Abstract
Using the high-resolution imaging instrument, 'Alopeke, at the Gemini-N telescope, we obtained simultaneous two-channel time-series observations of the binary exoplanet host star Kepler13-AB. Our optical observations were obtained during a transit event of the exoplanet Kepler-13b and light curves were produced using both speckle interferometric and aperture photometry techniques. Both techniques confirm that the transiting object orbits the star Kepler-13A while different transit depths are seen across the optical wavelength range, being ∼2 times deeper in the blue. These measurements, as well as mass determinations in the literature, are consistent with Kepler-13b being a highly irradiated gas giant with a bloated atmosphere. Our observations highlight the ability of high-resolution speckle imaging to not only assess binarity in exoplanet host stars but robustly determine which of the stars the transiting object actually orbits.
1. Introduction
The discovery of planets orbiting other stars—exoplanets—has changed the view of our place in the universe. The NASA Kepler mission (Borucki et al. 2011) and its follow-up K2 mission (Howell et al. 2014) used the transit technique to discover more than 4000 exoplanets. Currently, NASA's Transiting Exoplanet Survey Satellite (TESS) mission (Ricker et al. 2015) is carrying on the search, focusing on the discovery of exoplanets orbiting nearby and bright stars.
Since the beginning of the Kepler mission, our research team has been furnishing critical ground-based follow-up observations consisting of high-resolution speckle imaging (Howell et al. 2011). Such observations, providing the highest spatial resolution imaging available on any single telescope whether on the ground or in space, have revealed that exoplanet host stars are not all single like our Sun.
One of the major discoveries of this research is that approximately one-half of all exoplanets orbit stars that reside in binary star systems (Horch et al. 2014; Matson et al. 2018). The discovered exoplanets orbit only one of the two stars in the system and it is often difficult or even completely impossible to determine which one. Statistical and transit shape arguments suggest that it is more likely that the vast majority of the discovered planets orbit the brighter star of any pair (Bouma et al. 2018), however, this has yet to be confirmed observationally.
The Kepler mission also discovered ∼10 circumbinary exoplanets, that is planets that orbit both stars in a very close binary pair. Circumbinary exoplanets are challenging to discover as the exoplanet transits are hidden in the eclipsing binary light curve, are aperiodic, and change depth and shape depending on which star they transit (Welsh et al. 2015). Discovery of circumbinary exoplanets is strongly biased to detection in close eclipsing systems and for large, long-period exoplanets. Our work herein is not related to circumbinary exoplanets.
For exoplanets orbiting one star in a binary system in which there is a substantial mass ratio (brightness) difference between the two stars, the measured transit depth (i.e., used to determined the exoplanet radius) is not too far from the correct value. However, for host stars that are nearly equal mass (brightness), the observed transit depth is too shallow due to third-light contamination, yielding an incorrect value for the planet radius (Ciardi et al. 2015).
Additional ramifications in the determined physical parameters assigned to such exoplanets also come into play. Teske et al. (2018) showed that the radius distribution of the Kepler discovered planets, of which ∼46% are incorrect (too small), cannot be precisely known due to unresolvable binaries. Additionally, Furlan & Howell (2017) examined how the exoplanet radius, if not corrected, leads to a large uncertainty in the mean density of the planet (∝R3) and atmospheric models will get mislead as well due to the fact that the scale height depends on the radius squared.
Given the above scenarios, we undertook an experiment to obtain high-resolution imaging observations of a blended exoplanet host star binary, Kepler-13AB. We obtained light curve measurements during a transit event for the well-studied Kepler-13AB system—a binary containing a purported hot-Jupiter exoplanet, Kepler-13b. Our goals were to unambiguously determine which star (A or B) the transiting object orbits and attempt to reveal Kepler-13b's true nature—exoplanet or low-mass star.
2. Kepler-13AB
Kepler-13AB (BD+46 2629, CCDM J19079+4652AB) is a long known binary star system discovered by Aitken (1904). Aitken found two nearly equal brightness stars (V = 9.9 and V = 10.2; Szabo et al. 2011) separated by ∼1
0. The A and B components are hot A stars (∼8000 K), with masses near 2 M⊙ each and (out of transit) magnitude differences of 0.20 (562 nm) and 0.14 (832 nm). Kepler-13AB is known to be a common proper motion system (Hess et al. 2018) with an estimated binary period of 9500 yr (assuming a distance of 638 pc, a projected binary separation of 733 au, and a total mass of approximately 4M⊙). The fainter star, Kepler-13B, has its own companion, Kepler-13C (Santerne et al. 2012), consisting of a low-mass star (<0.75 M⊙) orbiting star B every 65.8 days.
This binary system, located in the Kepler field of view by happenstance and not initially identified as a binary, was discovered early in the Kepler mission to contain a planetary size body (KOI-13) in a close-in orbit. Early validation observations of KOI-13 recognized it as a binary star (Howell et al. 2011) harboring the exoplanet (Kepler-13b) orbiting one of the two nearly equal brightness stars. Table 1 gives the basic parameters of the two bright stars in the Kepler-13AB system (see Szabo et al. 2011; Santerne et al. 2012; Esteves et al. 2015).
Table 1. Recent Stellar Parameters of Kepler-13AB
| Parameter | Kepler-13A | Kepler-13B | Kepler-13A | Kepler-13B |
|---|---|---|---|---|
| Santerne et al. (2012) | Shporer et al. (2014) | |||
| V | 9.9 | 10.2 | 9.9 | 10.2 |
| Teff (K) | 8511 | 8222 | 7650 | 7530 |
| M/M⊙ | 2.05 | 1.95 | 1.72 | 1.68 |
| R/R⊙ | 2.55 | 2.38 | 1.71 | 1.68 |
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Kepler-13AB has been well studied in the recent literature (Barnes et al. 2011; Shporer et al. 2011; Szabo et al. 2011, 2012; Johnson et al. 2014; Esteves et al. 2015). The transiting object has an orbital period of 1.76 days and is generally believed to orbit the brighter, primary star of the pair. Radius estimates of Kepler-13b, based initially on Kepler photometric transit data and the stellar parameters from the Kepler Input Catalogue (Brown et al. 2011), assumed Kepler-13 to be a single star. Various follow-up studies (reviewed in Johnson et al. 2014) made corrections to the stellar parameters and thus to the transit depth (i.e., exoplanet radius) as well as accounting for third-light blending in the binary. These corrections led to revising the physical parameters for Kepler-13b such as radius, >0.75–2.2 RJ, and mass, spanning 8–10 MJ (Johnson et al. 2014). The reported radius of the transiting object has increased over time, as the binarity of the host star system was brought into play and third-light corrections, applied to the transit depth were accepted as critically needed. Kepler-13b is thus a victim of its environment—existing in a nearly equal brightness binary star system producing a contaminated transit depth and causing the object to appear smaller in radius than it really is.
3. Gemini 'Alopeke Observations
We observed Kepler-13 on 2018 August 13/14 UT at the Gemini-N telescope using the high-resolution imaging instrument 'Alopeke. 'Alopeke is a dual-channel imager using two electron-multiplying CCDs (EMCCDs) as the detectors and containing filter wheels providing bandpass limited observations (see Scott et al. 2018 and 'Alopeke web pages4 ). The observations of Kepler-13 were planned to provide two types of time-series data at once: speckle interferometric observations (e.g., Horch et al. 2012) and traditional time-series transit photometry (Howell et al. 1988).
For Kepler-13, we obtained time-series observations consisting of a near continuous stream of simultaneous, two-channel, 60 ms integrations covering a 4 hr period. The observations were interrupted every 15 minutes for 1–2 minutes to observe point-spread function (PSF; HR 7468 and HR 7210) and binary star (HR 7053) standards. These stars were chosen to be close to but spanning the target R.A. and were used to monitor PSF shape and photometric quality as well as provide checks on any systematics (perhaps small changes in plate scale, rotation, or detector gains) throughout the sequence. No instrument systematics were discovered. The entire data set produced a total of 335 GB of data during the transit observation.
Our Kepler-13AB observations, as well as each standard star observation, were collected in sets of 1000, 60 ms frames, and stored on a disk as multi-extension FITS files. Unique FITS files were produced for each channel of the instrument over the entire time of the run resulting in ∼300 multi-extension FITS files for each channel (or 300,000 total image files). We made all observations in the blue channel using the 562/54 nm filter and in the red channel using the 832/40 nm filter.
Our observations began at 8:42 UT on 2018 August 13/14 and lasted until 12:49 UT. The Kepler-13AB observations, spanning 4 hr in time, ranged in airmass from 1.1 (start) to 2.0 (end). We know from past experience that airmass values larger then about 1.5 begin to quickly reveal atmospheric dispersion blurring and noncorrelated speckle patterns, especially for stars as widely separated (for speckle work) as Kepler A and B (see below).
4. Data Analysis
4.1. Speckle Analysis
The 'Alopeke instrument is fundamentally a speckle imaging camera, capable of delivering diffraction-limited image information. Thus, our observations were collected in speckle mode, that is sets of 1000, 60 ms exposures of the binary star Kepler-13AB (Figure 1). We note that this double star system appears in the Washington Double Star Catalog (Mason et al. 2001) as Aitken 704 (A 704, also ADS 12085), with the first measurement of position angle and separation in 1904. Using our speckle analysis techniques and the Gemini data set, we provide current epoch astrometric values for the Kepler-13AB binary system and list our results in Table 2.
Figure 1. One of our typical 60 ms red channel images of Kepler-13. The box is 3'' × 3'' in size with the two stars separated by 11. The field is displayed with north to the left and and east is down; star A is at the bottom.
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Standard image High-resolution imageTable 2. 'Alopeke Astrometry for Kepler-13AB
| Parameter | Value |
|---|---|
| Separation | 1163 ± 0003 |
| Position Angle | 279 56 ± 010 |
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The potential advantage of speckle analysis for a close binary star that also hosts an exoplanet is that when diffraction-limited information is obtained, it is in theory possible to unambiguously determine whether the transit occurs in the primary or secondary star of a binary star system, even if the system is highly blended and difficult to impossible to analyze in seeing-limited images. If the transit occurs in the primary star, then fewer correlations will be seen in the autocorrelation function at the location of the primary star while the transit occurs, leading to a smaller magnitude difference between the two stars in a speckle analysis. On the other hand, if the secondary star is the one in which the transit occurs, then there will be fewer correlations in the secondary peaks of the autocorrelation function, leading to a larger magnitude difference between the stars during the transit. Kepler-13 has a large enough separation for both speckle and seeing-limited photometric analyses to be completed and compared. If a speckle analysis yields results consistent with the seeing-limited analysis in this regime (Section 4.2), that would give some confidence that it could then be extended to other smaller-separation systems, where the seeing-limited analysis is either more difficult or not possible.
For typical exoplanet transit depths, such a measurement would necessarily have to be very sensitive in order to be successful, something that presents a challenge for a speckle analysis. Estimates of the magnitude differences of binary stars made by seasoned speckle observers have typical uncertainties of ∼0.1 mag even in the best of circumstances. (This value is appropriate for a single speckle sequence taken of a reasonably bright source, usually representing ∼1000 individual speckle frames taken in a ∼2-minute time frame.) In addition, the standard speckle reduction relies on the assumption of space invariance over the field of view, meaning that the speckle pattern of any star within a certain radius of the primary star would produce an identical speckle pattern to that of the primary star. This is also known as the isoplanatic assumption, and the angular radius over which it is valid is known as the isoplanatic angle.
In the visible range, the isoplanatic angle has a size of at most a few arc seconds (see, e.g., Roddier 1988). As the separation between the primary star and secondary increases and the isoplanatic assumption begins to fail, one expects that, due to the increasing variation between the primary and secondary stellar speckle patterns, a loss of correlations will occur in the secondary peaks of the autocorrelation function, leading to an overestimate of the magnitude difference between the stars. This is illustrated in Figure 2.
Figure 2. Illustration of the effect of speckle decorrelation on the autocorrelation function obtained for a wide (∼1'' separation) binary star. Panel (a) shows a simulated speckle pattern with observational parameters similar to Gemini and assuming the observation is perfectly isoplanatic, and panel (b) shows an autocorrelation function obtained from many such frames. In this case, one can see very clear diffraction-limited peaks in the autocorrelation at the positive and negative vector separation of the two stars. This is because the speckle patterns of the primary and secondary are identical. Panels (c) and (d) illustrate the opposite regime. Here, the primary and secondary speckle patterns differ in panel (c), leading to a loss of correlations at the positive and negative vector separation of the two stars in the average autocorrelation, shown in (d). This loss of correlations then translates into a systematic error in the magnitude difference obtained.
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Standard image High-resolution imageHorch et al. (2004, 2011) have discussed the breakdown of the isoplanatic assumption and its subsequent effect on differential photometry of binary stars in their analyses of Kitt Peak 3.5 m WIYN speckle data, and have suggested, for example, that the degree to which an observation of a binary star is isoplanatic can be given by the ratio of the separation to the size of the isoplanatic angle. In this case, roughly speaking, the observation is isoplanatic or quasi-isoplanatic if this ratio is much less than 1, and anisoplanatic if it is greater than one. An observationally derived parameter that scales with this ratio is seeing-times-separation, called q'. This follows from the fact that the seeing is inversely proportional to the Fried parameter, r0, and that the isoplanatic angle scales with r0. Therefore, if ρ represents the separation of the stars, ω represents the seeing, and δω the isoplanatic angle, then the ratio of the separation to the isoplanatic angle scales as
In the above references, graphical evidence is presented showing the difference in Δm obtained from speckle observations to space-based observations for a large number of binary star systems. It is found that the difference is small for values of q' under approximately 06 squared, and grows roughly linearly with q' above that point. While no similar study has yet been done with speckle data at Gemini due to the lack of a comparably large speckle data set on binary stars, if the same relationship were to hold at Gemini, then for systems with separations under roughly 08 and average or better seeing at Gemini (05–06), speckle magnitude differences would not be severely affected by decorrelation. Thus, one could expect essentially unbiased results with uncertainties in magnitude difference of ∼0.1 mag per 2 minutes of observation. For separations larger than this, some mitigation for the speckle magnitude difference would need to be attempted. Given the earlier speckle results at WIYN, the roughly linear trend in the systematic error indicates that it may be possible to calibrate out the effect of speckle decorrelation, at least under certain circumstances.
We have attempted to understand such systematic uncertainties for the case of Kepler-13, as an illustration of what may be possible with speckle imaging in other (tighter) binary star systems that host exoplanets. Additionally, we provide a way forward on the question of how to correct the diffraction-limited image reconstructions obtained with speckle data for photometry as a function of position on the image plane. We have confined our attention only to the 832 nm filter observations here, as the systematic effects described are more tractable in that case due to the longer wavelength rather than the other bluer channel of the instrument.
4.1.1. Methodology
The Kepler-13 system presents a near perfect example of the challenges that can occur when deriving photometry from speckle data as discussed above. With a separation of 116 and seeing conditions for our observing sequence of approximately 07–1'', the seeing-times separation values for all data files are well above the nominal limit of q' = 0.6–0.8 arcsec2; the photometry is expected to be substantially affected by speckle decorrelation. In addition, much of the data sequence was taken when the star was at relatively high airmass, ending with a value of greater than 2.1. This presents an additional complication because standard speckle theory suggests that
where Δh is the measure of the altitude dispersion of the turbulent layers in the air above the telescope aperture. In turn, one expects due to geometry that
where z is the zenith angle of the observation (Dainty 1975). Thus, even after making a correction to the photometry based on seeing, a second correction due to the zenith angle would be needed, especially if the zenith angle is large. That is, when the star is observed at high zenith angle, the value of Δh increases, so that even at fixed seeing, the speckles within the seeing disk lose contrast. Nonetheless, if corrections for q' and are made in sequence, it can correct the photometry to the point where it could be examined for evidence of a transit signature.
To begin this procedure, we reduced the Kepler-13 data files using our standard reduction pipeline, described most recently in Horch et al. (2019). In this pipeline, the final parameters for a binary star are found with a weighted least-squares fringe fit to the spatial frequency power spectrum. This power spectrum has been divided by the power spectrum of a point source observed near in time and in sky position to the science target; this effectively performs the deconvolution so that the fringes fitted can be fitted in the Fourier domain by a function of the form
where a and b represent the brightness of the primary and secondary, respectively, and the vector separation of the two components on the image plane is given by . The brightness ratio b/a for the binary star is then calculated from the final parameters, a and b, from the fit and the magnitude difference follows as
4.1.2. Analysis of the Data
Application of the Seeing Correction. In order to obtain magnitude differences for the Kepler-13 binary system that are corrected for the effect of the parameter q', we calculated fringe fits for each file in the sequence and derived a speckle magnitude difference from the fringe fits. We also made integrated images from the speckle data cubes by summing the frames. From these, we computed an estimate of the seeing-limited magnitude difference by performing a 2D Gaussian fit of the two stellar profiles in the integrated image. While a 2D Gaussian function is not a perfect match to the stellar profiles in this case, the ratio of the two Gaussian amplitudes still appears to match reasonably well with what one would obtain using a more sophisticated functional form. The error in the magnitude difference inherent in the fringe-fitting results is then assumed to be the difference between the fringe-fit result and the average of all of the integrated image results. The latter was found to be 0.154 ± 0.003 mag at 832 nm, which agrees reasonably well with the Gaia DR2 GRP-magnitude difference for this pair, 0.118 mag, and that found by Shporer et al. (2014) of 0.14 mag.
The seeing in each data set was estimated by measuring the width of a smoothed version of the speckle autocorrelation function. It is assumed that the FWHM of the seeing can be estimated as the FWHM of the autocorrelation divided by , a relation that matches well with simulated stellar profiles. Figure 3 shows the error in magnitude difference as a function of q' obtained in this way. As expected from the work discussed in Section 4.1, this relation shows a quasi-linear relationship with q'. We averaged the results for files at each q' and represented and computed the standard errors, δ(Δm), of those. The weight of each point in the linear fit was given by 1/(δ(Δm))2. We then used the linear relation obtained to correct the magnitude difference for the effect of seeing for all files, regardless of zenith angle.
Figure 3. Error in magnitude difference plotted as a function of q' = seeing-times separation for the subset of data files taken at a zenith angle less than 45°. The results above are for the 832 nm filter. Green diamonds indicate these observations, while black filled circles indicate the average value in the error for each q' measure. The error bars drawn are the standard errors obtained.
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Standard image High-resolution imageApplication of the Zenith Angle Correction. The seeing-corrected magnitude differences are plotted in Figure 4 as a function of the secant of the zenith angle (equivalently, the airmass) for all 125 observations in the sequence. The plot shows that, starting at , a nearly linear trend is noted in the error of the magnitude difference. A least-squared best-fit line for this region of the plot was obtained, with all data points receiving equal weight. This was then used to correct the Δm values in the range above (z > 45°), and the resulting magnitude differences are shown in green.
Figure 4. Seeing-corrected values of the magnitude difference, shown as a function of the secant of the zenith angle for all 125 observations of Kepler-13 in the sample. Black diamonds are the raw values obtained. The dashed line indicates the line of best fit for values where sec(z) is larger than (equivalent to a zenith angle of 45°). The green squares indicate values corrected for the linear trend at high zenith angle.
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Standard image High-resolution image4.1.3. Speckle Interferometric Photometry Results
In Figure 5, we show the final magnitude differences plotted as a function of time, for all data files. The Kepler-13AB speckle observing sequence was such that standard star observations were interspersed with the data files taken of Kepler-13 (see Section 3). There were a total of 10 separate pointings to Kepler-13, each of which was deconvolved with a different point-source observation. The first pointing consisted mainly of files completed before ingress, and the last when the system was out of transit after egress. Pointings 2 and 9 in the sequence mainly occurred during ingress and egress, respectively, and pointings 3 through 8 occurred during the transit. In Figure 5, the red filled circles mark the average magnitude difference obtained for each pointing, with error bars indicating the standard error for that group of observations. Excluding pointings 2 and 9, we averaged the results from pointings 1 and 10 as being the out-of-transit measurement, and the average of pointings 3 through 8 as being the in-transit measurement. The final values obtained at 832 nm are as follows:
Figure 5. Final values of the magnitude difference obtained in this analysis as a function of time during the transit. The green diamonds represent values for each of the 125 data files. Red circles are the average value obtained for each pointing toward Kepler-13 as described in the text. The red lines indicate average values for the pointings in and out of transit. The ingress, egress, and midpoint of the transit are shown with vertical lines.
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Standard image High-resolution imageOut of transit: Δmout = 0.152 ± 0.008.
In transit: Δmin = 0.132 ± 0.017.
The uncertainties listed here are the standard error for the two groups of measurements. These results are consistent with the brightness of the primary star decreasing during the transit, indicating that the transiting object (exoplanet) orbits the star Kepler-13A. Combining these results with the assumption that the brightness of the B component of the system does not change, one may derive a ratio of the brightness of A star in transit versus out of transit, and that calculation yields 0.982 ± 0.017 or in other words, the implied transit depth is 0.018 ± 0.017.
The above results carry too large of an uncertainty to be of scientific value in this case, but if repeated over several transits, they could presumably be improved. Given this level of uncertainty and assuming statistics apply, observing 16 transits in a similar fashion would result in, for example, an uncertainty of 0.004 in the transit depth. This level of precision would be sufficient for a high-confidence determination of which star the planet orbited in the system, if not already known.
However, the Kepler-13 system has a large separation by speckle standards, and the analysis has required correction for systematic errors expected in that regime. Speckle imaging would have much more of an advantage if the separation were smaller, so that the observation occurs in a regime where speckle correlation and differential photometry are better understood. In that case, speckle imaging would be a superior technique to a seeing-limited analysis, given that the components would be highly blended or inseparable in seeing-limited images. For example, Horch et al. (2011) and papers cited therein describe that in the range of q' < 0.6, uncertainties per 2-minute speckle observations at the WIYN telescope are in the range of 0.1 mag in many cases. Taking this value and assuming no systematic error, a magnitude difference measure carrying an uncertainty of 0.005 mag could in theory be obtained with 800 minutes of observing.
Within each pointing in Figure 5, one can see trends in the magnitude differences obtained. From this, one can surmise that there are other systematics not addressed in this paper that may be limiting the final precision of the results. A leading candidate for uncorrected systematic error is the degree to which the point source used for the deconvolution matches the true speckle transfer function of the science observation. Again, these observations of Kepler-13 represent a worst-cast scenario due to the fact that many of the data files are taken at high airmass, where there is some residual dispersion (∼005 at X = 1.5; Howell 2006). This produces an asymmetry in the speckle transfer function that depends on both azimuth and zenith angle. If the binary and the point source are observed with differences in these angles of a few degrees, this can result in an imperfect division in the Fourier plane during the deconvolution step, which would potentially affect the fringe depth. A related effect, that of the loss of the signal-to-noise ratio in reconstructed images due to imperfect deconvolution, is discussed in Scott et al. (2018). A comprehensive study of both systematic error in binary star parameters and the loss of signal-to-noise in the reconstructed image is currently being undertaken, but is beyond the scope of this paper. However, these problems are minimized when the zenith angle of the observation is kept small.
4.2. Aperture Photometry
The seeing at Gemini during our Kepler-13AB observations generally ranged from 05 to 10, getting very poor near the end of the observing sequence and producing some difficulty for aperture photometry given the 116 separation of the component stars in Kepler-13AB. However, we had the opportunity to use the same data set as described above to also perform standard aperture photometry (Howell 2006). To do so, we started by producing mean average images of each of the 1000, 60 ms data set throughout the transit. This resulted in 140 1-minute sampled images covering transit ingress to egress for the object Kepler 13b. Figure 1 presented a single 60 ms red channel speckle image in which the speckles are easily seen. Figure 6 shows a typical 1000 frame mean average image also from the red channel, yielding an equivalent 1-minute integration of Kepler-13AB. All observations were obtained with telescope guiding on, so the star had a relatively stable position on the EMCCD array, however, seeing changes redistribute light across the underlying fixed pattern (accentuated when using high-speed readout and EM gain; see Scott et al. 2018) and this effect set the final aperture photometric uncertainty limit. As the airmass increased, the two stars became less distinct as separate PSFs.
Figure 6. Typical red frame median average of 1000, 60 ms exposures, yielding approximately 1 minute of total exposure time. The vertical lines are fixed pattern noise inherent in the EMCCD. The box is 3'' × 3'' in size and the field is displayed with north to the left and and east as down; star A is at the bottom.
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Standard image High-resolution imageThe generally good seeing and excellent plate scale of 'Alopeke (001 pixel−1), allowed aperture photometry to be robustly performed on most of the 1-minute mean red and blue images obtained during the transit. The effective seeing of the 1-minute mean images varied between 06 and 10, with occasional excursions above 1''–14. The time-varying seeing we experienced can be seen in Figure 5. Stars A and B were measured separately using a fixed aperture radius of 70 pixels and a sky annulus of a width of 20 pixels. To estimate the mean sky value, we employed 3σ Lucy smoothing sky pixel rejection (Howell 2006). This technique was needed as the sky annulus between the two stars contained their overlapping stellar wings, not an actual sky background. The typical raw stellar flux varied between 1.5 and 2 million counts in the red and over 3 million counts in the blue for each 1-minute sampled stellar image. Twenty of the 1-minute samples were rejected in producing the final three-point running boxcar average light curves as they contained variable seeing above 12, causing them to be unsuitable for our fixed radius simple aperture photometry.
4.2.1. Aperture Photometry Results
Using the aperture photometry measurements for Kepler-13AB during the transit event and forming a differential light curve of the two stars in each filter measurement, we obtained the transit light curves shown in Figures 7 and 8 with our time-series photometric values listed in Table 3.
Figure 7. Differential blue channel (562 nm) light curve of Kepler-13A. The symbols are the three-point running boxcar averages. The dashed lines show the predicted times of transit ingress and egress. The error bars represent the standard error, i.e., within each bin.
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Figure 8. Differential red channel (832 nm) light curve of Kepler-13A. The symbols are the three-point running boxcar averages. The dashed lines show the predicted times of transit ingress and egress. The error bars represent the standard error, i.e., within each bin.
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Standard image High-resolution imageTable 3. Kepler-13AB Aperture Photometry
| Mean UT | ΔMag 562 nm | Mean UT | ΔMag 832 nm | ||
|---|---|---|---|---|---|
| 8.88 | −0.192 | 0.0053 | 8.88 | −0.137 | 0.0029 |
| 8.91 | −0.200 | 0.0041 | 8.91 | −0.1378 | 0.0030 |
| 8.93 | −0.1955 | 0.0041 | 8.93 | −0.1383 | 0.0028 |
| 8.95 | −0.196 | 0.0041 | 8.95 | −0.1388 | 0.0028 |
| 8.97 | −0.190 | 0.0041 | 8.97 | −0.1415 | 0.0029 |
| 8.99 | −0.1793 | 0.0041 | 8.99 | −0.1408 | 0.0030 |
| 9.01 | −0.1738 | 0.0047 | 9.01 | −0.1395 | 0.0029 |
| 9.05 | −0.1658 | 0.0041 | 9.04 | −0.1358 | 0.0030 |
| 9.08 | −0.1633 | 0.0041 | 9.06 | −0.1294 | 0.0030 |
| 9.13 | −0.1653 | 0.0042 | 9.08 | −0.1275 | 0.0028 |
| 9.18 | −0.1687 | 0.0041 | 9.10 | −0.1283 | 0.0029 |
| 9.21 | −0.1703 | 0.0041 | 9.14 | −0.1258 | 0.0028 |
| 9.24 | −0.1663 | 0.0040 | 9.18 | −0.129 | 0.0029 |
| 9.26 | −0.1705 | 0.0042 | 9.21 | −0.130 | 0.0041 |
| 9.35 | −0.1703 | 0.0041 | 9.24 | −0.1248 | 0.0035 |
| 9.43 | −0.1705 | 0.0040 | 9.26 | −0.126 | 0.0040 |
| 9.52 | −0.1665 | 0.0041 | 9.35 | −0.1253 | 0.0029 |
| 9.60 | −0.1713 | 0.0053 | 9.43 | −0.1224 | 0.0028 |
| 9.67 | −0.1685 | 0.0047 | 9.52 | −0.127 | 0.0030 |
| 9.73 | −0.165 | 0.0041 | 9.60 | −0.1263 | 0.0029 |
| 9.80 | −0.1708 | 0.0042 | 9.67 | −0.127 | 0.0029 |
| 9.96 | −0.1628 | 0.0040 | 9.73 | −0.1286 | 0.0030 |
| 10.08 | −0.1646 | 0.0040 | 9.80 | −0.1285 | 0.0041 |
| 10.19 | −0.1693 | 0.0041 | 9.96 | −0.128 | 0.0029 |
| 10.38 | −0.169 | 0.0042 | 10.08 | −0.1273 | 0.0034 |
| 10.49 | −0.170 | 0.0041 | 10.19 | −0.1258 | 0.0029 |
| 10.57 | −0.1667 | 0.0041 | 10.38 | −0.1263 | 0.0036 |
| 10.67 | −0.164 | 0.0047 | 10.49 | −0.1286 | 0.0042 |
| 10.70 | −0.168 | 0.0041 | 10.57 | −0.129 | 0.0035 |
| 10.75 | −0.166 | 0.0047 | 10.67 | −0.128 | 0.0034 |
| 10.83 | −0.1642 | 0.0059 | 10.75 | −0.127 | 0.0029 |
| 10.88 | −0.1685 | 0.0047 | 10.83 | −0.126 | 0.0034 |
| 11.10 | −0.1682 | 0.0045 | 10.98 | −0.128 | 0.0041 |
| 11.17 | −0.1649 | 0.0053 | 11.10 | −0.129 | 0.0034 |
| 11.18 | −0.1676 | 0.0041 | 11.17 | −0.127 | 0.0040 |
| 11.22 | −0.1669 | 0.0042 | 11.18 | −0.128 | 0.0047 |
| 11.32 | −0.1688 | 0.0046 | 11.22 | −0.125 | 0.0041 |
| 11.45 | −0.1673 | 0.0053 | 11.32 | −0.127 | 0.0034 |
| 11.70 | −0.1777 | 0.0065 | 11.39 | −0.126 | 0.0040 |
| 11.80 | −0.1650 | 0.0047 | 11.46 | −0.127 | 0.0053 |
| 11.83 | −0.1659 | 0.0053 | 11.66 | −0.128 | 0.0041 |
| 11.88 | −0.1724 | 0.0046 | 11.77 | −0.127 | 0.0042 |
| 11.92 | −0.1733 | 0.0051 | 11.83 | −0.125 | 0.0040 |
| 12.08 | −0.1763 | 0.0059 | 11.88 | −0.126 | 0.0047 |
| 12.10 | −0.1797 | 0.0060 | 11.92 | −0.126 | 0.0041 |
| 12.15 | −0.1825 | 0.0065 | 12.08 | −0.127 | 0.0035 |
| 12.32 | −0.1988 | 0.0053 | 12.10 | −0.130 | 0.0040 |
| 12.43 | −0.1953 | 0.0058 | 12.15 | −0.134 | 0.0042 |
| 12.53 | −0.1997 | 0.0054 | 12.32 | −0.139 | 0.0048 |
| 12.58 | −0.1963 | 0.0057 | 12.37 | −0.141 | 0.0047 |
| ⋯ | ⋯ | ⋯ | 12.53 | −0.140 | 0.0053 |
| ⋯ | ⋯ | ⋯ | 12.58 | −0.139 | 0.0059 |
Download table as: ASCIITypeset image
The drop in light seen in each differential light curve confirms that the transit event occurs on the primary star, Kepler-13A. The blue data (562 nm) had slightly poorer seeing, and as such, slightly larger uncertainties in the mean values of the transit light curve. The variable seeing throughout data accumulation resulted in the best uncertainties for each 1-minute average binned point of ±0.007 mag in blue (562 nm) and ±0.005 mag in red (832 nm). Table 4 lists our differential photometric measured transit depths at 562 and 832 nm, our speckle transit depth measurement at 832 nm (see Section 4.1.3), and the depth measured at 700 nm by Szabo et al. (2011).
Table 4. Kepler-13A Transit Depth
| Waveband | Transit Depth ±1σ (mag) | Source |
|---|---|---|
| 562 nm | 0.0231 ± 0.0029 | This paper |
| 700 nm | 0.014 ± 0.06a | Szabo et al. (2011) |
| 832 nm | 0.0126 ± 0.0020 | This paper |
| 832 nm (speckle) | 0.018 ± 0.017 | This paper |
Note.
aUncertainty estimated from Figure 4 (Szabo et al. 2011).Download table as: ASCIITypeset image
We note that the unblended transit depth,
varies across the optical bandpass, being 1.8 times deeper in the blue (562 nm). All of the depths measured here are deeper then the original Kepler measurement of 0.008 mag, due to the fact that Kepler's light curve was a blend of both stars A and B. The third light from star B caused the transit depth to appear shallower then it really is, leading to a calculated smaller planet radius for Kepler-13b. Taking the Kepler transit depth times the third-light correction factor of 1.818 (Ciardi et al. 2015; Furlan et al. 2017), tells us that the unblended transit depth should be near 0.0145 mag, essentially the value we find in the red part of the optical spectrum.
Szabo et al. (2011) performed a study of the orbital obliquity and transit curve asymmetries seen in the Kepler light curve of Kepler-13AB. They also produced a differential light curve for Kepler-13AB using a Johnson–Cousins R filter (λC = 700nm) and measured a transit depth of 0.014 mag (see Table 4). Based on detailed analysis and model fits of the transit and secondary eclipse in the Kepler light curve, Szabo et al. (using a radius for star A of 2.5 R⊙ and a temperature of ∼3150 K) suggested that the object transiting Kepler-13A had a radius near 2.2 RJ and properties more consistent with a low-mass star (or an irradiated brown dwarf) than an exoplanet.
Using the transit depths measured in this study and a radius for Kepler-13A of 1.71 R⊙ (see Table 1), we find an effective radius for Kepler-13b of 2.57 ± 0.26 RJ (562 nm) and 1.91 ± 0.25 RJ (832 nm). If the transit is caused by a cool object, we can set a limit on the temperature of the eclipsing object as ≤3100 K, corresponding to a M4V or later spectral type, or a brown dwarf. This is a similar result to that found by Szabo et al. However, the deeper transit depth toward the blue could indicate that the orbiting object is a highly irradiated exoplanet with a very extended atmosphere, producing an effectively larger radius object. Given the mass measurement of Kepler-13b by Shporer et al. (2014), Mp = 4.94–8.09 MJ, we conclude that the transiting object is a highly irradiated, bloated exoplanet.
A proper solution for such a highly irradiated exoplanet will require detailed modeling of the transit light curves using a realistic irradiated gas giant model of atmospheres. This effort is beyond the scope of the current paper.
5. Conclusions
Approximately one-half of all exoplanets orbit a star residing in a binary system, yet in most cases, we are at a loss to robustly determine which star hosts the planet.
High-resolution speckle observations of Kepler-13AB have allowed us to produce both speckle interferometric and aperture photometric transit light curves. While the speckle analysis was hampered by the large (>1'') separation of the two stars, it shows consistent results with the aperture photometry and great promise for future work on close (<1'') stellar pairs.
Both photometric solutions of Kepler-13AB nicely reveal the transit signal and definitively prove that the purported exoplanet orbits star A. Given the nonequal transit depths across the optical and the measured mass of Kepler-13b, we conclude that Kepler-13b is a highly irradiated gas giant with a puffed-up atmosphere.
Based on the analysis here, we find that speckle imaging will be a useful tool in determining which star an exoplanet orbits in a binary star system, if the transit depth can be detected, depths of the order of a percent. To give the best chance of success, the observation should be kept at as low of an airmass as possible, certainly under 45°, and the systematic error will be further minimized in cases where the angular separation of the binary system is small compared to the size of the seeing disk. In wider separated stars, the excellent plate scale of 'Alopeke allows robust aperture photometry of the component stars and it too can reveal which star hosts the planet. The simultaneous, two-color observations allow additional science to be achieved, such as unblended transit depth determinations across the optical.
We wish to thank John Blakeslee, Jen Miller and Meg Schwamb at Gemini, Robert Szabo for providing photometric details from his work, and Elise Furlan and Claire Hebert for providing ancillary information. The results presented herein are based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). The observations were obtained via remote operation of the 'Alopeke instrument under Gemini proposal 18B-DD-101.