PLANET HUNTERS. VI. AN INDEPENDENT CHARACTERIZATION OF KOI-351 AND SEVERAL LONG PERIOD PLANET CANDIDATES FROM THE KEPLER ARCHIVAL DATA^*

Once a system is identified as having a possible transit signal, we perform a full analysis of the system using the Kepler light curve (data validation; Batalha et al. 2010) and any other publicly available archival data. This includes using the PyKE package (Still & Barclay 2012) and screening the surrounding field for background eclipsing binaries by ensuring that the flux-weighted centroid remains stationary during an object's transit (Bryson et al. 2013). By measuring the flux centroid shift between in- and out-of-transit, a limit can be put on the angular separation of a possible contamination source. This method has limitations when the target star is brighter than 11th magnitude or if it is in a crowded field (Wang et al. 2014). The flux-weighted centroid method reported large (>3σ) flux centroid offsets for the aforementioned cases even for confirmed planet candidates. However, all but one objects in this paper are fainter than 13th magnitude. Our own flux-weighted centroid analysis package is described in Wang et al. (2013) and Wang et al. (2014).

We use UKIRT and Two Micron All Sky Survey images to search for nearby contaminating sources and asymmetric point spread functions, necessary for probing nearby unresolved sources due to the low-resolution of the Kepler CCD detector. Two of the stars have a visual companion within 4'': KIC 6372194 and 10255705 (see Figure 1 for the UKIRT images and Table 1). If these companions are outside the computed confusion radius, the candidates are unlikely to be orbiting the contaminating sources. If they are orbiting the contaminating sources and outside the confusion radius, an apparent pixel centroid offset should have been detected. However, KIC 10255705 has a 3σ confusion radius of 32 and a companion at 14, meaning that no apparent pixel centroid offset would be seen, so we cannot be sure the planet is truly orbiting the brighter star. The neighboring stars for both KIC 6372194 and 10255705 are at least 2 mag fainter than the central star. The uncertainty caused by the flux contamination is smaller than the one from the stellar radius estimation, so we did not include the dilution factor in our parameter estimates. Afterward, the light curves are then fully modeled and inspected for variations in even–odd transit depth, the presence of secondary eclipses, and misshaped transit profiles, any of which can indicate a falsely identified planetary candidate with tools from Still & Barclay (2012).

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The revised set of Kepler stellar parameters provides estimates of T_eff, log(g), mass, radius, and [Fe/H] of all stars in the Kepler field (Huber et al. 2014). We adopt these as stellar inputs for the Wang et al. (2013) transit fitting routine from the Kepler stellar data hosted by the NEA Exoplanet Archive.¹³ Table 2 lists the primary stellar parameters. We use the values in Table 2 as inputs for our own transit fitting routine (Wang et al. 2014, 2013) developed to iterate between the light curve solution and the Yonsei–Yale (Y²) isochrones (Demarque et al. 2004) for a range of ages spanning from 0.08 to 15 Gyr, with [α/Fe] =0. The high T_eff of KIC 5522786, T = 8941 K, fell on the upper edge of the temperature range for our stellar models, which caused error bars to be clipped. As such, we retain the Huber et al. (2014) stellar parameters for KIC 5522786. We ran 1000 trials of Monte Carlo simulations using the Y² isochrones to obtain stellar properties such as effective temperature, mass, radius, metallicity, and luminosity. The distributions of the inputs are assumed to follow a Gaussian function. The mean and standard deviation are the reported value and error bar in the Kepler stellar parameter table. The distributions of the outputs are used to constrain the transit light curve fitting, excluding mathematically acceptable fits that are physically unlikely. The formal error bars sometimes result in unrealistically low error bars for log(g), radius, and mass, so we adopt a floor on the log(g) error bar of ±0.10, 20% for the radius error, and 10% for the mass error. The outputs of the transiting light curve fitting (e.g., stellar density) can also be used to constrain the Y² isochrone. Thus, the iterative transit fitting routine is able to provide a set of self-consistent stellar and orbital solutions.

Table 2. Stellar Parameters

	Input Values							Derived Values
Star	Kp	(g − r)	Teff	log g	M*	R*	[Fe/H]	Teff	log g	M*	R*	[Fe/H]	L*	ρ*
(KIC)	(mag)	(mag)	(K)	(cgs)	(M☉)	(R☉)	(dex)	(K)	(cgs)	(M☉)	(R☉)	(dex)	(L☉)	(g cm−3)
2437209	16.353	1.001	4822	4.56	0.73	0.74	−0.04	$4842^{+157}_{-90}$	$3.07^{+0.60}_{-0.15}$	$1.16^{+0.75}_{-0.30}$	$4.97^{+2.09}_{-1.14}$	$0.07^{+0.45}_{-0.23}$	$10.68^{+14.48}_{-5.52}$	2.33 ± 0.49
5010054	13.961	0.631	5944	4.22	1.05	1.32	0.02	$5948^{+145}_{-81}$	$4.37^{+0.15}_{-0.15}$	$1.07^{+0.11}_{-0.11}$	$1.05^{+0.38}_{-0.21}$	$0.01^{+0.20}_{-0.08}$	$1.17^{+1.15}_{-0.12}$	1.30 ± 0.66
5094412	15.772	0.633	5511	4.60	0.83	0.76	−0.34	$5572^{+109}_{-96}$	$4.58^{+0.15}_{-0.15}$	$0.82^{+0.08}_{-0.08}$	$0.76^{+0.15}_{-0.15}$	$-0.42^{+0.20}_{-0.11}$	$0.46^{+0.07}_{-0.05}$	2.64 ± 0.70
5522786a	9.350	−0.146	8941	4.12	2.10	2.08	0.07	...	...	...	...	...	$24.78^{+17.88}_{-17.88}$	$0.328^{+0.234}_{-0.223}$
5732155	15.195	0.550	6140	4.45	1.09	1.03	−0.04	$6065^{+131}_{-77}$	$4.41^{+0.15}_{-0.15}$	$1.02^{+0.10}_{-0.21}$	$1.06^{+0.21}_{-0.11}$	$-0.12^{+0.15}_{-0.10}$	$1.17^{+0.31}_{-0.12}$	1.37 ± 0.36
6372194	15.870	0.698	5314	4.62	0.80	0.72	−0.34	$5308^{+187}_{-68}$	$4.62^{+0.15}_{-0.15}$	$0.79^{+0.08}_{-0.08}$	$0.71^{+0.14}_{-0.14}$	$-0.44^{+0.22}_{-0.09}$	$0.35^{+0.07}_{-0.04}$	3.17 ± 0.73
6436029	15.768	1.007	4817	4.50	0.80	0.83	0.42	$4878^{+173}_{-31}$	$4.55^{+0.15}_{-0.15}$	$0.83^{+0.08}_{-0.08}$	$0.81^{+0.16}_{-0.16}$	$0.42^{+0.05}_{-0.03}$	$0.36^{+0.09}_{-0.04}$	2.20 ± 0.69
6805414	15.392	0.555	6108	4.47	1.07	1.00	−0.08	$6029^{+133}_{-68}$	$4.43^{+0.15}_{-0.15}$	$1.00^{+0.10}_{-0.10}$	$1.02^{+0.20}_{-0.20}$	$-0.25^{+0.20}_{-0.06}$	$1.20^{+0.20}_{-0.12}$	1.36 ± 0.60
9662267	14.872	0.534	6032	4.49	1.06	0.97	−0.06	$5870^{+172}_{-43}$	$4.44^{+0.15}_{-0.15}$	$1.02^{+0.10}_{-0.10}$	$0.98^{+0.20}_{-0.20}$	$-0.21^{+0.17}_{-0.08}$	$1.02^{+0.20}_{-0.10}$	1.56 ± 0.65
9704149	15.102	0.540	5897	4.53	0.98	0.89	−0.16	$5738^{+165}_{-47}$	$4.50^{+0.15}_{-0.15}$	$0.91^{+0.09}_{-0.09}$	$0.88^{+0.18}_{-0.18}$	$-0.37^{+0.18}_{-0.07}$	$0.79^{+0.11}_{-0.08}$	1.89 ± 0.39
10255705	12.950	0.698	5286	3.96	0.90	1.64	−0.12	$5339^{+153}_{-84}$	$3.73^{+0.80}_{-0.15}$	$1.34^{+0.31}_{-0.26}$	$2.53^{+1.13}_{-0.58}$	$-0.20^{+0.35}_{-0.10}$	$4.29^{+4.76}_{-1.71}$	0.11 ± 0.10
11152511	13.618	0.640	5568	4.27	0.86	1.12	−0.08	$5548^{+161}_{-58}$	$4.44^{+0.15}_{-0.15}$	$0.92^{+0.10}_{-0.09}$	$0.92^{+0.25}_{-0.18}$	$-0.08^{+0.28}_{-0.09}$	$0.64^{+0.46}_{-0.06}$	1.53 ± 0.99
11442793	13.804	0.398	6238	4.38	0.97	1.05	−0.40	$6258^{+150}_{-103}$	$4.39^{+0.15}_{-0.15}$	$0.99^{+0.10}_{-0.10}$	$1.04^{+0.21}_{-0.21}$	$-0.48^{+0.23}_{-0.09}$	$1.47^{+0.48}_{-0.18}$	1.24 ± 0.43
12454613	13.537	0.617	5530	4.56	0.94	0.84	0.00	$5436^{+144}_{-54}$	$4.55^{+0.15}_{-0.15}$	$0.87^{+0.09}_{-0.09}$	$0.82^{+0.16}_{-0.16}$	$-0.17^{+0.18}_{-0.08}$	$0.55^{+0.06}_{-0.06}$	2.34 ± 0.69

Notes. Stellar inputs (Huber et al. 2014) and outputs from the iterative light curve and stellar isochrone fitting routine. See Section 3.2 for details. ^aKIC 5522786 has a T_eff above the limits of our stellar modeling, so we used the stellar parameters from Huber et al. (2014).

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All available long-cadence light curves from Kepler quarters 1–16 were flattened, normalized, and phase-folded using the PyKE package (Still & Barclay 2012). We used a custom-made package (Wang et al. 2013) to find the best fit values for the orbital period (P), the ratio of the planet radius to the stellar radius (R_PL/R_*), the ratio of the semi-major axis to the stellar radius (a/R_*), inclination (i), eccentricity (e), longitude of periastron (ω), and midtransit times. Quadratic limb darkening parameters are determined by interpolating a table provided by Claret & Bloemen (2011). The best fit parameters were determined through a Levenberg–Marquardt least square algorithm, while the error bars are estimated with a bootstrapping method in the following way. We repeatedly fit the simulated transiting light curves, which were generated from the observations but perturbed by photon noise. In order to reduce the dependence of the initial guess of orbital parameters, we perturbed the initial guess based on the standard deviation of previous runs. We used a range of five times the standard deviation to explore a large phase space. The reported orbital solutions in Table 3 are the weighted averages based on the goodness of fit.

Table 3. Orbital Parameters

Star	T0	Period	Impact	RPL/R*	e	ω	i	a/R*	a	RPL	S	Depth	Duration
KIC	(MJD)	(days)	Parameter			(radian)	($\deg$)		(AU)	(R⊕)	(S0)	(ppm)	(hr)
2437209	55329.2790	$281.3290^{+0.0012}_{-0.0040}$	$0.48^{+0.10}_{-0.48}$	$0.1154^{+0.0006}_{-0.0017}$	$0.43^{+0.23}_{-0.43}$	$4.72^{+0.50}_{-2.38}$	$89.31^{+0.24}_{-1.26}$	$39.79^{+25.10}_{-7.25}$	0.88 ± 0.13	62.64 ± 19.61	14.39 ± 11.76	13115 ± 1137	73.56
5010054a	55188.9590	$904.0905^{+0.0114}_{-0.0533}$	$0.03^{+0.84}_{-0.03}$	$0.0257^{+0.0006}_{-0.0010}$	$0.31^{+0.68}_{-0.31}$	$3.72^{+1.43}_{-3.72}$	$90.00^{+0.00}_{-0.31}$	$372.31^{+38.58}_{-8.93}$	1.86 ± 0.09	2.92 ± 0.48	0.37 ± 0.07	789 ± 136	21.23
5094412	55009.0210	$276.8800^{+0.0000}_{-0.0000}$	$0.99^{+0.01}_{-0.09}$	$0.0895^{+0.0187}_{-0.0591}$	$0.04^{+0.10}_{-0.04}$	$5.97^{+0.32}_{-5.97}$	$89.74^{+0.21}_{-0.17}$	$220.60^{+12.59}_{-13.51}$	0.77 ± 0.03	7.38 ± 3.24	0.77 ± 0.17	2014 ± 280	3.77
5522786a	55115.4928	$757.1570^{+0.0089}_{-0.0299}$	$0.36^{+0.40}_{-0.29}$	$0.0089^{+0.0003}_{-0.0014}$	$0.45^{+0.41}_{-0.45}$	$1.53^{+2.79}_{-1.53}$	$89.91^{+0.09}_{-0.28}$	$236.70^{+25.98}_{-20.35}$	2.07 ± 0.06	1.86 ± 0.25	4.85 ± 0.98	90 ± 13	14.71
5732155a	55369.2000	$644.1978^{+0.0077}_{-0.0182}$	$0.39^{+0.12}_{-0.39}$	$0.0573^{+0.0021}_{-0.0028}$	$0.52^{+0.20}_{-0.24}$	$4.40^{+0.34}_{-0.52}$	$89.93^{+0.03}_{-0.12}$	$307.37^{+22.70}_{-13.83}$	1.47 ± 0.09	6.34 ± 0.48	0.59 ± 0.10	3644 ± 398	24.03
6372194	55375.9140	$281.5904^{+0.0031}_{-0.0094}$	$0.97^{+0.03}_{-0.11}$	$0.1027^{+0.1905}_{-0.0086}$	$0.27^{+0.09}_{-0.27}$	$2.34^{+3.95}_{-2.34}$	$89.76^{+0.01}_{-0.07}$	$232.59^{+12.76}_{-10.00}$	0.78 ± 0.02	7.90 ± 7.68	0.59 ± 0.18	10515 ± 344	5.90
6436029	55290.6000	$505.4611^{+0.0152}_{-0.0340}$	$0.56^{+0.43}_{-0.56}$	$0.0470^{+0.0680}_{-0.0228}$	$0.63^{+0.36}_{-0.63}$	$4.63^{+1.66}_{-4.63}$	$89.90^{+0.08}_{-0.08}$	$308.28^{+11.00}_{-29.10}$	1.17 ± 0.04	4.16 ± 4.04	0.26 ± 0.07	1972 ± 389	13.49
6805414	55137.9480	$200.2473^{+0.0010}_{-0.0027}$	$0.39^{+0.12}_{-0.02}$	$0.1083^{+0.0001}_{-0.0006}$	$0.74^{+0.09}_{-0.05}$	$4.86^{+0.27}_{-0.57}$	$89.84^{+0.02}_{-0.03}$	$142.17^{+12.84}_{-8.93}$	0.67 ± 0.04	11.91 ± 1.58	2.67 ± 0.50	12482 ± 296	23.72
9662267a	55314.3800	$466.1710^{+0.0112}_{-0.0370}$	$0.74^{+0.19}_{-0.26}$	$0.0426^{+0.0052}_{-0.0094}$	$0.65^{+0.34}_{-0.65}$	$5.37^{+0.92}_{-5.37}$	$89.83^{+0.02}_{-0.11}$	$257.93^{+22.65}_{-16.43}$	1.18 ± 0.04	4.50 ± 0.98	0.77 ± 0.15	1511 ± 229	10.55
9704149a	55252.2220	$697.0159^{+0.0000}_{-0.0000}$	$0.38^{+0.34}_{-0.38}$	$0.0524^{+0.0039}_{-0.0018}$	$0.03^{+0.11}_{-0.03}$	$6.29^{+0.00}_{-6.29}$	$89.94^{+0.02}_{-0.05}$	$367.03^{+23.65}_{-10.04}$	1.49 ± 0.06	5.01 ± 0.39	0.33 ± 0.09	3214 ± 406	13.86
10255705a	55378.2200	$707.8201^{+0.0000}_{-0.0000}$	$0.57^{+0.09}_{-0.57}$	$0.0362^{+0.0010}_{-0.0120}$	$0.52^{+0.18}_{-0.52}$	$4.82^{+1.47}_{-4.82}$	$89.76^{+0.07}_{-0.19}$	$136.78^{+55.92}_{-6.74}$	1.69 ± 0.13	10.08 ± 3.09	1.67 ± 0.66	1118 ± 102	39.72
11152511	55193.2608	$287.3377^{+0.0348}_{-0.0837}$	$0.36^{+0.49}_{-0.36}$	$0.0187^{+0.0113}_{-0.0166}$	$0.00^{+0.08}_{-0.00}$	$0.00^{+6.16}_{-0.00}$	$89.89^{+0.11}_{-4.14}$	$190.60^{+4.72}_{-48.07}$	0.83 ± 0.05	1.93 ± 1.50	1.06 ± 0.80	463 ± 95	9.38
11442793	55087.1710	$124.9199^{+0.0236}_{-0.0540}$	$0.54^{+0.05}_{-0.43}$	$0.0239^{+0.0147}_{-0.0215}$	$0.69^{+0.30}_{-0.69}$	$4.73^{+0.25}_{-1.22}$	$89.69^{+0.31}_{-3.86}$	$99.70^{+10.81}_{-4.08}$	0.49 ± 0.03	2.70 ± 2.07	5.82 ± 1.70	480 ± 87	10.48
12454613a	55322.7620	$736.3819^{+0.0065}_{-0.0211}$	$0.37^{+0.42}_{-0.37}$	$0.0289^{+0.0064}_{-0.0015}$	$0.16^{+0.21}_{-0.16}$	$0.00^{+0.17}_{-0.00}$	$89.95^{+0.03}_{-0.18}$	$399.19^{+22.45}_{-17.10}$	1.54 ± 0.04	2.56 ± 0.42	0.23 ± 0.04	1006 ± 142	12.79

Notes. Orbital fit to the Kepler light curves from the iterative light curve and stellar isochrone fitting routine. ^aPlanet candidates with only two transits. Of these, KIC 9704149 actually only has 1.5 transits due to a data gap interrupting the second transit.

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Table 4. KOI-351 Candidates

Candidate	T0	Period	Impact	RPL/R*	i	a/R*	a	RPL	S	Depth	Duration
	(MJD)	(days)	Parameter		($\deg$)		(AU)	()(R⊕)	(S0)	(ppm)	(hr)
KOI-351.01	54972.98	331.64	0.326	0.0833	89.95	180	0.94	9.4 ± 4.0	1.67	8277	14.54
KOI-351.02	54979.55	210.60	0.313	0.0584	89.95	133	0.69	6.6 ± 2.9	3.09	4073	12.23
KOI-351.03	54991.45	59.74	0.01	0.0217	89.95	57.4	0.30	2.5 ± 1.1	16.3	567	8.12
KOI-351.04	54966.82	91.94	0.29	0.0192	89.95	76.5	0.40	2.2 ± 1.0	9.12	432	8.97
KOI-351.05	54971.96	8.72	0.36	0.0116	88.81	15.9	0.083	1.3 ± 0.51	213	148	3.97
KOI-351.06	54970.17	7.01	0.34	0.0099	88.81	13.8	0.072	1.1 ± 0.48	284	104	3.71
KOI-351.07	55087.22	124.92	0.54	0.0239	89.69	99.8	0.49	2.7 ± 2.07	6.12	480	10.48

Notes. KOI-351.01 through KOI-351.06 values are directly from the public KOI data (http://exoplanetarchive.ipac.caltech.edu, last accessed 2014 March 11), scaled to our model's stellar parameters of M = 0.99 ± 0.10 M_☉, $R=1.04^{+0.12}_{-0.10}\,R_{\odot }$, and $T_{\rm {eff}}=6258^{+150}_{-103}$ K.

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The phase-folded solutions for each star are shown in Figure 2. Odd and even transits are colored blue and red, respectively, and there is no significant odd–even depth variation, which would be indicative of an eclipsing binary star system. The strongest odd–even depth variation is 1.49σ for KIC 5522786, a two transit candidate. Table 3 contains best fit parameters for the new planet candidates.

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Planet Hunters has produced a relatively large proportion of the known long period candidates from the Kepler data (see Figure 3). Importantly, it is these longer periods that probe the HZs of G- and K-type stars. The inner edge of the HZ is typically defined as the orbital radius of the water-loss limit, the point at which a terrestrial planet will quickly lose its water, and the outer edge is defined by a maximum greenhouse effect from CO₂ (Kasting et al. 1993). These two boundaries define the "conservative" HZ. "Empirical" HZ estimates expand the HZ by assuming Venus had water for much of its history ("Recent Venus") and that Mars had water early in its history ("Early Mars"). A revised estimate of the HZ by Kopparapu et al. (2013) proposes to define the HZ by its level of incident flux, S, rather than the equilibrium temperature of the planet, removing the dependency on Bond albedo. The HZ also varies with spectral type as the peak wavelength of the stellar emission changes. As such, cooler stars have slightly more distant HZs relative to the incident flux on the planet.

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In this revised HZ estimate, only the a/R_* and T_eff are required to determine whether the planet resides in its host's HZ. Seven planet candidates lie directly in the conservative HZ: KIC 2437209, 5010054, 5094412, 5732155, 6372194, 9662267, and 9704149. KIC 11152511 sits in the Recent Venus HZ with error bars into the conservative HZ. KIC 6436029 and KIC 10255705 are outside of the HZ, but are within 1σ of the Early Mars and Recent Venus HZs, respectively. See Figure 4 for the location of each planet candidate relative to its host star's HZ.

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Of these, KIC 11152511 has the lowest radius, R = 1.93 ± 1.50 R_⊕. The best-fit value falls very near or on the transition zone between high density super Earths with thin atmospheres and low density mini-Neptunes with thick atmospheres, which recent studies show is likely between 1.5 and 2.0 R_⊕ (Lopez & Fortney 2013; Weiss & Marcy 2014; Marcy et al. 2014). However, this candidate is likely shrunk due to neglected light dilution from its neighboring star. KIC 5522786's planet candidate also lies in this transition zone (R = 1.86 ± 0.25 R_⊕), leaving uncertainty as to whether this candidate would be a super Earth or mini-Neptune. However, although it lies outside the T_eff range studied by Kopparapu et al. (2013), it certainly orbits too close to the star, with S ≈ 5S₀ (five times the solar incident flux).

In quarters 1–16, the light curve for KIC 2437209 has four large (∼14, 000 ppm) and long transits (duration of 71 hr; see Figure 2, Table 3). Although there were three transits (and a fourth in a data gap), one transit was de-emphasized due to a sudden pixel sensitivity dropout detector in TPS, leaving it without the requisite three detected transits to be labeled a TCE (J. M. Jenkins 2014, private communication). With a fourth transit in Q14, the Q1–16 TPS search (Tenenbaum et al. 2014) has detected this signal, and it is now a KOI candidate.

KIC 2437209's transit duration, approximately equivalent to the duration of Neptune transiting the Sun, is extremely long for a 281 day orbit. Our first attempts at modeling this system resulted in a degeneracy in the stellar and planetary radius. This system was consistent with two scenarios: an evolved star on the giant branch with a stellar companion in a circular orbit or with a main sequence dwarf with a planetary companion in a highly eccentric e = 0.974 orbit viewed at apastron, an unfavorable probability of occurrence. In the evolved star interpretation, the stellar parameters were $\rm {log({g})}=3.07^{+0.60}_{-0.10}$, $R_{*}=4.97^{+2.09}_{-1.14}\,R_{\odot }$, R_PL = 62.64 ± 19.61 R_⊕, $e=0.43^{+0.23}_{-0.43}$, while the dwarf interpretation had best-fit values of log(g) = 4.56 ± 0.10, R_* = 0.80 ± 0.10 R_☉, R_PL = 9.79 ± 0.62 R_⊕, $e=0.974^{+0.013}_{-0.029}$, similar to the Huber et al. (2014) stellar parameters.

This degeneracy led us to obtain one spectrum of the star with Keck/HIRES (Vogt et al. 1994) in an attempt to better determine the stellar parameters. We used Spectroscopy Made Easy (SME; Valenti & Piskunov 1996; Valenti & Fischer 2005) to model the spectrum; however, due to the faintness of the star (K_p = 16.353), the resulting signal to noise ratio was ∼15, well below the preferred regime for reliable SME analysis. Nevertheless, our results fitting the spectrum with SME gave T_eff = 4965 ± 100 K, log(g) = 3.75 ± 0.2, and [Fe/H] = 0.564 ± 0.10. This has overlapping error bars with our evolved star interpretation and is inconsistent with input stellar parameters from Huber et al. (2014).

KIC 2437209 has six quarters of short-cadence data and likely belongs to the open cluster NGC 6791. With g' = 17.239 and (g' − r') = 1.001 given by the Kepler Input Catalog, KIC 2437209 is placed on the giant branch of NGC 6791 on the g' versus (g' − r') color–magnitude diagram (Platais et al. 2011). Evolved cluster stars are usually targets for short-cadence Kepler observations to study pulsations. Assuming that the star is a member of NGC 6791, the stellar parameters become T_eff = 4664 ± 100, R = 3.89 ± 0.22 R_⊕, and log(g) = 3.34 (D. Huber 2014, private communication), which is consistent with our evolved star fit. Therefore, KIC 2437209 is very likely to be a giant star with a smaller stellar companion. However, should this planet indeed have e = 0.974, then this planet may be one of the super-eccentric planets predicted in Socrates et al. (2012) caught in the act of high eccentricity migration.

Planet Hunters volunteers discovered an additional transit signal in Q16 at 2496333.91 JD, a signal consistent with a second planet in the system. No accompanying transit is seen. A TAP analysis (Carter & Winn 2009; Gazak et al. 2012; Eastman et al. 2013) suggests a period of $P=504^{+170}_{-160}$ days, meaning an earlier transit may have been located in a data gap. The TAP fit with the modeled stellar parameters gives this signal a radius of R = 2.9 ± 0.48 R_⊕.

KIC 5094412 has the shortest transit duration of candidates in this paper (3.77 hr), leading to few in-transit data points. We note that two of the four transits appear V-shaped, a shape that can be produced by a grazing eclipsing binary system, but one is an even numbered transit and the other is an odd numbered transit. The transit morphology of this system is unclear due to the under-sampling induced by the short duration transits. This is the only candidate in our sample that has such a potential V-shaped transit profile. With three transits in Q1–12 (and one in the data gap between Q6 and Q7), one transit was de-emphasized for a reaction wheel zero crossing due to possible false alarms caused by such events. It has since been shown that a reaction wheel zero crossing does not cause false alarms, so they are no longer de-emphasized (J. M. Jenkins 2013, private communication). This change and an extra transit in Q14 led to a detection by TPS in the latest run. As such, it is now an undispositioned KOI.

KIC 5522786 has only two transits and both exhibit a very sharp ingress and egress. This is the second smallest candidate in this paper, a planet on the super-Earth/mini-Neptune transition zone at R = 1.86  ±  0.25 R_⊕. Despite a depth of only 90 ± 13 ppm, the transits are visually apparent due to the host star's brightness, a Kepler-magnitude =9.350 star. A third transit of this candidate would be extremely valuable and is expected to take place at about 2457387.7614 JD (2015 December 31). We also note that the star has the highest effective temperature in our sample with $T_{\rm {eff}} = 8941^{+258}_{-396}$ K.

KIC 6372194 was undetected in the Q1–12 TPS search due to a bug in the Robust Statistic code (J. M. Jenkins 2014, private communication). The star was not observed until Q4. However, the bug resulted in the code checking the expected transit in Q3, for which KIC 6372194 was not observed. As such, it was rejected. This bug has since been corrected, and the signal is now detected and is designated an undispositioned KOI.

KIC 6436029 already has one KOI candidate (KOI-2828.01; P = 59.5 days, R = 4.1 ± 2.0 R_⊕). We have detected three transits of another planet around this star with P = 505.45 days. This new planet candidate possibly lies in the outer HZ; its upper error bar overlaps the Early Mars zone of the optimistic HZ. It has a radius of R = 4.16 ± 4.04 R_⊕.

There are four transits in Q1–12 (a fifth was in the data gap between Q9 and Q10). Two of these were de-emphasized due to the TPS sudden pixel sensitivity dropout detector (J. M. Jenkins 2014, private communication). It was subsequently detected in the Q1–16 search and is now an undispositioned KOI. This candidate was also independently discovered in Huang et al. (2013).

KIC 11442793 has six listed KOI candidates (KOI-351) at periods of 7.01, 8.72, 59.74, 91.94, 210.60, and 331.64 days (see Table 4 for transit parameters). Planet Hunters has detected an additional 124.92 day signal with five full transits and two partial transits. However, after the first transit (Q2), the next transit fell within a data gap. The following transit contained only the egress due to a data gap within Q5. In the next transit at the end of Q6, only the ingress is observed. The next transit fell into a data gap. Two other transits were de-emphasized due to the aforementioned reaction wheel zero crossings. Furthermore, the large number of candidates in the system caused the data validation to time out. All these conspired together and led to its non-detection in the Q1–12 TPS search (J. M. Jenkins 2014, private communication). While this paper was being reviewed, Cabrera et al. (2014) and Lissauer et al. (2014) independently discovered the 124.92 day signal and characterized all seven candidates claiming confirmation, with Lissauer et al. (2014) statistically confirming all seven with high confidence. For the 124.92 day signal described in this paper, both of the previous works agree well with each other and with our analysis.

To test whether the seventh signal is merely an alias of one or more of the previous six candidates, we assumed a linear ephemeris for all planets and calculated each planet's midtransit points (see Table 5). None of the planets matched the seventh candidate. In fact, somewhat surprisingly, only one midtransit of the previously known six planet candidates comes within 24 hr of a midtransit of the seventh candidate, but unsurprisingly, it is the candidate with the shortest period (7.01 days). However, we recognize the fact that we cannot assume a perfectly linear ephemeris on account of transit timing variations, or TTVs (Miralda-Escudé 2002; Agol et al. 2005; Holman & Murray 2005; Holman et al. 2010).

We therefore analyzed the system using the IDL program TAP to determine transit midpoints and compared the observed midtransits to the midtransits expected from the KOI epochs and periods. A plot of the observed midtransit times minus calculated midtransit times (O − C) shows deviations from a perfectly linear ephemeris due to TTVs for the outer three planets, indicating significant gravitational interactions between planets. Figure 5 shows the O − C plot for the outer three planet candidates of KOI-351. The last transit of KOI-351.02 has O − C = +14.4 hr, while the second-to-last transit has O − C = −9.4 hr, a change of 24 hr over the course of one orbit. KOI-351.02 has one of the largest TTVs known, excluding circumbinary planets (Mazeh et al. 2013). The presence of TTVs significantly increases the likelihood that our planet candidates are real, as they show mutual gravitational interactions with their neighbors. A more in-depth analysis can likely be used to determine masses and confirm several planets in this system, but this is left for future studies.

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The TTVs show that we cannot rely solely on comparisons of linear ephemerides. Therefore, we also compared the transit depths and transit durations of all seven candidates. The transit depth for KOI-351.07, 480 ± 87 ppm, is only consistent with two of the KOI candidates, KOI-351.03 and KOI-351.04, but the duration of the seventh candidate is hours longer than either. These two candidates also have significantly different midtransit times and thus cannot be the same object as KOI-351.07. The depths and durations are compared in Table 5, which also shows the phase information of each KOI-351.07 transit relative to the other six candidates. If KOI-351.07 were in fact a secondary eclipse from one of the other six objects, we would see a constant phase offset of KOI-351's transit relative to the primary eclipses. No such phase offset is observed. A combination of looking at the differences in duration, depth, midtransit points, and phases of KOI-351.07 relative to the other six candidates clearly demonstrates that KOI-351.07 is a distinct object. Simply put, the seventh candidate is not an alias of any of the other six candidates.

We also performed two stability tests to assess the feasibility of this system. Hill stability is a simple stability diagnostic that can be used to determine whether this somewhat compact system is at least feasible. To test the stability of the system, the masses of the planets must be assumed. For the inner five planets, which all have R < 4.0 R_⊕, we used the recent (Weiss & Marcy 2014) mass–radius relationship shown below based on the masses and radii of confirmed planets, which was valid for 1.5 R_⊕ ⩽ R ⩽ 4.0 R_⊕. The middle three planets fall into this range, while the inner two are within 1σ of this range.

$$\begin{equation} \frac{M_P}{M_{\oplus }}= 2.69 \left(\frac{R_P}{\,R_{\oplus }}\right)^{0.93},\quad R<4\,R_{\oplus }. \end{equation} \tag{ 1 }$$

The masses of the upper two planets were calculated with the same equation used by Lissauer et al. (2011b), shown below. This equation was determined by fitting for the solar system planets Earth, Uranus, Neptune, and Saturn. However, the upper error bar on the outermost planet is consistent with a Jupiter radius where the mass–radius relationship breaks down, meaning the mass could be significantly larger.

$$\begin{equation} \frac{M_P}{M_{\oplus }}= \left(\frac{R_P}{\,R_{\oplus }}\right)^{2.06},\quad R>4\,R_{\oplus }. \end{equation} \tag{ 2 }$$

Again using the same method as Lissauer et al. (2011b), we measured the mutual Hill radii for the six consecutive planet pairs. When the following holds true, the pair of planets are Hill stable, meaning that they will never develop crossing orbits, assuming circular, coplanar orbits. Whether the equation holds true depends more heavily on stellar radius (via the R_PL/R_* and the mass–radius relationship) than stellar mass (via a/R_* and Newton's Third Law). The best fit values for these two parameters from Y² interpolation are $R=1.04^{+0.12}_{-0.10}\,R_{\odot }$ and $M=0.99^{+0.10}_{-0.10}\,M_{\odot }$, consistent within 1σ of the stellar parameters from Huber et al. (2014). The Hill stability metric, where a is the semi-major axis of the planet and R_H is the Hill radius, is:

$$\begin{equation} \Delta = \frac{a_{\rm {outer}} - a_{\rm {inner}}}{R_{H}} > 2\sqrt{3} \approx 3.46. \end{equation} \tag{ 3 }$$

Because of the extremely large TTVs, we might expect that the mutual Hill spheres of the outer two planets are very close to the Hill stability criterion. As expected from the TTVs, the least Hill stable pair of planets are KOI-351.01 (P = 331.6 days) and KOI-351.02 (P = 210.6 days), the outer two planets, with Δ = 5.60. All planet pairs remain Hill stable across the 3σ range of stellar radius and mass.

Lastly, we ran an orbital integration with the Mercury code (Chambers 1999) using the best fit values and for planetary masses corresponding to ±1σ in stellar mass and radius, assuming coplanarity and circular orbits. The systems were stable for >100 Myr. However, doubling the mass of the outer planet resulted in instability, suggesting that the mass of the outer planet is on the less massive end of the flat part of the mass–radius relationship for gas giants. These orbital integrations are only feasibility tests and are by no means an exhaustive analysis proving dynamic stability.

KOI-351 is also interesting as it is close to being a compact analog to the solar system; see Figure 6 for an orbital representation of the system. The nominal radius values of the inner five planet candidates are all in the Earth to mini-Neptune regime (≲ 3.0 R_⊕), while the outer two candidates are gas giants. This differs from Kepler-11 (Lissauer et al. 2011a), in that all of Kepler-11's planets are in the super-Earth to Neptune sizes. However, we stress that the error bars on the KOI-351's stellar radius and thus the planetary radii are very large at roughly 50% each. The new candidate has a radius of R = 2.70 ± 2.07 R_⊕. KOI-351 deserves a strong follow-up observation to better constrain the radii, analyze the TTVs, and confirm these planets. This new candidate also exemplifies how complicated signals that may confuse or overload computers can be deciphered by visual checks. We also note that Planet Hunters had independently discovered the 8.72 and the 91.94 day signals. However, during preparation of this paper, both were upgraded to KOI candidate status.

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