Sixty Validated Planets from K2 Campaigns 5–8

Our team successfully proposed K2 General Observer (GO) targets for Campaigns 5–8.¹⁶ In brief, we used data from the TESS Dwarf Catalog (Stassun et al. 2014), the SUPERBLINK proper-motion database (Lépine & Shara 2005), the PanSTARRS-1 survey (Kaiser et al. 2002; Chambers et al. 2016), 2MASS, and WISE, applying color and proper-motion cuts in order to select solar- and late-type dwarf stars while minimizing contamination from background giants (for a more detailed description, see Crossfield et al. 2016 and P18). As the K2 data from all GO programs are public, we have included data besides those from our own proposals in our search for candidate planet transit signals. For reference, we have listed all GO programs associated with each of the targets in this work in Table 1.

As described in P18, we used the publicly available software packages k2phot¹⁷ (Petigura et al. 2015) and TERRA¹⁸ to produce calibrated photometric time series from the K2 pixel data for 87,913 stars from C5–8 and identify planet candidates. In brief, each calibrated light curve is iteratively searched for transit-like signals by masking the transits of each successive candidate identified and repeating the search. This iterative approach allows us to detect multi-candidate systems. These "threshold-crossing events" (TCEs) are then subjected to further scrutiny in order to identify obviously spurious signals and minimize the number of false positives in our candidate sample. Figure 1 presents an overview of how our photometry and transit search fit into the process of candidate identification, follow-up observations, and detailed analyses. For a full description of our photometry, transit search, and candidate vetting procedures, see Crossfield et al. (2016) and P18. In addition to the 151 planet candidates reported by P18, we identified four candidates in the light curves of stars already reported to have at least one candidate by P18. The analysis that follows considers the resulting set of $155$ planet candidates orbiting the same set of 141 stars as analyzed by P18. Figure 2 shows 1' × 1' r-band image stamps from PanSTARRS-1 with k2phot optimal apertures overplotted for the stars we analyze here.

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From 2016 January 26 to 2017 August 20 UT, we performed high-resolution imaging follow-up observations to identify stellar companions. We employed adaptive optics (AO) techniques using the following near-infrared (NIR) cameras: NIRC2 (Wizinowich et al. 2014) on the 10 m Keck II telescope, PHARO (Hayward et al. 2001) on the 5 m Hale telescope, and NIRI on the 8 m Gemini North (Hodapp et al. 2003). For all instruments, initial detection of diluting companions is conducted by observing in the K band (centered at 2.196 μm), K_cont (centered at 2.27 μm), or Brγ (centered at 2.168 μm). Some targets were also observed in J (centered at 1.248 μm) in order to obtain NIR colors of any detected secondary sources. Efforts are currently underway to obtain multiband observations of targets with diluting companions so as to ascertain the bound or unbound nature of the companion. For further details of the NIR AO imaging follow-up, see G18.

Speckle-interferometric observations were also conducted in the optical for most targets using the Differential Speckle Survey Instrument (DSSI; Horch et al. 2009, 2012) on the Gemini 8 m telescopes and the NN-EXPLORE Exoplanet and Stellar Speckle Imager (NESSI; Howell et al. 2011; Scott et al. 2016) on the WIYN 3.5 m telescope. For further details of the optical speckle-interferometric follow-up, see Matson et al. (2018).

The contrast curves derived from these high-resolution images are an important constraint on the calculation of statistical FPPs, as they place limits on the existence of nearby bound stellar companions or background stars that could be the source of the observed transit signals. To illustrate the typical strength of these constraints, we compute the median z- and K_s-band contrast curves used in this work, derived from speckle imaging and AO, respectively. We plot these median contrast curves along with their 16th–84th percentile ranges in Figure 3.

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We obtained high-resolution optical spectra for most of the targets in this work using Keck/HIRES, described in detail in P18. From these spectra, we derive stellar parameters using SpecMatch-syn (Petigura et al. 2017) for stars hotter than 4200 K and SpecMatch-emp (Yee et al. 2017) for cooler stars. In addition, we refer the reader to Dressing et al. (2017a) and Martinez et al. (2017), in which spectroscopic analyses of many of the M dwarfs in the sample were presented. As an input to vespa, we adopt the constraints on secondary stars determined by ReaMatch (Kolbl et al. 2015; presented in P18), which are typically ΔV ≤ 5 mag for $v\sin i\geqslant 10$ km s⁻¹. We show a plot illustrating this analysis in Figure 4. For a subset of 21 late-type stars in this work, we adopt the stellar parameters of Dressing et al. (2017a) and Martinez et al. (2017), who obtained medium-resolution NIR spectra with IRTF/SpeX and NTT/SOFI. In total, 119 of the host stars we analyze here have spectroscopically derived parameters.

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To facilitate a uniform analysis of all the candidates, we utilized the Python package isochrones to infer stellar parameters using priors from the aforementioned spectroscopic analyses, 2MASS JHK photometry (Skrutskie et al. 2006), and Gaia DR2 parallaxes (Gaia Collaboration et al. 2016, 2018). This step is important because we have a heterogeneous set of parameters derived from spectroscopy, and 22 stars lack spectra entirely. From SpecMatch-syn, we have the parameter effective temperature ${T}_{\mathrm{eff}}$, surface gravity $\mathrm{log}g$, and metallicity [Fe/H], whereas SpecMatch-emp yields ${T}_{\mathrm{eff}}$, [Fe/H], and radius ${R}_{\star }$. The NIR spectroscopic analyses of Dressing et al. (2017a) and Martinez et al. (2017) are based on empirical relations calibrated to nearby stars with interferometrically measured radii and yield the parameters of interest: ${T}_{\mathrm{eff}}$, ${R}_{\star }$, and mass ${M}_{\star }$. For each star, we estimated the missing parameters using isochrones, which uses MultiNest (Feroz et al. 2013) in conjunction with the Dartmouth stellar evolution models (Dotter et al. 2008), effectively combining prior knowledge from spectroscopy, photometry, and parallax to constrain all parameters of interest. The resulting stellar parameters used in this work are listed in Table 1.

For the 22 stars in this sample that lack spectroscopic constraints, we compare the parameters we derive from Gaia DR2 parallax and 2MASS JHK photometry to the parameters from the Ecliptic Plane Input Catalog (EPIC; Huber et al. 2016), which were based on photometry, proper motion, and models of the distribution of stars in the Milky Way. We plot these parameters in Figure 5, highlighting the significance of parallax for stars lacking spectroscopy. The additional constraint from parallax reveals that several of these are late-type stars with underestimated radii in the EPIC. Huber et al. (2016) were aware of this systematic effect, which was the result of their choice of isochrones; this bias was later empirically shown to be ∼40% for M dwarfs by Dressing et al. (2017a). Including parallax also eliminates most of the potential for misclassifying dwarfs and subgiants, a frequent problem with the parameters in the EPIC. However, spectroscopic observations would be useful to more precisely constrain the radii of planets orbiting these stars.

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We describe our analysis of the K2 light curves in detail in Crossfield et al. (2016) and P18. In brief, we use MCMC to explore parameter space using the Python packages emcee and batman, an implementation of the analytic light-curve model of Mandel & Agol (2002). Parameter estimates resulting from our transit analyses are listed in Table 2. Throughout this work, we make heavy use of the Python scientific computing stack (i.e., numpy, scipy, and matplotlib). We plot the phase-folded data and best-fit transit models of each candidate in Figure 6.

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Figure 2 shows the optimal photometric apertures selected by k2phot, which are determined according to an algorithm described in P18. In addition to performing a transit analysis of each candidate using the light curves extracted from these optimal apertures, we also analyzed the light curves produced by circular apertures of varying sizes. This helps to ensure that the transit signal is indeed coming from the target star and not from another nearby source within the aperture, such as the cases identified by Cabrera et al. (2017). In such a case, one would expect the measured transit depth to increase as a function of aperture radius. Another possibility is that there is significant photometric dilution from other sources within the aperture, which would result in a decrease in transit depth with larger aperture radius.

To perform this analysis, we extracted light curves using circular apertures with radii of 1.5, 3.0, and 8.0 Kepler pixels (60, 119, and 318, respectively) for each candidate host star. We then fit the transit model to each light curve using the best-fitting parameters from the optimal apertures, with the radius ratio (R_p/${R}_{\star }$) allowed to float. To determine the value of R_p/${R}_{\star }$ and its uncertainty for each aperture extraction, we used the Python package lmfit, which utilizes the Levenberg–Marquardt nonlinear least-squares minimization in scipy (Jones et al. 2001). By comparing the results from fitting the 1.5, 3.0, and 8.0 pixel radius light curves, we found no evidence of a significant radius dependence for any of the planets we validate in this work (at the 5σ level).

Compared to the optimal k2phot apertures, these circular apertures typically include substantially different sets of pixels, often resulting in significantly degraded light-curve quality. For some targets, this reduces the strength of the constraints from this analysis; a less automated approach and/or a different photometric pipeline could potentially produce better-quality light curves for comparison, but this is beyond the scope of this work. We do not validate any systems that exhibit a suspicious radius dependence or for which nearby bright stars exist, but the result of this analysis is ambiguous. For several candidates we classify as false positives, we found evidence of increasing R_p/${R}_{\star }$ with increasing aperture radius, suggesting that these are actually the eclipses of a nearby eclipsing binary (EB). For some unvalidated candidates, we found a similar radius dependence, which suggests that the signals do not originate from the presumed target star. In some cases, we partially rely on the clear absence of a radius dependence to validate a system with a nearby bright star, as the smallest aperture excludes the flux of the neighbor without resulting in a diminished transit depth. We discuss these specific cases at length in the Appendix.

To compute FPPs, we use the open-source Python package vespa. We build off of the methodology of Crossfield et al. (2016), who used this approach to compute FPPs for 197 planet candidates from K2's first year (Campaigns C0–C4). The result is a complementary catalog of validated planets, candidates, and false positives for the second year of the K2 mission (C5–C8). We adopt the commonly used FPP criteria of 1% and 99% for planet validation and false-positive designation, respectively (see, e.g., Rowe et al. 2014; Montet et al. 2015; Morton et al. 2016). A candidate with 1% < FPP < 99% is designated as neither a validated planet nor a false positive and thus remains a planet candidate. Figure 7 shows the distributions of radius and orbital periods for validated planets, candidates, and false positives.

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At the heart of vespa is a robust statistical framework to compute the likelihood of several astrophysical false-positive scenarios, both with and without the effect of transit depth dilution caused by additional sources within the photometric aperture: EBs, hierarchical triple systems (HEBs), and background eclipsing binaries (BEBs). Here vespa uses simulations of the galaxy from the TRILEGAL population synthesis code (Girardi et al. 2005). We emphasize that the inclusion of Gaia parallaxes significantly impacts the stellar parameters for some candidate host stars and thus also affects the FPPs; our vespa results should therefore be more reliable than any previous analyses that did not include parallax. Because vespa assumes that the input photometry, parallax, and spectroscopic information corresponds to the true host of the transit signals, the FPPs it computes are only reliable when this assumption is valid. We list the likelihoods of false-positive scenarios considered by vespa in Table 3.

An important distinction between this work and the validation framework of Crossfield et al. (2016) is that we have taken extra steps to ensure that our sample of validated planets is pure. Recent work by Cabrera et al. (2017) and Shporer et al. (2017b) showed that several statistically validated planets from Crossfield et al. (2016) were in fact false-positive eclipsing binary scenarios. Therefore, to ensure the high purity of the validated planet sample in this work, we analyzed the light curves from multiple K2 apertures, as described in Section 4.1, and also included a planet radius upper limit in our validation criteria, as described in Section 5.4. These steps ensure that the FPPs are robust for the validated planet sample. However, the unvalidated planet sample contains candidates with low FPPs that we do not validate because of uncertainty about which star is the host; the FPPs for the unvalidated candidate sample are thus inherently less reliable than those of the validated sample, as the assumptions made by vespa may sometimes be in violation. We thus urge caution in the interpretation of the FPPs of such unvalidated candidates, in particular for the unvalidated candidates from Campaign 7, whose lower galactic latitudes resulted in frequent contamination from background stars within the photometric apertures. Further observations may help establish which stars are the signal hosts and could thus enable some of these candidates to be validated or confirmed.

Stars with multiple transiting planet candidates have been shown to have much lower FPPs than their single-planet counterparts (e.g., Lissauer et al. 2011, 2014). In this work, we take into account the (transiting) planet candidate multiplicity of each system when computing FPPs. Because the FPPs from vespa do not reflect multiplicity, we apply a "multiplicity boost" to the planet scenario, following previous validation papers (e.g., Crossfield et al. 2016; Sinukoff et al. 2016). Lissauer et al. (2012) estimated this boost factor as 25 for systems of two planet candidates and a factor of 100 for systems of three or more candidates based on the observed false-positive rate for the Kepler field. We apply the boost factors to the planet probability of each member of a multi-candidate system, which reduces the FPP of each individual candidate. Sinukoff et al. (2016) estimated the multiplicity boost for K2 using data from fields 1–2 and found values comparable to those found for the Kepler field by Lissauer et al. (2012). To check that the factors are not too high for fields 5–8, we used Equations (2) and (4) of Lissauer et al. (2012) to estimate them from our candidate sample. Based on the FPPs calculated by vespa, we have a sample purity of ∼75%. In conjunction with the observed fraction of candidates detected in multi-candidate systems ($24$/$155$), this yields multiplicity boost factors higher than that of the original Kepler field. While the true value of the multiplicity boost is field-dependent, the average values for fields 5–8 appear to be comparable to those of the Kepler field, similar to what was found for fields 1 and 2 by Sinukoff et al. (2016). Thus, we apply the boost factors estimated by Lissauer et al. (2012) to all candidates from K2 fields 5–8. We note, however, that none of the planets we validate in this work require this boost in order to meet our validation criterion of 1%. Figure 8 shows the light-curve and phase-folded transits of K2-187, a validated system of four planets detected in Campaign 5.

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The FPPs we compute with vespa are only valid for systems without detected stellar companions within the K2 photometric apertures. The high-resolution imaging presented in G18 enabled us to detect companions as close as 01 and up to 9 mag fainter. If the apparent transit signal originates from a secondary star within the photometric aperture, the large uncertainties on the stellar parameters of the host result in a highly uncertain planetary radius. Furthermore, in most such cases, the primary star is much brighter than the host, so the true transit depth would be underestimated by orders of magnitude, making the deep eclipse of a stellar mass object appear more similar to the shallow transit of a planet. We do not validate any planet candidates for which we cannot rule out all detected companions (either from AO or archival imaging) as the source of the signal. To rule out such scenarios, we consider the relationship between the observed transit depth δ' and the true transit depth δ given dilution γ from a secondary star Δm magnitudes fainter than the primary star (in the Kepler bandpass):

$$\begin{eqnarray}&&\delta ^{\prime} =\displaystyle \frac{\delta }{\gamma }=\displaystyle \frac{\delta }{1+{10}^{0.4{\rm{\Delta }}m}}.\end{eqnarray} \tag{ 1 }$$

To be conservative, we assume a maximum eclipse depth of 100% (i.e., δ = 1), so if $\delta ^{\prime} \gt {\gamma }^{-1}$, then the observed depth is too deep to have originated from the secondary star. Otherwise, the true host of the transit-like signals is uncertain, which in turn induces large uncertainties on the planet radius. Table 4 lists these cases, along with the transit depths and the dilution factors ${\gamma }_{\mathrm{pri}}$ and ${\gamma }_{\sec }$, which assume the signal originates from the primary or secondary star, respectively. We also indicate these cases of nonvalidated candidates (regardless of their FPP) by "AO" in the Note column of Table 2.

This analysis relies on the results of our extensive high-resolution imaging observations (see Section 3.1). The multi-aperture light-curve analysis presented in Section 4.1 is sensitive to problems of the variety pointed out by Cabrera et al. (2017), in which the AO imaging field of view is too small to detect more widely separated stars that nonetheless contribute flux to the K2 photometric aperture. However, as described in Section 4.2, the quality of the light curves produced with nonoptimal apertures was not always high enough to enable a robust constraint from this analysis. We thus made use of the high precision and completeness of Gaia DR2 to perform an additional check on the possibility of photometric dilution or false-positive contamination from nearby sources. For each target star, we searched for Gaia DR2 sources within 2' of the target star positions taken from the EPIC. We then determined the subset of these sources contributing flux to the K2 photometric aperture using a 2D Gaussian profile to model the point-spread function (PSF). According to Kepler documentation,¹⁹ the full width at half maximum (FWHM) of the PSF varies from 31 to 75, so we used a value of 6'' as a reasonable approximation for the FWHM across the focal plane. This approach accounts for "edge cases" involving a star outside of the aperture but still contributing significant flux. Finally, we determined the set of stars contributing enough flux to the aperture to be the source of the observed signals, taking into account dilution from other stars and the observed transit depth (assuming a maximum eclipse depth of 100%, as before). We show the positions of Gaia DR2 sources in Figure 2, and we color-code each Gaia source according to the following: red squares are sources bright enough (and contributing enough flux) to be the host of the signals, and green squares are sources that are either too faint to be the signal hosts or do not contribute enough flux to the aperture. We indicate cases of multiple stars bright enough to be the host by "Gaia" in the Note column of Table 2.

Several cases of low-mass eclipsing stellar companions that were initially classified as planets via statistical validation have recently come to light (Shporer et al. 2017b); these stars have radii in the range 0.9–1.9 ${R}_{\mathrm{Jup}}$, consistent with planets in the Jovian size regime (see also Mordasini et al. 2012). Thus, to err on the side of caution, we do not validate any planet candidate with a radius larger than 10 ${R}_{\oplus }$ (0.89 ${R}_{\mathrm{Jup}}\,$). This cautionary radius threshold can also be seen as an empirically sound choice based on the FPPs of the Kepler candidates presented by Morton et al. (2016), which rise quickly from ∼1% above 10 ${R}_{\oplus }$ in aggregate (see, e.g., Figure 4 of Morton et al. 2016). Candidates with radii larger than this in Table 2 are indicated by "LR" in the Note column. Many candidates with large radii are clear false positives based on their FPPs, but we do not validate several candidates with large radii in spite of their low FPPs. Future RV measurements of these unvalidated candidates are likely to reveal many of them to be giant planets.

Our validated planet sample includes $18$ planets smaller than 2 ${R}_{\oplus }$, several of which orbit bright host stars (J ≈ 7–9). These small planets thus present opportunities for detailed studies of terrestrial worlds via either RV measurements or transmission spectroscopy. Our sample also contains $24$ validated planets in 11 multi-planet systems, some of which orbit near low-order mean-motion resonances. In particular, further transit monitoring could reveal TTVs in systems such as EPIC 211562654bc, which is within 5% of a 2:1 period commensurability. This growing population of resonant systems (e.g., TRAPPIST-1, Gillon et al. 2017; K2-138, Christiansen et al. 2018) provides important clues for planet formation theories.

Also present in the validated planet sample are three planets with periods less than 1 day, commonly referred to in the literature as ultrashort-period planets (USPs; e.g., Sanchis-Ojeda et al. 2013). These planets may have migrated to their current orbital locations, or their orbits could be the result of a scattering event followed by tidal circularization. In particular, we validate the previously confirmed USP K2-96 b (HD 3167 b; Vanderburg et al. 2016a; Christiansen et al. 2017), which is part of a system with a rich dynamical history. We also validate the previously confirmed USP K2-106 b (EPIC 220674823 b; Adams et al. 2017; Sinukoff et al. 2017a), which is part of a multiplanet system. The newly validated four-planet system in our sample, K2-187, also contains a USP, making it a potentially interesting system from a dynamical point of view. However, given the low mutual inclinations implied by the presence of four transiting planets in this system, it is likely that the system has a quiet dynamical history, perhaps similar to what has been seen in other multiplanet USP-hosting systems, such as WASP-47 (Sinukoff et al. 2017b; Vanderburg et al. 2017).

To identify compelling targets for future characterization studies, we predicted masses using the mass–radius relation of Wolfgang et al. (2016) and then used these to predict RV semi-amplitudes. The following validated planets are the top three most compelling targets for future RV mass measurements, in the sense that they orbit relatively bright stars ($J\lt 10$, $V\lt 10.7$), have expected semi-amplitudes within reach of current and planned precision spectrographs (${K}_{\mathrm{pred}}\gt 1\,{\rm{m}}\,{{\rm{s}}}^{-1}$), and currently lack a mass determination: 211594205.01 (K2-184 b), 212357477.01, and 220709978.01 (K2-222 b). Additionally, these are interesting targets because their radii place them near the recently observed gap in the radius distribution (Fulton et al. 2017; Fulton & Petigura 2018; Van Eylen et al. 2018). Precise mass measurements would yield planet densities and therefore provide insights into the possibility of having been sculpted by photoevaporation (e.g., Owen & Wu 2013; Lopez & Fortney 2014). Such tests of photoevaporation theories will in turn help to clarify the extent to which the diversity of planet densities can be explained by planetesimal accretion (Inamdar & Schlichting 2016) or core-powered mass loss (Ginzburg et al. 2018), as well as probing core compositions (Jin & Mordasini 2018).

Of the $60$ validated planets in our sample, $40$ have previously been validated in the literature, and we include the default names of these planets as they are listed in the NASA Exoplanet Archive alongside their candidate IDs in Table 2. We found overall good agreement with literature parameter estimates but also some discrepancies that are likely attributable to some combination of differences in stellar characterization and photometric extraction, time-series detrending, and transit fitting. One interesting example is K2-97 b, for which our estimate of R_p/${R}_{\star }$ is ∼3σ different from the value found by Grunblatt et al. (2016); K2-97 is an evolved star exhibiting asteroseismic oscillations detectable in the K2 photometry.

Besides these discrepancies with the parameter estimates from the literature, we found one case of system parameters arising from the misidentification of a candidate's orbital period. Mayo et al. (2018) recently reported two small validated planets orbiting K2-189 (EPIC 212394689), which is also a star in our sample. We also validated two small planets orbiting this star, but we found that the orbital period of the inner planet reported by Mayo et al. (2018) is twice the true period. To check the validity of this conclusion, we fitted the light curve at both the period we detected and the period reported by Mayo et al. (2018). We then visually inspected the fits, as well as compared the resulting fit parameters. Our estimates of the planet-to-star radius ratio (R_p/${R}_{\star }$) are in 1σ agreement, but our estimate is the larger of the two. If the true orbital period were in fact twice our estimate, one would expect our estimate of R_p/${R}_{\star }$ to be significantly smaller due to the presence of out-of-transit photometry at the location of every other presumed transit. When we fold the light curve on the period reported by Mayo et al. (2018), we find that our best-fit model is a good fit to the data at both phase 0.0 and phase 0.5, indicating that the data were folded on twice the true period (see Figure 10). We also analyzed the light curve analyzed by Mayo et al. (2018), which was produced by K2SFF (Vanderburg & Johnson 2014) and is publicly available²¹ ; however, we came to the same conclusion. Besides the case of K2-189 b, there is good agreement in planet parameters ($\lt 3\sigma$) for the other planets in our validated sample that are also validated by Mayo et al. (2018).

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The K2 C16 observed a field overlapping C5 from 2017 December 7 to 2018 February 25. We used kadenza²² to process the K2 raw cadence data and then analyzed the resulting target pixel files with our team's standard pipelines, as described in detail in Yu et al. (2018). A subset of our C5 candidates were also observed by K2 during C16, so to demonstrate the increase in precision of orbital period estimates from a second observing campaign 18 months later, we conducted a joint analysis of both the C5 and C16 light curves for this subset of targets.²³ Table 5 lists the resulting period estimates, along with the C5-only estimates for comparison. We find that the median precision in the orbital period is 26 times greater. This illustrates the utility of follow-up transit observations; such improvements in ephemeris estimates greatly facilitate efficient scheduling of atmospheric transmission spectroscopy with expensive telescope assets, e.g., JWST. For deep enough transits, similar improvements are possible with ground-based transit follow-up observations, but for many interesting targets, such follow-up will need to be conducted from space, e.g., with Spitzer or CHEOPS. A similar overlap exists between K2 C6 and C17, and this type of space-based self-follow-up will likely continue with the TESS extended mission.

The newly validated planets in this work bring the total number of planets discovered by K2 to over ∼360 (see footnote 20). Our sample of $155$ candidates has an integrated FPP of ∼35, and we identified 18 of these as false positives; thus, 17 additional false positives can reasonably expected to be found among the $77$ unvalidated candidates. By extrapolation of the true-positive rate implied by our integrated FPPs for C5–C8, we expect that K2 will have discovered ∼600 planets by the end of 2018 (i.e., by the end of Campaign 19), which is approximately when K2 will run out of the fuel required for three-axis pointing control (Howell et al. 2014). Many of these planets will remain as unvalidated candidates until sufficient follow-up observations can be made. Many are potential targets for RV mass measurement using current and upcoming high-precision spectrographs in the optical and near-IR, especially given the relatively bright host stars typically surveyed by K2. These planets are complementary to those expected to be discovered by the upcoming NASA TESS mission, due to the fact that K2 surveys the ecliptic plane and TESS will survey most of the remainder of the celestial sphere.