KEPLER OBSERVATIONS OF THREE PRE-LAUNCH EXOPLANET CANDIDATES: DISCOVERY OF TWO ECLIPSING BINARIES AND A NEW EXOPLANET

The Kepler photometric time series are initially fit to a transit (when the companion moves in front of the star) model to determine the scaled radius (R_p/R_⋆), scaled semimajor axis (a/R_⋆), impact parameter (b), and the period (P) and epoch (T₀) of the companion. Our transit model uses the analytic formulae of Mandel & Agol (2002) for a nonlinear limb-darkening law and best fits are found using a Levenberg–Marquardt algorithm (Press et al. 1992). Limb-darkening coefficients were adopted from fits to Atlas 9 spectra (Sbordone et al. 2004) convolved with the Kepler bandpass (A. Prsa 2010, private communication). We model the occultation (when the companion moves behind the star) by computing the fraction of the companion occulted by the star as a function of the star–planet projected distance and fitting for the brightness of the companion relative to the star. We assume the planet is a uniformly illuminated disc during occultation. In cases where we detect a significant occultation we allow for eccentric orbits and appropriately adjust the depth of the transit model to account for dilution. Uncertainties for the model parameters were derived from a Markov-Chain Monte Carlo (MCMC) analysis (Ford 2005). We refer the reader to Koch et al. (2010) for a full description of the transit modeling procedure.

We also compute an odd–even transit depth and occultation depth statistic that provide useful diagnostics in the identification of stellar binaries. The odd–even statistic determines the significance of a change of depth of odd and even-numbered transits. If the transit depths are found to be changing in such a fashion, then we have strong evidence that we are seeing a stellar binary where the two components have slightly different surface flux densities and the true orbital period is twice as long. The odd–even effects were measured at 0.7σ, 1.6σ, and 0.5σ confidence levels for KIC 9595827, KIC 9838975, and KIC 9597095, respectively. No significant odd–even effect was found for the three candidates described in this paper.

The occultation depth statistic attempts to measure the significance of an occultation of the companion. The search is done by first removing photometric measurements during transit and then phasing the remaining data at the orbital period and computing the maximum displacement of a segment of phased data with a length equal to the transit duration. No displacements are found for KIC 9595827 (the largest displacement had a 0.7σ significance) level, while strong displacements were identified for KIC 9597095 and KIC 9838975.

The scaled semimajor axis is related to the mean density of the primary star and companion by

$$\begin{equation} \left(\frac{a}{R_\star }\right)^3 \frac{\pi }{3 G P^2} = \frac{(M_\star +M_p)}{\frac{4 \pi }{3}R_\star ^3}. \end{equation} \tag{ 1 }$$

If M_⋆ ≫  M_p, then it is a simple matter to estimate the mean stellar density ($\bar{\rho _\star }$) of the primary star and deduce its stellar parameters by matching to a set of theoretical stellar evolution models with an independent measurement of the stars' effective temperature (Sozzetti et al. 2007). For KIC 9838975 and KIC 9597095, the depth of the occultation is used to estimate the temperature of the companion by assuming the companion radiates as a blackbody and correcting for the Kepler bandpass. We estimate temperatures for the companion of ∼2700 and ∼4000 K, respectively. Such temperatures suggest companions with masses of ∼0.1 and ∼0.5 M_☉. For a Jupiter-mass companion an error of 0.02% will be incurred on the measurement of $\bar{\rho _\star }$, a 0.1 M_☉ companion would skew our estimate of $\bar{\rho _\star }$ by ∼2%, and a 0.5 M_☉ companion would induce a systematic error of 41% on $\bar{\rho _\star }$. It should also be noted that we have assumed a circular orbit for KIC 9595827. Should the companion exist in an eccentric orbit, our estimate of the scaled semimajor axis could exhibit large systematic errors (cf., Tingley et al. 2010).

We adopt estimates for the masses of the companions listed above and calculate $\bar{\rho _\star }$. For KIC 9597095, we also carry through an error of 10% to account for our uncertainty in the mass of the companion. We then proceed to determine the stellar parameters of the primary stars by matching T_eff (see Table 2) with an adopted error of 150 K with the mean stellar density to the Yonsei–Yale stellar evolution tracks (Demarque et al. 2004) to calculate the range of stellar parameters consistent with the observation (e.g., Borucki et al. 2010b). This calculation produces a Markov Chain of 100,000 samples of M_⋆, R_⋆ pairs. These values are then used to determine new fits for T₀, P, R_p, orbital inclination (i), and occultation depth as well as uncertainties in our model fits to light curves as listed in Table 3.

Examination of the Kepler pixel images within the aperture of an exoplanet candidate star provides powerful extra constraints that can eliminate false positives. The stars KIC 9597095 and KIC 9838975 have already been eliminated as false positives for exoplanet candidates by virtue of their Kepler light curves alone. However, the exoplanet candidate KIC 9595827, not shown to be a false positive event based on the folded light curves and transit models discussed above, can be subjected to additional testing by making use of the downloaded image pixel data. The use of Kepler image pixel data for false positive elimination is described in Batalha et al. (2010). Details of initial image centroiding and difference image use are discussed by Jenkins et al. (2010b) and make for additional methods by which false positives can be identified. We have improved on those techniques as discussed below.

The pixel image aperture containing KIC 9595827 is shown in Figure 5 (top two panels) and is seen to contain 24 pixels in a 6 × 4 arrangement. Formation of these two images is done by first detrending and then folding the pixel time series and finally averaging over several in-transit (5 in this case) and out-of-transit (20) points. This improvement from the original analysis provides more robust images. The small change in flux of the target star between in and out of transit is too small to be noted here given the image stretch and the fact that a Kepler star is purposely slightly out of focus with an FWHM value near 4 arcsec (see Bryson et al. 2010). Since each pixel is 3.98 arcsec in size (Koch et al. 2010), the total aperture used here is 24 by 16 arcsec and is seen to contain our target star and a piece of a close companion. This brighter neighbor star can also be seen in Figure 1. The central source seen in Figure 5 is our target, KIC 9595827, while the other source, only partially in the aperture (at 1090, 552), is KIC 9595844 with r ∼13. This star has its own Kepler light curve and shows no variation consistent with the transit observed in KIC 9595827. Its constant third light contribution to the total aperture flux is responsible for, and consistent with, the observed very small centroid shift seen in KIC 9595827 during transit (−0.43 ± 0.06, −0.99 ± 0.09 millipixels).

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Making use of Kepler pixel images for KIC 9595827 when in and out of transit, we can form a difference image and check to see if the target star is indeed the one changing in flux during the transit. We note in Figure 1 an additional close, faint companion to KIC 9595827 that will be well blended with the target star in the Kepler aperture. This star is 2.5–3 mag fainter than the primary object and would, if an eclipsing binary, have to have an eclipse depth of 14% in order to mimic the observed transit. This change in light would easily be observed in the difference image but is not seen. The bottom left panel of Figure 5 shows the difference image and reveals that indeed only KIC 9595827 varies during the transit.

A final and very informative use we can make from the pixel data is to produce individual pixel time series light curves. These are shown in Figure 6 in the same pixel arrangement as that of the Kepler pixel images in Figure 5. The transit event is clearly seen in the pixels containing KIC 9595827 but not observed in the brighter companion star partially in the aperture.

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The BOKS survey discovered this source as an r = 16 variable showing a few percent exoplanet-like transit with a period near 2.7 days. The star, designated BOKS-r.45069, is revealed through optical spectroscopy (Figure 7) to be an F8–F9 main-sequence star with an effective temperature near 6400 K and a distance estimate of 2500 pc. There is no evidence in our spectrum of a secondary star suggesting a large luminosity ratio. The Kepler light curve (Figure 2) shows an easily noted V-shaped primary eclipse and a clear secondary eclipse providing a deterministic diagnostic that this star is a grazing eclipsing binary. Knowing the primary star parameters, the eclipses allow the companion star and its orbit to be modeled. The secondary star has a radius of 5.9 R_Jupiter with an effective temperature near 4100 K, consistent with a late K or early M-dwarf, having 0.83% of the luminosity of the F star primary. The orbital inclination is 79° and the companion is likely heated by its close proximity to the F star. We note that the secondary eclipse depth in this system is ∼1%, a level which is challenging but doable from the ground (cf., Weldrake et al. 2008). The low-mass companion star will be greatly out-shined by the F star in the optical and near-IR and a radial velocity solution for the binary will be required to fully determine the secondary star mass.

There is variability related to the orbital period of the companion that has a peak-to-peak amplitude of ∼1.8 mmag. Measuring the first two harmonics at 2.75 and 1.37 days gives amplitudes of 0.7 and 1.8 mmag, respectively. The second harmonic shows amplitude modulation over the timescale of the Kepler Q1 observations. If we interpret the cause of these interactions as ellipsoid distortions and Doppler boosting (Rowe et al. 2010; van Kerkwijk et al. 2010) then we can estimate a mass of approximately 0.4 M_☉.

Discovered in the BOKS survey, this r = 16 star showed an exoplanet transit-like event in its light curve but with only one transit observed, and its orbital period was unknown. Spectroscopy (Figure 7) determines the star, designated as BOKS-r.45069, to be a K0V (±one subclass in spectral type) with an effective temperature near 5000 K and a distance of ∼1 kpc. The Kepler light curve (Figure 3) shows a U-shaped transit event as well as a clearly off-centered secondary eclipse suggestive of an elliptical orbit. The secondary eclipse in this system would be extremely difficult to observe from the ground as it has a depth near one-half of 1%. Thus, this object would be extremely difficult to eliminate as an exoplanet using ground-based photometry alone. The companion causing the transit event has a radius of 1.4 R_Jupiter and a modeled effective temperature of 2760 K. The orbital eccentricity is ∼0.1, making the difference between aphelion and perihelion change by approximately 20%. Thus, at an average distance from the K0V star of ∼0.13 AU, the companion is not close enough for irradiation to account for the observed temperature. At this low effective temperature, a low-mass red or brown dwarf is the most likely companion star in a near 90° elliptical orbit with a period of 18.7 days. Additional Kepler observations and a radial velocity study should be able to easily confirm the elliptical nature of the orbit as well as provide a good mass estimate for the companion star.

The best exoplanet candidate from the BOKS survey, BOKS-1, is an r = 15 variable showing an exoplanet transit-like event with a period near 4 days. Ground-based spectroscopy (Figure 7) shows the host star to be a G8V(±one subclass) with an effective temperature of 5500 K at a distance of ∼800 pc. Spectroscopic observations of this target obtained on two consecutive nights in 2008 June (roughly 0.5 apart in phase) and three nights in 2010 May reveal no statistically significant radial velocity trends at the ∼7 km s⁻¹ level or larger. This limit rules out a companion star with a mass greater than 0.1 M_☉, i.e., virtually all dwarf stars.

Our speckle imaging was aimed at a search for background (or real) companions which may be the cause of the transit signal. To robustly estimate the background limit we reach in each reconstructed speckle image, we use the metrics derived from the top plot in Figure 8. If a companion is present, it will appear in the reconstructed image as a "point" like source, similar to the central source. As in a normal image, the value of pixels in the target and any companion star images will lie above the local "sky" background. If a nearby source appears and is approximately 3–5σ above the background (the line in the top plot is a 5σ limit from the mean of the distribution of background points) we will easily see it and can robustly measure its properties. If, however, a source is barely detected (say at 1.5σ), then we will just be able to note its presence, but would derive only approximate information for it. Local minima are also plotted mainly as a check to see if the minimum and maximum points are normally distributed (as would be the case for a well-produced reconstructed "sky").

Using our simultaneous two-color speckle camera we can detect companions, for bright targets, below the diffraction limit (0.035 arcsec at 5000 Å) by detection of a single fringe in both cameras that provides the same solution. For fainter targets (R ≳ 13.5–14.5) and good observing conditions, our inner detection limit ranges from 005 to 015 depending on the magnitude difference of the companion. Thus, for multi-fringe images, a very conservative inner limit for robust detections is near 0.2 arcsec. Our high-resolution ground-based speckle observations allow us to eliminate any possible companion stars to 4.2 mag in R and 5.0 mag in V fainter and from i ∼0.05 to 1.8 arcsec of KID 9595827. Thus, the observed transit depth of 1.2% cannot be mimicked by a variable or eclipsing binary background star even if it showed a 50% dimming. Taken together with the Kepler light curve model results, no companion star is present that can be the cause of the observed exoplanet transit event.

Image analysis of the Kepler pixel data for KIC 9595827 reveals that it is the source of variation within its aperture during the transit event and that its small centroid motion is consistent with the star itself dimming in the presence of a nearby constant light neighbor. Additionally, pixel time series light curves clearly reveal that the transit event is centered on our target star. No evidence from the image data suggests any explanation for the observed variation except as that of an exoplanet transit.

The Kepler light curve observations (Figure 4) show the typical U-shaped exoplanet transit and reveal no evidence for a secondary eclipse. The transiting body has a radius of 1.12 R_Jupiter orbiting every 3.9 days at nearly 90° to the plane of the sky. If this exoplanet is similar to other "hot Jupiters," it is likely to have a mass near one to a few Jupiter masses. The raw Kepler light curve shows evidence for a rotational modulation of the host star with a period near 17–18 days, and we note possible evidence of starspots seen as slight wiggles at the bottom of the exoplanet transit.

We tested the possibility of hierarchical triples, by adding a dilution factor to our models. The dilution factor accounts for inclusion of third light from an unseen stellar companion in the system. The effect is that the observed transit can be much shallower than reality. For example, if two stars of equal brightness are found within the Kepler aperture, the measured transit would need to be made twice as deep. We modeled the transit of KID 9595827 with dilution factors ranging from 0 to 0.7, in increments of 0.05, where 0.7 means 70% of the observed flux comes from an additional star within the photometric aperture. Comparing chi-squared values we find models with dilution factors greater than 0.1 are ruled out at the 99.97% confidence level. In particular, the egress and ingress of the models are incompatible with the size of the companion inferred from the depth of the transit. While there may be third light contamination due to a hierarchical triple scenario, the unseen companion must contribute less than 10% of the light in the photometric aperture. At such dilution factors, the planet radius would increase by 5% but still be compatible with being a bona fide planet.

In addition, the Kepler pixel data are not consistent with a nearly perfectly aligned (within ∼0.05 arcsec) background eclipsing binary (BGEB) being the cause of the transit. To estimate the possibility of a chance alignment, we can take the mean local star density observed near KIC 9595827 (0.0122 stars arcsec⁻² to r ∼20) times the likelihood that a background star would be an eclipsing binary (1.2% of stars are eclipsing binaries; Torres et al. 2010). The product of these values yields a probability of only 0.015% that a BGEB could be the cause of the transit event. If we assume a near circular orbit for the stars in any BGEB, we can estimate this probability in another way. The observed transit time restricts the background population of confounding EBs to only G8 stars or earlier. Using the Besancon Galactic model, we calculate a stellar density of possible (G8 and earlier) pollutants to be 2e-4 stars arcsec⁻². Taking the same likelihood as above that a background star could be an EB, this approach suggests only a 0.00024% chance that the transit could be caused by a BGEB. Given that these conservative estimates of a chance alignment of a BGEB or a hierarchical triple can be the cause of the observed transit event are essentially zero, we again conclude that KIC 9595827 (BOKS-1) does indeed harbor an exoplanet.

Kepler is still monitoring this source and revealing continuous transits leaving no doubt as to its periodic nature and constant transit shape and depth. Phase folding of all the data to date reveals no secondary eclipse eliminating essentially all possible binary star configurations. Future Kepler observations will hopefully detect the occultation allowing one to determine the companions orbit. At r = 15, it is unlikely that high-precision radial velocities will soon be forthcoming for this system.