ABSTRACT
High-resolution imaging is an important tool for follow-up study of exoplanet candidates found via transit detection with the Kepler mission. We discuss here Hubble Space Telescope imaging with the WFC3 of 23 stars that host particularly interesting Kepler planet candidates based on their small size and cool equilibrium temperature estimates. Results include detections, exclusion of background stars that could be a source of false positives for the transits, and detection of physically associated companions in a number of cases providing dilution measures necessary for planet parameter refinement. For six Kepler objects of interest, we find that there is ambiguity regarding which star hosts the transiting planet(s), with potentially strong implications for planetary characteristics. Our sample is evenly distributed in G, K, and M spectral types. Albeit with a small sample size, we find that physically associated binaries are more common than expected at each spectral type, reaching a factor of 10 frequency excess in M. We document the program detection sensitivities, detections, and deliverables to the Kepler follow-up program archive.
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1. INTRODUCTION
The NASA Kepler mission has presented a catalog of over 2000 stars with over 2700 planetlike transit signatures (Borucki et al. 2011; Batalha et al. 2013; Burke et al. 2014). The number of planets confirmed (much more likely to be a real exoplanet than a false positive) from the Kepler sample has reached 977, with the vast majority of these following from the Lissauer et al. (2014) and Rowe et al. (2014) validation of planets in systems showing more than one set of periodic transits. Perhaps more impressive than these large numbers that have qualitatively expanded the sample of exoplanets are the large number of specific cases for which detailed studies have allowed qualitatively new discoveries, e.g., circumbinary planets (Doyle et al. 2011), planet properties constrained by transit timing variations (Holman et al. 2010), density constraints across the rocky to gaseous planet domain using radial velocities (Marcy et al. 2014), and significant improvements that follow from Kepler asteroseismology results for planet hosts (Huber et al. 2013).
Clearly the spectacular time-series data collected from the Kepler mission (Borucki et al. 2010; Koch et al. 2010; Jenkins et al. 2010) have been the primary basis for new advances. Also important has been an emphasis from the missionʼs start to carefully discriminate between planet candidates as found from apparent transits and validated or confirmed planets. The chance for false positives in transit detection experiments is high, with numerous channels potentially contributing apparent results that are not in fact due to extrasolar planets (Brown 2003).
The Kepler data are used directly to eliminate the vast majority of false positives arising from the most common case of blended, background eclipsing binaries through measurement of centroid motion (Bryson et al. 2013) in difference images in- and out-of-transit. Although very powerful, the Kepler data centroiding still allows for both false positives to slip through and for blended stars, whether physically associated or chance superpositions, to introduce dilution that needs to be corrected for in arriving at accurate interpretations of planets.
Fundamental to the Kepler mission results has been a vigorous program to obtain supporting spectroscopy and high-resolution imaging for recognizing false positives, for confirming planets, and for refining parameters of detected exoplanets. Spectroscopy is particularly important for detecting tight binaries via induced radial velocity variations, and blended objects in cross-correlations with templates. High-resolution imaging gains relevance in picking up wider bound components and chance superpositions (Morton & Johnson 2011) important to establishing planetary status.
The primary Hubble Space Telescope (HST ) program, data characteristics, and basic image analyses are discussed in Section 2. Defining point-spread functions, conducting searches, avoiding spurious detections, establishing completeness limits for the HST high-resolution imaging, and placing these results within the context of other similar observations are topics in Section 3. Section 4 presents results on using isochrone matching to assess the probability of spatially close stars being physically associated and documents all companions that could be the transit host or source of false positives for our sample.
2. PROGRAM, DATA, AND BASIC IMAGE ANALYSES
In early 2012, when this GO-12893 program was proposed, the Kepler mission follow-up programs were relying on 3–6 m telescopes and adaptive optics (AO) or speckle imaging for high-resolution imaging. Many of the Kepler targets are rather faint—with the interesting M-dwarf hosts of candidates often near V = 16. With transits of only a few hundred parts per million (ppm), deep imaging to delta magnitudes of at least eight was needed to securely detect all possible false positives. This need for many Kepler objects of interest (KOIs) to reach the equivalent of V = 24 severely challenged then available ground-based resources. A test (Gilliland & Rajan 2011) showed that HST imaging over half an orbit could provide superior results to full-night efforts from the ground for the most challenging targets. In later seasons with the more capable Keck AO imaging in routine use, some aspects of the HST advantage have gone away with comparable resolution and depth limits. HST retains an advantage of allowing imaging in optical bandpasses that are standard and well-calibrated, allowing accurate transformation to the Kepler bandpass as needed for use in establishing dilution corrections.
The HST imaging program was proposed to concentrate on a small subset of the Kepler planet candidates: (1) those that were faint with shallow transits severely challenging available ground-based imaging resources and (2) planet candidates that had estimated parameters Rp below and equilibrium temperatures below 500 K, thus emphasizing candidates with a chance of being rocky and, in some cases, within habitable zones (HZ; Kasting et al. 1993). The GO-12893 SNAPshot program contained 158 targets, with the bulk being G-type stars mirroring the overall Kepler target list. In the end, and contrary to advertised expectations, the executed SNAPshot visits often corresponded to our faintest stars and longest visits. Thus, the M dwarf targets were executed at a higher relative fraction. HST observations were obtained for only 22 of the proposed sample of 158, however, those executed were among both the most interesting and most challenging for ground-based studies. For example, our sample of 22 KOIs included 6 of 11 highlighted in the Dressing & Charbonneau (2013) study of M dwarf KOIs with candidates in or near the HZ, and all 3 (KOIs 854, 1422, and 2626) that were identified as most favorably placed with respect to the HZ. The observations listed in Table 1 span 2012 October 27–2014 January 7; any further visits that occurred after 2014 May 1 will be processed with deliveries made as discussed in Section 3.3, but are not included in this paper.
Table 1. KOIs with HST High-Resolution Imaging
KIC | KOI | Kepler | Np | Kp | Depth | δ-mag | Def555 | Def775 | Teff | Dist |
---|---|---|---|---|---|---|---|---|---|---|
2853029 | 3259 | ⋯ | 1 | 15.68 | 872 | 7.53 | ⋯ | 0.15 | 5494 | 1325 |
4139816 | 812 | 235 | 4 | 15.95 | 554 | 8.03 | 0.17 | 0.14 | 4023 | 495 |
4813563 | 1959 | ⋯ | 1 | 14.25 | 859 | 7.55 | ⋯ | ⋯ | 4915 | 480 |
5358241 | 829 | 53 | 3 | 15.39 | 422 | 8.32 | ⋯ | 0.03 | 6266 | 1765 |
5942949 | 2525 | ⋯ | 1 | 15.70 | 810 | 7.61 | ⋯ | 0.10 | 4595 | 715 |
6026438 | 2045 | 354 | 3 | 15.55 | 356 | 8.51 | ⋯ | ⋯ | 4621 | 710 |
6149553 | 1686 | FP | 1 | 15.89 | 631 | 7.89 | 0.32 | ⋯ | 3510 | 235 |
6263593 | 3049 | ⋯ | 1 | 15.04 | 540 | 8.05 | ⋯ | ⋯ | 4582 | 690 |
6435936 | 854 | ⋯ | 1 | 15.85 | 1692 | 6.81 | 0.26 | ⋯ | 3580 | 265 |
7455287 | 886 | 54 | 3 | 15.85 | 448 | 8.26 | 0.22 | ⋯ | 3654 | 290 |
8150320 | 904 | 55 | 5 | 15.79 | 436 | 8.29 | 0.00 | 0.11 | 4404 | 645 |
8890150 | 2650 | 395 | 2 | 15.99 | 357 | 8.50 | 0.23 | 0.10 | 3825 | 390 |
8973129 | 2286 | ⋯ | 1 | 15.06 | 504 | 8.13 | ⋯ | ⋯ | 5452 | 975 |
9838468 | 2943 | ⋯ | 1 | 13.85 | 213 | 9.06 | ⋯ | ⋯ | 6036 | 820 |
10004738 | 1598 | 310 | 3 | 14.28 | 168 | 9.32 | ⋯ | ⋯ | 5657 | 780 |
10118816 | 1085 | ⋯ | 1 | 15.23 | 307 | 8.67 | ⋯ | ⋯ | 3820 | 275 |
10600955 | 2227 | ⋯ | 1 | 14.87 | 523 | 8.09 | ⋯ | ⋯ | 5848 | 1090 |
11306996 | 3256 | FP | 1 | 14.81 | 333 | 8.58 | ⋯ | ⋯ | 4021 | 290 |
11497958 | 1422 | 296 | 5 | 15.92 | 787 | 7.65 | 0.29 | ⋯ | 3690 | 340 |
11768142 | 2626 | ⋯ | 1 | 15.93 | 818 | 7.60 | 0.32 | ⋯ | 3620 | 400 |
12256520 | 2264 | ⋯ | 1 | 14.48 | 334 | 8.58 | ⋯ | ⋯ | 5556 | 800 |
12470844 | 790 | 233 | 2 | 15.34 | 962 | 7.43 | ⋯ | ⋯ | 5208 | 970 |
12557548 | 3794 | ⋯ | 1 | 15.69 | 3186 | 6.13 | ⋯ | ⋯ | 4242 | 550 |
Note. KIC and corresponding KOI numbers are given for all targets, with the Kepler planet number given for validated cases. The number of multiple candidates or planets (Np), Kp, and the shallowest transit depth (Depth in ppm) over multiple systems are taken from CFOP. The δ-mag shows how much fainter a false positive source could be assuming 90% deep eclipses, and hence the relative depth to which high-resolution imaging is needed. Def555 and Def775 are the net shortfalls in magnitudes in reaching standard depth due to slightly truncated exposure times. Teff is from the KIC, and Dist (in pc) is calculated using the HST photometry as discussed in the text.
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An advantage of our HST imaging is a very uniform data set. All observations were acquired with a standard set of five dithered exposures in each of the WFC3 filters F555W and F775W, chosen to sample the Kepler bandpass optimally. Four exposures used the DITHER-BOX pattern with exposure times chosen to reach 90% of saturation for cases with the image centered on a pixel. A fifth exposure at six times the length of those in the pattern, thus saturating the core, was added to bring up signal-to-noise (S/N) in the wings and allow reaching delta magnitudes near 10. For about one-half of the faintest targets, the long exposure was limited to 300 s in one of the two filters (three targets were limited in both filters), thus yielding slightly shallower depths as listed in Table 1. The lost depth due to truncated exposure times is calculated separately as Def555 and Def775 for the two filters by using the WFC3 Exposure Time Calculator provided by STScI. This takes into account the five exposures in each bandpass and realistic background levels. The deficits are defined as the difference in magnitudes required to reach a S/N of 5 at the actual exposure time compared to the exposure time that would have been used for the full, standard depth. The deficit applies to a 2'' radius and beyond. At closer offsets from the target star, deficits are likely smaller since other factors enter to limit relative depth, but for discussion purposes, we conservatively assume these apply everywhere. Also included in Table 1 is KIC-12557548 added from GO-12987 (PI: Rappaport, Croll et al. 2014) for which nearly identical exposures were available. Image FWHM values (Gaussian fit) are 0077 ± 0004 for F555W and 0079 ± 0003 for F775W with no outliers to statistically unexpected deviations. WFC3/UVIS consists of two backside illuminated 2048 × 4096 CCDs with a scale of 004 per pixel and a full well depth of about 72,000 electrons. For a centered stellar image in our bandpasses, ∼15%–18% of the light falls on the central pixel in F555W and F775W, respectively. Further details of WFC3 may be found in Dressel (2014).
Figure 1 illustrates the very similar data for each target, KIC-10004738 in particular.
Discussion of data processing through drizzle combinations of all available exposures to a scale of 003333 is presented in Cartier et al. (2014). Critical to this study, the final drizzled image products were all shifted to be nearly (to within a few 0.01 of a WFC3 UVIS pixel) centered on a pixel, thus allowing all images to be "stacked" as discussed in Section 3.1 for an empirical point-spread function (PSF) definition.
The WFC3 UVIS images were obtained using the 1024 × 1024 subarray nearest the readout amplifier of UVIS2, thus minimizing the effects of charge transfer efficiency. To further minimize limitations from the loss of charge transfer efficiency, all exposures used a post-flash (a brief illumination using an LED internal to WFC3 immediately after the exposure, and before CCD readout) to generate a physical background of about 12 electrons per pixel including an allowance for the expected small sky background.
The UVIS subarray spans just over × . A few pixels near the boundary were trimmed to retain an area of exactly 1600 square arcseconds searched for companions to simplify later statistics.
3. COMPANION DETECTIONS AND COMPLETENESS
The primary product to be obtained from these HST observations is a list of all stars within the field of view, pushing as close to the bright target as allowed by the data and PSF and providing accurate photometry and positions. Associated with this will be extensive simulations and analyses to quantify limits to false detections, detection completeness as a function of depth in delta magnitudes relative to the target star, and offset (angular separation from the primary) distance from the target.
3.1. Empirically Defined PSF and Subtraction
HST imaging is characterized by great stability compared to ground-based imaging, whether direct or with adaptive optics. However, over the course of HST orbits, the telescope is thermally stressed and the focus varies by an amount that does influence the cores of PSFs in a significant way. Also, through broadband filters, the PSFs will vary slightly as a function of the underlying spectral energy distribution. A goal of these HST observations is to make use of the general imaging stability, account for deviations from this, and thereby enable deep relative imaging near the core of the bright KOIs by subtracting a model PSF from each individual image.
We define a model PSF for each individual image by "stacking" all available images, except for those in which close-in companions are found, and then for each pixel relative to the target centers developing the PSF model as a function of target color, telescope focus, and minor deviations with respect to the sub-pixel phase of the target centering. Photometry in the standard WFC3 Vegamag system (see Section 3.3) was developed for each target as discussed in Cartier et al. (2014). We then adopted the F555W–F775W magnitudes as the color. For telescope focus, we utilized STScIʼs Observatory Support portal5 which provides an estimated secondary–primary mirror despace at the time of observations using a modeling of observatory support structure temperature changes. For residual offsets from perfect centering, we used an initial guess based on first moments over the central 3 × 3 pixels. We used 20 of the 23 targets for the PSF definition, ignoring KIC-6263593, KIC-11497958, and KIC-11768142 for which the binary or triple nature with small delta magnitudes and offsets <05 made these useless for determining a PSF. For five of the other targets, we pre-subtracted a total of six much fainter companions that, if left, would have perturbed the resulting PSF model. A sample of 20 images in each filter to define the PSF as a function of color, focus, and residual centering is smaller than desired, but clearly works well for eliminating to near perfection diffraction spikes and any filter artifacts.
The model PSFs in F555W and F775W are developed over an area of 201 × 201 for the 003333 pixels, thus including an area of at least 333 in radius extending to 47 on the diagonals to include the full domain of diffraction spike influence. Although other options were experimented with, we adopted a PSF model that was a linear function of color, focus, and the always small x and y offsets from perfect image-to-image alignment.
After an initial fit at each pixel to determine a zero point plus the four coefficients of linear terms, the solution was iterated for each image by fitting the model PSF to each individual target, providing updated linear coefficients for focus and offset positions, with the known color being held fixed. With revised focus and offset coefficients for each target in hand, the model PSF at each pixel was again derived. This was iterated four times at which point convergence was reached.
The result of this approach can be assessed from inspection of Figure 1 showing one of the input images; the model PSF evaluated at the color, focus, and offset applicable to this target; and the result of subtracting the scaled PSF to create a difference image. The PSF resulting from stacking 20 individual images shows a much lower noise level than the single target drizzled image—as should be the case. Also, as should be the case, easily recognized features such as the diffraction spikes, and a filter artifact are sufficiently well subtracted that they leave no discernible trace with careful inspection of difference images, while nearby faint stars are preserved. However, within the inner ∼02, the PSF subtraction does not leave residuals that are near the Poisson limit, although detection sensitivity is gained even at these small offsets from using the PSF model subtraction. This lack of reaching a fundamental limit at small offsets could follow from a number of things. Our model for the PSF might be inadequate, e.g., perhaps other terms than the assumed linear dependence of color, focus, and small offsets should apply. We did try a quadratic dependence on focus with no improvement. Perhaps the sample size of 20 targets spanning a significant range of color (mid-G through mid-M stars), focus (deviations to about ±5 μ predicted), and residual centering imperfections to 0.05 pixels was insufficient for a solid solution; we had argued that 50 targets observed would be a good number for supporting robust PSF subtractions. In the end, though, the limiting factor seems likely to be the extent to which each individual exposureʼs position relative to the other four to be drizzled together could be determined. Given the small sub-array, there are generally only a small handful of other stars in the field of view at magnitudes remotely comparable to the target from which to establish relative positions. Minor errors at the order of 0.01 pixels in determining relative offsets of the undersampled component dithered exposures would suffice to introduce errors to the PSF of individual combined drizzle products that would not be amenable to correction through our stacking process. Our PSF subtractions are, in fact, quite good, and there is a ready explanation for subpar performance in the core. Given that, coupled with small sample size, we have not exhaustively pursued improvements in this area. Rather, we focus on properly quantifying the detection limits that follow from the data subtractions as described.
3.2. DAOFIND Searches, Avoiding False Detections
We use the DAOFIND task within IRAF based on Stetson (1987) to find stellar sources within our difference images from which the primary target has been suppressed. We have adopted a four-fold approach to avoiding false detections: (1) a number of images equal to our target set (23) have been simulated using simple Gaussian noise at the level of nine electrons characterizing our real data. We then run DAOFIND on these images adopting increasingly conservative cuts on the adjustable parameter threshold for the feature detection in sigma until no false detections result over the full sample. A value of threshold = 5.0 resulted in no false detections for this null limit test, but is recognized as perhaps not sufficiently conservative for the real data. (2) Our goal is to retain most stars to a delta magnitude beyond 9.0, but to reject background galaxies to the extent possible. We therefore generated a grid of 2500 delta-mag nine stars at a random sub-pixel centering phase per each of the 23 pure Gaussian noise simulated, 1024 × 1024 images and then plotted the distribution of DAOFIND output parameters on sharpness, sround, and ground and adopted bounds on these as tight as possible while eliminating no more than ∼1% of these targets near the expected limiting depth. We adopted a range of [0.4,0.85] for sharpness, for sround, and for ground. (3) We performed extensive inspections of results on the actual images after using the above parameters. The only change following from this was to adopt a more conservative threshold of 6, rather than 5σ, on the underlying detection significance to minimize detections which, upon inspection, seemed to not always be confidently stellar. (4) Near bright stars we boosted the required magnitude returned from DAOFIND based on a fifth order polynomial fit to the mean noise in annuli spanning 01–20 away from target stars on average. Without this step, a large number of spurious detections occur at small offsets in the difference images simply from increased Poisson noise levels, but also from increasingly imperfect PSF subtractions at small offset radius.
This approach results in high completeness in detecting any stellar companions that could result in a false positive for the shallow transits in question. That is, outside of ∼14 where noise from the stellar wings provides little lost sensitivity, 22 of 23 cases in Table 1 are imaged deeply enough to exclude EBs with 90% depth. Closer to the stellar core at a working radius of ∼04, the detection limit (adjusted for deficits due to shortened exposures) is at about the median of depths needed to fully probe for the worst case 90% deep eclipsing binaries. At the same time, we have been rather liberal in the retention cuts in the sense that we likely are not pushing as near the limiting depth as might be possible. In this approach, we are placing a greater emphasis on avoiding false detections than reaching the limiting depth and will rely upon quantified completeness simulations to characterize the results. Furthermore, we will individually discuss in Section 4 any close-in detections that are not unambiguously real.
In setting up the difference images upon which DAOFIND is run to detect stars, we not only subtract the primary target, but also perform PSF fits to and subtract all other stars within a delta-magnitude of three of the primary. This was found to be necessary to avoid spurious detections, e.g., along diffraction spikes on any stars within the images. For the three cases in which tight binaries or triples were detected, we performed simultaneous fits of the PSF to these to create the difference image as discussed in Cartier et al. (2014).
3.3. Photometric Results—Deliverables to CFOP
We use DAOFIND only to locate the approximate position of stars to be analyzed. Photometry and astrometry are then developed using least squares fits of the PSF derived for each image based on the discussion in Section 3.1. Photometry of individual stars makes use of bi-cubic polynomial interpolation shifts of the PSFs as solved for in the least squares fitting, with the count level then following directly from the scale. Formal errors on the count levels and positions are adopted from the least squares fitting (Bevington 1969). Transformation to the VEGAmag system is based on the STScI published zero points6 based on encircled energy in 20 radii relative to an infinite aperture along with published zeropoints. The vega magnitude of a star with flux F is −2.5 log() where Fvega is the calibrated spectrum (Bohlin & Gilliland 2004) of Vega. We verified that our PSF fits accurately reproduced results for 2'' radius aperture photometry on isolated bright stars.
Table 2 shows an example for KOI-3049, KIC-6263593 of a delivered detections table. The photometry described in this paper is performed on the target star and provided in the tables. The improved target star magnitudes take into account the contributions of the newly discovered field and companion stars. Our goal for this paper is not to show all of the results for each target, but rather to document the general approaches and highlight any interesting results. Figure 2 shows the drizzled images from which the detections were developed. Both the fits images and the source tables (extension of .src) have been delivered to the primary archive for Kepler results, CFOP.7 For this example, the delivered files are named: 3049Ic-rg20130214v.fits, 3049Ic-rg20130214i.fits, and 3049Ic-rg20130214HST.src; in addition, a 3 × 3'' clipout is available as 3049Ic-rg20130214i.jpg. The ‵‵v'' and ‵‵i'' in the above names are shorthand for F555W and F775W, respectively.
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Standard image High-resolution imageTable 2. Example Source Detection Table for CFOP Delivery
R.A. | Decl. | Dist | PA | F775 W | F775W_e | Color | Color_e | Kp | Kp_e | d_Kp | KIC | KIC_Kp |
---|---|---|---|---|---|---|---|---|---|---|---|---|
282.9975209 | 41.6785572 | 0.000 | 0.000 | 14.806 | 0.020 | 1.198 | 0.020 | 15.537 | 0.020 | 0.000 | 6263593 | 15.037 |
282.9974699 | 41.6784340 | 0.478 | 196.900 | 15.284 | 0.020 | 1.362 | 0.020 | 16.080 | 0.020 | 0.543 | ⋯ | ⋯ |
282.9974496 | 41.6783548 | 0.757 | 194.804 | 20.592 | 0.061 | 1.280 | 0.111 | 21.355 | 0.076 | 5.818 | ⋯ | ⋯ |
282.9970876 | 41.6784729 | 1.207 | 255.271 | 22.400 | 0.045 | 0.916 | 0.062 | 23.017 | 0.045 | 7.480 | ⋯ | ⋯ |
282.9977796 | 41.6788370 | 1.221 | 34.638 | 19.712 | 0.015 | 1.242 | 0.022 | 20.460 | 0.018 | 4.923 | ⋯ | ⋯ |
282.9971164 | 41.6793261 | 2.972 | 338.496 | 20.773 | 0.019 | 1.126 | 0.027 | 21.474 | 0.022 | 5.937 | ⋯ | ⋯ |
282.9936923 | 41.6799497 | 11.450 | 295.946 | 22.764 | 0.054 | 2.436 | 0.152 | 23.992 | 0.100 | 8.455 | ⋯ | ⋯ |
282.9961378 | 41.6818506 | 12.423 | 342.573 | 22.942 | 0.060 | 3.001 | 0.293 | 24.397 | 0.188 | 8.860 | ⋯ | ⋯ |
282.9999390 | 41.6750932 | 14.065 | 152.477 | 20.422 | 0.017 | 2.654 | 0.032 | 21.738 | 0.024 | 6.201 | ⋯ | ⋯ |
282.9954610 | 41.6749528 | 14.112 | 203.117 | 22.913 | 0.046 | 3.500 | 0.721 | 24.568 | 0.458 | 9.031 | ⋯ | ⋯ |
283.0023335 | 41.6769730 | 14.141 | 113.799 | 21.039 | 0.021 | 2.055 | 0.034 | 22.114 | 0.025 | 6.576 | ⋯ | ⋯ |
282.9980917 | 41.6746183 | 14.266 | 173.831 | 18.003 | 0.013 | 2.083 | 0.019 | 19.090 | 0.017 | 3.552 | 6263597 | 19.349 |
282.9921937 | 41.6778002 | 14.583 | 259.217 | 20.707 | 0.035 | 2.763 | 0.068 | 22.067 | 0.047 | 6.530 | ⋯ | ⋯ |
282.9921506 | 41.6777921 | 14.702 | 259.189 | 20.875 | 0.042 | 2.694 | 0.080 | 22.207 | 0.055 | 6.670 | ⋯ | ⋯ |
282.9974078 | 41.6831811 | 16.646 | 358.948 | 23.466 | 0.072 | 1.841 | 0.160 | 24.455 | 0.107 | 8.913 | ⋯ | ⋯ |
282.9966051 | 41.6739474 | 16.780 | 188.445 | 19.552 | 0.015 | 0.619 | 0.020 | 20.050 | 0.018 | 4.513 | 6263592 | 19.659 |
282.9933695 | 41.6821712 | 17.141 | 319.361 | 20.528 | 0.018 | 2.625 | 0.033 | 21.832 | 0.025 | 6.294 | ⋯ | ⋯ |
283.0013226 | 41.6738763 | 19.711 | 148.768 | 20.743 | 0.018 | 1.238 | 0.026 | 21.490 | 0.021 | 5.952 | ⋯ | ⋯ |
282.9901758 | 41.6794287 | 19.998 | 279.017 | 23.558 | 0.072 | 2.672 | 0.330 | 24.881 | 0.212 | 9.343 | ⋯ | ⋯ |
282.9909203 | 41.6828850 | 23.615 | 311.271 | 17.305 | 0.012 | 0.572 | 0.017 | 17.784 | 0.015 | 2.247 | 6263577 | 17.742 |
282.9904070 | 41.6824301 | 23.669 | 306.081 | 21.840 | 0.029 | 2.158 | 0.056 | 22.956 | 0.039 | 7.429 | ⋯ | ⋯ |
Notes. R.A. and Decl. = position of HST source (J2000, decimal degrees). Dist and P.A. = distance (arcseconds) and position angle (deg. E of N) of HST source from KOI. F775 W and F775W_e = HST (Vega) magnitude and error of HST source. Color and Color_e = F555W–F775W HST -based color and error. Kp and Kp_e = derived Kepler magnitude from F555W, F775W and error. d_Kp = number of Kepler magnitudes fainter (or brighter) than KOI in HST -based Kp. KIC = KepID likely corresponding to HST source. KIC_Kp = KIC value of Kp for likely match.
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3.4. Simulations to Define Completeness
To define completeness, we have chosen to insert an equal number of simulated targets on each of 22 (of 46 total) images, half in the F555W filter and half in F775W. We use all images for this simulation except: (1) the three cases of obvious binary and triple stars, (2) the KIC-12557548 images from GO-12897, since these went slightly deeper than the GO-12893 set, and (3) the ∼1/4 of images from Table 1 for which one or both filters were not taken to the full nominal depth. This leaves exactly half of the images from GO-12893, all of which by design used identical dither patterns and exposure times that were designed to take the primary target to the same count level. Since the F555W and F775W images were designed to reach the same exposure level, we do not separate detection completeness by filter. The background level is nearly identical by design in that post-flash is used across all cases . The number of cosmic rays will of course vary frame to frame, but the longest total integration time in any filter was 673 s summed over five exposures, and cosmic rays have been well eliminated in the drizzling process and so are not a major factor. Nor do we take into consideration differences in stellar crowding image to image; while at the Kepler pixel scale of 40 many of these are quite crowded fields, at the HST WFC3 scale of 004 per pixel these are all sparse. While minor deviations in completeness level surely exist between images, this is likely below the level of fidelity to which any reasonable effort could quantify it.
We have chosen to determine completeness on a relatively fine grid of offset positions from the primary targets: 010, 012, 016, 02, 03, 04, 06, . . . 18, and positions at and larger than 20. Simulated images are generated at a series of delta magnitudes using the PSF appropriate (Section 3.1) for each image. The simulated images are always placed at random positions with respect to sub-pixel centering. The positions of real stars, other than the primary target, in the real-data difference images were ignored when placing the simulated stars. Different approaches to accumulating a sufficient number of simulations were adopted for different offset positions. Outside of 20, simulated stars in each of the 22 images were placed on a regular grid (set at random sub-pixel positions for each realization) every 25 pixels in x and y per image, thus resulting in over 50,000 cases. For the smallest offsets, the central 41 × 41 pixels in each difference image were rastered into standard sized images, thus replicated over 900 times per image, and one simulated star was added at the correct radial offset for the trial, but at a random position angle. For intermediate offsets, a few realizations were placed on the offset circle at a non-interfering separation in angle. A sufficient number of simulations were used to result in Poisson counting statistic errors of ≲1% for the smallest and largest offset positions up to ∼5% for a few intermediate offset separations.
Our simulated images use difference images from which the target has been subtracted as the basis. For small offsets and magnitude differences, a concern existed that the presence of a nearby companion might influence the primary target fit and subtraction, thus invalidating use of difference images as the basis. We therefore also performed a large number of simulations based on injections to the original images and found no difference with respect to conclusions using the difference images.
After setting up the simulated images at any offset and delta magnitude combination, the images were processed with DAOFIND, and the same cuts on output parameters as used on the real images were applied. A target returned from DAOFIND was counted as real if it falls within 007 of the known position of the simulation input.
The resulting completeness levels are shown in Figure 3. At an offset of 010, 90% of stars with a delta magnitude of 2.0 are detected, while the 50% recovery level occurs at about δ-mag of 3. At and outside of 2'', 90% completeness is at δ-mag 8.9 and 50% at 9.4 per filter. Clearly beyond an offset of 08, the completeness levels change very little, with most of the sensitivity change for offsets ≲05.
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Standard image High-resolution imageWe believe that at ≳02, these completeness levels have been reached with essentially no chance of false positives coming in. That view is based on having performed careful visual inspections of all such detections in both F555W and F775W images and assuring that all detections are qualitatively secure. At still lower offsets, we expect few if any false positives, but cannot argue that none have occurred in the real data given non-Gaussian behavior of the difference images in the PSF cores or at least PSF variations that are not adequately captured by our modeling.
Figure 4 shows a sensitivity curve developed as the 70% completeness level (following this use in the Lillo-Box et al. (2014) comparative study) for all offsets as plotted in Figure 3, as well as all detections within 25 offsets shown as δ-magnitude deviations from the target Kp. The dashed line in Figure 4 corresponds to the boosted magnitude near bright stars (as discussed in Section 3.2) based on the noise in annuli spanning 01–2'' in steps of 008 near the bright targets in the PSF-subtracted images. The dashed line is 2.5 × log(noise/reference), where reference is the mean noise level of 9.0 electrons per drizzled pixel at > 15.
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Standard image High-resolution image3.5. Comparison with Other High-resolution Imaging
Although the high-resolution imaging observations available under CFOP in support of vetting and interpreting Kepler exoplanet candidates is expanding rapidly, these HST observations fill a useful niche. These observations are of very interesting targets in general, and are unique in covering both a large 40 × 40'' domain, and providing resolution better than 008 in well-calibrated optical bandpasses that can be robustly mapped to the Kepler bandpass.
A recent paper by Lillo-Box et al. (2014) compared all primary published results for high-resolution imaging of Kepler targets. Included were the authors own lucky imaging results picking off the best 10% of very short, diffraction-limited exposures obtained with the 2.2 m telescope at Calar Alto Observatory, near-IR adaptive optics results of Adams et al. (2012, 2013), and Dressing et al. (2014) using the 6.5 m Multiple Mirror Telescope on Mt. Hopkins, speckle imaging (Howell et al. 2011) with the 3.5 m WIYN telescope on Kitt Peak and (Horch et al. 2012) with the 8 m Gemini North telescope on Mauna Kea, as well as the extensive robotic AO observations (optical) obtained by Law et al. (2014) with the 1.5 m Palomar telescope on Mt. Palomar. We will also comment on Keck 10 m telescope on Mauna Kea near-IR adaptive optics imaging, which is extensively used in the Kepler literature, although lacking an over-arching summary paper.
An ideal set of high-resolution imaging observations would include all KOIs and a large enough area (40'' would be good) to cover all potential companions of interest for analyzing KOIs. At the same time, it should build up observational statistics on background object density across the Kepler field, reaching limiting depths of 9–10 magnitudes beyond the target brightness in order to detect (with a comfortable margin) all possible sources of false positives (shallower is acceptable for deeper transit cases), use at least two well-calibrated bandpasses in the optical, allowing robust transformation to Kp and interpretation with published stellar isochrones, and have near diffraction-limited resolution on large telescopes to probe as near to the target as possible. All existing high-resolution surveys analyzing the Kepler targets fail in at least one of the attributes of an ideal program. The primary weakness of our HST program is that it provides data for only 23 (<1% of total sample) KOIs, but is probably better than any other program on the balance of other desired attributes. Therefore, these HST results may provide useful insights through comparison of overlapping observations from other programs.
A valuable observational element available through CFOP for nearly all KOIs are UKIRT near-IR images and resulting source tables. However, those were based on rather shallow, natural seeing imaging. In Figure 2, we have highlighted two detections at offsets and position angles from the KOI of about 14'' and 203°and 197 and 149°. In the UKIRT-based source tables, both of those were flagged as probable galaxies and had Kp magnitudes projected from J of 21.5 and 21.0 respectively. On the much deeper, much higher resolution HST images, both objects are stellar in appearance and have more accurately determined Kp magnitudes of 24.5 and 21.5 respectively.
We have only one target in common with the 6.5 m AO (Dressing et al. 2014), the unusually faint (for MMT Observatory AO) KOI-886 at Kp = 15.85. The MMT AO provide a primary working angle of 03–10'' to a contrast usually better than 5 magnitudes in Ks. Within the 10'' radius where Dressing et al. (2014) report no detections, we see four. Three of these have δKp ≳8, while a fourth has an offset angle from the target of 37, δKp = 3.86 and is fairly blue. None of these should have been reported from the MMT AO given the listed sensitivity limits for this faint star.
We have six targets in common with Robo AO (Law et al. 2014): KOIs 854, 886, 1085, 1422, 1598, and 2045. Within the typical offset working angle of ∼02–25 and limiting depth of about six magnitudes for Robo AO, no detections were made for these six targets. For the same set, we have three detections within the same offset distance. The KOI-1422 δ-Kp 1.56 companion at 022 that deeper HST imaging reveals was not found by Robo AO . This is a very interesting target (Dressing & Charbonneau 2013) hosting multiple planets in or near the habitable zone, that will be strongly modified in interpretation (Cartier et al. 2014) through the recognition that this is a stellar binary. This is near the advertised working domain for Robo AO, but in the low-performance domain, this faint KOI detection was not expected. Also not found was the 23 offset δ-Kp of a 7.36 physical companion to KOI-1598—this is fainter than the claimed Robo AO limit. Similarly, the 13 δ-Kp of 6.9 detection near KOI-2045 is not detected by Robo-AO. Although strong in covering many KOIs (eventually, all is the goal), the Robo-AO program by design does not succeed in detecting a large number of relevant companions.
We have no overlap with the lucky imaging (Lillo-Box et al. 2014), but note that the sensitivity curve of Figure 4 for HST is much better than lucky imaging, especially at offsets < 1''; see their figure 11.
Lillo-Box et al. (2014) discuss the limitations of the extensive 3.5 m speckle imaging (Howell et al. 2011) which has neither a field of view large enough nor a detection depth deep enough to provide much of an effect in delimiting possible target contamination. We have KOIs 812 and 3259 in common with the more capable Gemini 8 m speckle imaging discussed in Horch et al. (2012). The speckle imaging does not result in any detections for either of these targets. For KOI-3259, the HST imaging turns up a companion at 136 just inside the speckle field of view, but at a δ-Kp of 7.8 is some 3.8 magnitudes beyond the 5-σ limiting depth as quoted on CFOP for either of these Gemini speckle targets. For the two targets in common with our HST program, the Gemini speckle imaging appears relatively uninteresting from the perspective of field of view and limiting depth. However, the speckle imaging provides the best resolution limit of any other available options in common use.
J. Lillo-Box provided an evaluation of the blended source confidence (BSC) parameter used in Lillo-Box et al. (2014) for our HST observations. The BSC parameter measures how effectively high-resolution imaging observations eliminate the phase space of background objects bright enough to be false positives. Gilliland & Rajan (2011) had introduced a similar parameter and estimated that HST observations would eliminate 95%–98% of possible background sources. The Lillo-Box et al. (2014) BSC result came out quite similar, with typical rejections above 99%, and averaging well above 95%. In contrast, the other high-resolution imaging observation programs discussed in Lillo-Box et al. (2014) succeed in eliminating only a small fraction of possible background objects bright enough to matter.
Finally we note that several of our targets have been observed with the Keck NIRC2 AO system of the 10 m Mauna Kea telescope, which was used for all of the objects discussed in Marcy et al. (2014). The Keck AO images generally have an FWHM some 30% better than the HST value, and reach a comparable limiting depth in many uses. However, the field of view and limitation to near-IR bandpasses introduces limitations relative to the ideal. Our most challenging target, KOI-2626 (see also Cartier et al. 2014), with a triple at the 02 level, was first detected in Keck AO imaging, then in short order, was also observed with Gemini 8 m speckle and our HST imaging. In all three of these observation sets, the triple is cleanly resolved. Arguably, the HST imaging is most valuable in providing well-calibrated optical photometry supporting a determination of the light fraction of each component in the Kepler bandpass as well as matching up with published stellar isochrones.
4. TESTING FOR PHYSICAL ASSOCIATION
Spatially close companions near and below the arcsecond offset level are common in our high-resolution imaging. Since knowing whether a given companion is a chance superposition or a star likely bound in physical association with the target influences the interpretation of planetary candidates, we seek a means of determining this nature. Canonical approaches would be to check for common proper motions or similar radial velocities—neither is available in this study. We know only the angular separation, and photometry in two HST bandpasses with WFC3, F555W, and F775W. Since the companions are fainter than the targets and many of our targets are already K and M dwarfs, if physically bound, the companions will often be M dwarfs. We will use matching of closely separated stars to isochrones, arguing that if the multiple stars can be represented by a single isochrone, then they are likely a bound system. We also adopt a Bayesian argument, providing odds ratios in individual cases for the associations being a physical companion versus chance alignment.
4.1. Use of Isochrones—M Dwarfs and Optical Bandpasses
If two stars can be placed on a common stellar evolution isochrone, then this is solid evidence (in an Occamʼs razor sense) that the two objects are at nearly the same distance, likely share similar ages and metallicities, and hence, are likely to be physically bound. The Dartmouth stellar evolution isochrones (Dotter et al. 2008; Feiden et al. 2011) conveniently include magnitudes in our WFC3 bandpasses and have been extensively used for the interpretation (Dressing & Charbonneau 2013) of Kepler M dwarf KOIs. Modeling of M dwarfs is challenging: especially problematic is obtaining the correct spectral energy distribution at short wavelengths where the complexity of molecular opacities couples with a part of the spectrum containing only a small fraction of the stellar flux.
Figure 5 illustrates the problems arising for interpretation of early- to mid-M dwarfs, roughly those beyond F555W–F775W of 2.0, using standard isochrones. In this figure, about 50 very nearby stars with V, Ic photometry and large, accurately known parallaxes from the RECONS project (Henry et al. 1999, 2006; Cantrell et al. 2013; Jao et al. 2014) are shown following application of a minor transformation to F555W and F775W based on synthetic photometry using the Pickles (1998) spectra and the IRAF/STSDAS SYNPHOT package. The Dartmouth isochrones at [Fe/H] = 0.0 and -0.5 perform reasonably well in matching the spectral energy distribution of earlier type stars, but fail spectacularly in the optical in representing early- to mid-M dwarfs (M3 is at F555W–F775W ∼2.4); see also similar comparisons and a more extensive discussion in Boyajian et al. (2012). Recognizing this disconnect for the M dwarfs which will likely be the most common companions in these analyses, we used the Pickles (1998) set of standardized, composite spectra to develop synthetic photometry using the SYNPHOT package under IRAF/STSDAS. This empirical approach to setting an isochrone results in a curve that at least parallels the observed color–magnitude distribution in Figure 5, but by mid-M is offset by over a magnitude.
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Standard image High-resolution imageFor our purposes we only care about whether the stars at small spatial offsets are at near equal distances, and thus likely to be physically associated. We are not attempting to derive accurate stellar parameters. Thus we are free to adopt a purely empirical fit within the F775W, F555W–F775W CMD to represent a mean solar neighborhood isochrone. The adopted fit shown in Figure 5 is a fourth order polynomial over F555W–F775W = 0.5–3.3 with a linear extension beyond this. Although there is a significant scatter of individual stars around this empirical fit, likely due to generally unknown star-to-star metallicities, this represents the empirical CMD much better than more direct options such as the Dartmouth isochrones or our attempt to obtain an empirical isochrone from published composite spectra.
Figure 5 should raise a strong note of caution in using the Dartmouth isochrones to interpret M dwarfs if relying on optical bandpass photometry. The reddest stars plotted in Figure 5 extend only to M6.
4.2. Odds Ratios for Companion versus Chance Alignment
We follow the approach used by Torres et al. (2011) and Fressin et al. (2011) to establish the probability that planetary candidates are real exoplanets, instead of false positives. In their case an odds ratio based upon the established frequency of exoplanets, and the frequency of potential false positives was established. In our case, this will be very similar—a ratio based on the known physically associated companion rate, compared to our own empirically developed rate of false associations:
The recent synthesis of extensive literature on the commonality of binary and higher order associations by Duchêne & Kraus (2013) is adopted to provide the prior expectation on the frequency of bound systems and thus for each target. Duchêne & Kraus (2013) present results that FGK dwarfs have a mean companion frequency of 0.62, while M dwarfs have a lower fraction of 0.33 companions per star. For the G dwarfs, companions follow a log-normal distribution with a mean semimajor axis of 45 AU and a σ on log(Period) in days of 2.3 and 5.3 AU and σlog(Period) of 1.3 for M dwarfs.
Our high-resolution imaging is sensitive primarily to binaries at relatively large physical separations, the high period tail of the log-normal distributions. To evaluate the statistically expected number of companions for each of our targets, we proceeded as follows. (1) For each target, we estimated its distance using the observed F775W magnitude, the reddening given in the KIC (Brown et al. 2011), and the empirical fit to absolute F775 W versus color as in Figure 5. These distances are shown in Table 1. (2) For each companion, we mapped the observed spatial offset and estimated distance into AU ignoring projection effects. (3) We integrate over the G and M distributions of companion frequency separately from 0.5 to 2.0 times the offset distance in AU. (4) If the spectral type of the target was G, we used the G star result, if the spectral type was M, we used the M star result, and if it was K, we used the geometric mean of G and M. We used the KIC Teff from Table 1 and 5250 K as the G–K boundary, and 3850 K (Pickles 1998) as the K–M boundary. The expected number of companions, , within the search range is usually 0.02–0.08, i.e., an order of magnitude smaller than the integral number of companions expected on average over all possible offsets.
Assessing the is developed from our own stellar detections and depends on three factors: (1) the mean stellar density (number per unit area) as a function of galactic latitude, (2) the mean stellar density as a function of apparent brightness, and (3) how often unassociated stars reach various levels of consistency with isochrone matching. For the odds ratio of a companion versus a chance association, we used the full set of GO-12893 images to establish the frequency at which two physically unrelated stars match to a given in:
where the color differences are F555W–F775W per star minus the same quantity for the fit to local stars as in Figure 5 for the two stars tested, A and B, and the magnitude difference is the observed B-A value minus the corresponding value of the absolute F775 W from the fit. For each of the 23 primary targets, test matches were made to each of the non-primary targets in the other 22 images. For each evaluation, a minimum was evaluated by testing against all colors in the underlying fit of Figure 5. In addition, the observed colors were dereddened by all possible values (in steps of 0.01) from zero to twice the KIC value for of the primary star.
From our set of 23 images, the smallest separation between two images on the sky is about 0.75°. Our targets have a mean distance of ∼660 pc. Thus, the physical separation between stars in the two images nearest each other would be of order 10 pc. We thus assumed that no stars in any image are physically associated with stars in other images. Using all detected stars in each of the 23 images to evaluate Equation (2) against all target stars in separate images gave about 11,000 matches. For the σʼs in Equation (2), we adopted formal estimates of precision from fitting a PSF to the data with a floor of 0.015. At 21st magnitude, errors were ∼0.02, increasing to typically 0.1 at 24th magnitude. The comparison of two physically unassociated stars was usually large, with the most common values of order 1000 indicative of extremely poor matches relative to the empirical isochrone. The cumulative fraction of matches as a function of is shown in Figure 6. Random pairings of stars do occasionally have good matches to the isochrone, e.g., 5% have ≲1.0. Since these stars cannot be physically associated, it is clear that merely having a close match with the isochrone does not suffice to argue for physical association.
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Standard image High-resolution imageThe test matching of ∼11,000 pairs covered an equivalent of 23 × 22 times the 1600 square arcseconds of each image. To evaluate the denominator for the odds ratio, we adopted the same annulus area used for the prior expectation of companions discussed above and multiplied this by the number density per unit solid angle of test matches up to the level of the star in question. We adjusted this value by two additional factors affecting the number density of stars: (1) a general dependence on galactic latitude as shown in Figure 7 after normalization to a mean of unity, and (2) the dependence of number counts as a function of brightness Kp as shown in Figure 8 evaluated up to the estimated brightness of the test star plus a 1σ error.
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Standard image High-resolution imageThis approach to evaluating an odds ratio for likelihood that a given companion is physically associated as opposed to a chance alignment provides a good indication of status, but for a few ambiguous cases, additional input would be needed to establish the true nature. The results of testing the 481 total detections over 23 images for physical association is shown in Table 3 for all cases in which the odds ratio favors association, and for which the value is less than 10. (Two cases had odds ratios of 1.1 and 2.3, respectively, for which the corresponding isochrone were at 27 and 154.)
Table 3. Companions with a Likely Physical Association
KIC | KOI | Offset | PA | δ-mag | Color | Odds Ratio | |
---|---|---|---|---|---|---|---|
5358241 | 829 | 0.107 | 239.9 | 2.39 | 1.034 | 1.123 | 3703.9 |
5358241 | 829 | 3.311 | 335.4 | 6.00 | 2.659 | 0.032 | 1.3 |
6263593 | 3049 | 0.478 | 196.9 | 0.54 | 1.362 | 0.011 | 1923.7 |
10004738 | 1598 | 2.275 | 65.9 | 7.36 | 2.933 | 0.038 | 6.3 |
11497958 | 1422 | 0.217 | 217.3 | 1.56 | 2.478 | 0.008 | 4101.6 |
11768142 | 2626 | 0.161 | 181.6 | 1.44 | 2.389 | 1.019 | 928.1 |
11768142 | 2626 | 0.201 | 212.7 | 0.61 | 2.299 | 0.107 | 2832.9 |
12256520 | 2264 | 0.949 | 103.8 | 6.53 | 2.838 | 0.038 | 62.5 |
Note. KIC and corresponding KOI numbers are given for all stars having a positive odds ratio for a physical association as discussed in Section 4.2. Offset is in arcseconds, P.A. is in degrees E of N, δ-mag in Kp, color is F555W–F775W, with and odds ratio as in Section 4.2.
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The split in Figure 4 between dominance by companions within 05 and chance alignments prevailing outside of 05 is striking. At the distances of our targets, 05–25 already projects to the high-period tail of the log-normal, physically associated distributions. Given the values from Duchêne & Kraus (2013), we expect about twice as many physically associated companions within 05 as within 05–25, i.e., consistent with Figure 4. The density of chance alignments should be uniform, and the area over 05–25 is 25 times that at <05. In qualitative terms, the split in Figure 4 is fully expected.
4.3. Close Companions That Could be Transit Hosts
We now consider all detections that complicate consideration of the true transit host based on our high-resolution imaging. For close companions that we have determined are likely to be physically associated with the target, the complication would be not knowing the true host star of the planet candidates. For chance alignments, the nearby star remains as a false positive possibility. In tabulating these cases of interest, we consider two factors: (1) whether the offset distance of the companion star is within the 3σ centroiding error based on analysis of difference images in- and out-of-transit (Bryson et al. 2013) and (2) whether the companion star is bright enough such that even with 90% eclipse depths it could produce the observed transit depth when diluted by the target.
We take the 3σ centroiding error from the data validation reports for quarters 1–16 from CFOP. Two entries from Table 3 are not included here, since for both the 33 offset star for KIC-5358241, and the companion to KIC-10004738 the Kepler -based centroiding eliminates these from contention. On the other hand, we find that newly detected close companions to KIC-6263593 = KOI-3049 that are not physically associated with the target cannot be eliminated as possible false positive sources for the apparent transits.
The primary and companions for the six targets in Table 3 are shown in relation to each other in the CMD Figure 9. KOI-3049/KIC-6263593 provides a good illustration—the closest companion in physical offset and δ-mag has an odds ratio of nearly 2000 favoring physical association. The other three companions in Table 4 have odds ratios favoring chance alignment and isochrone match values (Equation 2) of 154–816.
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Standard image High-resolution imageTable 4. Target in which Host is Uncertain from High-resolution Imaging
KIC | KOI | 3σ error | Offset | δKp | Depth if Host | Bound? |
---|---|---|---|---|---|---|
5358241 | 829 | 0.57 | 0.11 | 2.39 | 4235 | yes |
6263593 | 3049 | 1.39 | 0.48 | 0.54 | 1428 | yes |
6263593 | 3049 | 1.39 | 0.76 | 5.82 | 115460 | no |
6263593 | 3049 | 1.39 | 1.21 | 7.48 | 530684 | no |
6263593 | 3049 | 1.39 | 1.22 | 4.92 | 50704 | no |
11497958 | 1422 | 1.03 | 0.22 | 1.56 | 4098 | yes |
11768142 | 2626 | 2.07 | 0.16 | 1.44 | 3899 | yes |
11768142 | 2626 | 2.07 | 0.20 | 0.61 | 2253 | yes |
12256520 | 2264 | 2.31 | 0.95 | 6.53 | 137027 | yes |
Note. KIC and corresponding KOI numbers are given for all stars leading to ambiguity as to the host star. The 3σ error is the extreme offset still allowed from Kepler centroid analysis, the offset is in arcseconds, the "Depth if host" is the intrinsic transit or eclipse depth (for the shallowest transit of multi-planet systems) in ppm if the star is the host, and the final column indicates whether the companion is physically associated with the primary target star.
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Over the 23 KOIs considered in this paper, we find that five have physically associated companions that could be the true transit host, and one of these has additional chance alignments that could be the source for a false positive. The results are summarized in Table 4. Refined analyses, e.g., application of BLENDER (Torres et al. 2011), might well eliminate some of these possibilities.
The "Depth if host" column in Table 4 follows from the observed depth in an unrecognized blend and the correction for dilution. Daemgen et al. (2009) provide the now often used correction for dilution in the case of the host being the brighter star. With the assumed host being the fainter star, the Equation takes the same form, with a change of sign in the exponent:
For several cases, the inferred depth if the companion is the host exceeds 10%, making a planet interpretation unlikely, although this must be balanced by considering the host star radius as well which is beyond the scope of this paper.
Of the stars listed in Tables 3 or 4, one deserves a special note of caution. The companion to KIC-5358241 at an offset of 0107 and a δKp of 2.39 is in a region of detection parameter space where reliability is difficult to assess. Until this detection is confirmed by a second high-resolution imaging experiment, the reality of this star remains open to question. All of the other detections listed in these tables are considered unambiguously real with parameters as listed within nominal uncertainties.
4.4. Statistics on Physical Association
As shown in Table 3, we have detected six companions to five targets that have odds ratios above 50, which we take as confirmation of physical associations. Two additional cases have positive indications of being bound to the target, but are not certain. We wish to tabulate here the total number of detections as a function of target spectral type and compare this with the a priori number of expected companions (Duchêne & Kraus 2013). For the two cases with modest odds ratios of 1.3 and 6.3, we assign fractional detections as 1-1/(odds ratio + 1). We also only count the KIC-5358241 source offset by 0107 as 0.5 of a detection from conservatism as to the basic reality of its existence.
Over the 21 targets considered, ignoring the two sources (KIC-6149553 and KIC-11306996) that in the interim had been shown to be false positives, we have seven, eight, and six stars at G, K, and M spectral types respectively. To evaluate the expected number of companions in our data, we sum over the log-normal distributions (Duchêne & Kraus 2013) corresponding to search offsets of 012 to 2257. This yields an expected total number of companions of: 1.52, 0.67, and 0.31 for the G, K, and M stars in our sample. We detect 1.93, 2.0, and 3.0 across the three spectral types. Overall we detect 6.93 compared to an expected number of 2.50, for an over-detection ratio of ×2.8. The fraction of times that Poisson fluctuations with an expectation of 2.5 exceed 7 is 1.4% suggesting that the general over-abundance of companions is significant at >98%. For the M dwarfs in isolation, the overabundance is ×9.7, and the nominal significance is 99.6%, or 3σ.
It is clear that (a) this experiment yields only small number statistics with 6–8 targets per spectral type bin, and (b) we find more physically associated companions than would be expected. The overabundance of physically associated companions is a monotonically increasing factor over the G (near nominal) to K and M (order of magnitude excess) spectral types. These targets were selected on the basis of being strongly suspected of hosting one or more small and cool exoplanets. A direct interpretation is that widely spaced stellar binaries, and higher order systems are over-represented among planetary hosts. Such an interpretation from this limited sample would be consistent with stellar multiples being more favorable sites for exoplanet formation than are single stars. Another factor is that with knowledge of binarity, these planets are actually larger than reported in the exoplanet archive. There has thus been a selection effect of including larger planets in the sample due to unrecognized binarity initially.
Kraus et al. (2014), however, find from an interferometric survey of 600 Kepler planet candidate hosts sensitive to 5–50 AU binaries (our sensitivity is primarily to binaries near and mostly beyond 50 AU, and therefore disjoint to their sample) that stellar binarity has a strong influence suppressing the planet frequency by a factor of about four.
G. W. Marcy (2014, private communication) suggests an alternative view that multiple stars within the Kepler aperture simply increases the probability of transits existing, e.g., doubled for a binary since either of the stars might host planets at random orientations. In this approach, one might expect binaries to be over-represented in the KOI list by a factor of two if the individual components have the same intrinsic planet hosting frequency as single stars. Since our overabundance of M dwarfs is nearly a factor of 10 a discrepancy persists that, simply interpreted, suggests wide binaries favor the formation of small planets.
5. SUMMARY
The stable, high-resolution imaging provided by WFC3 UVIS on HST has allowed a careful survey for stellar companions to KOIs selected for having small and cool exoplanet candidates. In most cases, no close-in companions were found that could be false positives for transits through blending of background eclipsing binaries. Our sensitivity to such companions reached 90% completeness for delta-magnitudes of 4 at 02 separation, 8 at 04, and >9 magnitudes at ≳08, with the latter usually exceeding the general brightness ratio that could physically be a false positive for these transits. However, in several cases we find close-in companions that are physically associated with the target star. These smaller, associated stars would not likely be a concern regarding potential false positives for exoplanets, but do call into question which of the multiple stars hosts the planet candidates with strong implications for the resulting exoplanet properties as presented by Cartier et al. (2014).
We also find, especially for our sample of M dwarf stars, that stellar multiplicity is over-represented in association with our sample having been selected as likely exoplanet hosts. Resolving whether the implied proclivity of wide multiple stars, as can be found in high-resolution imaging surveys, to form exoplanets is merely a fluke of small number statistics awaits larger studies.
Funding for Kepler , the 10th Discovery mission, was provided by NASAʼs Science Mission Directorate. The many people contributing to the development of the Kepler mission are gratefully acknowledged. The individuals who joined as co-investigators on this HST proposal in early 2012 are recognized. Andrea Dupree, Francois Fressin, Matthew Holman, Jack Lissauer, Geoff Marcy, and Jason Rowe contributed directly to development of the proposal, provided extensive background discussion, or assisted in target selection. We thank Jorge Lillo-Box for providing a note about his detection metric for our HST imaging. R.L.G. and K.M.S.C. have been partially supported through grant HST-GO-12893.01-A from STScI. P.K. is grateful for the support from NASA NNX11AD21G and NSF AST-0909188. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. CFOP is funded by NASA through the NASA Exoplanet Science Institute. Data presented in this paper were obtained from the Mikulski Archive for Space Telescopes.
Facilities: HST (WFC3) - Hubble Space Telescope satellite, Kepler - The Kepler Mission.
Footnotes
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Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, operated by AURA, Inc., under NASA contract NAS 5-26555.
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