ROBOTIC LASER ADAPTIVE OPTICS IMAGING OF 715 KEPLER EXOPLANET CANDIDATES USING ROBO-AO

We selected targets from the KOIs catalog based on a Q1–Q6 Kepler data search (Batalha et al. 2013). Our initial targets were selected randomly from the Q1–Q6 KOIs, requiring only that the targets are brighter than m_i = 16.0, a restriction which removed only 2% of the KOIs. While it is our intent to observe every KOI with Robo-AO, this initial target selection provides a wide coverage of the range of KOI properties. Given Robo-AO's low time overheads, we took the time to re-observe KOIs which already had detected companions, to produce a complete and homogenous survey.

In Figure 1 we compare the Robo-AO imaged KOIs to the distribution of all Batalha et al. (2013) KOIs in magnitude, planetary period, planetary radius, and stellar temperature. The Robo-AO list closely follows the KOI list in the range of magnitude covered, with the exception of the three brightest stars (which have already been covered in detail by other non-laser adaptive optics systems), and a reduced coverage of the faintest KOIs, which Robo-AO requires excellent weather conditions to reach. Robo-AO's target distribution closely matches the full KOI list in planetary radius, planetary orbital period, and stellar temperature.

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We obtained high-angular-resolution images of the 715 Kepler targeted planet candidate host stars in summer 2012. We performed all the observations in a queue-scheduled mode with the Robo-AO laser adaptive optics system (Baranec et al. 2012, 2013; Riddle et al. 2012) mounted on the robotic Palomar 60 inch telescope (Cenko et al. 2006). The survey and system specifications are summarized in Table 1.

Table 1. The Specifications of the Robo-AO KOI Survey

KOI Survey Specifications
KOI targets observed	715
Exposure time	90 s
Observation wavelengths	600–950 nm
FWHM resolution	012–015
Field of view	44'' × 44''
Pixel scale	43.1 mas pixel−1
Detector format	10242 pixels
Detectable magnitude ratio	Δm = 5 mag. at 05 (typical)
Observation date range	2012 Jun 17 – 2012 Oct 6
Targets observed/hr	20

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Robo-AO observed the targets between 2012 June 17 and 2012 October 6, on 23 separate nights (detailed in Table 5 in the Appendix). We chose a standardized 90 s exposure time to provide a snapshot image which would contain all sources likely to affect the Kepler light curve, including close-in sources up to ∼5 mag fainter than the Kepler target. For the observations described here, we used either a Sloan i'-band filter (York et al. 2000) or a long-pass filter cutting on at 600 nm (LP600 hereafter). The latter filter roughly matches the Kepler passband (Figure 2) at the redder wavelengths while suppressing the blue wavelengths which have reduced adaptive optics performance (except in the very best seeing conditions). Compared to near-infrared adaptive optics observations, this filter more closely approximates direct measurement of the effects of unresolved companions on the Kepler light curves.

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Two dominant factors affect Robo-AO's imaging performance: the seeing and the brightness of the target. During the 23 nights of observing, the median seeing was 12, with minimum and maximum values of 08 and 19, respectively. We developed an automated routine to measure the actual imaging performance and to classify the targets into the imaging-performance classes given in the full observations list; this classification can be used with the contrast curve for each class to estimate the companion-detection performance for each target (Section 3.4).

The Robo-AO imaging pipeline (Law et al. 2012; Terziev et al. 2013) is based on the Lucky Imaging reduction system described in Law et al. (2006a, 2006b, 2009). The recorded EMCCD-frames are dark-subtracted and flat-fielded, and are then corrected for image motion using a bright star in the field. For the KOI observations the relatively crowded fields often led to the automatic selection of a different guide star from the KOI. To avoid having to account for the effects of tip/tilt anisoplanatasism, we manually checked the location of the KOI in Digital Sky Survey images and selected the KOI itself as the guide star in each observation. To produce more consistent and predictable imaging performance for groups of similar KOIs, we used the KOI even if a brighter guide star was nearby and offered potentially increased performance.

The KOI target stars are all in similar parts of the sky, have similar brightness, and were observed at similar airmasses. Because it is unlikely that a companion would be found in the same position for two different targets, we can use each night's ensemble of (at least 20) KOI observations as PSF references without requiring separate observations.

We use a custom locally optimized PSF subtraction routine based on the Locally Optimized Combination of Images algorithm (Lafrenière et al. 2007). For each KOI target we select 20 other KOI observations obtained in the same filter and closest to the target observation in time. We divide the region around the target star into sections based on polar coordinates: five upsampled pixels (110 mas) in radius and 45° in angle. Similar sections are extracted from each PSF reference image.

We then generate a locally optimized estimate of the PSF in each section by generating linear combinations of the reference PSFs. In each section, an initial PSF is generated by averaging all the reference PSFs. We then use a downhill simplex algorithm to optimize the contribution from each PSF image, searching for the combination which provides the best fit to the target image. This optimization is done on several sections simultaneously (in a region three sections in radius and two sections in angle) to minimize the probability of the algorithm artificially subtracting out real companions. After optimization in the large region, only the central section is output to the final PSF. This provides smooth transitions between adjacent PSF sections because they share many of the image pixels used for the optimization.

This procedure is iterated across all the sections of the image, producing a PSF which is an optimal local combination of the reference PSFs and which can then be subtracted from the target star's PSF. The PSF subtraction typically leaves residuals that are consistent with photon noise only (for these relatively short exposures). Figure 3 shows an example of the PSF subtraction performance.

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We limited the detection radius of this initial search to a 25 radius from the target KOIs, covering the range of separations between seeing-limited surveys and ≈015 (subsequent papers will present an analysis of wider-radius companions in Robo-AO imaging).

To more easily and robustly find companions in this large data set, we developed a new automated companion detection algorithm for Robo-AO data. We first measure the local image noise as a function of distance from the target star, by covering the PSF-subtracted target image with four-pixel-diameter apertures and measuring the rms of the pixel values in each aperture, along with the average PSF-subtraction residual signal. We then fit a quadratic to interpolate the changes in noise and residual values as a function of radius from the target star position. For each pixel in the PSF-subtracted image we then use the noise and residual fits to estimate the significance of that pixel's signal level. This procedure generates a significance image where bright pixels in regions of high photon noise (i.e., in the core of the star) are down-weighted compared to those in lower-noise areas.

The significance image yields the pixels which have some chance of denoting detections of stars, but does not take into account the shapes of the detections—a single bright pixel surrounded by insignificant pixels is more likely to be due to a cosmic ray hit than a stellar companion, and a tens-of-pixels-wide blob is likely due to imperfect PSF subtraction. We quantify this by cross-correlating the significance image by a Gaussian corresponding to the diffraction limit of the Robo-AO observation. We then select the pixels which show the most significant detections (>5σ) as possible detections, and amalgamate groups of multiple significant pixels into single detections.

After automated companion detection we also manually checked each image for companions, to check the performance of the automated system and to search for faint but real companions which could have been fit and removed by spurious speckles in the PSF references. The automated system picked up every manually flagged companion, and had a 3.5% false-positive rate from all the images, mainly due imperfect PSF subtraction.

We evaluated the contrast-versus-radius detection performance of the PSF-subtraction and automated companion detection code by performing Monte Carlo companion-detection simulations. The time-consuming simulations could only be performed on a group of representative targets, and so we established a quantitative image quality metric that allows each of our observations to be tied into the contrast curves for a particular test target. We first parameterized the performance of each observation of our data set by fitting a two-component model to the PSF based on two Moffat functions tuned to separately measure the widths of the core and halo of the PSF. We then picked 12 single-star observations to represent the variety of PSF parameter space in our data set. For each test star, we added a simulated companion into the observation at a random separation, position angle and contrast, ran the PSF subtraction and automated companion detection routines, and measured the detection significance (if any) of the simulated companion. We repeated this for 1000 simulated companions.⁸ We then binned the simulated detections as a function of separation from the target star, and in each radial bin fit a linear significance-versus-contrast relation. We use the intersection of the fitted relation with a 5σ detection to provide the minimum-detectable contrast in each radial bin.

We found that the PSF core size was an excellent predictor of contrast performance, while the halo size did not affect the contrast significantly. The halo is effectively removed by the PSF subtraction, and the contrast is thus chiefly limited by the companion signal-to-noise ratio (S/N), which scales with the achieved PSF core size (rather than the image FWHM, which we found is a weak predictor of contrast performance in Robo-AO data). On this basis, we use the PSF core size to assign targets to contrast-performance groups (low, medium and high). As the imaging-performance degrades, we found that the relative contribution of the fitted core PSF decreases, while the core itself shrinks. The somewhat counter-intuitive size decrease is because poor imaging quality inevitably corresponds to poor S/N on the shift-and-add image alignment used by Robo-AO's EMCCD detector. This leads to the frame alignments locking onto photon noise spikes, and thus produces a single-pixel-sized spike in the images (Law et al. 2006b, 2009). We therefore assign images with a diffraction-limited-sizes core (∼015) to the high-performance groups; smaller cores, where the imaging performance is degraded, were assigned to the lower-performance groups.

Figure 4 shows the contrast curves resulting from this procedure, for clarity smoothed with fitting functions of form a − b/(r − c) (where r is the radius from the target star and a, b, and c are fitting variables). The i-band observations obtain better contrast close-in than the LP600 filter, because of their improved Strehl ratios, while the broader LP600 filter allows somewhat improved contrast at wider radii under all but the poorest conditions.

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3.5.1. Contrast Ratios

3.5.2. Separations and Position Angles

Lillo-Box et al. (2012, hereafter L12) observed 98 KOIs using a Lucky Imaging system. Seven of the targets for which they discovered companions within a 25 radius are also in our survey. Both surveys detect KOI-401 at a separation of 20 and at a contrast of 2.6 mag (L12 i-band) or 2.9 mag (Robo-AO LP600). The companions to KOI-628 were visible in our survey but at contrasts that placed them in the "likely detections" group. L12 detected a companion to KOI-658 at 19 radius and a contrast of 4.6 mag in i-band. At that radius, for the performance achieved on KOI-658, the Robo-AO snapshot-survey limiting magnitude ratio is ∼4.0 mag and so we do not re-detect that companion. For the same reason we also do not re-detect the companions to KOI-703 (6.4 mag contrast), KOI-704 (5.0 mag contrast) and KOI-721 (3.9 mag contrast). The 013 radius companion to KOI-1537 detected in Adams et al. (2013) is at too close a separation to be detectable in our survey. The L12 companion to KOI-1375 is visible in our data set, but has a contrast ratio of 4.0 mag, under our formal detection limit and well below the 2.75 mag i-band contrast measured by L12. The target is not strongly colored according to L12 and it is not obvious why the companion is so much fainter in our survey.

The detection of a previously unknown star within the photometric aperture of a KOI host star will affect the derived radius of any planet candidate around that host star, because the Kepler observed transit depth is shallower than the true depth due to dilution. The degree of this effect depends upon the relative brightness of the target and secondary star, and which star is actually being transited. In particular, if there is more than one star in the photometric aperture and the transiting object is around a star that contributes a fraction F_i to the total light in the aperture, then

$$\begin{equation} \delta _{\rm true} = \delta _{\rm obs} \left(\frac{1}{F_i} \right), \end{equation} \tag{ 1 }$$

where δ_true is the true intrinsic fractional transit depth and δ_obs is the observed, diluted depth. Since δ∝(R_p/R_⋆)², the true planet radius in the case where the transit is around star i is

$$\begin{equation} R_{p,i} = R_{\star,i} \left(\frac{R_p}{R_\star }\right)_0 \sqrt{{{A^A}^A}\smash{{{\displaystyle\frac{1}{F_i}}}}}, \end{equation} \tag{ 2 }$$

where R_{⋆, i} is the radius of star i, and the 0 subscript represents the radius ratio implied by the diluted transit, or what would be inferred by ignoring the presence of any blending flux.

Thus, for each planet candidate in KOI systems observed to have close stellar companions, the derived planet radius must be corrected—and there are two potential scenarios for each candidate: the eclipsed star is either star A (the brighter target star) or star B (the fainter companion).

In case A, the corrected planet radius is

$$\begin{equation} R_{p,A} = R_{p,0} \sqrt{\vphantom{{A^A}^A}\smash{{{\displaystyle\frac{1}{F_A}}}}}, \end{equation} \tag{ 3 }$$

and in case B,

$$\begin{equation} R_{p,B} = R_{p,0} \frac{R_B}{R_A} \sqrt{\vphantom{{A^A}^A}\smash{{{\displaystyle\frac{1}{F_B}}}}}. \end{equation} \tag{ 4 }$$

Case A is straightforward, with nothing needed except the observed contrast ratio (in order to calculate F_A). It should be noted, however, that this assumes that the estimated host stellar radius R_A is unchanged by the detection of the companion star. As the radii for most Kepler stars are inferred photometrically, this may not be strictly true, as light from the companion might cause the primary stellar type to be misidentified. We do not attempt to quantify the extent of this effect in this paper. We do, however, note that it is likely to be negligible for larger contrast ratios where the colors of the blended system are dominated by light from the primary.

Case B, in addition to needing F_B, needs also the ratio R_B/R_A. If the observed companion is an unassociated background star, then the single-band Robo-AO observation does not constrain R_B. However, under the assumption that the companion is physically bound, then we can estimate its size and spectral type, given assumed knowledge about the primary star A.

In order to accomplish this, we use the Dartmouth stellar models (Dotter et al. 2008) and the measured primary KOI star properties listed in the NASA Exoplanet Archive. For the mass and age of the primary, we use the Dartmouth isochrones to find an absolute magnitude in the observed band (approximating the LP600 bandpass as Kepler band), then we inspect the isochrone to find the mass of a star that is the appropriate amount fainter (according to the observed contrast ratio), and assign the stellar radius R_B accordingly.

Table 4 summarizes how the planet radii change under both case A and B for each KOI in all the systems in which we detect companions. We also list an additional case B_bg for the situation in which the eclipsed star is not physically bound—since we do not have a constraint on R_B in this situation, we simply list the planet radii for the case of R_B = 1 R_☉, which allows for simple scaling.

Table 4. Implications on Derived Radius of Kepler Planet Candidates

KOI	Pa	Rpa	R⋆a	Δm	sep	R⋆, Bb	Rp, Ac	Rp, B	$R_{p,B_{bg}}$d
–	(d)	(R⊕)	(R☉)	(mag)	('')	(R☉)	(R⊕)	(R⊕)	(R⊕)
1.01	2.471	14.40	1.06	4.0	1.13	0.50	14.6	42.0	84.9
13.01	1.764	23.00	2.70	0.2	1.16	2.70	31.2	34.0	12.6
97.01	4.885	16.10	1.78	4.6	1.90	0.57	16.2	43.6	76.1
98.01	6.790	10.00	1.63	0.8	0.29	1.26	12.2	13.4	10.7
119.01	49.184	3.90	0.94	0.9	1.05	0.76	4.7	5.6	7.5
119.02	190.313	3.40	...	...	...	...	4.1	4.9	6.5
141.01	2.624	5.43	0.93	1.4	1.10	0.72	6.1	9.0	12.5
162.01	14.006	2.54	0.96	0.8	0.29	0.79	3.1	3.7	4.7
174.01	56.354	1.94	0.63	4.4	0.60	0.21	2.0	5.1	24.0
177.01	21.060	1.84	1.06	1.0	0.24	0.84	2.2	2.7	3.2
191.01	15.359	11.00	0.88	3.1	1.69	0.55	11.3	29.3	53.4
191.02	2.418	2.30	...	...	...	...	2.4	6.1	11.2
191.03	0.709	1.24	...	...	...	...	1.3	3.3	6.0
191.04	38.652	2.30	...	...	...	...	2.4	6.1	11.2
268.01	110.379	1.73	0.79	3.8	1.81	0.33	1.8	4.3	13.0
306.01	24.308	2.29	0.87	4.2	2.06	0.39	2.3	7.0	18.0
356.01	1.827	5.73	1.60	2.9	0.56	0.66	5.9	9.4	14.2
401.01	29.199	7.23	1.58	2.9	1.99	0.66	7.5	11.9	18.0
401.02	160.017	7.31	...	...	...	...	7.6	12.0	18.2
401.03	55.328	2.66	...	...	...	...	2.8	4.4	6.6
511.01	8.006	2.80	1.08	3.3	1.28	0.61	2.9	7.5	12.3
511.02	4.264	1.58	...	...	...	...	1.6	4.2	6.9
628.01	14.486	3.10	1.29	5.2	1.83	0.38	3.1	10.1	26.5
640.01	30.996	2.44	0.89	0.6	0.44	0.80	3.1	3.6	4.5
687.01	4.178	1.46	0.93	2.0	0.70	0.64	1.6	2.8	4.3
688.01	3.276	2.28	1.35	2.2	1.71	0.77	2.4	3.8	4.9
712.01	2.178	1.08	0.84	1.2	0.47	0.76	1.3	1.9	2.6
984.01	4.287	3.19	0.92	0.0	1.80	0.92	4.5	4.5	4.9
987.01	3.179	1.28	0.92	4.1	2.05	0.42	1.3	3.9	9.3
1002.01	3.482	1.36	1.01	2.3	0.30	0.66	1.4	2.7	4.1
1050.01	1.269	1.40	0.76	2.7	2.09	0.46	1.5	3.1	6.6
1050.02	2.853	1.40	...	...	...	...	1.5	3.1	6.6
1150.01	0.677	1.10	1.09	2.4	0.39	0.66	1.2	2.1	3.2
1151.01	10.435	1.46	0.97	3.5	0.75	0.50	1.5	3.8	7.7
1151.02	7.411	1.15	...	...	...	...	1.2	3.0	6.0
1151.03	5.249	0.70	...	...	...	...	0.7	1.8	3.7
1151.04	17.453	0.87	...	...	...	...	0.9	2.3	4.6
1151.05	21.720	0.97	...	...	...	...	1.0	2.5	5.1
1152.01	4.722	19.56	0.65	0.3	0.59	0.54	25.9	24.9	45.7
1274.01	362.000	4.73	0.79	3.8	1.10	0.37	4.8	12.6	34.3
1359.01	37.101	3.50	0.92	3.8	1.43	0.58	3.6	13.0	22.2
1359.02	104.820	7.30	...	...	...	...	7.4	27.1	46.3
1375.01	321.214	6.78	1.17	4.4	0.77	0.50	6.8	22.0	44.0
1442.01	0.669	1.23	1.00	6.7	2.24	0.20	1.2	5.2	26.8
1613.01	15.866	1.07	1.04	1.3	0.22	0.78	1.2	1.7	2.1
1613.02	94.091	1.08	...	...	...	...	1.2	1.7	2.2
1619.01	20.666	0.80	0.62	2.8	2.10	0.33	0.8	1.6	4.9
1677.01	52.070	2.18	0.85	4.8	0.61	0.43	2.2	9.8	23.1
1677.02	8.512	0.81	...	...	...	...	0.8	3.7	8.6
1845.01	1.970	1.50	0.70	5.0	2.06	0.19	1.5	4.0	21.2
1845.02	5.058	21.00	...	...	...	...	21.1	56.2	297.4
1880.01	1.151	1.49	0.52	3.7	1.70	0.18	1.5	2.8	15.6
1884.01	23.120	5.00	0.92	3.6	0.95	0.55	5.1	16.3	29.7
1884.02	4.775	2.63	...	...	...	...	2.7	8.6	15.6
1890.01	4.336	1.50	1.32	3.4	0.41	0.62	1.5	3.5	5.7
1891.01	15.955	1.85	0.69	4.5	2.09	0.33	1.9	6.9	21.1
1891.02	8.260	1.26	...	...	...	...	1.3	4.7	14.4
1916.01	20.679	2.16	0.96	2.7	0.27	0.67	2.2	5.5	8.2
1916.02	9.600	1.89	...	...	...	...	2.0	4.8	7.2
1916.03	2.025	0.92	...	...	...	...	1.0	2.4	3.5
1979.01	2.714	1.13	0.94	3.2	0.84	0.52	1.2	2.8	5.4
2009.01	86.749	2.20	0.97	4.1	1.51	0.48	2.2	7.3	15.2
2059.01	6.147	0.83	0.67	1.1	0.38	0.60	1.0	1.4	2.4
2059.02	2.186	0.60	...	...	...	...	0.7	1.0	1.7
2143.01	4.790	1.14	0.81	3.5	2.16	0.54	1.2	3.9	7.2
2159.01	7.597	1.07	0.88	4.0	2.00	0.48	1.1	3.8	7.7
2159.02	2.393	0.99	...	...	...	...	1.0	3.5	7.2
2413.01	12.905	1.32	0.65	2.1	0.31	0.46	1.4	2.7	5.8
2413.02	31.200	1.26	...	...	...	...	1.3	2.6	5.5
2443.01	6.792	1.20	1.09	5.4	1.39	0.41	1.2	5.3	13.1
2443.02	11.837	1.02	...	...	...	...	1.0	4.5	11.1
2463.01	7.467	1.02	0.97	0.8	0.62	0.94	1.2	1.7	1.8
2486.01	4.268	2.71	1.17	0.5	0.24	1.08	3.5	4.0	3.7
2641.01	3.556	1.20	1.10	2.6	1.42	0.66	1.3	2.5	3.7
2657.01	5.224	0.60	0.80	0.3	0.73	0.89	0.8	1.0	1.1

Notes. ^aValues taken from the NASA Exoplanet Archive. ^bEstimated radius of the stellar companion in the scenario where it is physically bound to the target star. Estimate made according to the absolute magnitude difference in the Kepler band, according the Dartmouth stellar models (Dotter et al. 2008). ^cEclipsing object radius in the scenario where the companion star is the eclipsed object and is physically bound to the target star, assuming the stellar radius of star B as estimated in this table. ^dEclipsing object radius in the scenario where the companion star is the eclipsed object and is a chance-aligned background star with radius 1 R_☉. We note that a background or foreground object is perhaps unlikely to be solar-type, but this quantification allows for simple scaling of the implied eclipsing object radius.

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Interestingly, under case B where the transit is assumed to be around a bound companion, in many cases the implied planet radius is not indicative of a false positive. This is because in order to get a large radius correction there must be a large contrast ratio, which then (in the physically associated scenario) implies that the secondary is a small star, which shrinks the radius correction factor. In fact, the only candidates which attain clearly non-planetary radii under case B are those which already have radii comparable to or larger than Jupiter to begin with. On the other hand, case B_bg often suggests a non-planetary radius, as the stellar radius in this case is not bound to shrink as the contrast ratio grows.

We leave a quantitative analysis exploring the relative probability of scenario B being a physically bound or chance-aligned companion to future work. However, we note qualitatively that relatively bright, small-separation companions are more likely to be physically associated, whereas more distant and higher contrast ratio companions are more likely to be foreground/background objects.

There are several KOIs with detected companions which we note as being of particular interest, some of which might represent rare false-positive scenarios. Future work will quantitatively assess the true nature of these particular KOIs (e.g., the probability that any given KOI is a false positive).

5.2.1. KOI-191: A Probable "Coincident Multiple"

5.2.2. KOI-268: Habitable Zone Candidate?

5.2.3. KOI-628: Possible Triple-system

5.2.4. KOI-1151: Another Possible Coincident Multiple

5.2.5. KOI-1442: Largest Contrast Ratio Companion

5.2.6. KOI-1845: One Likely False Positive in a Two-candidate System

5.2.7. Systems with Secure Small Planets

Our detection of 53 planetary candidates with nearby stars, from 715 targets, implies an overall nearby-star probability of 7.4% ± 1.0%, within the detectable separation range of our survey (015–25, Δm ≲ 6).

In this section we go on to search for broad-scale correlations between stellar multiplicity and planetary candidate properties. The companions we detect may not be physically bound, nor are we sensitive to binaries in all possible orbital locations around these KOIs. This multiplicity rate, therefore, should not be expected give a full description of the physical stellar multiplicity of Kepler planet candidates; however, we can use the current survey results to compare the multiplicity rates of different populations of planet candidates. Future papers from the ongoing Robo-AO survey will investigate the multiplicity properties of Kepler candidates in more detail, including quantifying the effects of association probability and incompleteness.

The above nearby-star probability calculation and the following sections use the binomial distribution to calculate the uncertainty ranges in the multiplicity fractions (e.g., Burgasser et al. 2003) and Fisher exact tests (e.g., Feigelson & Jogesh Babu 2012) to evaluate the significance of differences in multiplicity between different populations.

5.3.1. Stellar Multiplicity Rates versus Host-star Temperature

Figure 8 shows the fraction of multiple stellar systems around Kepler-detected planetary systems as a function of stellar temperature from the Kepler Input Catalog (Brown et al. 2011). The hottest stars appear to have an increased stellar multiplicity fraction, but there is a 16% probability this is due to chance. We thus do not detect any significant change in the stellar multiplicity fraction with KOI temperature, although the initial survey presented here does not yet cover the entire Kepler sample of non-solar-type stars.

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5.3.2. Stellar Multiplicity and Multiple-planet Systems

It is expected that multiple-planet systems detected by Kepler are less likely to be false positives than single-planet systems because there are far fewer false-positive scenarios which can lead to multiple-period false positives. In Figure 9 we show the stellar multiplicity rates for single and multiple planet detections. There is a difference in stellar multiplicity between the single and multiple planet detections, but a Fisher exact test shows a 13% probability of this being a chance difference due to small-number statistics. At least in the current data set we cannot distinguish stellar multiplicity between single and multiple planet systems.

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5.3.3. Stellar Multiplicity and Close-in Planets

Stellar binarity has been hypothesized to be important in shaping the architectures of planetary systems, both by regulating planet formation and by dynamically sculpting planets final orbits, such as forcing Kozai oscillations that cause planet migration (Fabrycky & Tremaine 2007; Katz et al. 2011; Naoz et al. 2012) or by tilting the circumstellar disk (Batygin 2012). If planetary migration is induced by a third body, one would expect to find a correlation between the presence of a detected third body and the presence of short-period planets.

Figure 10 shows the fraction of Kepler planet candidates with nearby stars as a function of the period of the closest-in planet, grouping the planets into two different size ranges. From these raw binarity fractions, where we have not accounted for the probability of physical association, it appears that while small planets do not show a significant change in third-body probability with the orbital period of the Kepler candidate, giant planets show a significant increase at periods less than ∼15 days. Binning all our targets into only four population groups allows us to search for smaller changes in the binarity statistics (Figure 11). We arbitrarily split "small" planets from "giant" planets at Neptune's radius (3.9 R_⊕), but the exact value of the split does not significantly affect the results; only two of the detected systems have planetary radii within 20% of the cutoff value. We see that small planets at short periods share the same binarity fraction as all sizes of planets with >15 days periods (within statistical errors). However, the short-period giant planets again show a significantly increased binarity fraction. A Fisher exact test rejects the hypothesis that the two planetary populations have the same binarity fraction, at the 95% level.

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We can attempt to remove the background asterisms by selecting on the basis of magnitude ratio, as faint background stars are more likely to be chance alignments than roughly equal-brightness companions. Our survey displayed an excess of close-separation bright companions: there are 13 companions with Δm < 2 with separations <15, and only one at larger radii (Figure 6), while the numbers of fainter companions do not show such a bias. We suggest that this excess reveals a bright-companion population which is more likely to be physically associated than an average companion in the survey.

Selecting the companions with Δm < 2 and separation <15 leads an increased difference in stellar multiplicity between the planetary populations (Figure 12), increasing the significance to 98%. This approach does not fully account for the probability of each companion being physically associated, and so its results should be interpreted with caution. For example, close-in companions are less likely to be rejected by the Kepler centroid-based false-positive tests, but it is not obvious why this rejection would be different for planetary systems with short-period (<15 days) and longer-period KOIs (with a median period of 54 days for the KOIs we surveyed). In fact, the shorter-period systems have more eclipse events in the Kepler data set and it should therefore be easier to detect a small centroid shift from close-in companions.

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On the basis of our current analysis, we suggest that the difference of multiplicity rates between the planetary populations may be tentative evidence for third bodies in stellar systems producing an excess of close-in giant planets. We expect the full Robo-AO surveys to be able to evaluate this possibility at more than the 3σ confidence level.