PLANETARY CANDIDATES OBSERVED BY KEPLER. VII. THE FIRST FULLY UNIFORM CATALOG BASED ON THE ENTIRE 48-MONTH DATA SET (Q1–Q17 DR24)

In Figure 1, we plot a histogram of the number of Q1–Q17 DR24 TCEs identified as a function of period (Seader et al. 2015). We also plot the TCE populations from the two previously published searches, which used data from Q1–Q16 (Tenenbaum et al. 2014) and Q1–Q12 (Tenenbaum et al. 2013), processed by previous versions of the Kepler pipeline. Given that the observed period distribution of transiting planets is thought to be relatively flat and smooth in log-space (Howard et al. 2012; Fressin et al. 2013), and that the population of TCEs has varied significantly between successive data releases and pipeline versions, it is clear that all of these TCE catalogs contain a large number of FPs.

Zoom In Zoom Out Reset image size

For Q1–Q17 DR24 and Q1–Q12, there is a particularly large excess at short periods principally due to short-period, quasi-sinusoidal variable stars, e.g., rapid rotators with strong starspots and pulsating stars, as well as eclipsing binary (EB) stars. Spikes seen in this short-period regime are due to contamination from bright variable stars (Coughlin et al. 2014), such as RR Lyrae at 0.567 days (−0.25 in log-space), V2083 Cyg at 0.934 days (−0.03 in log-space), and V380 Cyg at 12.426 days (1.09 in log-space). For Q1–Q12 and Q1–Q16 there is a large spike of excess TCEs at ∼372 days (2.57 in log-space), which is due to quasi-sinusoidal-like red noise produced by "rolling-band" instrumental artifacts (Van Cleve & Caldwell 2009) that repeat at Kepler's orbital period. For Q1–Q16, and to a lesser extent Q1–Q17, there is a broad excess of long-period TCEs at periods ≳200 days. These are due to short-duration systematics (caused by cosmic rays, flares, starspots, stellar pulsation, edge effects around gaps, and similar features) that occur throughout the light curves and produce a TCE when three events happen to be equally spaced in time. In the Q1–Q17 data, a spike at ∼459 days (2.66 in log-space) can be seen, corresponding to TCEs that were generated due to edge effects from three equally spaced data gaps, and thus this ∼459 day systematic is common to many stars across the entire field.

The injection of artificial transits into the pixel-level data is crucial to fully characterize the false negative rate and compute accurate occurrence rates. The completeness (i.e., how often a transiting planet signal is recovered) of the Kepler pipeline has been measured for both individual transit events (Christiansen et al. 2013a) and multiple transit events spanning a year of data (Christiansen et al. 2015). An injection run for the entire Q1–Q17 DR24 data set has been completed and the results are publicly available (Christiansen 2015). We employ these results in quantifying the accuracy of our PC catalog (see Section 5.3).

In the Q1–Q17 DR24 version of the Kepler pipeline, a new veto was added called the "statistical bootstrap test," which adjusts the detection threshold of the pipeline to account for the presence of non-Gaussian noise—see the appendices of Jenkins (2002), Seader et al. (2015), and Jenkins et al. (2015) for details. While this test was successful in eliminating many long-period FPs compared to the previous Q1–Q12 and Q1–Q16 runs (see Figure 1), a subtle flaw introduced excess noise into the statistic. This eliminated a significant number of valid long-period, transit-like signals, especially at low signal-to-noise ratio (S/N), which may have included some previously designated near Earth-size PCs in the habitable zones of their host stars from Rowe et al. (2015) and Mullally et al. (2015a). Results from the Q1–Q17 DR24 transit injection run (Christiansen 2015) also indicate that the bootstrap test introduced a period-dependent, non-uniform planet search, which complicates the computation of planetary occurrence rates. Future Kepler pipeline runs will not employ the bootstrap test as a veto within the transiting planet search (TPS) module, but rather retain a correctly implemented version as a diagnostic metric.

While they are not true false negatives, as they are not transiting planets, we also note that the on-target, contact EB candidates identified by the Kepler Eclipsing Binary Working Group¹⁷ (EBWG; Prša et al. 2011; Slawson et al. 2011; Kirk et al. 2016) were purposely excluded from this transit search, as sinusoidal and quasi-sinusoidal signals are not considered to be transit-like for mission purposes, and significantly increase processing time. There was a total of 1033 targets excluded, which we list in Table 1. "Contact" is defined as having a morphology parameter (Matijevič et al. 2012) greater than 0.6. Detached eclipsing binaries were not excluded as they are sufficiently transit-like to include in this catalog. Stars that were not searched for transits can also be identified by lacking a value for "duty cycle" in the Q1–Q17 DR24 stellar table, which is publicly available at the NASA Exoplanet Archive.

If a TCE under examination is not the first one in a system, then the robovetter checks if there exists a previous TCE with a similar period that was designated as an FP due to a significant secondary (see Section 3.3). To compute whether two TCEs have the same period within a given statistical threshold, we employ the period matching criteria of Coughlin et al. (2014, see Equations (1)–(3)), σ_P, where higher values of σ_P indicate more significant period matches. Here, we re-state the equations as

$$\begin{eqnarray}&&{\rm{\Delta }}P=\displaystyle \frac{{P}_{A}-{P}_{B}}{{P}_{A}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{P}^{\prime }=\mathrm{abs}({\rm{\Delta }}P-\mathrm{rint}({\rm{\Delta }}P)),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\sigma }_{P}=\sqrt{2}\cdot \mathrm{erfcinv}({\rm{\Delta }}P^{\prime} ),\end{eqnarray} \tag{ 3 }$$

where P_A is the period of the shorter-period TCE, P_B is the period of the longer-period TCE, rint() rounds a number to the nearest integer, abs() yields the absolute value, and erfcinv() is the inverse complementary error function. We consider any value of σ_P > 3.25 to indicate significantly similar periods.

If the current TCE is (1) in a system that has a previous TCE dispositioned as an FP due to a significant secondary, (2) matches the previous TCE's period with σ_P > 3.25, and (3) is separated in phase from the previous TCE by at least 2.5 times the transit duration, then the current TCE is considered to be a secondary eclipse. In this case, it is designated as an FP and is classified into both the not transit-like and significant secondary FP categories—a unique combination that can be used to identify secondary eclipses while still ensuring that they are not assigned Kepler Object of Interest (KOI) numbers (see Section 4.2). Note that since the Kepler pipeline identifies TCEs in order of their S/N, from high to low, a TCE identified as a secondary can sometimes have a deeper depth than the primary, depending on their relative durations and shapes.

There are two cases where we modify the three criteria above. First, it is possible that the periods of two TCEs will meet the period matching criteria, but be different enough to have their relative phases shift significantly over the ∼4 year mission duration. Thus, the potential secondary TCE is actually required to be separated in phase by at least 2.5 times the previous TCE's transit duration over the entire mission time frame in order to be labeled as a secondary. Second, the Kepler pipeline will occasionally detect the secondary eclipse of an EB at a half, third, or some smaller integer fraction of the orbital period of the system, such that the epoch of the detected secondary coincides with that of the primary. Thus, for the non-1:1 period ratio cases, we do not impose the phase separation requirement. (Note that Equations (1)–(3) allow for integer period ratios.)

A very large fraction of FP TCEs have light curves that do not resemble a detached transiting or eclipsing object. These include quasi-sinusoidal light curves from pulsating stars, starspots, and contact binaries, as well as more sporadic light curves due to instrumental artifacts. In previous PC catalogs, a process called "triage" was employed whereby the human vetters looked at the phased light curves to determine whether the TCEs were not transit-like or should be given KOI numbers, which are used to keep track of transit-like systems over multiple Kepler pipeline runs. We thus employ a series of algorithmic tests to reliably identify these not transit-like FP TCEs, as shown by the flowchart in Figure 3.

Zoom In Zoom Out Reset image size

3.2.1. Not Transit-shaped

The human members of TCERT were given training and diagnostic plots that allowed them to quickly distinguish between a quasi-sinusoidal shaped light curve and one that is more detached due to a transit or eclipse. Also, they were trained to recognize if an individual event is due to a transit or a systematic feature, such as a sudden discontinuity in the light curve. As such, we sought metrics for the robovetter that would similarly detect quasi-sinusoidal light curves and systematics.

3.2.1.1. The LPP Metric

Many short-period FPs are due to variable stars that exhibit a quasi-sinusoidal phased light curve. Matijevič et al. (2012) used a technique known as Local Linear Embedding (LLE), a dimensionality reduction algorithm, to classify the "detachedness" of Kepler EB light curves on a scale of 0–1, where 0 represented fully detached systems with well-separated, narrow eclipses and 1 represented contact binaries with completely sinusoidal light curves. We use a similar technique, known as Local Preserving Projections (LPP; He & Niyogi 2004), to distinguish transit-like signals from not transit-like signals (Thompson et al. 2015b). LPP returns a single number that represents the similarity of a TCE's shape to that of known transits. Unlike LLE, LPP can be applied to any TCE, not just those that lie within the parameter space of the training set. Thus, LPP is more suitable for separating transit-like TCEs from all of the other not transit-like TCEs, and can be run on artificially injected transits.

To calculate the LPP metric, we start with detrended Kepler light curves. We then fold and bin each light curve into 141 points, ensuring adequate coverage of both the in- and out-of-transit portions of the light curve. We exclude points near a phase of 0.5, as the presence of a secondary eclipse in a short-period binary may unduly influence the LPP value, and we seek to classify detached eclipsing binaries as transit-like. These 141 points act as the initial number of dimensions that describe each TCE. Using a subset of known transit-like TCEs, we create a map from the initial 141 dimensions down to 20 dimensions. We apply this map to all TCEs and measure the average Euclidean distance of each to the 15 nearest known transit-like TCEs. This average distance is the value of the LPP metric. When small, it means other transit-like TCEs are nearby in the 20-dimensional space, and thus it is likely to be shaped like a transit. We calculate this LPP transit metric for all TCEs using both the DV and the alternate detrending, as described in Section 3.2.

In order to quantitatively determine a threshold between transit-like and not transit-like, we run the LPP classifier on both detrendings of the injected transits (see Section 5.3), which we know a priori are all transit-shaped, barring any light-curve distortion due to detrending. We then fit a Gaussian to the resulting distribution, computing its median and standard deviation. We then select a maximum LPP cutoff such that we expect less than one false negative in 20,367 TCEs, via

$$\begin{eqnarray}&&{\sigma }_{{\rm{LPP}}}=\sqrt{2}\cdot \mathrm{erfcinv}(1/{N}_{{\rm{TCEs}}}),\end{eqnarray} \tag{ 4 }$$

where N_TCEs = 20,367, yielding σ_LPP = 4.06. Any TCE with an LPP value greater than the median plus 4.06 times the standard deviation, using either detrending, is considered to be not transit-like.

3.2.1.2. The Marshall Metric

A number of long-period FPs are the result of three or more systematic events that happen to be equidistant in time and produce a TCE. There are two prominent types of systematic events in Kepler data: sudden pixel sensitivity dropouots (SPSDs) and step-wise discontinuities. SPSDs are due to cosmic-ray impacts that temporarily reduce the detection sensitivity of the impacted pixels, resulting in a sudden drop in flux followed by an asymptotic rise back to the baseline flux level over a timescale of a few hours (Van Cleve & Caldwell 2009). Step-wise discontinuities are sudden jumps in the baseline flux level, in either the positive or negative flux direction, and are typically due to imperfect detrending, but may have other causes. If a TCE is due to several of these events that are of similar S/N, then they will not be flagged as FPs without examining the shape of their individual events.

In order to detect TCEs due to SPSDs and step-wise discontinuities, we developed the "Marshall" metric (Mullally et al. 2015b). Marshall fits a transit, SPSD, and step-wise discontinuity model to each individual event of a long-period TCE. The Bayesian Information Criterion (BIC; Schwarz 1978) is then used to select which model best fits each individual transit event given each model's number of degrees of freedom. If either the SPSD or step-wise discontinuity model have a lower BIC value than the transit model by a value of 10 or more for a given transit event, then that event is determined to be due to a systematic rather than a transit. After evaluating each individual event, if there are fewer than three events that are determined to be due to transits, then the TCE is dispositioned as a not transit-like FP. This is in agreement with the Kepler mission requirement of detecting at least three valid transits in order to generate a TCE.

3.2.2. Previous TCE With Same Period

3.2.3. The Model-shift Uniqueness Test

If a TCE under investigation is truly a PC, then there should not be any other transit-like events in the light curve with a depth, duration, and period similar to the primary signal, in either the positive or negative flux directions, i.e., the transit event should be unique in the phased light curve. Many FPs are due to quasi-sinusoidal signals (see Section 2), and thus are not unique in the phased light curve. In order to identify these cases, TCERT developed a "model-shift uniqueness test" and used it extensively for identifying FPs in both the Q1–Q12 (Rowe et al. 2015) and Q1–Q16 (Mullally et al. 2015a) PC catalogs.

See Section 3.2.2 of Rowe et al. (2015) and page 20 of Coughlin (2014) for figures and a detailed explanation of the "model-shift uniqueness test;" in brief, after removing outliers, the best-fit model of the primary transit is used as a template to measure the best-fit depth of the transit model at all other phases. The deepest event aside from the primary (pri) transit event is labeled as the secondary (sec) event, the next-deepest event is labeled as the tertiary (ter) event, and the most positive (pos) flux event (i.e., shows a flux brightening) is labeled as the positive event. The significances of these events (σ_Pri, σ_Sec, σ_Ter, and σ_Pos) are computed assuming white noise as determined by the standard deviation of the light-curve residuals. Also, the ratio of the red noise (at the timescale of the transit duration) to the white noise (F_Red) is computed by examining the standard deviation of the best-fit depths at phases outside of the primary and secondary events. When examining all of the events among all of the TCEs, the minimum threshold for an event to be considered statistically significant is given by

$$\begin{eqnarray}&&{\sigma }_{{\rm{FA}}}=\sqrt{2}\cdot \mathrm{erfcinv}\left(\displaystyle \frac{{T}_{{\rm{dur}}}}{P\cdot {N}_{{\rm{TCEs}}}}\right),\end{eqnarray} \tag{ 5 }$$

where T_dur is the transit duration and P is the period. (The quantity P/T_dur represents the number of independent statistical tests for a single target.) When comparing two events from the same TCE, the minimum difference in their significances in order to be considered distinctly different is given by

$$\begin{eqnarray}&&{\sigma }_{{\rm{FA}}}^{\prime }=\sqrt{2}\cdot \mathrm{erfcinv}\left(\displaystyle \frac{{T}_{{\rm{dur}}}}{P}\right).\end{eqnarray} \tag{ 6 }$$

In the robovetter, we disposition a TCE as a not transit-like FP if ${\sigma }_{{\rm{Pri}}}/{F}_{{\rm{Red}}}\lt {\sigma }_{{\rm{FA}}}$, ${\sigma }_{{\rm{Pri}}}-{\sigma }_{{\rm{Ter}}}\lt {\sigma }_{{\rm{FA}}}^{\prime }$, or ${\sigma }_{{\rm{Pri}}}-{\sigma }_{{\rm{Pos}}}\lt {\sigma }_{{\rm{FA}}}^{\prime }$ for either the DV or alternate detrending. 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.

3.2.4. Dominated by Single Event

The depths of individual transits of PCs should be equal to each other, and thus, assuming constant noise levels, the S/Ns of individual transits should be nearly equivalent as well. In contrast, most of the long-period FPs that result from three or more equidistant systematic events are dominated in S/N by one of those events. The Kepler pipeline measures detection significance via the Multiple Event Statistic (MES), which is calculated by combining the Single Event Statistic (SES) of all of the individual events that comprise the TCE—both the MES and SES are measures of S/N. Assuming that all of the individual events have equal SES values,

$$\begin{eqnarray}&&{\rm{MES}}=\sqrt{{N}_{{\rm{Trans}}}}\cdot {\rm{SES}},\end{eqnarray} \tag{ 7 }$$

where N_Trans is the number of transit events that comprise the TCE. Thus, SES/MES = 0.577 for a TCE with three transits, and less for a greater number of transits. If the largest SES value of a TCE's transit events, SES_Max, divided by the MES is much larger than 0.577, then this indicates that one of the individual events dominates when calculating the S/N.

In the robovetter, for TCEs with periods greater than 90 days, if SES_Max/MES > 0.9, then it is dispositioned as a not transit-like FP. The value of 0.9 was empirically chosen based on the results of transit injection (Section 5.3) to reject a minimal number of valid planetary candidates, accounting for natural deviations of SES values due to light-curve systematics and changes in local noise levels. The period cutoff of 90 days is applied because short-period TCEs can have a large number of individual transit events, which dramatically increases the chance of one event coinciding with a large systematic feature, thus producing a large SES_Max/MES value despite being a valid planetary signal.

If a TCE is deemed to be transit-like by passing all of the tests presented in Section 3.2 on both detrendings, then it is given a KOI number. However, many of these KOIs are FPs due to eclipsing binaries and contamination from nearby variable stars. In order to produce a uniform catalog, we do not designate any TCE as an FP on the basis of its transit depth or inferred radius—see Section 7 item 6 of Mullally et al. (2015a) for more detail. Thus, being agnostic to stellar parameters, the only way to definitively detect an EB via a Kepler light curve is by detecting a significant secondary eclipse. We employ a series of robotic tests to detect secondary eclipses, as shown by the flowchart in Figure 4.

Zoom In Zoom Out Reset image size

3.3.1. Subsequent TCE With Same Period

3.3.2. Secondary Detected in Light Curve

3.3.3. Odd/Even Depth Difference

If the primary and secondary eclipses of an EB are similar in depth, and the secondary is located near phase 0.5, then the Kepler pipeline may detect them as a single TCE at half the true orbital period of the EB. In these cases, if the primary and secondary depths are dissimilar enough, then it is possible to detect it as an FP by comparing the depths of the odd- and even-numbered transit events. Thus, we compute the following statistic, for both the DV and alternate detrending,

$$\begin{eqnarray}&&{\sigma }_{{\rm{OE}}}=\displaystyle \frac{{d}_{{\rm{odd}}}-{d}_{{\rm{even}}}}{\sqrt{{\sigma }_{\mathrm{odd}}^{2}+{\sigma }_{\mathrm{even}}^{2}}},\end{eqnarray} \tag{ 8 }$$

where d_odd is the median depth of the odd-numbered transits, d_even is the median depth of the even-numbered transits, σ_odd is the standard deviation of the depths of the odd-numbered transits, and σ_even is the standard deviation of the depths of the even-numbered transits. For the alternate detrending with a trapezoidal fit, we use all of the points that lie within ±30 minutes of the central time of transit, as well as any other points within the in-transit flat portion of the trapezoidal fit. For the DV detrending, we use all of the points within ±30 minutes of the central time of transit. (This threshold corresponds to the long-cadence integration time of the Kepler spacecraft. Including points farther away from the central time of transit degrades the accuracy and precision of the test.) If σ_OE > 1.7 for either the DV or alternate detrending, then the TCE is labeled as an FP due to a significant secondary. The value of 1.7 was empirically derived utilizing manual checks and transit injection.

Given that Kepler's pixels are 398 square (Koch et al. 2010) and the typical photometric aperture has a radius of 4–7 pixels (Bryson et al. 2010), it is quite common for a given target star to be contaminated by light from another star. If that other star is variable, then that variability will be visible in the target aperture at a reduced amplitude. If the variability due to contamination results in a TCE, then it is an FP, whether the contaminator is an EB, planet, or other type of variable star (Bryson et al. 2013). For example, if a transit or an eclipse occurs on a bright star, then a shallower event will be observed on a nearby, fainter star. Similarly, a star can be mistakenly identified as experiencing a shallow transit if a deep eclipse occurs on a fainter, nearby source.

The DV module of the Kepler pipeline produces "difference images" for each quarter, which are made by subtracting the average flux in each pixel during each transit from the flux in each pixel just before and after each transit (Bryson et al. 2013). If the resulting difference image shows significant flux change at a location (centroid) other than the target, then the TCE is likely an FP due to a centroid offset. In prior catalogs, TCERT members manually examined the difference images to look for evidence of a centroid offset, as fully described in Bryson et al. (2013) and Sections 3.2.3–3.2.6 of Rowe et al. (2015). In this catalog, the search for centroid offsets was fully robotized and confirmed to reproduce the results of earlier catalogs using human vetting (F. Mullally et al. 2016, in preparation).

In our robotic procedure to detect FPs due to centroid offsets, we first check that the difference image for each quarter contains a discernible stellar image and is not dominated by background noise. This is done by searching for at least three pixels that are adjacent to each other and brighter than a given threshold, which is set by the noise properties of the image. We use an iterative σ clipping approach to eliminate bright pixels when calculating the background noise, as the star often dominates the flux budget of a substantial number of pixels in the aperture.

For those difference images which are determined to contain a discernible stellar image, we first search for evidence of contamination from sources that are resolved from the target. Since resolved sources near the edge of the image may not be fully captured, Pixel Response Function (PRF—Kepler's point-spread function convolved with the image motion and the intra-pixel CCD sensitivity) fitting approaches do not often work well to detect them. Instead, we check if the location of the brightest pixel in the difference image is more than 1.5 pixels from the location of the target star. If at least two-thirds of the quarterly difference images show evidence of an offset by this criterion, we disposition the TCE as an FP due to a centroid offset. Note that FPs due to stars located many pixels from the target, i.e., far outside the target's image, are not detected by this approach, but rather through ephemeris matching (see Section 3.5).

If no centroid offset is identified by the previous method, we then look for contamination from sources that are unresolved from the target. We measure the PRF-fit centroid of the difference images and search for statistically significant shifts with respect to the PRF centroid of both the out-of-transit images as well as the catalog position of the source. Following Bryson et al. (2013), a TCE is marked as an FP due to a centroid offset if there is a 3σ significant offset larger than 2'', or a 4σ offset larger than 1''. F. Mullally et al. (2016, in preparation) show that when simulated transits are injected at the catalog positions of Kepler stars, these robotic methods result in <1% of valid PCs being marked incorrectly as FPs.

Note that if there are less than three difference images with a discernible stellar image, then no tests are performed and the TCE is not declared an FP by the centroid module.

Another method for detecting FPs due to contamination is to compare the ephemerides (periods and epochs) of TCEs to each other, as well as to other known variable sources in the Kepler field. If two targets have the same ephemeris within a specified tolerance, then at least one of them is an FP due to contamination. Coughlin et al. (2014) used Q1–Q12 data to compare the ephemerides of KOIs to each other and eclipsing binaries known from both Kepler- and ground-based observations. They identified over 600 FPs via ephemeris matching, of which over 100 were not known as FPs via other methods. They also identified four main mechanisms of contamination. The results of Coughlin et al. (2014) were incorporated in Rowe et al. (2015, see Section 3.3). Mullally et al. (2015b, see Section 5.3) slightly modified the ephemeris matching process of Coughlin et al. (2014) and applied it to all of the Q1–Q16 TCEs, as well as to known KOIs and EBs, identifying nearly 1000 TCEs as FPs.

In this Q1–Q17 DR24 catalog, we use the same method as Coughlin et al. (2014), with the modifications of Mullally et al. (2015b, see Section 5.3), to match the ephemerides of all Q1–Q17 DR24 TCEs (Seader et al. 2015) to the following sources.

• •  
  Themselves.
• •  
  The list of 7348 KOIs from the NASA Exoplanet Archive cumulative KOI table after the closure of the Q1–Q16 table and publication of the last catalog (Mullally et al. 2015a).
• •  
  The Kepler EBWG of 2605 true EBs found with Kepler data as of 2015 March 11 (Prša et al. 2011; Slawson et al. 2011; Kirk et al. 2016).
• •  
  J.M. Kreiner's up-to-date database of ephemerides of ground-based eclipsing binaries as of 2015 March 11 (Kreiner 2004).
• •  
  Ground-based eclipsing binaries found via the TrES survey (Devor et al. 2008).
• •  
  The General Catalog of Variable Stars (GCVS Samus et al. 2009) list of all known ground-based variable stars, published 2015 February 06.

Through ephemeris matching, we identify 1910 Q1–Q17 DR24 TCEs as FPs. Of these, 189 were identified as FPs only due to ephemeris matching. We list all 1910 TCEs in Table 2, as this information is valuable for studying contamination in the Kepler field. (Note that each TCE identified consists of its KIC ID and planet number, separated by a dash.) We also list in Table 2 each TCE's most likely parent, the period ratio between child and parent (P_rat), the distance between the child and parent in arcseconds, the offset in row and column between the child and parent in pixels (ΔRow and ΔCol), the magnitude of the parent (m_Kep), the difference in magnitude between the child and parent (ΔMag), the depth ratio of the child and parent (D_rat), the mechanism of contamination, and a flag to designate unique situations. In Figure 5, we plot the location of each FP TCE and its most likely parent, connected by a solid line. TCEs are represented by solid black points, KOIs are represented by solid green points, EBs found by Kepler are represented by solid red points, EBs discovered from the ground are represented by solid blue points, and TCEs due to a common systematic are represented by open black points. The Kepler magnitude of each star is shown via a scaled point size. Note that most parent-child pairs are so close together that the line connecting them is not easily visible on the scale of the plot.

Zoom In Zoom Out Reset image size

The larger number of matches compared to the Q1–Q12 and Q1–Q16 catalogs is predominately the result of a much larger short-period FP population compared to Q1–Q16, and an extended baseline compared to Q1–Q12, coupled with matching all TCEs and not just KOIs. In Q1–Q17 DR24, we identify an additional contamination mechanism, which we label "Common Systematic." As mentioned in Section 2, these are over 200 TCEs that are caused by 3 systematic events that are common to all Kepler CCDs and happen to be equidistant in time with a spacing of ∼459 days.

We also identify 119 examples of "Column Anomaly," which is a previously identified mechanism where a parent is able to contaminate a child at large distances if they both lie on the same column of a CCD. This mechanism is particularly pernicious because it does not result in a visible centroid offset; the apparent location of the transit signal via the difference images coincides with the target. If the parent is not observed by Kepler, then the child could go undetected as an FP due to the column anomaly, as was recently the case for KOI 6705.01 (Gaidos et al. 2016). The large number of examples of column anomaly now available in the Q1–Q17 DR24 catalog reveals the following.

• •  
  Despite equally searching for matches in row and column, no instance of "row-anomaly" has been found to occur.
• •  
  The CCDs are read out in the column direction.
• •  
  In 91.6% of cases, the child is at a higher row number than the parent, and thus the parent's pixels are read out before the child's. (The remaining 8.4% of cases may not have the true parent identified, but rather a sibling, as only the most likely parent is listed, and many parents are unobserved by the spacecraft.)
• •  
  Most cases show that the depth of the child increases over time.
• •  
  The effect appears to exhibit seasonal depth variations in most cases.
• •  
  The average depth ratio between parent and child is a factor of ∼10⁴, and typically the parent and child have similar magnitudes.

Combining these details leads to our conjecture that the column anomaly is due to decreasing charge transfer efficiency over time, likely due to cosmic-ray impacts. When the CCD is read out, some charge from the parent is left behind due to charge transfer inefficiency. As the child is read out and its electrons pass through the pixels where the parent was, the child picks up some of the parent's left-behind electrons. Thus, the variable signal from the parent is induced in the child. As more cosmic-ray impacts accumulate over time, the amount of charge left behind by the parent increases, resulting in an increase in contamination, and thus an increase in the observed depth of the child. Seasonal variation is seen as the parent and child rotate between four CCDs with season, and the amount of degradation varies with CCD. The average depth ratio, along with the delta magnitudes observed, indicate that a charge transfer efficiency of ∼99.99% is consistent with the observed contamination, i.e., a degradation of ∼0.01%. This is well within the range observed on Hubble's Advanced Camera for Surveys and other space-based detectors (see Section 3.7 of Sirianni et al. 2005 and references therein).

In Table 3, we list each of the 20,367 Q1–Q17 DR24 TCEs and all of the parameters that were used by the robovetter. These include the following:

• •  
  the period of the TCE in days, epoch in Barycentric Kepler Julian Date (BKJD), and duration of the transit in hours, all from the DV module of the Kepler pipeline;
• •  
  the MES, and maximum SES value used in determining the MES, from the Kepler pipeline;
• •  
  the LPP value using the DV detrending (LPP_DV) and the alternate detrending (LPP_Alt);
• •  
  the value of the Marshall metric;
• •  
  the odd/even depth statistic (σ_OE) for both the DV and alternate detrendings;
• •  
  the metrics produced from the model-shift uniqueness test (see Section 3.2.3) for both the DV and alternate detrending;
• •  
  the radius of the planet in R_⊕, calculated by multiplying the radius ratio from the DV module of the Kepler pipeline and the stellar radius value from Huber et al. (2014);
• •  
  the albedo (A), primary depth (D_pri), secondary depth (D_sec), and secondary's phase (Ph_sec) for the DV and alternate detrendings (see Section 3.3.2);
• •  
  the disposition value from the centroid module (a value of 1 indicates that a significant centroid offset was detected, while a value of 0 indicates no offset).

Table 3.  The Robovetter Input Parameters for the 20,367 Q1–Q17 DR24 TCEs

TCE	Period	Epoch	Duration	SESMax	MES	LPPDV	LPPAlt	Marshall	${\sigma }_{{\rm{OE,DV}}}$
	(Days)	(BKJD)	(hr)
000757450-01	8.884923	134.452041	2.078	1.130e+02	5.240e+02	2.370e–04	4.100e–05	0.000e+00	0.000e+00
000892667-01	2.262112	132.171131	7.509	3.890e+00	8.037e+00	4.608e–03	1.884e–03	0.000e+00	6.794e–02
000892772-01	5.092598	133.451376	3.399	3.810e+00	1.562e+01	1.337e–03	1.081e–03	0.000e+00	1.692e–01
001026032-01	8.460442	133.774329	4.804	4.957e+02	3.889e+03	4.660e–04	8.300e–05	0.000e+00	1.244e–01
001026032-02	4.230222	133.998093	4.606	1.704e+02	1.440e+03	3.030e–04	3.900e–05	0.000e+00	0.000e+00
001026133-01	1.346292	132.841605	1.626	4.530e+00	1.051e+01	3.540e–03	6.126e–03	0.000e+00	6.815e–02
001026133-02	2.691910	132.267127	5.530	3.320e+00	1.135e+01	4.856e–03	7.933e–03	0.000e+00	6.316e–02
001026957-01	21.761298	144.779125	1.277	2.383e+01	1.034e+02	2.570e–04	1.230e–04	0.000e+00	1.615e–01
001028018-01	0.614378	131.652061	1.448	6.850e+00	1.281e+01	6.614e–03	6.647e–03	0.000e+00	8.698e–04
001160891-01	0.940463	132.400156	3.354	4.010e+00	1.203e+01	7.627e–03	2.202e–03	0.000e+00	7.456e–03

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.

Download table as:  DataTypeset image

Transit-like signals found over the course of the Kepler mission are given KOI numbers in order to facilitate the tracking of these objects over multiple runs of the Kepler pipeline. Using the same procedure as in Mullally et al. (2015a, see Section 4.1), which examines the number of overlapping in-transit cadences between two ephemerides, we federate 5992 Q1–Q17 DR24 TCEs to existing KOIs.

Given that there were 7348 KOIs known prior to the Q1–Q17 DR24 pipeline run, this indicates, at first glance, a 81.5% KOI recoverability rate. Unrecovered KOIs can be planets in systems with large TTVs, or transit-like systems in regions of parameter space that are affected by Kepler pipeline changes (see Section 2). However, some unrecovered KOIs could have been dispositioned as not transit-like FPs after being promoted to KOI status in previous catalogs, and thus are rightfully not recovered by the pipeline due to additional data and improvements in the data processing and detection algorithms. (As a rule, once a KOI number is designated, it is never removed from the catalog.) Thus, given that there were 6491 transit-like KOIs known prior to the Q1–Q17 DR24 pipeline run, of which 5854 federated, this indicates a 90.2% transit-like KOI recoverability rate.

With respect to the Q1–Q17 DR24 the robovetter, we assign new KOI numbers to nearly all of the transit-like TCEs (i.e., those that were not designated not transit-like) that did not federate with previously known KOIs. New KOIs on stars that had previously associated KOIs were given the same base KOI number with the next-highest unused planet number. New KOIs on stars that did not have any previously associated KOIs were given numbers of 6252.01 and higher. The only TCEs deemed to be transit-like by the robovetter that did not receive KOI numbers were the 25 systems listed in Table 4. These systems were so complicated or unusual (e.g., extreme TTV systems, circumbinary planets, seasonally dependent contamination, severe detrending issues) that the resulting TCEs did not accurately correspond to the underlying transit-like signal. In total, we created 1478 new KOIs, thus extending the total number of KOIs from all of the KOI catalogs to 8826. Note that while developing the robovetter, some KOI numbers were assigned to TCEs that were initially dispositioned as transit-like but, due to code changes, were later dispositioned as not transit-like, and thus there are some new KOIs in this catalog that are dispositioned as not transit-like FPs.

In Table 5, we list all 20,367 TCEs, their assigned KOI numbers (if transit-like), their the robovetter dispositions (PC or FP), the values of the four major flags (as described in Section 3), and a comment field that has mnemonic flags that describe the result of each individual the robovetter test. Detailed descriptions for each mnemonic flag are located in Appendix B. Note that every FP will have at least one major flag set, and could have any combination of all four. When both the not transit-like and significant secondary flags are set, it indicates that the TCE corresponds to the secondary eclipse of a system (e.g., TCE 001026032-02 in Table 5). While we do not assign new KOI numbers to TCEs that are dispositioned as secondary eclipses in this catalog, there are pre-existing KOIs that federate with Q1–Q17 DR24 TCEs dispositioned as secondary eclipses. PCs will not have any major flags set, unless the system is a hot Jupiter with a visible secondary eclipse due to planetary reflection and/or thermal emission, in which case the significant secondary flag will be set. This information is also publicly available at the NASA Exoplanet Archive in the Q1–Q17 DR24 KOI table.

In order to obtain transit-model fits with robust uncertainties, we model every KOI in the same manner as described in Rowe et al. (2015, see Section 5) and Mullally et al. (2015b, see Section 6.2). To summarize briefly, we fit all of the available PDC data from DR24 at MAST after detrending via a polynomial filter as described in Section 4 of Rowe et al. (2014). We use the transit model of Seager & Mallén-Ornelas (2003), assuming a circular orbit, with the quadratic limb-darkening law of Claret & Bloemen (2011), calculated for the Kepler passband. Uncertainties are calculated using a Markov Chain Monte Carlo (MCMC; Ford 2005) method with four chains of 10⁵ fits each, discarding the first 20% of each chain, to construct the posterior distributions. The transit-model fit parameters are then combined with the stellar parameters to produce planetary parameters. The MCMC chains are publicly available and documented in Rowe & Thompson (2015).

KOIs that existed prior to Q1–Q17 DR24 were not re-fit in this work, and thus use stellar values from the Q1–Q16 stellar catalog (Huber et al. 2014) and contain values for their fit parameters identical to those given in Mullally et al. (2015a). Newly designated KOIs are fit using the DR24 light curves and use stellar values from the updated Q1–Q17 DR24 stellar catalog (Huber 2014). The best-fit value and 1σ uncertainties of each parameter are listed at the NASA Exoplanet Archive, along with the MCMC chains themselves. Note that not all KOIs could be modeled, which typically occurs when the polynomial filter (a separate detrending used specifically for the MCMC fitting) does not recover the transit events with sufficient S/N. These cases are designated in the KOI catalog by a value of "none" for the "fittype" parameter, and only the period, epoch, and duration of the federated TCE are reported.

Of the 5854 transit-like KOIs that existed prior to the Q1–Q17 DR24 activity and were detected as TCEs by the Q1–Q17 DR24 Kepler pipeline, 5700 were dispositioned by the robovetter as transit-like, yielding a 97.4% transit-like KOI recoverability rate for the robovetter. Similarly, of the 3772 pre-existing PCs that were re-detected, 3654 were dispositioned as PCs, yielding a 96.9% PC the robovetter recoverability rate. Finally, of the 2220 pre-existing FPs that were re-detected, 1983 were dispositioned by the robovetter as FPs, yielding a 89.3% FP the robovetter recoverability rate.

Compared to past catalogs, the dispositions of 118 KOIs changed from PC to FP, and 237 went from FP to PC. Examining these KOIs, we note that many changed dispositions due to the robovetter out-performing the human vetters. For example, the robovetter reliably detects very small secondary eclipses that the humans tended to miss. Also, the robovetter does not declare FPs based on transit depth alone, which was a directive given to the human vetters, but not followed by all of the vetters. Thus, the Q1–Q17 DR24 catalog contains more PCs with very deep depths compared to previous catalogs. We also note that the Q1–Q6 and Q1–Q8 catalogs were not solely based on the TCE list from the Kepler pipeline, and included KOIs found by other transit search techniques as well as manual light curve inspection.

5.2.1. The Eclipsing Binary Working Group Catalog

5.2.2. The False Positive Working Group Catalog

5.2.3. The Kepler Autovetter

5.2.4. Planet Hunters

5.2.5. Confirmed Planets

The primary method of measuring the efficiency of a transit detection pipeline is to inject artificial transit signals into the calibrated pixel-level data, with a range of parameters, and determine what fraction are detected as a function of those parameters. For the Kepler pipeline, Christiansen et al. (2013a) measured the detection efficiency of individual transit events, finding that they were generally recovered to a high fidelity of ∼99.7%. Christiansen et al. (2015) then extended this work by injecting full time-series transit signals into a year of Kepler data, and were able to map out the actual Kepler pipeline recoverability rate as a function of MES, which is crucial for accurately determining planet occurrence rates (Burke et al. 2015).

In Q1–Q17 DR24, artificial transits were injected into the entire Kepler data set at the pixel level, one injected transiting planet signal per star, with periods between 0.5 and 500 days and planetary radii between 0.25 and 20 R_⊕ (Christiansen 2015). A small fraction of these were purposely injected up to ∼10'' away from the target star in order to simulate FPs due to a centroid offset. The exact same version of the Kepler pipeline that produced the Q1–Q17 DR24 TCEs was used to search this injected data set. In total, there were 42,264 injected signals detected by the Kepler pipeline, which we refer to as "injTCEs."

We disposition the injTCEs with the exact same version of the robovetter that was used to disposition the Q1–Q17 DR24 TCEs (Coughlin 2015b). In Table 6, we list each injTCE via its KIC number, along with the resulting the robovetter disposition, major flags, and all injected and recovered parameters. In Figure 6, we plot the fraction of on-target injTCEs that were labeled as PCs by the robovetter (the PC recovery fraction) as functions of their MES, period, planetary radius, planetary insolation flux, stellar radius, and stellar temperature.

Zoom In Zoom Out Reset image size

The robovetter dispositioned 34,210 of the 35,917 injTCEs without centroid offsets as PCs, yielding a 95.25% pass rate. Examining Figure 6, specifically the top left panel, it can be seen that the PC recovery fraction increases with increasing MES. (Note that the Kepler pipeline has a minimum detection threshold of 7.1 MES, and very few transit signals were injected with MES greater than 100.) While very low MES detections pass ∼90% of the time, the highest MES detections pass ∼98% of the time, as the vetting metrics become more reliable at higher MES values. Examining the top right panel, the PC recovery fraction increases with decreasing period. (Note that no signals were injected with periods greater than 500 days.) These two trends can also be seen in the middle left panel where the PC recovery fraction is shown as a function of both period and MES, and in the middle right panel where the PC recovery fraction is shown as a function of planet radius and period. The bottom left panel indicates that planets around higher-temperature and more evolved stars, particularly the instability strip at ∼7500 K, may also have decreased PC recovery fractions compared to cooler, main-sequence stars, likely due to increased systematic noise from stellar pulsation that is not fully corrected by either of the two detrendings employed by TCERT.

Finally, we examine the PC recovery fraction of on-target injTCEs with radius (R_p) and insolation flux (S_p) values within 25% of that of Earth's values (0.75 > R_p > 1.25 R_⊕ and 0.75 > S_p > 1.25 S_⊕). There are 118 on-target injTCEs that meet these R_p and S_p criteria, of which 116 are designated as PCs by the robovetter, therefore yielding a 98.3% PC recovery fraction. This can be seen graphically in the bottom right panel of Figure 6, where the area around Earth's values (1.0 R_⊕, 1.0 S_⊕) shows a very high PC recovery fraction. If we add the additional constraint that the host star's effective temperature (T_⋆) is within 500 K of the Sun's (5300 < T_⋆ < 6300 K), in addition to the previous radius and insolation flux constraints, then the TCERT detection efficiency is 96.1%, as 49 of 51 on-target injTCEs that meet these criteria are designated as PCs.

Note that one could make a the robovetter with a 100% detection efficiency by simply passing every TCE as a PC—however, this would be a very poor the robovetter, as it would not identify any FPs! We have specifically designed the robovetter to identify as many FPs as possible while still correctly identifying at least ∼95% of true planetary signals. This means that correcting for the robovetter's detection efficiency will only affect derived occurrence rates at the ∼5% level for the entire population, which is small compared to other systematic effects that influence the determination of planetary occurrence rates (see Figure 10 of Burke et al. 2015). We note that specific regions of interest may have higher or lower detection efficiencies.

At present (i.e., for DR24), we do not have a complete measure of how many true, underlying FPs that the robovetter dispositions as PCs. This injection-only run included signals purposely injected off-target to simulate FPs due to centroid offsets, and found a ∼50% detection rate at a separation of 2'' (0.5 pixels) when recovered with an MES of 20 (F. Mullally et al. 2016, in preparation). To assess other types of FPs, we recommend (1) injecting EB signals to simulate FPs due to significant secondaries, (2) inverting the light curve and performing a transit search to simulate the population of not transit-like FPs, operating under the general observation that most not transit-like FPs tend to be symmetrical, and (3) shuffling the Kepler data by season and performing a transit search to simulate long-period FPs. Such activities are likely vital to fully evaluate the FP rate of the Kepler pipeline and the robovetter, and thus determine accurate occurrence rates, especially for those with radii and insolation fluxes comparable to the Earth.

In the Q1–Q17 DR24 catalog, there are a total of 4293 PCs in 3355 systems. Of these systems, 636 contain 2 or more PCs, with a total of 1632 PCs in multi-PC systems. Compared to past catalogs, looking at systems that increased in PC count, we find the following:

• •  
  47 systems went from 1 $\to$ 2 PCs;
• •  
  1 system went from 1 $\to$ 3 PCs;
• •  
  9 systems went from 2 $\to$ 3 PCs;
• •  
  4 systems went from 3 $\to$ 4 PCs;
• •  
  1 system went from 4 $\to$ 5 PCs.

The system of five PCs, KOI 4032, appears to be a particularly interesting compact, multi-planet system, as all five PCs have periods between 2.9 and 7.2 days, with inferred radii between 0.8 and 1.0 R_⊕, around a solar-type star (5575 K, 1.06 R_⊙).

Of the 7470 KOIs in the Q1–Q17 DR24 catalog, 5864 are in single KOI systems, and 1786 are in multi-KOI systems (at least two KOIs associated with the same target). Of the 5864 KOIs in single systems, 2661 are dispositioned as PCs and 3023 as FPs, yielding a 51.6% FP rate. Of the 1786 KOIs in multiple systems, 1632 are dispositioned as PCs and 154 as FPs, yielding a 8.6% FP rate. The lower FP rate is expected for multi-KOI systems, as systems with multiple KOIs are more likely to contain actual PCs (Rowe et al. 2014). While expected, this analysis provides a valuable check that the robovetter is not dispositioning a significant number of KOIs as FPs simply due to the fact they are in multi-KOI systems.

In Figure 7, we plot every Q1–Q17 DR24 TCE that was dispositioned as a PC by the robovetter as a function of its inferred planetary radius (R_p) and insolation flux (S_p). We also utilize point size to represent the S/N of each candidate, and the color of the point to indicate the effective temperature of the host star. We use vertical dashed lines to indicate the insolation flux levels of Mars and Venus as a broad guide to a potential habitable zone. We use a horizontal dashed line to mark the radius at which a planet has about an even chance of being a terrestrial, rocky planet (Rogers 2015).

Zoom In Zoom Out Reset image size

As can be seen, while there are thousands of PCs, only a small percentage lie within the potential habitable zone. Smaller planets with lower insolation flux levels are predominately found around late-type stars. This is primarily an observational bias, as planets with shorter periods and larger radii relative to their host stars are more easily detected. Many of the small, low insolation flux planets have an S/N of ∼10 or less. In this low S/N regime, the odds of the TCE being an FP that is undetectable by the robovetter is enhanced, and thus these candidates should continue to be treated with caution. More work is needed to obtain a quantitative measure of the rate of undetected low S/N FPs residing in the catalog.

Potentially rocky, habitable planets are the most important targets for follow-up observations to determine the frequency of Earth-size planets in the habitable zones of other stars. In Table 7, we list all of the PCs in the Q1–Q17 DR24 catalog that have R_p < 2.0 R_⊕ and S_p < 2.0 S_⊕. We list the values for their transit-model S/N, inferred planet radius, insolation flux, and host star effective temperature and radius from the Q1–Q17 DR24 KOI catalog. In addition, as discussed in Section 5.2.5, the NASA Exoplanet Archive maintains a list of KOIs that have been confirmed as planets via follow-up observations and/or statistical analyses, and assigns them Kepler confirmed planet numbers, e.g., Kepler-1b. (Again, note that the KOI PC/FP disposition and the NExScI confirmed planet designation are completely independent.) If the planet is listed as a confirmed planet at the NASA Exoplanet Archive confirmed planets table, we also list its Kepler confirmed planet number, reference for the confirmation, and values for the planetary radius, planetary insolation flux, and host star effective temperature and radius from the reference. If insolation flux was not given in the reference, then we derive it from other values given in the reference via

$$\begin{eqnarray}&&{S}_{p}=\displaystyle \frac{{R}_{p}^{2}\cdot {({T}_{\star }/5777)}^{4}}{{a}^{2}},\end{eqnarray} \tag{ 9 }$$

where a is the semimajor axis of the planet's orbit in au, T_⋆ is in Kelvin, 5777 K is the effective temperature of the Sun, and S_p and R_p are in Earth units.

There are a number of PCs in Table 7 that are new in the Q1–Q17 DR24 catalog. A much larger fraction of them orbit solar-like stars compared to previously known PCs in the table, as well as having lower insolation flux values. Specifically, KOIs 6343.01, 6425.01, 7016.01, 7223.01, 7235.01, and 7470.01 have inferred radii between 1.13 and 1.90 R_⊕, insolation fluxes between 0.56 and 0.75 S_⊕, and orbit stars with T_⋆ between 5128 and 6117 K. We first note that they are generally also at lower S/N compared to previously known PCs which, coupled with being in single systems, puts them at higher risk for being undetected, low S/N FPs. We also note that if any of them are confirmed to be planets by subsequent observations and analyses, then their resulting radii and insolation fluxes could change significantly as a result of more accurate stellar parameters. However, the fact that there are a significant number of new PCs that orbit Sun-like stars and have insolation fluxes even less than that of Earth's represents great progress by the Kepler mission in determining the fraction of Earth-size planets in the habitable zones of Sun-like stars. In order to facilitate the prioritization of follow-up observations, in the subsections below, we examine in detail each PC from Table 7 that is new in the Q1–Q17 DR24 catalog. We utilize both the TCERT vetting forms (Coughlin 2015a, publicly available for every Q1–Q17 DR24 TCE at the Exoplanet Archive), as well as the PDC data from MAST.

5.5.1. KOI 1126.02

5.5.2. KOI 1681.04

5.5.3. KOI 2719.02

5.5.4. KOI 5475.01

5.5.5. KOI 6343.01

KOI 6343.01 is a newly detected single PC in Q1–Q17 DR24 with an inferred size of 1.90 R_⊕ and insolation flux of 0.61 S_⊕, given its period of 569 days around a 0.95 R_⊙, 6117 K star. Manual inspection of its PDC light curve reveals that, of its three transit events, the second event is likely a low-amplitude SPSD and the other two events may be smaller amplitude systematic events. The SPSD feature is not as readily visible in either the DV or alternate detrending, though it is perhaps not surprising given the KOI's low S/N of 9.9. We note the value of the Marshall metric is 8.1 for KOI 6343.01, which is very close to the threshold value of 10.0, above which the robovetter classifies TCEs/KOIs as FPs due to systematic events. For clarity, in Figure 8, we plot the distribution of the Marshall metric for injTCEs (see Section 5.3) where it can be seen that very few injected transiting planets have Marshall metrics near 10 or higher, even at low S/N. Overall, we deem it very likely that this object is actually a result of low-amplitude systematics.

Zoom In Zoom Out Reset image size

5.5.6. KOI 6425.01

5.5.7. KOI 6676.01

5.5.8. KOI 6971.01

5.5.9. KOI 7016.01

5.5.10. KOI 7179.01

5.5.11. KOI 7223.01

5.5.12. KOI 7235.01

5.5.13. KOI 7470.01

5.5.14. KOI 7554.01

5.5.15. KOI 7567.01

5.5.16. KOI 7591.01

5.5.17. KOI 7592.01