STELLAR AND PLANETARY PROPERTIES OF K2 CAMPAIGN 1 CANDIDATES AND VALIDATION OF 17 PLANETS, INCLUDING A PLANET RECEIVING EARTH-LIKE INSOLATION

With the exception of one star in our sample (K2-18), we do not have spectroscopic data with which to characterize the stellar properties. Additionally, there are no measured parallaxes for any of these stars. Instead, we rely on photometry. For each system, we query the VizieR database of astronomical catalogs (Ochsenbein et al. 2000). We record the B, V, g', r', and i' magnitudes and their uncertainties from the AAVSO Photometric All-sky Survey DR6 (Henden & Munari 2014), as reported in the UCAC4 Catalog (Zacharias et al. 2012). We also record the J, H, and K magnitudes and their uncertainties as found in the 2MASS All-sky Catalog of Point Sources (Cutri et al. 2003) and the $W1-W3$ WISE magnitudes and uncertainties from the ALLWise Data Release (Cutri et al. 2013). For all except two of our targets, the W4 band is only an upper limit, and in the remaining two cases, the photometric uncertainity in W4 is at least an order of magnitude larger than those in $W1-W3$, so we do not use W4 for any system. These data are reported in Table 1, and a color–color diagram showing the $r$–$J$, $J$–$K$ colors of our candidates is included as Figure 1.

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To convert the observed photometric data into physical properties for each star, we used the new publicly available isochrones Python module,¹⁰ a general-purpose interpolation tool for the fitting of stellar models to photometric or spectroscopic parameters (Morton 2015a). This software does trilinear interpolation in mass–age–[Fe/H] space for any given set of model grids, thus being able to predict the value for any physical or photometric property provided by the models at any values of mass, age, and [Fe/H] within the boundaries of the grid.

This enables a set of observed properties ($\left\{{x}_{i},{\sigma }_{i}\right\}$), either spectroscopic, photometric, or both, to define a likelihood function to be sampled:

$$\begin{eqnarray}&&\mathrm{ln}{\mathcal{L}}({\boldsymbol{\theta }})\propto -\displaystyle \frac{1}{2}\displaystyle \sum _{i}\displaystyle \frac{{\left({x}_{i}-{I}_{i}({\boldsymbol{\theta }})\right)}^{2}}{{\sigma }_{i}^{2}},\end{eqnarray} \tag{ 1 }$$

where ${I}_{i}({\boldsymbol{\theta }})$ is the isochrone model prediction of property i at the given parameters ${\boldsymbol{\theta }}$. If the observed properties include any apparent magnitudes, then ${\boldsymbol{\theta }}$ includes distance and extinction in addition to mass, age, and [Fe/H] .

In this work, we use grids from the Dartmouth Stellar Evolution Database (Dotter et al. 2008) at Solar values of [α/Fe] = 0.0 and helium abundance Y = 0.2741, which come packaged with the isochrones module. We then infer the stellar parameters using MULTINEST (Feroz et al. 2009), an implementation of a multimodal nested sampling algorithm, for each host star conditioned on the observed photometric properties as presented in Table 1. MULTINEST is designed to sample multimodal posteriors, where other samplers such as MCMC algorithms often struggle. Given the multimodal nature of our posteriors, this scheme is optimal for capturing parameter space on the subgiant branch where these stars could reside. We include a prior on stellar metallicity representative of the observed metallicities of stars within 1 kpc of the Sun, following the results of Hayden et al. (2015), and a Salpeter-slope prior on mass up to the maximum mass available in the model grids of $3.7{M}_{\odot }$.

During the sampling process, we fit for Galactic extinction as one of our physical parameters. We include the WISE bandpasses by applying the relative extinction values between SDSS, 2MASS, and WISE calculated by Davenport et al. (2014). In each step of our fitting process, we draw a value for A_V, calculate the expected extinction in all bandpasses A_X assuming the R_V = 3.1 reddening law of (Fitzpatrick 1999), and then measure the likelihood of our model stellar fit to the observed apparent magnitudes. We apply a uniform prior ranging from zero to a maximum extinction value of 0.2 and marginalize over extinction in our final determination of stellar parameters. The NASA/IPAC Extragalactic Database, which reports the Schlafly & Finkbeiner (2011) recalibration of the Schlegel et al. (1998) extinction map as measured by COBE/DIRBE and IRAS/ISSA, suggests that typical A_V extinction values to the edge of the galaxy at this high Galactic latitude are ∼0.1 mag, so our upper limit appears to be justified.

Such a scheme enables us to infer the statistical uncertainties on the mass, radius, and effective temperature. However, we are subject to biases induced by systematics in the models themselves. There is some evidence that the Dartmouth models may under-predict radii of M dwarfs by $\sim 15\%$ when compared to other methods (Montet et al. 2015; Newton et al. 2015). Such an effect may be the result of the Dartmouth model reliance on BT-Settl atmospheres, which are based on incomplete molecular line lists and have been shown to predict near-IR colors that are too blue (Thompson et al. 2014).

As our stellar results are model-dependent, we caution users who intend to use these parameters for other works, such as exoplanet population studies. When available, stellar parameters inferred through other techniques such as asteroseismology or spectroscopy should supersede these values. We note the observed photometric parameters are consistent with spectroscopically derived parameters for stars with published spectra, and consistent with typical model-dependent uncertainties from photometric data (e.g., Huber et al. 2014). We provide full samples of our posteriors on the physical parameters for each star.¹¹

Bastien et al. (2014) use the "granulation flicker" in the Kepler light curves to suggest that approximately 50% of planet host stars have evolved off the main sequence onto the subgiant branch, so that both the host stars and their planets are larger than previously reported. Similarly, in K2 Campaign 1 we may expect to find evolved stars in a sample of planet candidates, although we may expect the effect to be lessened due to the high Galactic latitude of Campaign 1. Indeed, we find this to be the case. Two stars, EPIC 201257461 and 201649426 are definitively evolved stars, with inferred masses less than 2 M${}_{\odot }$ but radii above 8 R${}_{\odot }$. For approximately one third of the others, we find the stellar radius posterior distribution to be bimodal, with both main sequence and subgiant models of the stars being consistent with the photometric data. This number is consistent with our expectations of the number of subgiant contaminants in the Campaign 1 field (K. Stassun 2015, private communication). Future observations to measure the parallaxes of these stars, such as with Gaia, will be helpful in differentiating between these two models to determine more precisely the stellar, and thus the planetary, radii.

A near-infrared spectrum of K2-18 was obtained using the upgraded SpeX spectrograph (Rayner et al. 2003) on the NASA Infrared Telescope Facility on 2015 January 29 (UT). SpeX observations were taken using the short cross-dispersed mode and the $0\buildrel{\prime\prime}\over{.} 3\times 15^{\prime\prime}$ slit, which provides simultaneous coverage from 0.7 to 2.5 μm at $R\simeq 2000$. The target was observed at two positions along the slit to subsequently subtract the sky background. Eight spectra were taken following this pattern, which provided a final signal-to-noise ratio (S/N) of $\gt 150$ per resolving element. The spectrum was flat fielded, extracted, wavelength calibrated, and stacked using the Spextool package (Cushing et al. 2004). An A0V-type star was observed immediately after the target, which was used to create a telluric correction using the xtellcor package (Vacca et al. 2003).

An optical spectrum was obtained using SNIFS (Aldering et al. 2002; Lantz et al. 2004) on the University of Hawai'i 2.2 m telescope on the night of 2015 January 30. SNIFS provides simultaneous coverage from 3200–9700 Å at a resolution of $\simeq 1000$. Final S/N of the spectrum was $\gt 100$ per resolving element in the red (∼6000 Å). Details of the SNIFS reduction, including dark, bias, and flat-field corrections, cleaning the data of bad pixels and cosmic rays, and extraction of the one-dimensional spectrum are described in Bacon et al. (2001) and Aldering et al. (2006). Flux calibration was performed using a separate pipeline described in Mann et al. (2015).

T_eff was calculated by comparing our optical spectra with the CFIST suite¹² of the BT-SETTL version of the PHOENIX atmosphere models (Allard et al. 2013), which gave a temperature of 3503 ± 60 K. More details of this procedure are given in Mann et al. (2013b) and Gaidos et al. (2014). This method was used because it is known to accurately reproduce empirical T_eff values from long-baseline optical interferometry Boyajian et al. (2012).

Metallcity was determined using the procedures from Mann et al. (2013a), in which the authors provide empirical relations between atomic features and M dwarf metallicity, calibrated using wide binaries. We adopted the weighted mean of the $H$- and $K$-band calibrations, which yielded a metallicity of 0.09 ± 0.09.

We combined the derived T_eff and [Fe/H] values with the empirical T_eff-[Fe/H]-R_* relation from Mann et al. (2015) to compute a radius. Accounting for measurement and calibration errors in [Fe/H] and T_eff we calculated a radius $0.394\pm 0.038{R}_{\odot }$. We use these parameters instead of the derived photometric properties for this target, although we note the two are consistent at the $1\sigma$ level.

The full list of stellar parameters adopted in this paper is included in Table 2.

Table 2.  Stellar Properties for All Objects of Interest

Name	R.A. (J2000)	Decl. (J2000)	Mass	Radius	Teff	[Fe/H]	Distance
	(Degrees)	(Degrees)	(${M}_{\odot }$)	(${R}_{\odot }$)	(K)	(dex)	(pc)
201208431/K2-4	174.745639	−3.905585	${0.63}_{-0.03}^{+0.03}$	${0.60}_{-0.02}^{+0.02}$	${4197}_{-43}^{+45}$	$-{0.12}_{-0.12}^{+0.10}$	${218}_{-10}^{+11}$
201257461	178.161110	−3.094936	${1.50}_{-0.02}^{+0.04}$	${10.96}_{-0.93}^{+0.82}$	${5141}_{-42}^{+38}$	$-{0.21}_{-0.01}^{+0.01}$	${1651}_{-134}^{+121}$
201295312	174.011629	−2.520881	${1.07}_{-0.07}^{+0.07}$	${1.09}_{-0.11}^{+0.20}$	${5989}_{-81}^{+100}$	$-{0.02}_{-0.18}^{+0.15}$	${331}_{-35}^{+61}$
201338508/K2-5	169.303502	−1.877976	${0.53}_{-0.01}^{+0.01}$	${0.52}_{-0.01}^{+0.01}$	${4102}_{-41}^{+45}$	$-{0.51}_{-0.06}^{+0.04}$	${181}_{-7}^{+7}$
201367065/K2-3	172.334949	−1.454787	${0.53}_{-0.02}^{+0.02}$	${0.52}_{-0.02}^{+0.02}$	${3951}_{-38}^{+33}$	$-{0.30}_{-0.06}^{+0.07}$	${42}_{-2}^{+2}$
201384232/K2-6	178.192260	−1.198477	${0.97}_{-0.07}^{+0.07}$	${0.96}_{-0.09}^{+0.14}$	${5850}_{-98}^{+79}$	$-{0.14}_{-0.20}^{+0.17}$	${343}_{-33}^{+52}$
201393098/K2-7	167.093771	−1.065755	${0.97}_{-0.06}^{+0.06}$	${0.96}_{-0.08}^{+0.17}$	${5772}_{-91}^{+72}$	$-{0.07}_{-0.16}^{+0.16}$	${433}_{-38}^{+75}$
201403446	174.266345	−0.907261	${1.01}_{-0.06}^{+0.08}$	${1.12}_{-0.14}^{+0.26}$	${6445}_{-111}^{+81}$	$-{0.50}_{-0.13}^{+0.15}$	${362}_{-48}^{+86}$
201445392/K2-8	169.793666	−0.284375	${0.79}_{-0.04}^{+0.03}$	${0.74}_{-0.03}^{+0.02}$	${4890}_{-58}^{+38}$	$-{0.01}_{-0.13}^{+0.11}$	${405}_{-16}^{+14}$
201465501/K2-9	176.264467	0.005301	${0.24}_{-0.03}^{+0.05}$	${0.25}_{-0.03}^{+0.04}$	${3468}_{-19}^{+20}$	$-{0.46}_{-0.10}^{+0.12}$	${66}_{-7}^{+11}$
201505350/K2-19	174.960319	0.603575	${0.84}_{-0.04}^{+0.04}$	${0.81}_{-0.05}^{+0.09}$	${5519}_{-82}^{+49}$	$-{0.27}_{-0.10}^{+0.10}$	${291}_{-20}^{+33}$
201546283	171.515164	1.230738	${0.89}_{-0.07}^{+1.15}$	${0.88}_{-0.10}^{+7.37}$	${5422}_{-93}^{+194}$	$-{0.09}_{-0.15}^{+0.31}$	${251}_{-29}^{+2138}$
201549860	170.103081	1.285956	${0.73}_{-0.03}^{+0.03}$	${0.69}_{-0.02}^{+0.02}$	${4523}_{-47}^{+43}$	${0.05}_{-0.14}^{+0.15}$	${249}_{-9}^{+9}$
201555883	176.075940	1.375947	${0.54}_{-0.01}^{+0.07}$	${0.52}_{-0.01}^{+0.08}$	${4419}_{-33}^{+29}$	$-{0.98}_{-0.11}^{+0.62}$	${289}_{-9}^{+46}$
201565013	176.992193	1.510249	${0.51}_{-0.03}^{+0.13}$	${0.50}_{-0.03}^{+0.12}$	${3987}_{-68}^{+142}$	$-{0.44}_{-0.08}^{+0.47}$	${506}_{-38}^{+154}$
201569483	167.171300	1.577513	${0.83}_{-0.05}^{+0.05}$	${0.79}_{-0.05}^{+0.06}$	${5192}_{-70}^{+55}$	$-{0.09}_{-0.15}^{+0.17}$	${152}_{-10}^{+12}$
201577035/K2-10	172.121957	1.690636	${0.94}_{-0.06}^{+0.04}$	${0.93}_{-0.07}^{+0.16}$	${5647}_{-89}^{+60}$	$-{0.04}_{-0.17}^{+0.14}$	${271}_{-21}^{+48}$
201596316/K2-11	169.042002	1.986840	${1.35}_{-0.56}^{+0.04}$	${5.15}_{-4.39}^{+0.20}$	${5433}_{-144}^{+49}$	$-{0.12}_{-0.17}^{+0.01}$	${2019}_{-1728}^{+71}$
201613023/K2-12	173.192036	2.244884	${1.01}_{-0.06}^{+0.05}$	${1.01}_{-0.09}^{+0.27}$	${5800}_{-90}^{+53}$	${0.03}_{-0.17}^{+0.13}$	${294}_{-27}^{+78}$
201617985	179.491659	2.321476	${0.52}_{-0.03}^{+0.03}$	${0.49}_{-0.03}^{+0.03}$	${3742}_{-36}^{+31}$	$-{0.08}_{-0.11}^{+0.10}$	${111}_{-9}^{+8}$
201629650/K2-13	170.155529	2.502696	${0.80}_{-0.04}^{+0.04}$	${0.78}_{-0.05}^{+0.09}$	${5698}_{-82}^{+45}$	$-{0.54}_{-0.14}^{+0.12}$	${290}_{-18}^{+34}$
201635569/K2-14	178.057026	2.594245	${0.47}_{-0.01}^{+0.01}$	${0.45}_{-0.01}^{+0.01}$	${3789}_{-16}^{+17}$	$-{0.37}_{-0.04}^{+0.03}$	${219}_{-8}^{+8}$
201649426	177.234262	2.807619	${1.29}_{-0.02}^{+0.02}$	${8.15}_{-0.23}^{+0.32}$	${5086}_{-26}^{+24}$	$-{0.17}_{-0.01}^{+0.01}$	${2537}_{-68}^{+92}$
201702477	175.240794	3.681584	${0.87}_{-0.06}^{+0.06}$	${0.85}_{-0.08}^{+0.11}$	${5618}_{-85}^{+86}$	$-{0.26}_{-0.18}^{+0.17}$	${673}_{-63}^{+87}$
201736247/K2-15	178.110796	4.254747	${0.72}_{-0.03}^{+0.06}$	${0.68}_{-0.03}^{+0.06}$	${5131}_{-65}^{+69}$	$-{0.46}_{-0.14}^{+0.20}$	${437}_{-22}^{+43}$
201754305/K2-16	175.097258	4.557340	${0.67}_{-0.03}^{+0.04}$	${0.64}_{-0.03}^{+0.03}$	${4761}_{-57}^{+50}$	$-{0.40}_{-0.17}^{+0.12}$	${324}_{-16}^{+16}$
201779067	168.542699	4.988131	${0.91}_{-0.04}^{+0.03}$	${0.92}_{-0.07}^{+0.20}$	${6166}_{-51}^{+30}$	$-{0.54}_{-0.12}^{+0.07}$	${188}_{-15}^{+39}$
201828749	175.654343	5.894323	${0.74}_{-0.04}^{+1.06}$	${0.71}_{-0.06}^{+9.64}$	${5552}_{-97}^{+87}$	$-{0.69}_{-0.23}^{+0.34}$	${146}_{-12}^{+1996}$
201855371/K2-17	178.329776	6.412261	${0.71}_{-0.05}^{+0.02}$	${0.66}_{-0.03}^{+0.02}$	${4320}_{-47}^{+56}$	${0.15}_{-0.22}^{+0.09}$	${134}_{-6}^{+5}$
201912552/K2-18a	172.560461	7.588391	${0.413}_{-0.043}^{+0.043}$	${0.394}_{-0.038}^{+0.038}$	${3503}_{-60}^{+60}$	${0.09}_{-0.09}^{+0.09}$	${34}_{-4}^{+4}$
201929294	174.656968	7.959611	${0.73}_{-0.09}^{+0.06}$	${0.70}_{-0.08}^{+0.04}$	${4786}_{-53}^{+48}$	$-{0.16}_{-0.34}^{+0.22}$	${197}_{-24}^{+13}$

Notes. These values and their uncertainties are derived from MULTINEST analysis and the numbers are computed as the 0.158, 0.500, and 0.842 posterior sample quantiles. The coordinates are retrieved directly from the EPIC. These data are available in interactive form at https://filtergraph.com/k2_planets_montet.

^aParameters inferred from spectroscopic observations.

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One of the definitive signatures of a false positive binary star system masquerading as a transiting planet is the presence of a secondary eclipse. While a nondetection of a secondary does not exclude the possibility of a binary system (the orbit may be eccentric, or the companion too faint for a secondary eclipse to be detectable in the noise), such a nondectection reduces the probability of each of the EB false positive scenarios.

To attempt to eliminate each EB scenario, we first search each K2 light curve to determine which secondary eclipse signals are not allowed by the data. We mask the transit signal of the planet in question and search for the most significant signal at the same period. Such a scheme does not assume circular orbits: we return the most significant signal at any phase, not only at the midpoint between consecutive transits.

We report these maximum allowable secondary eclipse depths in Table 5. These values are used by vespa as limits on the allowable secondary eclipse. Any models that cause a larger event, such as a background EB consisting of two equal-mass stars in a circular orbit, can be excluded by the data. We note that with the exception of K2-19c (EPIC 201505350.01), all systems with a maximum eclipse depth of at least one part per thousand have FPPs of 0.866 or larger. The exception, K2-19, is a two-planet system with the two planets near a 3:2 period commensurability, so in this case the "secondary" is actually the transits of the other planet.

We obtained high resolution images of seven stars with the Palomar High Angular Resolution Observer (PHARO) infrared detector (Hayward et al. 2001) behind the PALM3000 adaptive optics system (Dekany et al. 2013) at the Palomar 5.1 m Hale telescope on the nights of 2015 February 3 and 4 UT. Sky conditions were mostly clear with light cirrus and ≈10–13 seeing on both nights. We used the smallest plate scale of 25 mas pixels⁻¹ which resulted in a field of view of 256 × 256 across the 1024² pixels² array. All observations were obtained with the 32x pupil sampling mode, resulting in Strehl ratios of ≈20%–30% in K_S for our V = 11–13 mag targets as measured by the Strehl monitor at the telescope in real time. We obtained unsaturated dithered frames of each target in ${K}_{S}$-band with typical integration times of 2–10 s. Except for EPIC 201828749 and EPIC 201546283, which had nearby candidate binary companions, we also acquired deep saturated images (5–10 frames at 60 s each) to search for fainter companions.

Images were registered and contrast curves were generated following Bowler et al. (2015). For the saturated data, the star's position in each image was found by masking the saturated region and fitting a 2D bivariate Gaussian to the PSF wings. Contrast curves for the median-combined image are calibrated using the unsaturated frames. The typical sensitivity is 6.5–7.5 mag at $1^{\prime\prime}$. The images were astrometrically calibrated using dithered observations of the Trapezium cluster centered on ${\theta }^{1}$ Ori C taken on 2015 February 3 UT. Based on the reference astrometry for pairs of stars in the field from McCaughrean & Stauffer (1994), we measure a plate scale of 25.2 ± 0.4 mas pixels⁻¹ and north orientation of –02 ± 03. Since this latter value is consistent with being aligned with the detector columns, we adopt a value of 00 ± 03 for this work. Relative photometry of nearby stars is carried out using aperture photometry with an aperture radius of 12 pixels (03). For EPIC 201828749, we also acquired J- and H-band images. Astrometry and photometry is derived separately for each image, and the mean and standard deviation of these measurements is adopted for our final values listed in Table 4.

Images for all systems AO data was obtained for is shown in Figure 3, while contrast curves showing the $5\sigma$ limits for detection as a function of orbital separation are given in Figure 4.

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The PHARO AO system has a field of view of 25 arcsec. Each K2 pixel is a square, $3\buildrel{\prime\prime}\over{.} 98$ on a side. A background EB within a few K2 pixels of our target stars could mimic a transit signal inside our aperture while evading detection by PHARO. Such wide EBs should appear in seeing-limited ground-based surveys.

To investigate the possibility that such wide companions exist, we query the ninth data release of the Sloan Digital Sky Survey (SDSS DR9, Ahn et al. 2012). For each target, from the depth of the observed transit we determine how bright a background object must be to cause the event if the background object were an equal mass totally eclipsing binary. We then search for all stars within 25'' that are within this brightness limit relative to the candidate host star. All apertures we use in our K2 analysis are smaller than 20'' so this search should encompass the region where possible background contaminants could reside. Of the 31 stars in our sample, eleven have such a companion, plus one detected in AO imaging.

Unlike the original Kepler field, the field for K2 Campaign 1 is well out of the Galactic plane, so the rate of giant, distant background stars is significantly lower. We include all potential contaminants in Table 4. We validate or eliminate each of these as a possibility based on the transit shape. For example, the events near EPIC 201546283 could only be caused by a background binary if the background object was a completely eclipsing system (so that the eclipse depth was 50%). In this case, the transit would be perfectly V-shaped. Since it is not, this background object likely does not cause the transit event.

In Table 4, the "maximum depth" column represents the maximum observed "transit" depth if the transit were actually caused by a total eclipse of the hypothetical background binary system, inducing a 50% flux decrement in the background star's apparent brightness.

The photometric apertures used to detect these candidates range in radius from $10\buildrel{\prime\prime}\over{.} 0$ to $19\buildrel{\prime\prime}\over{.} 9$. In order to be a plausible contaminant, any companion star must be either within this aperture or just outside but bright enough for signficant flux to leak in. Evaluating each of the systems listed in Table 4, we judge that we cannot yet rule out contamination as a potential source of the transit signal for four candidates: 201295312.01, 201403446.01, 201546283.01, and 201828749.01. Despite receiving low FPP scores from vespa, we list these systems as candidates in Table 5, rather than planets. Further updates to the vespa code will allow consideration of "specific" false positive scenarios; that is, scenarios that correspond to actually detected stars such as these, rather than hypothetical background or bound companions.

The candidates with identified companions that we judge to not be plausible sources of potential contamination are the following.

• 1.  
  201546283.01—for this system, the "maximum depth" is nearly identical to the observed transit depth, which would require a perfectly V-shaped eclipse to explain. As this is not the case (see Figure 2), this signal cannot be caused by contamination from this star.
• 2.  
  K2-13b (201629650.01)—the companion to this star is $17\buildrel{\prime\prime}\over{.} 3$ from the EPIC target. As this is outside the aperture (radius $15\buildrel{\prime\prime}\over{.} 9$) and the background star is not particularly bright, we rule out contamination for this system.
• 3.  
  201702477.01—the companion to this star is $12\buildrel{\prime\prime}\over{.} 15$ from the EPIC target, and the aperture size is $10\buildrel{\prime\prime}\over{.} 0$. In addition, the maximum depth in this system is almost identical to the transit depth. For these two reasons we rule out contamination in this case.

SDSS is 95% complete at r = 22.2 mag and the telescope has a PSF of $1\buildrel{\prime\prime}\over{.} 4$. For the purposes of the vespa calculation, we thus treat nondetection in SDSS data as providing a contrast curve at wide separations down to a limiting magnitude of r = 22.2 mag.

For the stars with AO nondetections, there is still the possibility that a background binary could be positioned directly behind the target star, evading detection. The probability is small, given the $0\buildrel{\prime\prime}\over{.} 1$ diffraction limit of the Hale Telescope at 2 μm, but nonzero. While the vespa calculations quantify this probability for this to occur, we can also rule out the possibility of such chance alignments, down to a certain contrast, with archival imaging data.

Five of the stars in our sample have proper motions larger than 50 mas ${\mathrm{yr}}^{-1}$, so they have moved across the sky by $\gtrsim 2\buildrel{\prime\prime}\over{.} 5$ since they were imaged during the first Palomar Observatory Sky Survey (POSS) in the 1950s. To rule out background companions, we download data from the POSS I and II surveys, which imaged these targets in 1952–1955 and 1989–1998, respectively. We also download data from the Sloan Digital Sky Survey, which imaged these fields between 2000 and 2009. As shown in Figure 5, we do not detect any background targets at the present-day location of any of these stars in any of these images.

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For this target, we can extend our contrast curves to zero present-day orbital separation and rule out the possibility that these transit events are caused by a background EB. By combining present-day seeing-limited photometric survey data, adaptive optics imaging, and archival photometry, the only stellar companions we would not detect would be those that are gravitationally bound to the target star and positioned in their orbits so that their projected separation is smaller than the diffraction limit of the Hale Telescope. Such an alignment would require the orbital inclination of the binary to be nearly 90° and the phase $\varpi +\theta \approx \pi /2$ or $3\pi /2$. While we cannot fully rule out this possibility, the vespa calculations confirm that its probability is negligibly small.

We observed EPIC 201912552 on 2015 February 04 and 25 UT with TRES on the 1.5 m Tillinghast Reflector at the Fred L. Whipple Observatory. These dates were chosen to be near the times of largest RV variations, corresponding to phases of 0.72 and 0.32 relative to the time of transit. The spectra were taken with a resolving power of R = 44,000 and integration times ranging from 2800 to 3600 s, resulting in S/N between 17 and 29 per resolution element.

The spectra were extracted as described in Buchhave et al. (2010). The relative RVs were derived by cross-correlating the spectra against the strongest observed spectrum (in this case, the first) over the wavelength range 4700–6800 Å. We selected 19 echelle orders in the analysis, being careful to reject orders with telluric absorption lines, fringing in the far red and those with very low SNR in the blue.

The two observed spectra have RVs that differ by 47 ± 42 m s⁻¹. If the RVs were caused by a stellar companion, the RV shift between these observations would be on the order of km s⁻¹. Therefore, we can rule out any stellar-mass companions that would be able to create this transit signal.

The planet orbiting K2-18 may be an interesting target for atmospheric studies of transiting exoplanets.

By combining archival and modern seeing-limited data with adaptive optics imaging, we can exclude the possibility these transit events are caused by a background EB. The apparent transits must be caused by an object co-moving with K2-18; radial velocities eliminate the possibility the companion is nonplanetary. Therefore, we confirm the planetary nature of this system.

This star is an M2.8 dwarf at a distance of 34 ± 4 pc. Of our planet candidate hosts, only K2-3 (originally discovered by Crossfield et al. 2015) is brighter in K-band. This star is only 0.1 mag fainter in K than GJ 1214 (Charbonneau et al. 2009). Due to the relative brightness of the host star, this target is likely to become a prime target for atmospheric characterization studies and is ideal as a target for future space-based missions such as JWST.

The planet is slightly smaller than GJ 1214b, but unlike that planet, K2-18b is not highly irradiated. Instead, it is at a reduced semimajor axis $a/{R}_{\star }$ $=\;83.8\pm 9.0$. Its equilibrium temperature is then, assuming zero albedo, ${T}_{\mathrm{eq}}=272\pm 15$ K, meaning its bulk insolation is 94% ± 21% that of the Earth's. Although the planet is likely too large to be rocky (Rogers 2015), its atmosphere is likely to be the focus of many future observations, providing a cool analogue to the highly irradiated planets of a similar size found by Kepler.

The method of Foreman-Mackey et al. (2015) assumes that all variability in the light curves are caused by either the motion of K2, in which case the variability is shared by all stars, or transits of planets, in which case the variability is intrinsic to only one star. This assumption breaks down for extremely spotted stars where the astrophysical variability is larger than the instrumental magnitude. In that regime, the starspot modulations can be incorrectly fit by the systematic model, causing spurious transits to appear. This appears to be the case with EPIC 201929294, which has coherent starspots that appear to have the same rotation period as the transit period reported previously. Because the starspots are so periodic and coherent, these spurious transits were falsely identified as a planet candidate; we consider that system a false positive in this work.

The candidate object possibly orbiting EPIC 201555883 has a period, time of transit, and transit duration consistent with EPIC 201569483. Such effects are not uncommon in Kepler data. Coughlin et al. (2014) identify 685 KOIs as false positives and outline four physical reasons why these anomalies may occur. EPIC 201555883 is a unique case in that it does not appear to fall under any of these cases. It falls on module 23, while EPIC 201569483 is on module 8, neither 180° away from nor on the same column as this candidate. Moreover, there is not any evidence of a mechanism that could cause a third star to induce both the appearance of a 7% eclipse on one module and an additional anomalous transit event on a different module. Instead, this candidate could be a false positive caused by a different systematic mechanism.

Foreman-Mackey et al. (2015) modeled the systematic effects in the K2 light curves using a linear combination of "eigen light curves" generated empirically by running a PCA on the light curves of every star. This means that the training set includes the light curves for variable stars, EBs, and even transiting planets. Again, this star has significant variability caused by starspots. In this case, the fitting procedure tries to account for stellar variability using the eigen light curves. This overfit gives undue weight to eigen light curves that include the transits of EPIC 201569483, causing this spurious transit to occur. Again, we consider this system to be a false positive. As stated in Section 3, by including an empirical Gaussian prior on the weights for the eigen light curves in the linear systematics model, the signals observed on 201555883 and 201929294 are mitigated, suggesting such a scheme should be employed in searching for planet candidates in future campaigns.

The problem of over-fitting stellar variability using eigen light curves can also be solved by adding a stellar activity model to our fitting procedure. In this case, the spacecraft motion could be fit simultaneously with a model of starspot modulation, astroseismic oscillations, and planet transits. Such a model is currently under development (R. Angus et al. 2015, in preparation).

Five of the systems reported by Foreman-Mackey et al. (2015) have more than one transiting candidate. One of these is K2-3, a three-planet system originally announced by Crossfield et al. (2015). Another of these is K2-19 (Armstrong et al. 2015), a two-planet system with the orbital periods of the two planets near a 3:2 period commensurability. The remaining three are all representative of the multiple-planet systems observed by Kepler (Lissauer et al. 2011; Fabrycky et al. 2014). Two of the systems are near a period commensurability and all three consist of mini-Neptune sized planets.

We do not detect any significant transit timing variations (TTVs) in any of these systems from the K2 data alone. K2-5 (EPIC 201338508) would be expected to have a TTV period of 117 days, but is likely too far from commensurability to have an observable TTV signal. K2-8 (EPIC 201445392) is expected to have a TTV period of 234 days, so this system may be a candidate for additional follow-up to constrain the system masses dynamically. The transiting planets orbiting K2-16 (EPIC 201754305) are near a 5:2 period commensurability. There is no evidence from Kepler of an abundance of planets near this period ratio, and so this may be coincidence. Follow-up observations may be warranted to search for an additional planet in this system forming a resonant chain, similar to those observed around other stars (e.g., Swift et al. 2013; Campante et al. 2015).

One of the primary goals of K2 is the detection of transiting planets around bright stars that can be followed up from the ground or with future space-based observatories such as JWST (Howell et al. 2014). Of our sample, two systems orbit stars with $K\lt 9$ mag: K2-3 (Crossfield et al. 2015) and K2-18. An additional planet candidate may orbit EPIC 201828749, a star with $K=9.93\pm 0.03$ mag. These targets are ideal for ground-based followup and may be useful targets for Spitzer and JWST to probe planetary atmospheres.