, it is possible to detrend and re-whiten the data and avoid any loss in S/N that would otherwise occur because of the effect of the signal on the estimated trend and the whitening coefficient estimates. Although this will not make the problem of detecting the signal any easier, since it can only be done after the initial detection, it does improve the discriminating power of the other statistical tests, or vetoes (discussed subsequently), that TPS subjects each candidate event to. Prior to calculation of the veto statistics, the ephemeris of the candidate event is used to identify in-transit cadences (with some small amount of padding). These in-transit cadences are then filled using an adaptive auto-regressive gap prediction algorithm. A trend line is then estimated using a piecewise polynomial fitting algorithm that employs Akaike's Information Criterion to prevent over-fitting. After removing this trend from the data, the whitening coefficients are then re-computed. After removing the trend from the in-transit cadences, they are restored to the trend-removed data which are then whitened using the new whitening coefficients. The potential candidate is then subjected to a suite of four statistical tests described below in Section 2.3.

Mismatch between any true signal and the template used to filter the data degrades S/N. This degradation due to signal-template mismatch can be decomposed into two separate types: shape mismatch, and timing mismatch. The transit duration and assumed transit model affect the shape mismatch, while the template search grid spacing in orbital period and epoch affect the timing mismatch.

TPS searches a total of 14 transit durations: 1.5, 2.0, 2.5, 3.0, 3.5, 4.5, 5.0, 6.0, 7.5, 9.0, 10.5, 12.0, 12.5, and 15 hr. These are logarithmically spaced, rounded to the nearest half hour (roughly the time per cadence), and augmented by a requirement to always search for 3, 6, and 12 hr pulses. Prior to this run of the pipeline, TPS has simply used a square-wave transit model. In Seader et al. (2013), it was shown through a Monte Carlo study, that with perfect duration and timing match, the square wave, on average, mismatches a true signal by $\;3.91$%. This translates directly into S/N loss. This same Monte Carlo study was used to compute the integral average of all astrophysical models based on the Mandel & Agol geometric transit model (Mandel & Agol 2002) with limb darkening of Claret (Claret 2000), over the parameter space of interest (Seader et al. 2013). TPS now uses this averaged model to construct templates, which lowers the shape mismatch to only $\;1.49$%. Lowering this shape mismatch also improves the sensitivity of the ${{\chi }^{2}}$ vetoes (discussed in the next section) which currently assume a perfect match between the signal and template. In the next pipeline code release, the calculation of the ${{\chi }^{2}}$ vetoes will take into account the signal-template mismatch as described first in Allen (2004) and later in Seader et al. (2013). Using the new templates, the total shape mismatch (transit duration included) is only $\;1.66$% compared to $\;4.32$% for the square wave model.

The mismatch in timing is a function of the template spacing in the period-epoch space. This is controlled by a mismatch parameter which is essentially the Pearson Correlation Coefficient between two mismatched pulse trains (Jenkins et al. 1996, 2010). Previously, TPS required a match of 90%, which gave a timing mismatch alone of $\;2.65$% with the new astrophysically motivated templates for a total mismatch of $\;4.31$% including both shape and timing mismatches. Since we are now running TPS on the NAS however, we can afford to search a finer grid of templates and have therefore tightened up the period-epoch match to 95%. This parameter may be increased further in the future but by increasing the number of search templates the false alarm rate also increases. So there are tradeoffs to consider outside of just run time. The false alarm vetoes keep the total number of false alarms at a manageable level even with the increase to the period-epoch match.

The most substantial changes in terms of both impact on final results and extent in the codebase, are the changes to the false alarm vetoes since the last pipeline codebase release cycle. During the transiting planet search, TPS steps through potential candidates across period-epoch space with MES values exceeding the search threshold of $7.1\sigma$ in order of decreasing MES for each pulse duration. The search continues until either TPS runs out of time on that pulse duration, it hits the maximum allowable number of candidates to loop over (set to 1000), it exhausts the list without finding anything that passes all the vetoes, or it settles on something that passes all the vetoes. During the course of performing the search, TPS has the ability to remove up to two features in the data that contribute to detections that do not pass all the vetoes (Tenenbaum et al. 2013). After removing features, the period-epoch folding is re-done to generate a new list of candidates.

Candidate events are subjected to a suite of four statistical tests, two of which are new to this pipeline code release. First, the distribution of the MES under the null hypothesis at the detected period is estimated by a Bootstrap test outlined in detail in Appendix A and in J. M. Jenkins et al. (2015b, in preparation). From the estimated MES distribution, the threshold needed to achieve the false alarm probability equivalent to a $7.1\sigma$ threshold on a standard normal distribution ($\;6.28\times {{10}^{-13}}$) is calculated by either interpolation or extrapolation. If the whitener is doing its job perfectly, the MES distribution should be standard normal. When extrapolation is needed, a linear extrapolation in log probability space is done which yields values that are typically conservative. If any threshold values are suspect, or if the distribution can not be constructed for some reason, then this veto is not applied. Otherwise, we require that the MES exceeds the calculated threshold value to, in effect, ensure that we are making a detection that meets the false alarm criteria we have placed on the search. The threshold used in this run for the bootstrap veto is too strict given that many real transiting planets are found in multiple planet systems. The presence of transits for other candidate events, on a given target, in the null statistics will artificially elevate the threshold since they will add counts to MES bins above background. In future runs, after appropriate tuning, the threshold will be relaxed to reduce the likelihood of rejecting real planetary signatures.

This Bootstrap veto does an excellent job at removing long period false alarms that are related to rolling band image artifacts. The image artifacts render the MES distribution non-white and potentially non-Gaussian after whitening. This means that $7.1\sigma$ is not as significant in comparison to the background at a given period for a given target than it would be in a purely standard normal distribution so we must therefore require a higher threshold to achieve the desired false alarm rate. Under the Neyman–Pearson criterion, which is employed in our detection strategy, the search threshold is determined from a required false alarm rate. The Bootstrap veto allows us to map out a correction factor for each target and period so that we can ensure the required false alarm rate is met. This is sure to play an important role in upcoming planet occurrence rate studies where one must assess detectability of potential signals spanning the whole parameter space on every target. The Bootstrap shows us that the MES distribution, and therefore detectability, is highly variable from target-to-target and across period space as well.

Candidates that pass the Bootstrap veto are then subjected to the Robust Statistic (RS) veto after the detrending and re-whitening described in Section 2.1 above. This veto is described in detail in Appendix A of Tenenbaum et al. (2013). The fit S/N is derived from robustly fitting the whitened data to a whitened model pulse train constructed using the ephemeris of the candidate event. Previously, the threshold for this fit S/N was set to $6.4\sigma$ based on examination of the slope of the best fit line on a plot of MES versus RS for KOIs detected with the correct ephemeris. We found previously that $RS=0.9$ MES, hence the $6.4\sigma$ threshold since we have a $7.1\sigma$ threshold on MES. Now however, we find $RS=1.15$ MES, which means we could in principle set the RS threshold at $\;8.1\sigma$. This makes sense considering that the whitening process lowers S/N and the MES has not been re-computed with the new whitener as the RS has. For this run, we conservatively raised the threshold on the RS to $6.8\sigma$. There is an additional criterion applied during the RS test that affects only candidates with the minimum allowed number of transits (three transits). We require that each transit has no more than 50% of its cadences with data quality weights less than unity (Tenenbaum et al. 2014).

If the RS threshold is exceeded, the candidate event is subjected to two separate statistical ${{\chi }^{2}}$ tests. The first of these has been previously used and is described in Tenenbaum et al. (2013) as $\chi _{(2)}^{2}$ with modifications as discussed in Tenenbaum et al. (2014) and Seader et al. (2013). This test breaks up the MES into different components, one for each transit event, and compares what is expected from each transit to what is actually obtained in the data assuming that there is indeed a transiting planet. The current formulation assumes there is no mismatch between the signal and template. In the next pipeline release however, the mismatch will be explicitly accounted for by modifying the way the number of degrees of freedom (dof) are calculated as discussed in Allen (2004) and Seader et al. (2013). Since Tenenbaum et al. (2014), the use of $\chi _{(1)}^{2}$ has been dropped due to the deficiencies discussed in Seader et al. (2013). We have also dropped the use of $\chi _{(3)}^{2}$ as defined in Seader et al. (2013). We have however implemented a new ${{\chi }^{2}}$ veto, which tests the goodness of fit, that was presented in Baggio et al. (2000) and later discussed in Allen (2004). The new veto is dubbed $\chi _{({\rm GOF})}^{2}$ and details of its construction are presented in Appendix B. The thresholds used for both ${{\chi }^{2}}$ vetoes are $7.0\sigma$.

The number of targets with a MES above threshold was 126,153, or 63.5% of all the targets. The vetoes were then applied to this set of targets. The bootstrap veto rejected 107,846 targets, the RS rejected an additional 3553 targets, and the ${{\chi }^{2}}$ vetoes rejected an additional 2056 targets. Note that there is a lot of overlap across the different vetoes for targets that were rejected, for example most of the targets vetoed by the bootstrap would also be vetoed by the ${{\chi }^{2}}$ vetoes, and targets vetoed by one version of the ${{\chi }^{2}}$ veto would also be vetoed by the other. Together, this is a powerful set of false alarm vetoes each with a very firm theoretical basis, that complement each other well to discriminate against the myriad of potential types of noise that can masquerade as transiting planet signals. The vetoes are not perfect however, and do prevent the generation of TCEs for some number of legitimate transiting planets. We are in the process of fully characterizing their performance through transit injection studies.

For the 12,669 target stars which were found to contain a TCE, additional TPS searches were used to identify target stars which host multiple planet systems. The process is described in Wu et al. (2010) and in Tenenbaum et al. (2013). The multiple planet search incorporates a configurable upper limit on the number of TCEs per target, which is currently set to 10. This limit is incorporated for two reasons. First, limitations on available computing resources translate to limits on the number of searches which can be accommodated, and also on the number of post-TPS tests which can be accommodated. Second, applying a limit to the number of TCEs per target prevents a failure mode in which a flux time series is so pathological that the search process becomes "stuck," returning an effectively infinite number of nominally independent detections. The selected limit of 10 TCEs is based on experience: to date, the maximum number of KOIs on a single target star is 7, which indicates that at this time, limiting the process to 10 TCEs per target is not sacrificing any potential KOIs.

The additional searches performed for detection of multiple planet systems yielded 7698 additional TCEs across 5238 target stars, for a grand total of 20,370 TCEs. Figure 2 shows a histogram of the number of targets with each of the allowed numbers of TCEs. In this run, 16 targets produced 6 TCEs, 3 targets produced 7 TCEs, and 1 target had 8 TCEs. Note that all of these TCEs are subjected to the full TPS process of detection and vetoing described above.

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In the analyses below, 3 targets that produced TCEs are not included. This is due to the desire to limit the analysis presented here to TCEs for which there is a full analysis available from the DV pipeline module (Wu et al. 2010). These 3 targets failed to complete their DV analyses due to timing out and are thus excluded. The Kepler Input Catalog (KIC) numbers for these 3 targets are: 5513861, 8019043, 10095469. The TCEs found around KIC targets 5513861 and 10095469 were both short period ( 0.676 and 0.755 days respectively) and were found previously and are contained in the TCE catalogs at the NASA Exoplanet Archive. They were not made into KOIs by the TCE Review Team (TCERT). The other TCE found on KIC target 8019043 has been found previously and is contained in the KOI catalog at the NASA Exoplanet Archive and is labeled as being a false positive (KOI 6048.01). The 20,367 TCEs included in this analysis have been exported to the tables maintained by the NASA Exoplanet Archive.⁹

In what follows, comparisons are made between the TCEs returned by this latest pipeline run and the cumulative KOI catalog available at the NASA Exoplanet Archive.¹⁰ This archive of KOIs is built from many previous works including Borucki et al. (2010, 2011), Batalha et al. (2013), Burke et al. (2014), Rowe et al. (2015), and Mullally et al. (2015).

As in past analyses (Tenenbaum et al. 2012, 2013, 2014), we have identified a subset of the KOIs which we use as a set of test subjects for the TPS run. TPS does not receive any prior knowledge about detections on targets; therefore, the re-detection of objects of interest which were previously detected and classified as valid planet candidates is a valuable test to guard against inadvertent introduction of significant flaws into the detection algorithm.

The list of Q1–Q12, and Q1–Q16 KOIs has been analyzed and a set of high-quality "golden KOIs" identified for comparison to the Q1–Q17 TCEs. This subset of the full KOI list is a representative cross-section of all KOIs in the parameters of transit depth, S/N, and period. It builds upon the list used in Tenenbaum et al. (2014) but also now excludes those KOIs that are labeled as false positives at the NASA Exoplanet Archive.

The "golden KOI" set includes 1752 KOIs across 1483 target stars. Figure 8 shows the distribution of estimated transit depth, S/N, and period for the "golden KOIs." Out of these, 1411 target stars produced one or more TCEs, while 72 target stars did not. Of the 72 target stars which failed to produce a TCE, all but two produced one, and only one, KOI per target (total of 74 KOIs in all) in previous pipeline runs. Only 5 of the 74 KOIs had periods less than 10 days, so the issue described in Tenenbaum et al. (2014) of a stellar harmonics removal algorithm removing short period transits is not a likely culprit here. Out of the 74 missed KOIs, 48 ran through the search loop in TPS only a single time and so a precise determination of why they were missed can be made.

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For half of them, TPS failed to latch onto the correct period and therefore made no detection. The other half were vetoed evenly between the newly implemented bootstrap veto, and the ${{\chi }^{2}}$ vetoes. These were all very close to threshold, so re-tuning the thresholds would likely bring all these missed KOIs back. As discussed in Seader et al. (2013), the ${{\chi }^{2}}$ vetoes assume a perfect match between the signal and template. In the next pipeline development cycle, this assumption will no longer be made and the thresholds used on the ${{\chi }^{2}}$ vetoes will be adjusted to allow for mismatch. This adjustment will act to lower the threshold, thereby making it easier to detect valid transit signals that are near threshold. Injection studies so far have shown that this is very promising for flattening out the response of the vetoes across period space where previously there was a slight reduction in recoverability of injected signals at long periods.

3.1.1. Matching of Golden KOI and TCE Ephemerides

Detection of a TCE on a "golden KOI" target star is a necessary but not sufficient condition to conclude that TPS is functioning properly. An additional step is that the TCEs must be consistent with the expected signatures of the KOIs. This is assessed by comparing the ephemerides of the KOIs and their TCEs, as described in Tenenbaum et al. (2013); the ephemeris-matching process also implicitly compares the numbers of KOIs and TCEs on each target star, which exposes cases in which, on a given star, some but not all KOIs were detected.

There were 1678 "golden KOIs" (the full 1752 with the 74 that did not produce TCEs removed) on the 1411 target stars which produced TCEs, and for 1664 it was possible to find a match to a TCE. The fourteen KOIs which did not produce TCEs were KOI 1101.01, KOI 492.02, KOI 2971.02, KOI 649.02, KOI 6178.02, KOI 6182.02, KOI 3088.02, KOI 6191.02, KOI 600.02, KOI 1310.02, KOI 351.02, KOI 351.03, KOI 351.04, and KOI 351.05 . KOI 1101.01 is a short-period candidate (2.84 days) also missed in Tenenbaum et al. (2014), and was most likely removed by the narrow-band oscillation algorithm; the second candidate on this target, with a period of 11.4 days, was detected with a correct ephemeris match. KOI 351, aka Kepler-90, is a multi-planet system with significant transit timing variations (TTVs; Cabrera et al. 2014); since TPS requires highly periodic signals to produce a valid detection, its performance on this system has always been poor, and the bootstrap veto rejects the planets in this system affected by the large TTVs. The remaining KOIs were seen at the correct ephemeris by TPS but were vetoed by either the bootstrap or ${{\chi }^{2}}$ tests.

Figure 9 shows the value of the ephemeris match criterion for the 64 KOI-TCE matches where the value was less than 1, sorted into descending order. A total of 1600 KOI-TCE matches have a criterion value of 1.0, indicating that each transit predicted by one ephemeris corresponds to a transit predicted by the other, to within one transit duration. In these cases, it has been assumed that TPS correctly detected the "golden KOI" in question and no further analysis was performed.

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In the 64 cases in which the ephemeris match was imperfect, each KOI-TCE match was manually inspected. The disposition of the results is as follows.

• 1.  
  In 33 cases, the TCE actually matches the KOI, but the value of the match parameter does not reflect this; in general this is because the KOI ephemeris was derived with early flight data, requiring extrapolation to determine the transit times late in the mission and permitting an accumulation of error in the KOI transit timings relative to the actual timings.
• 2.  
  In 14 cases TPS detected the KOI at the correct period but the epoch was off by an integer multiple of periods.
• 3.  
  In 13 cases TPS failed to detect the KOI on the "golden KOI" list for a given target but did detect a different KOI on the same target.
• 4.  
  In 1 case TPS detected the planet but at twice the orbital period of the KOI.
• 5.  
  In 1 case TPS detected the planet but at a third of the period of the KOI.
• 6.  
  In 2 cases TPS failed to detect the KOI on the "golden KOI" list but the detections can not easily be dismissed as being false positives without further study and scrutiny.

In conclusion, out of the 64 KOI-TCE pairs which have imperfect ephemeris matches, 15 actually constitute a failure of the detection algorithm. Table 1 lists the KOIs used in the "golden KOI" set, KOI and TCE ephemerides, and the corresponding ephemeris match parameter.

Table 1.  Table of Golden KOI and TCE Matching Results

KIC #	KOI #	KOI Period	TCE Period	KOI Epoch	TCE Epoch	Ephemeris Match
		(Days)	(Days)	(KJD)	(KJD)
757450	889.01	8.8849	8.8849	169.9911	134.4485	1.00
1161345	984.01	4.2874	4.2874	262.0641	133.4537	1.00
1429589	4923.01	38.1690	38.1683	144.4650	144.4795	1.00
1431122	994.01	4.2989	4.2989	132.8642	132.8600	1.00
1432789	992.01	9.9316	9.9313	136.4865	136.5002	1.00
1432789	992.02	4.5784	4.5784	132.2933	132.2943	1.00
1717722	3145.01	4.5370	4.5370	132.1855	132.1829	1.00
1718189	993.01	21.8535	21.8536	144.3174	144.3195	1.00
1718189	993.03	86.7236	86.7244	195.3486	195.3454	1.00
1865042	1002.01	3.4815	3.4816	132.9944	132.9860	1.00

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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3.1.2. Matching of KOI and TCE Ephemerides

The detailed analysis of the performance of the search on the "golden KOI" set is useful in identifying problems and gives us an idea for how well the search should perform on the full set of KOIs. Here we examine the actual performance on almost the entire cumulative set of KOIs available at the NASA Exoplanet Archive. Currently, there are a total of 7305 KOIs, on a total of 6150 targets, in the cumulative KOI table. The "golden KOI" set is a subset of this largest set of KOIs. Since the purpose of this analysis is to assess the performance of the search, KOIs labeled as "false positive" or "not dispositioned" are removed from the set of KOIs. This leaves a set of 4173 KOIs across 3196 targets. It is important to note that we would not expect all of these to be detected since some have TTVs that made them more easily detectable with a smaller amount of data than the full 17Q used for this run. We make no effort to exclude these KOIs from the set (and in fact, even the "golden KOIs" analyzed above contain some KOIs that exhibit TTVs).

Of the 4173 KOIs in this set, it was possible to find matches for 3809, leaving 364 unmatched to any TCE. Of the 3809 for which matches were found, 3599 of them had an ephemeris match parameter of 1.0. Figure 10 shows the value of the ephemeris match criterion for the 210 KOI-TCE matches with a value less than 1, sorted into descending order. For the 210 with an ephemeris match less than 1.

• 1.  
  In 124 cases, the TCE actually matches the KOI, but the value of the match parameter does not reflect this; in general this is because the KOI ephemeris was derived with early flight data, requiring extrapolation to determine the transit times late in the mission and permitting an accumulation of error in the KOI transit timings relative to the actual timings.
• 2.  
  In 21 cases TPS detected the KOI at the correct period but the epoch was off by an integer multiple of periods.
• 3.  
  In 23 cases TPS detected the planet but at a harmonic or sub-harmonic of the orbital period of the KOI.
• 4.  
  In 42 cases TPS failed to detect the KOI.

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This means that TPS failed to detect 406 of the KOIs in this set. Figure 11 shows the distribution of KOI depth, KOI S/N, and KOI period (as given in the table at the NASA Exoplanet Archive). The majority of these missed KOIs are low S/N events skewed toward long period. A concerted effort is underway to tune the vetoes previously discussed, which should result in the recovery of these KOIs.

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On the 3196 targets with KOIs in this set, there were 280 TCEs that did not match with a KOI (in this set). Figure 12 shows the distribution of MES and period of the TCEs. These are primarily low MES events skewed toward short period. Expanding the set of KOIs to include every KOI (no matter what the disposition) shows that 51 of the 280 match a KOI labeled as a false positive or a KOI that has not yet been dispositioned. This leaves a total of 229 TCEs that do not match a KOI on the 3196 targets. Note that some of these new TCE's may actually have been found in previous runs but were excluded from becoming KOIs by the TCERT process. No effort has been made to trim those out since this is a new data set and a fresh look should be taken at them by TCERT. These new TCE's (along with all the other TCEs) will be vetted by TCERT soon for dispositioning. Some of them may become new KOIs. These 229 new TCEs will be briefly analyzed below in Section 4.

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3.1.3. Conclusion of TCE-KOI Comparison

During the DV step, a Levenberg–Marquardt algorithm is employed to search for the best astrophysical model across the parameter space of orbital period, transit duration, impact parameter, ratio of planet radius to host star radius, and the ratio of orbital semimajor axis to the host star radius. The astrophysical models are constructed using the geometric transit model of Mandel and Agol (Mandel & Agol 2002) with limb darkening of Claret (Claret & Bloemen 2011). The S/N of this fit should, in general, be slightly larger than the MES that TPS returns since the ephemeris is more refined, the signal-template mismatch should be lower (due to both barycentric time correction and the use of actual astrophysical models for the target star), and the whitener should not be degrading signal since it is recomputed for in-transit cadences after removing their effect. A fit S/N that is significantly different from the MES could indicate that the TCE was produced by some phenomenon other than a transiting planet. Figure 13 shows how the S/N from the fit compares to the MES for all 20,367 TCEs, 3599 TCEs that match existing KOIs with an ephemeris match of 1, and the 229 new TCEs. Note that the 1059 TCEs that failed to produce valid fits have been excluded and the axes have been restricted to focus on the bulk of the population.

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Using updated KIC parameters (Huber et al. 2014) and the results of the DV fitting process, the planet radius can be determined. Figure 14 shows planet radius versus orbital period for the same groups of TCEs. Clearly visible is the set of spurious long period TCEs as well a set of TCE's with both very large and very small planet radii which are clearly unphysical.

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Assuming perfect redistribution of heat and an albedo of 0.3, the planet equilibrium temperature can be calculated from

$$\begin{eqnarray}&&{{T}_{eq}}={{T}_{*}}{{(1-\alpha )}^{1/4}}\sqrt{\frac{{{R}_{*}}}{2a}},\end{eqnarray} \tag{ 1 }$$

where T_* is the effective temperature of the host star, α is the albedo, R_* is the radius of the host star, and a is the semimajor axis of the planet's orbit. Figure 15 shows a plot of the planet radius versus this equilibrium temperature for the same groups of TCEs.

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Here we report on eight of the new TCEs that have never been found in a prior run, six of which are interesting from the standpoint of habitability (near Earth size, planet effective temperature near Earth's, and fairly significant S/N), and two of which are interesting because they are sub-Earth size. It should be emphasized here that these are merely new TCEs and there is much work to be done on each of these in order for them to be promoted as planetary candidates. The one-page summaries produced by DV are given here but are also available at the NASA Exoplanet Archive, along with their full DV report counterparts that contain much more information about each.

• 1.  
  Figure 16 shows the one-page summary for a new TCE on KIC target 8311864. This TCE has an orbital period of 384.85 days, a planet radius of 1.19 ${{R}_{\oplus }}$, and an equilibrium temperature of 221 K. The bootstrap test measures this object as being significant at nearly the same level as a 7.1σ detection in a standard normal MES distribution (an improved version of the bootstrap shows that this object is even more significant). The true nature of many TCEs however, cannot be determined without some measure of followup observations.
• 2.  
  Figure 17 shows the one-page summary for a new TCE on KIC target 5094751. This TCE has an orbital period of 362.5 days, a planet radius of 1.6 ${{R}_{\oplus }}$, and an equilibrium temperature of 301 K. This is KOI 123 (Kepler-109) which already has 2 confirmed planets.
• 3.  
  Figure 18 shows the one-page summary for a new TCE on KIC target 5531953. This TCE has an orbital period of 21.91 days, a planet radius of 0.78 ${{R}_{\oplus }}$, and an equilibrium temperature of 288 K. This is KOI 1681 which already has 3 dispositioned planet candidates.
• 4.  
  Figure 19 shows the one-page summary for a new TCE on KIC target 8120820. This TCE has an orbital period of 129.22 days, a planet radius of 1.84 ${{R}_{\oplus }}$, and an equilibrium temperature of 290 K.
• 5.  
  Figure 20 shows the one-page summary for a new TCE on KIC target 9674320. This TCE has an orbital period of 317.05 days, a planet radius of 1.66 ${{R}_{\oplus }}$, and an equilibrium temperature of 222 K.
• 6.  
  Figure 21 shows the one-page summary for a new TCE on KIC target 7100673. This TCE has an orbital period of 7.24 days, a planet radius of 0.77 ${{R}_{\oplus }}$, and an equilibrium temperature of 948 K. This is KOI 4032 which already has 4 dispositioned planet candidates, all with periods shorter than this one.
• 7.  
  Figure 22 shows the one-page summary for a new TCE on KIC target 8105398. This TCE has an orbital period of 224.15 days, a planet radius of 1.71 ${{R}_{\oplus }}$, and an equilibrium temperature of 292 K. This is KOI 5475.01, for which a TCE was generated in the previous Q1–Q16 run (Tenenbaum et al. 2014) at twice the orbital period of this TCE. This KOI was dispositioned as a false positive at the longer period due to the presence of a secondary event, but at the period of this TCE, it appears to be consistent with a transiting planet.
• 8.  
  Figure 23 shows the one-page summary for a new TCE on KIC target 8105398. This TCE has an orbital period of 5.68 days, a planet radius of 0.55 ${{R}_{\oplus }}$, and an equilibrium temperature of 994 K. This is the second TCE detected on KOI 5475 and its presence may make the previous detection more likely to be a planet candidate rather than a false positive (Latham et al. 2011; Lissauer et al. 2012).

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