A SUPER-EARTH-SIZED PLANET ORBITING IN OR NEAR THE HABITABLE ZONE AROUND A SUN-LIKE STAR

The Transiting Planet Search (TPS; Jenkins et al. 2010c; Tenenbaum et al. 2012) and Data Validation (DV; Wu et al. 2010) modules of the Kepler pipeline (Jenkins et al. 2010b) identified two transit-like signatures in a search of Q1–Q10 data. The first signature was due to KOI-172.01, a planet candidate previously reported by Borucki et al. (2011b) and Batalha et al. (2013). The second signature was new and had a period of 242.4579 ± 0.0056 days and a depth of 258 ± 19 ppm and has been designated KOI-172.02 (C. J. Burke et al., in preparation). The planet radius provided by the Q1–Q12 DV report for KOI-172.02 was 1.4 R_⊕. A signal-to-noise ratio (S/N) of 73 was calculated for the transits of KOI-172.01 and 15 for KOI-172.02. The S/Ns for both planet candidates are significantly above the formal threshold of 7.1 (Jenkins et al. 2002), giving us very high confidence that neither of these detections are due to random or correlated noise.

There are instrumental features near two of the KOI-172.02 transits. One was a sudden pixel sensitivity dropout due to a cosmic ray hit (Stumpe et al. 2012a), the other is a coronal mass ejection (Thompson et al. 2012). Both aperture photometry and pre-search data conditioned (PDC; Stumpe et al. 2012a; Smith et al. 2012) flux time series data stored at the Mikulski Archive for Space Telescopes (MAST) insufficiently corrected the out-of-transit flux levels around the instrumental signals. This led to a measured transit depth that was underestimated by 20%. We instead chose to use a developmental version of the PDC error-corrected data that relies on error correction via wavelet-based band splitting (Stumpe et al. 2012b). This newly corrected data preserves stellar variability. We removed stellar variability using a numerically efficient discreet cosine transform (Garcia 2010) to implement a non-parametric penalized least squares smoothing of the flux time series. Data from individual quarters were normalized and then combined. Transits were treated as missing when smoothing the data.

We performed a fit of both planet candidates simultaneously using a Mandel & Agol (2002) transit model with quadratic limb darkening. Limb darkening parameters were computed by interpolating the tables of Claret & Bloemen (2011) and kept fixed.

The parameters included in our fit were mean stellar density, photometric zero point, and for each planet the transit epoch, orbital period, the planet-to-star radius ratio, impact parameter, and eccentricity vectors esin ω and ecos ω, where e and ω are the eccentricity and argument of periastron of the orbit, respectively. We utilized the emcee implementation (Foreman-Mackey et al. 2012) of an affine-invariant Markov Chain Monte Carlo (MCMC) algorithm (Goodman & Weare 2010) to calculate posterior distributions for these parameters. The mean stellar density measured from asteroseismology was used as a Gaussian prior. All other parameters were given uniform priors except for the two eccentricity vectors. Using the esin ω and ecos ω parameterization results in an implicit linear prior in e (Ford 2006; Burke et al. 2008; Eastman et al. 2013). We correct for this by enforcing a 1/e prior on eccentricity. Our likelihood function is therefore

$$\begin{equation} \mathcal {L} = \exp {\left(\frac{\chi ^{2}}{2} + \frac{(\rho _{a} - \rho _{m})^{2}}{\sigma _{\rho }^{2}} - \ln {e} \right)}, \end{equation} \tag{ 1 }$$

where ρ_a is the mean stellar density derived from asteroseismology and ρ_a is the model mean stellar density. χ² is the usual sum of squared deviation from the model weighted by the variance.

The median and central 68% of the posterior distribution (equivalent to the 1σ uncertainty) of each parameter are shown in Table 2. Uncertainty in the stellar radius was included as a component of these calculations. The best-fitting transit model and folded time series data are shown in Figure 1. This analysis yielded planet radii of $2.24^{+0.44}_{-0.29}$ and $1.71^{+0.34}_{-0.23}$ R_⊕ for KOI-172.01 and KOI-172.02, respectively.

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Table 2. Parameters from MCMC Analysis

Parameter	Kepler-69b (KOI-172.01)	Kepler-69c (KOI-172.02)
Stellar density (g cc−3)	$1.05^{+0.48}_{-0.27}$
Rp/R⋆	$0.02207^{+0.00023}_{-0.00018}$	$0.0168^{+0.00052}_{-0.00052}$
Mid-point of first transit (BJD − 2454833)a	$137.8414^{+0.0016}_{-0.0016}$	$150.870^{+0.016}_{-0.014}$
Period (days)	$13.722341^{+0.000035}_{-0.000036}$	$242.4613^{+0.0059}_{-0.0064}$
Impact parameter	$0.15^{+0.17}_{-0.10}$	$0.12^{+0.21}_{-0.09}$
ecos ω	$0.02^{+0.19}_{-0.14}$	$-0.01^{+0.14}_{-0.16}$
esin ω	$-0.07^{+0.09}_{-0.14}$	$-0.02^{+0.08}_{-0.15}$
Planet radius (R⊕)	$2.24^{+0.44}_{-0.29}$	$1.71^{+0.34}_{-0.23}$
a/R⋆	$21.8^{+2.9}_{-2.1}$	$148^{+20}_{-14}$
Semimajor axis (AU)	$0.094^{+0.023}_{-0.016}$	$0.64^{+0.15}_{-0.11}$
Inclination (deg)	$89.62^{+0.26}_{-0.45}$	$89.85^{+0.03}_{-0.08}$
Eccentricity	$0.16^{+0.17}_{-0.0010}$	$0.14^{+0.18}_{-0.10}$
Equilibrium temperature (K)b	$779^{+50}_{-51}$	$299^{+19}_{-20}$
Limb darkening parameters	{0.4012, 0.2627}

Notes. ^aBJD − 2454833 is the standard Kepler time system, known informally as BKJD. ^bEquilibrium temperature assumes an albedo of 0.3 and the thermal recirculation parameter of 1.0.

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The Kepler photometric data for KOI-172.01 and KOI-172.02 were examined for evidence suggestive of a false positive in the manner described in Batalha et al. (2013). No such evidence was found and hence both candidates were afforded a place within the most recent Kepler planet candidate list⁸ (C. J. Burke et al., in preparation). Specifically, odd and even numbered transits have consistent depths, there is no sign of a secondary transit, and there is no significant shift in the photo-centroid of the star in transit relative to out of transit (Jenkins et al. 2010a).

The DV module of the Kepler pipeline creates three images: an average out-of-transit image taken from nearby but not during the transit events, an average in-transit image, and a difference image which is the difference between the out-of-transit image and the in-transit image. A fit of the pixel response function (PRF) to the difference image gives the position of the transit source while a fit of the PRF to the out-of-transit image yields the position of the target star. The offset between the difference image position and the target star position can be used to identify false positive scenarios. Conversely, if no significant offset is detected, then the uncertainty in the difference image centroid position can be used to calculate a radius of confusion outside of which a false positive source can be excluded. No significant offsets are measured between the difference image and target position for KOI-172.01. The 3σ radius of confusion was measured by DV at 0.16 arcsec. Only two transits were included in the PRF centroid offset metric in the DV report for KOI-172.02 owing to data artifacts and transits of KOI-172.01 occurring near the transits of KOI-172.02. We wished to use all five transits of KOI-172.02 in our centroid analysis so we created difference images in the same manner used by the Kepler pipeline (Bryson et al. 2013) but included all observed transits of KOI-172.02. The significance of the offset from the remaining images was less than 3σ which is used as the warning threshold (Batalha et al. 2013; Bryson et al. 2013). The radius of confusion was estimated to be 1.5 arcsec. Given the above described tests, there is no reason to suspect KOI-172.01 or KOI-172.02 are false positives based on the Kepler data.

We measured a transit depth for KOI-172.02 of 350 ppm from the MCMC analysis. The faintest a star could be and still produce a transit of this depth can be calculated if we assume a total eclipse of that background star (Chaplin et al. 2013). Under this assumption, the faintest a false positive star could be is 7.9 mag fainter than Kepler-69. This is the limit we use in all false positive calculations for KOI-172.02. For KOI-172.01 the transit depth is 597 ppm, which sets the maximum brightness difference between the target star and a false positive of 7.3 mag.

We obtained optical V-band images of Kepler-69 using the Nickel 1 m telescope at Lick Observatory and searched for nearby stars. No stars are seen 2–5 arcsec from Kepler-69 brighter than 19th magnitude; stars closer than 2 arcsec could not be ruled out. Kepler-69 has a V-band magnitude of 14.0 (Everett et al. 2012), therefore we cannot exclude stars between V = 19–21.9 for KOI-172.02 and V = 19–21.3 for KOI-172.01 based on the Lick image and the transit depths.

There is a UK Infrared Telescope (UKIRT) J-band image of a field containing Kepler-69. The closest star is 3.2 arcsec west of Kepler-69 and is 9 mag fainter. This nearby star can be ruled out as the source of the transit signal from either planet candidate based on the PRF centroids. A magnitude dependent radius of confusion around Kepler-69 was calculated for use in false positive analysis. This confusion radius was converted to the Kepler magnitude system (Brown et al. 2011; Howell et al. 2012) and is shown in blue in Figure 2.

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The slit width used to collect the HIRES spectrum of Kepler-69 was 0.87 arcsec. This allowed us to search the HIRES spectrum for additional stars within 0.43 arcsec of the target. We calculated the best-fitting two-spectrum model using observed spectra with T_eff ranging from 3500 to 6000 K. We searched over a range of secondary star radial velocities and flux ratios relative to the target star. No second star was seen in the spectra down to the confusion limit of ΔK_P = 4.0. We then injected a range of observed spectra into the spectrum of Kepler-69. Given that we measure a radial velocity for Kepler-69 of −38.7 ± 0.1 km s⁻¹, virtually all sufficiently bright background stars would have been detected. G- and K-dwarf physical companions to Kepler-69 that are further than approximately 20 AU could evade detection owing to them having a radial velocity that we could not distinguish from Kepler-69. Companions with spectral type later than M0 are detected at any distance from the target (subject to falling into the spectrograph's slit) provided they are brighter than ΔK_P = 4.0.

Given that the KOI-172.01 and KOI-172.02 detections are unlikely to be due to noise (Jenkins et al. 2002), we can safely assume that they either represent planets or astrophysical false positives. Scenarios that could cause a transit-like signal that are not caused by a planet orbiting Kepler-69 are:

• 1.  
  Stellar binaries with grazing eclipses (the impact parameter >1).
• 2.  
  Background eclipsing binaries.⁹
• 3.  
  Background star-planet systems.
• 4.  
  An eclipsing binary physically associated with Kepler-69 in a hierarchical stellar triple system.
• 5.  
  A planet orbiting a stellar physical companion of Kepler-69.

We are immediately able to dismiss scenarios 1 and 4 because the best-fitting models representing these scenarios fit the observed data worse than the best-fitting transiting planet model at a level >3σ. This is because a stellar eclipse across Kepler-69 or a physical companion would be more V-shaped than we observe. Additionally, these scenarios are predicted to be very uncommon for sub-Jupiter-sized planet candidates (Fressin et al. 2013). The remaining false positive discussion is restricted to scenarios 2, 3, and 5.

To assess the probability that the transit-like signals we detect are not associated with the Kepler-69 system but are on a background star, we simulate the stellar background population that could be responsible. We simulated the number of stars within 1 deg of Kepler-69 using the Besançon Galaxy model with kinematics enabled (Robin et al. 2003). The Galactic model predicts there are 432,118 stars, of which 44,185 fall in the brightness range 14.0 < V < 22.0 and are not excluded by the secondary star test performed on the Keck spectrum. We integrated the area shown in white in Figure 2 to calculate the undetected stellar population in the background of KOI-172.02. The estimated number of stars in the background is 0.018. If we now consider that only 2.6% of stars observed by Kepler host either a transiting planet candidate or are an eclipsing binary, then excluding contact binaries (Batalha et al. 2013; Slawson et al. 2011; C. J. Burke et al., in preparation), the predicted number of background stars which could cause a false positive is 0.00046.

We used a Bayesian approach similar to that applied by Fressin et al. (2012) and Barclay et al. (2013) to the validation of the planets orbiting Kepler-20 and Kepler-37 to quantify the false positive probability. This technique compares the a priori chance of finding a planet the size of KOI-172.02 (the planet prior) to that of finding a background false positive. The ratio of the planet prior to the false positive probability is used to calculate our confidence in the planet interpretation. The population of super-Earth-sized planets orbiting with periods longer than 85 days is not well constrained. We assume that the super-Earth occurrence rate is the same at long orbital periods as it is at shorter orbital periods when period is measured in logarithmic units. There is evidence that the occurrence rate of super-Earth-sized planets is even high at longer orbital periods than at short periods. For example Cassan et al. (2012) find $62^{+35}_{-37}$% of stars host a super-Earth-mass planet. Therefore, using the statistics of Fressin et al. (2013), who derived a super-Earth occurrence rate of 23% ± 2.4%, may well lead to an underestimate of our planet prior.

There are 666 super-Earth-sized (1.25–2.0 R_⊕) planet candidates tabulated in Batalha et al. (2013). However, Fressin et al. (2013) predict that 8.8% of these are false positives which provides an estimated number of super-Earths found by Kepler of 607. The catalog of Batalha et al. (2013) was based on continuous (Q1–Q6) observations of 138,253 stars. Therefore, the occurrence rate of transiting super-Earth-sized planets is 0.0044 per star. We can compare this to the background/foreground false positive population which is 0.00046, as explained above. If KOI-172.02 were the only planet candidate associated with Kepler-69, then the likelihood of it being a true planet would be 0.0044/(0.0044 + 0.00046) = 0.91 . However, KOI-172.02 is in a two planet candidate system. As shown by Lissauer et al. (2012), having multiple transiting planet candidates associated with a star increases the probability that these candidates are real planets by a factor of ∼15 compared to single planet candidate systems. This multiplicity boost increases our confidence that KOI-172.02 is a bona fide planet physically associated with the Kepler-69 system to 99.3%.

We note that Kepler-69 has a lower metallicity than the Sun and for large planets a low metal content has been shown to hinder planet occurrence (e.g., Mayor et al. 2011). However, there appears to be no link between planet occurrence and stellar metallicity (Buchhave et al. 2012) for transiting super-Earth-sized planets. Therefore, we do not factor the stellar metallicity into our false positive calculations.

The centroid confusion radius for KOI-172.01 is much smaller than for KOI-172.02 (as shown in Figure 2). Using the approach outlined above, our confidence is 99.9% that KOI-172.01 is a planetary mass body physically associated with the Kepler-69 system. We can therefore conclude that the signals we observe are due to bona fide planets. The inner and outer planets are named Kepler-69b and Kepler-69c, respectively.

While the above analysis leads us to conclude that Kepler-69b and Kepler-69c are both substellar bodies physically associated with the target system, this does not exclude a scenario where one or both of the planets orbit a fainter stellar companion to Kepler-69.

We performed a series of MCMC transit analyses with no prior on the stellar density with the aim of constraining the range of stellar types the planets could orbit. First, we assumed that both planets orbit the same star. If this is the case, then this star would have a stellar density of $1.04^{+0.53}_{-0.31}$ g cm⁻³ with a 3σ upper limit of 3.6 g cm⁻³. This rules out both planets orbiting a star with a radius less than 0.64 R_☉, where the radius is calculated using Dartmouth isochrones (Dotter et al. 2008) and assumes Kepler-69 and stellar companion coevolved. We tried including a fixed dilution in the transit depth of 98% to simulate both planets being around a star 1/50th the brightness of the primary star in the system. In this case, we found a 3σ upper limit on the stellar density of 2.8 g cm⁻³. However, a companion hosting a transit whose light is diluted by 98% should have a density of 9.7 g cm⁻³ based on isochrones, therefore we can rule out a scenario where both planets orbits a much fainter companion. If both planets orbit a companion, then it must be a G or early K-type star.

We now consider the case that both planets orbit different stars. Fitting only the transits of Kepler-69b gave a stellar density upper limit of 6.2 g cm⁻³ which would place Kepler-69b around a star with a radius of at least 0.48 R_☉. This rules out Kepler-69c orbiting a star with a spectral type later than K9V. Fitting just for Kepler-69c implies a star with a mean stellar density of $1.3^{+1.1}_{-1.0}$ g cm⁻³ and the 3σ upper limit on density is 8.7 g cm⁻³. Including a dilution in the transit depth of 98% loosened our 3σ upper limit on the stellar density to 15.5 g cm⁻³. A star with a density of 15.5 g cm⁻³ that coevolved with Kepler-69 would have a radius of 0.31 R_☉—an M2-type star. Therefore, in the case of a physical companion, Kepler-69c cannot orbit a star cooler than an M2-type.

To quantify the probability that either of the planets orbit a companion star, we constructed three Monte Carlo simulations to estimate the properties of a stellar companion with different assumptions: both planets orbit a companion to Kepler-69; Kepler-69b orbits Kepler-69 and Kepler-69c orbits a companion; and Kepler-69c orbits Kepler-69 and Kepler-69b orbits a companion.

In the simulations, we assume the orbital period is described by a lognormal distribution with mean log P = 5.03 and standard deviation σ_log P = 2.28 where period is in days (Raghavan et al. 2010) and eccentricity is uniform from zero to one. The primary-to-secondary mass ratio q is assumed to be uniformly distributed (this approximates the distribution found by Halbwachs et al. 2003). The argument of periastron is taken to be uniformly distributed. We ran the simulation 10⁷ times. At each loop in the simulation, we calculated the radius, density, and brightness of the companion based on Dartmouth isochrones (Dotter et al. 2008). We calculated the binary separation from the orbital period and mass ratio. The radial velocity at the point of observation of the secondary was determined by calculating a radial velocity curve and selecting the time of observation at random.

We then calculated the proportion of secondary scenarios from our simulation that are unphysical or excluded based on observations. Unphysical scenarios are those where the binary separation is too small to allow a stable planetary orbit of 242.4 days (Rabl & Dvorak 1988; Holman & Wiegert 1999). We used the diluted MCMC transit analyses' 3σ upper limit on stellar density to exclude companions that are too dense or faint. Using the constraint from the Keck spectrum, if a companion had a brightness within 4 mag of Kepler-69 and a radial velocity difference between it and the primary of >10 km s⁻¹ (the limit from our analysis of the Keck spectrum), then it was excluded. Companions that would be seen by the J-band image or would induce a detectable centroid shift were also excluded. We find that a companion star is able to host Kepler-69b less than 0.01% of the time. Therefore, we are confident that Kepler-69b orbits the target star. However, in 1.9% of the simulations, Kepler-69 has a stellar companion capable of hosting Kepler-69c. If we assume that in scenarios with a viable planet hosting companion, half the time the planet orbits the primary and half the secondary, then our confidence that Kepler-69c orbits the primary is 99.1%. However, no multiplicity boost is included in the above calculation. It is unclear whether a companion is more likely to host transiting planets if the primary hosts transiting planets compared to a field star. However, if we were to apply this boost, the probability that Kepler-69c orbits Kepler-69 is 99.93%. The true probability that Kepler-69c orbits a companion star lies somewhere between 0.06% and 0.9%.

While we cannot conclusively rule out the possibility that Kepler-69c orbits a smaller star and therefore is larger and cooler, the chances are low. With more follow-up observations we may be able to further restrict the allowed parameter space and increase our confidence that Kepler-69c orbits the primary star. Specifically, continued non-detections in future radial velocity observations will increase the size of the region around Kepler-69 where we can rule out any companion star, while a deep adaptive optics observations can help rule out companions further from the star than around 0.5 arcsec.

In the remaining analysis, we will assume that Kepler-69c orbits the target star.