CHARACTERISTICS OF KEPLER PLANETARY CANDIDATES BASED ON THE FIRST DATA SET

The candidates discussed here do not include 400 stars selected as high-priority targets. These are primarily those amenable to ground-based follow-up observations and those with the smallest candidates. In particular, these stars include (1) those showing two or more sets of transit events at distinctly different periods, (2) those showing any indication of transit-timing variations that could lead to detection of additional planets, (3) stars cooler than 4000 K, (4) stars brighter than K_p = 13.9, (5) candidates with a likelihood of showing a secondary occultation event, and (6) stars with candidates smaller than 1.5 R_⊕. The likelihood of an occultation event is determined by computing the ratio of the stellar luminosity to the thermal emission of the planet assuming an even distribution of energy over the day and night side of the planet, an albedo of 0.1, and a circular orbit at a distance given by the stellar properties in the KIC and the period provided by the transit photometry. This ratio is then compared to the expected photometric noise given the apparent brightness of the star in question. Targets are flagged if the occultation depth is expected to be larger than 2σ. Collectively, these criteria yielded 400 stars, though the large majority of candidates were selected simply based on the brightness cutoff (e.g., amenability to ground-based follow-up observations). These targets will be released to the public in 2011 February, giving the team a full observing season to collect follow-up observations that will help to weed out astrophysical false positives. The remaining 305 stars comprise the sample described herein.

The Kepler photometric data contain a wide variety of both random and systematic noise sources. Random noise sources such as shot noise from the photon flux and read noise have (white) Gaussian distributions. Stellar variability introduces red (correlated) noise. For many stars, stellar variability is the largest noise source. There are also many types of instrument-induced noise: pattern noise from the clock drivers for the "fine-guidance" sensors, start-of-line ringing, overshoot/undershoot due to the finite bandwidth of the detector amplifiers, and signals that move through the output produced by some of the amplifiers that oscillate. The latter noise patterns (which are typically smaller than one least-significant-bit in the digital-to-analog converter for a single read operation) are greatly affected by slight temperature changes, making their removal difficult. Noise due to pointing drift, focus changes, differential velocity aberration, CCD defects, cosmic ray events, reaction wheel heater cycles, breaks in the flux time series due to desaturation of the reaction wheels, spacecraft upsets, monthly rolls to downlink the data, and quarterly rolls to re-orient the spacecraft to keep the solar panels pointed at the Sun are also present. These sources and others are treated in Jenkins et al. (2010b) and Caldwell et al. (2010). Work is underway to improve the mitigation and flagging of the affected data. Additional noise sources are seen in the short cadence data (Gilliland et al. 2010). In particular, a frequency analysis of these data often shows spurious regularly spaced peaks at 48.9388 day⁻¹ and their harmonics. Additionally, there appears to be a noise source that causes additive offsets in the time domain inversely proportional to stellar brightness.

Because of the complexity of the various small effects that are important to the quality of the Kepler data, prospective users of Kepler data are strongly urged to study the data release notes (hosted at the MAST) for the data sets they intend to use. Note that the Kepler data analysis pipeline was designed to perform differential photometry to detect planetary transits so other uses of the data products require caution.

Stars that show a pattern consistent with those from a planet transiting its host star are labeled "planetary candidates." Those that were at one time considered to be planetary candidates, but subsequently failed some consistency test, are labeled "false positives." Thus, the search for planets starts with a search of the time series of each star for a pattern that exceeds a detection threshold commensurate with a non-random event. After passing all consistency tests described below, and only after a review of all the evidence by the entire Kepler Science Team, does the candidate become a validated exoplanet. It is then submitted to a peer-reviewed journal for publication.

There are two general types of processes associated with false positive events in the Kepler data that must be evaluated and eliminated before a candidate planet can be considered a valid discovery: (1) statistical fluctuations or systematic variations in the time series, and (2) astrophysical phenomena that produce similar signals. A sufficiently high threshold has been used that statistical fluctuations should not contribute to the candidates proposed here. Similarly, systematic variations in the data have been interpreted in a conservative manner and only rarely should result in false positives. However, astrophysical phenomena that produce transit-like signals will be much more common.

The Transiting Planet Search (TPS) pipeline searches through each systematic error-corrected flux time series for periodic sequences of negative pulses corresponding to transit signatures. The approach is a wavelet-based, adaptive matched filter that characterizes the power spectral density (PSD) of the background process yielding the observed light curve and uses this time-variable PSD estimate to realize a pre-whitening filter and whiten the light curve (Jenkins 2002; Jenkins et al. 2010c, 2010d). Transiting Planet Search then convolves a transit waveform, whitened by the same pre-whitening filter as the data, with the whitened data to obtain a time series of single event statistics. These represent the likelihood that a transit of that duration is present at each time step. The single event statistics are combined into multiple event statistics by folding them at trial orbital periods ranging from 0.5 days to as long as one quarter (∼90 days). The step sizes in period and epoch are chosen to control the minimum correlation coefficient between neighboring transit models used in the search so as to maintain a high sensitivity to transit sequences in the data. The transit durations used for TPS through 2010 June were 3, 6, and 12 hr. These transit durations will be augmented to include 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 7.5, 9.5, 12.0, and 15.0 hr in order to maintain a similar degree of sensitivity as that achieved for epoch and period. This modification should increase the sensitivity to low signal-to-noise ratio (S/N) signals. Transiting Planet Search is also being modified to conduct searches across the entire mission duration by "stitching" quarterly segments together so that we can identify periods longer than one quarter in the data.

The maximum multiple event statistics is collected for each star and those with maximum multiple event statistics greater than 7.1σ are flagged as threshold crossing events (TCEs). The Data Validation (DV) pipeline fits limb-darkened transit models to each TCE and performs a suite of diagnostic tests to build or break confidence in each TCE as a planetary signature as opposed to an EB or noise fluctuation (Wu et al. 2010; Tenenbaum et al. 2010). Data Validation removes the transit signature from the light curve and searches for additional transiting planets using a call to TPS. Threshold crossing events with transit depths more than 15% are not processed by DV since they are most likely to be EBs. Also, currently light curves whose maximum multiple event statistics are less than 1.25 times the maximum single event statistic are not processed by DV since these are likely due to one large single event, and most of these cases are due to radiation-induced step discontinuities introduced at the pixel level.

Using these estimates and information about the star from the KIC, tests are performed to search for a difference in even- and odd-numbered event depths. If a significant difference exists, this would suggest that a comparable-brightness EB has been found for which the true period is twice that determined due to the presence of primary and secondary eclipses. Similarly, a search is conducted for evidence of a secondary eclipse or a possible planetary occultation roughly half-way between the potential transits. If a secondary eclipse is seen, then this could indicate that the system is an EB with the period assumed. However, the possibility of a self-luminous planet (as with HAT-P-7; Borucki et al. 2009) must be considered before dismissing a candidate as a false positive.

The shift in the centroid position of the target star measured in and out of the transits must be consistent with that predicted from the fluxes and locations of the target and nearby stars.

After passing these tests, the candidate is elevated to "Kepler Object of Interest" (KOI) status and is forwarded to the Threshold Crossing Event Review Team. They examine the information associated with each KOI, add any that they have found by visual inspection, judge the priority of each KOI, and then send the highest priority candidates to the Follow-up Observation Program (FOP) for various types of observations and additional analysis. These observations include the following.

• 1.  
  High-resolution imaging with adaptive optics or speckle interferometry to evaluate the contribution of other stars to the photometric signal and to evaluate the shift of the photocenter when a transit occurs.
• 2.  
  Medium-precision RV measurements are made to rule out stellar or brown dwarf mass companions and to better characterize the host star.
• 3.  
  A stellar blend model (Torres et al. 2004) is used to check that the photometry is consistent with a planet orbiting a star rather than the signature of a multi-star system.
• 4.  
  High-precision RV measurements may be made, as appropriate, to verify the phase and period of the most promising candidates and ultimately to determine the mass and eccentricity of the companion and to identify other non-transiting planets. For low-mass planets where the RV precision is not sufficiently high to detect the stellar RV variations, RV observations are conducted to produce an upper limit for the planet mass and assure that there is no other body that could cause confusion.
• 5.  
  When the observations indicate that the Rossiter–McLaughlin effect (Winn 2007) will be large enough to be measured in the confirmation process, such measurements may be scheduled, typically at the Keck Observatory.
• 6.  
  When the data indicate the possibility of transit-timing variations large enough to assist in the confirmation process, the multiple-planet and transit-timing working groups perform additional analysis of the light curve and possible dynamical explanations (Steffen et al. 2010).

This paper discusses the characteristics for the 311 candidates (associated with 305 stars) in the released list. These candidates have not been fully vetted through the steps described above, so a substantial fraction of the candidates could be false positives. The process of determining the residual false positive fraction for Kepler candidates at various stages in the validation process has not proceeded far enough to make good quantitative statements about the expected true planet fraction, or purity, of the released list but a modest improvement can be made over the broad estimate of 24%–60% good planets given in Gautier et al. (2010).

The candidates come from about 425 TCEs using the first three, pre-FOP, validation steps; i.e., check that the odd- and even-numbered transit depths have the amplitude, search for a secondary eclipse, and check that any centroid shift during the transits is consistent with a transit of the target star. Essentially no analysis of ground-based follow-up observations was applied to the released list. About 29% of the 425 TCEs were removed as false positives, mainly EB target stars and background eclipsing binaries (BGEBs) whose images were confused with those of the target stars. The false positives remaining in the 312 candidates should consist of BGEBs closer to the target star than the preliminary vetting could detect, EBs missed in the preliminary light curve analysis, and triple systems harboring an EB.

The analysis used to identify false positives in the 425 TCEs is not considered thorough. For instance, the centroid motion analysis to detect BGEBs in the released list is not particularly sensitive because only the KIC stars in the aperture used for the KOIs were used. A higher sensitivity to BGEBs is obtained when follow-up imaging of star fields around the KOIs is made using high spatial resolution imaging techniques. A rough estimate is that 70%–90% of the EBs and BGEBs were detected, leaving 14–53 EBs and BGEBs in the list. Analysis of medium-precision RV measurements of 268 of the 400 candidates sequestered by the Kepler team shows clear signs of 16 EBs that were not found in a relatively thorough light curve analysis. This fraction implies that 14–22 of these EBs are left in the released list. Brown & Latham (2008) estimate that the number of hierarchical triple systems expected to be seen by the proposed Transiting Exoplanet Survey Satellite (TESS) will be about equal to the number of planets. Almenara et al. (2009) find 6 hierarchical blends and 6 planets in a sample of 49 CoRoT candidates that were completely "solved." Combining these estimates yields an expectation of 52 ± 20 EBs and BGEBs in the 312 candidates leaving 249 ± 20 true planets plus hierarchical blends. Assuming a 1:1 ratio of planets to hierarchical blends, the fraction of planets in the released sample is estimated to be 41% ± 7%. This estimate might become as poor as 41% ± 17% if the uncertainty on the 1:1 ratio is as large as 40%, derived from the small number statistics used in the Almenara paper.

It is difficult to compare our estimated purity of 41% to purity estimates of other expolanet surveys at the same stage of candidate vetting. The sample of 49 CoRoT candidates in Almenara et al. (2009) is at roughly the same stage of vetting as our sample and yielded 6 planets for a purity of 12%. However, the Kepler analysis has been able to take advantage of centroid motion analysis in our vetting while the CoRoT sample had essentially no vetting for BGEBs. Reducing the 19 BGEBs in the CoRoT sample by 80% to make it similar to our sample produces a purity of 18%. The difference appears to come from the larger fraction of EBs in the CoRoT sample than we expect in ours. Estimates for TESS from Brown & Latham (2008) predict 28% purity, near the lower end of estimates for our list at a vetting stage similar to ours.

It is expected that many of the candidates listed in the Appendix will be followed up by members of the science community and that many will be confirmed as planets. To avoid confusion in naming them, it is suggested that the community refers to Kepler stars as KIC NNNNNNN (with a space between the "KIC" and the number), where the integer refers to the ID in the KIC archived at MAST. For planet identifications, a letter designating the first, second, etc., confirmed planet as "b," "c," etc. should follow the KIC ID number. At regular intervals, the literature will be combed for planets found in the Kepler star field, sequential numbers assigned, the IAU-approved prefix ("Kepler") added, and the information on the planet with its reference will be placed in the Kepler Results Catalog. Preliminary versions of this catalog will be available at the MAST and revised on a yearly basis.

We have conducted some statistical analyses of the 306 of the 311 released candidates to investigate the general trends and initial indications of the characteristics of the detected planetary candidates. Five of the 312 candidates were not considered in the analysis because they were at least twice the size of Jupiter and are likely to be M dwarf stars.

The readers are cautioned that the sample considered here contains many poorly quantified biases. Some of the released candidates could be false positives. Further, those candidates orbiting stars brighter than 13.9 mag and the small-size candidates (i.e., those with radii less than 1.5 R_⊕) are not among the released stars. Nevertheless, the large number of candidates provides interesting, albeit tentative, associations with stellar characteristics. Comparisons are limited to orbital periods of <33.5 days. For candidates with periods greater than 16.75 days and that have only a single transit during Q1, data obtained at a later date were used to compute the orbital period to provide necessary information for observers.

In the figures below, the distributions of various parameters are plotted and compared with values in the literature and those derived from the Extrasolar Planets Encyclopedia²⁸ (EPE; as of 2010 December 7).

The results discussed here for the 306 candidates are primarily based on the observations of 87,615 stars with K_p > 13.9 with effective temperature above 4000 K, and with size less than 10 times the size of the Sun. The latter condition is imposed because the photometric precision is insufficient to find Jupiter-size and smaller planets orbiting stars with 100 times area of the Sun. Stellar parameters are based on KIC data. The function of the KIC was to provide a target sample with a low fraction of evolved stars that would be unsuitable for transit work, and to provide a first estimate of stellar parameters that is intended to be refined spectroscopically for KOI at a later time. Spectroscopic observations have not been made for the released stars, so it is important to recognize that some of the characteristics listed for the stars are uncertain, especially surface gravity (i.e., log g) and metallicity ([M/H]). The errors in the star diameters can reach 25%, with proportional changes to the estimated diameter of the candidates.

In Figure 1, the stellar distributions of magnitude and effective temperature are given for reference. In later figures, the association of the candidates with these properties is examined.

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It is clear from Figure 1 that most of the stars monitored by Kepler have temperatures between 4000 and 6500 K; they are mostly late F, G, and K spectral types. This is because these types are the most frequent for a magnitude-limited survey of dwarfs and because the selection of target stars was purposefully skewed to enhance the detectability of Earth-size planets by choosing those with an effective temperature and magnitude that maximized the transit S/N (Batalha et al. 2010). Thus, the decrease in the number of monitored stars for magnitudes greater than 15.5 is due to the selection of only those stars in the field of view (FOV) that are likely to be small enough to show planets. In particular, A, F, and G stars were selected at magnitudes where they are sufficiently bright for their low shot noise to overcome the lower S/N for a given planet size due to their large stellar radii. After all available bright dwarf stars are chosen for the target list, many target slots remain, but only dimmer stars are available (Batalha et al. 2010). From the dimmest stars, the smallest stars are given preference. In the following figures, when appropriate, the results will be based on the ratio of the number of candidates to the number of stars in each category.

A comparison of the distributions shown in Figure 2 indicates that the majority of the candidates discovered by Kepler are Neptune-size (i.e., 3.8 R_⊕) and smaller; in contrast, the planets discovered by the transit method and listed in the EPE are typically Jupiter-size (i.e., 11.2 R_⊕) and larger. This difference is understandable because of the difficulty in detecting small planets when observing through Earth's atmosphere.

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The Kepler results shown in Figure 2 imply that small candidate planets with periods less than 33.5 days are much more common than large candidate planets with periods less than 33.5 days and that the ground-based discoveries are potentially sampling the upper tail of the size distribution (Gaudi 2005). Note that for a substantial range of planet sizes, an R⁻² curve fits the Kepler data well. Because it is much easier to detect larger candidates than smaller ones, this result implies that the frequency of planets decreases with the area of the planet, assuming that the false positive rate and other biases are independent of planet size for planets larger than 2 Earth radii.

In Figure 3, the dependence of the number of candidates on the semimajor axis is examined. In the upper panel, an analytic curve has been fitted to show the expected reduction in the integrated number in each interval due to the decreasing geometrical probability that orbits are correctly aligned with the line of sight. It has been fitted over the range of semimajor axis from 0.04 to 0.2 AU corresponding to orbital periods from 3 days to ∼33 days for a solar-mass star.

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Although the corrections necessary to normalize the observed distribution to an unbiased one are too lengthy to consider here, we performed a statistical analysis that corrected for the probability of orbital alignment. Although the sample sizes are small and thus the results are uncertain, it is interesting to correct the observations to get a lower limit to the occurrence frequencies.

The corrected number of candidates (Nc) in each 0.01 AU interval of the semimajor axis is estimated from

$$\begin{equation} Nc = {\rm Average}({{a_i /R_i } })N_{\rm obs}, \end{equation} \tag{ 1 }$$

where a_i is the semimajor axis of candidate "i," R_i is the stellar radius of the host star, N_obs is the number of detected candidates in the interval of the semimajor axis, and the index "i" counts only those candidates in each increment of the semimajor axis.

Considering only this correction and only for the range of the semimajor axis from 0.04 to 0.2 AU, the fraction of stars detected with candidates is nearly constant with the semimajor axis and equal to 6.8 × 10⁻².

Only a small decrease in the number of candidates with the logarithm of the semimajor axis is seen in the bottom panel of Figure 3. Appropriate corrections for the geometric probability showed a large increase in the number per logarithmic interval as expected from an examination of the upper panel. Thus, these observations are not consistent with a logarithmic distribution of candidates with semimajor axis.

A breakout of the number of candidates versus semimajor axis is shown in Figure 4. "Super-Earth-size" candidates are those with sizes from 1.25 R_⊕ to 2.0 R_⊕. These are expected to be rocky-type planets without a hydrogen–helium atmosphere. "Neptune-size" candidates are those with sizes from 2.0 R_⊕ to 6 R_⊕, and are expected to be similar to Neptune and the ice giants in composition. Candidates with sizes between 6 and 15 R_⊕ and between 15 and 22 R_⊕ are labeled Jupiter-size and very large candidates, respectively. The nature of the larger category of objects is unclear. No mass measurements are available. It is possible that they are small stars transiting large stars. It is also possible that these are ordinary Jovian planets whose stars have incorrectly assigned radii or that they are the tail of the distribution of large planets.

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A correction of these results for the probability of a geometrical alignment shows that the adjusted occurrence frequencies of candidate planets are 8 × 10⁻³, 4.6 × 10⁻², 1.2 × 10⁻², and 2 × 10⁻³ for super-Earth-size, Neptune-size, Jupiter-size, and the very large candidates, respectively. Substantial increases in the values for the smaller candidates are expected when more comprehensive corrections are made for low-level signals that are currently too noisy to produce detectable transits and when a larger range of semimajor axis is considered.

There are several references in the literature to the pile-up of giant planet orbital periods near 3 days (Santos & Mayor 2003) and a "desert" for orbital periods in excess of 5 days. Figure 5 is a comparison of distributions of frequency with orbital period for the Kepler results with that derived from the planets listed in the EPE. In this instance, the much larger number of planets listed in the EPE under RV discoveries was used in the comparison. The very compact distribution of frequency with orbital periods between 3 and 7 days seen in the EPE results is also seen in the Kepler results. However, there is little sign of the "desert" that has been discussed in the literature with respect to the RV results for giant planets. We note that the Kepler sample contains a much larger fraction of super-Earth-size candidates than does the EPE sample.

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In Figure 6, the dependences of the number of candidates with the size groups and orbital period are shown.

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The first four panels indicate that the observed number of candidates is decreasing with orbital period regardless of size and that there is a peak in concentration for orbital periods between 2 and 5 days for all sizes.

All panels in Figure 7 show a lack of candidates with radius less than 1.5 R_⊕. This result is mostly due to the sequestration of small candidates for follow-up observations during the summer of 2010. In the upper left panel, the decrease in the number of candidates with increasing orbital period and with decreasing size is evident. In contrast to the strong correlation of decreasing planet mass with orbital period found by Torres et al. (2008), no analogous dependence of candidate size with orbital period is evident.

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The vertical lines in the bottom right panel mark the edges of the HZ; i.e., temperatures of 273 and 373 K. The equilibrium temperatures for the candidates were computed for a Bond albedo of 0.3 and a uniform surface temperature. However, the computed temperatures have an uncertainty of approximately ±50 K, because of the uncertainties in the stellar size, mass, and temperature as well as the effect of any atmosphere. Over this wider temperature range, five candidates are present; two near super-Earth size, and three bracketing the size of Jupiter; see Table 1.

In Figure 8, the frequency of candidates in each magnitude bin has been calculated from the number of candidates in each bin divided by the total number of stars monitored in each bin. The number of stars brighter than 14.0 mag and fainter than 16.0 in the current list is so small that the count is not shown.

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The panel for super-Earth-size candidates shows a substantial decrease in frequency for magnitudes larger than 15.0 and is indicative of difficulty in detecting small candidates around dim stars.

Figure 9 shows that the number of candidates is a maximum for stars with temperatures between 5000 and 6000 K, i.e., G-type dwarfs. This result should be expected because a large number of G -type stars are chosen as target stars. The relatively large number of super-Earth- and Neptune-size candidates orbiting K stars (4000 K ≤ stellar temperature ≤ 5000 K) is likely the result of small planets being easier to detect around small stars than around large stars and the relatively large number of such stars chosen. Similarly, the paucity of candidates associated with stars at temperatures above 6000 K is likely to be due to the relatively small number of such stars in the survey.

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In Figure 10, the bias associated with the number of target stars monitored as a function of temperature is removed by computing the frequencies of the candidates as a fraction of the number of stars monitored.

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Note that the frequency for the total of all candidate sizes is nearly constant with increasing stellar temperature. However, for super-Earth candidates, the decrease with temperature is quite marked, as might be expected when considering the substantially lower S/N due to the increase of stellar size of main-sequence stars with temperature. It is unclear whether the decrease in occurrence frequency is real or a measurement bias. The observed increase in the frequency with stellar temperature for Jupiter-size candidates should not be biased because the signal level for such large candidates is many times the noise level associated with the instrument and shot noise. Thus, this increase could indicate a real, positive correlation of giant candidates with stellar mass (Johnson et al. 2010).

A study of the dependence of the frequency of the planet candidates on the stellar metallicity was not considered, because the metallicities in the KIC are not considered sufficiently reliable. In particular, the D51 filter used in the estimation of metallicity is sensitive to a combination of the effects of surface gravity and metallicity, especially within the temperature range from roughly late K to late F stars. However, the information generated by this filter was used to develop the association with log g, thereby making any estimate of metallicity highly uncertain.