KELT-1b: A STRONGLY IRRADIATED, HIGHLY INFLATED, SHORT PERIOD, 27 JUPITER-MASS COMPANION TRANSITING A MID-F STAR

The KELT-North survey instrument consists of a collection of commercially available equipment, chosen to meet the requirements of Pepper et al. (2003) and tuned to find the few brightest stars with transiting giant planets in the Northern sky. The optical system consists of an Apogee AP16E (4 K × 4 K 9 μm pixels) thermo-electrically cooled CCD camera attached using a custom mounting plate to a Mamiya camera lens with an 80 mm focal length and 42 mm aperture (f/1.9). The resultant field of view of the detector is 26° × 26° at roughly 23'' pixel⁻¹, allowing simultaneous observation of nearly 40,000 stars in typical high Galactic latitude fields. The medium-format image size is markedly larger than the CCD detector (which measures 37 × 37 mm) which greatly reduces the severity of vignetting across the large field of view. At the same time, the small aperture permits longer exposures, which improve observing efficiency (assuming fixed camera readout time). A Kodak Wratten #8 red-pass filter is mounted in front of the lens to further reduce the impact of atmospheric reddening (which primarily affects blue wavelengths) on our photometry. The resultant bandpass resembles a widened Johnson–Cousins R band. This optical system is mounted atop a Paramount ME robotic mount from Software Bisque on a fixed pier at Winer Observatory in Sonoita, AZ (Latitude 31° 39'56.08''N, Longitude 110° 36'06.42''W, elevation 1515.7 m). See Pepper et al. (2007) for additional details about the system hardware.

The primary KELT-North transit survey consists of 13 fields centered at +31.7 declination, spanning all 24 hr of right ascension. Including the slight overlap between fields, the total survey area is ≈40% of the Northern sky. Survey observations consist of 150 s exposures with a typical per-field cadence of 15–30 minutes. The KELT-North telescope has been collecting survey data in this manner since 2006 September and to date has acquired between 5000 and 9300 images per field. Given this quantity of data and the typical achieved photometric precision of ∼1% for V ≲ 11, the KELT-North survey is able to detect short-period giant transiting planets orbiting most FGK stars with magnitudes from saturation near V ∼ 8 down to V ∼ 12.

Relative photometry is generated from flat-fielded images using the ISIS image subtraction package (Alard & Lupton 1998; Alard 2000, see also Hartman et al. 2004), in combination with point-spread function (PSF) fitting using the stand-alone DAOPHOT II (Stetson 1987, 1990). Although highly effective, the image subtraction procedures are highly computer intensive. To improve reduction performance, the default ISIS scripts were modified to facilitate distributed image reduction across many computers in parallel. ISIS operation in this fashion permits thorough exploration of various reduction parameters, which would be intractable if executed serially. Other elements of the ISIS reduction package have also been modified or replaced with more robust alternatives. For example, the standard ISIS source-identification routines and utilities are ill equipped to deal with the nature and ubiquity of aberrations in KELT-North images. In response, we have replaced the ISIS "extract" utility with the popular SExtractor program (Bertin & Arnouts 1996). A more complete explanation of these modifications and driver scripts that implement them are available online.¹⁹

Once we have the light curves created by ISIS for all of the DAOPHOT-identified point sources in the reference image, we begin a series of post-processing steps before doing the initial candidate selection. To begin, we convert the ISIS light curves from differential flux to instrumental magnitude using the results of the DAOPHOT photometry on the reference image. We also apply 5σ iterative clipping to all of the light curves at this stage; this typically removes ∼0.6% of the data points. All of the uncertainties for the converted and clipped light curves in a given field are then scaled as an ensemble. The scaling is chosen such that the χ²/dof = 1 for the main locus of the light curves on a magnitude versus χ²/dof plot. Typically this scaling is around a factor of 1.2, implying that the uncertainties are somewhat underestimated.

We next attempt to match all of the DAOPHOT-identified point sources in the reference image to stars in the Tycho-2 catalog. We obtain a full-frame WCS with sub-pixel accuracy on our reference frame using Astrometry.net (Lang et al. 2010). Using this solution, we match stars by taking the closest Tycho-2 entry within 45''. This typically generates matches for 98% of the Tycho-2 stars within each field. A successful Tycho-2 match also will provide a Two Micron All Sky Survey (2MASS) ID. We use the proper motions and JHK apparent magnitudes from these two catalogs.

With this catalog information, we next identify and exclude giant stars by means of a reduced proper motion (H_J) diagram (Gould & Morgan 2003). Following the specific prescription of Collier Cameron et al. (2007b), we place each of our matched stars on a J versus H_J plot. We compute the reduced proper motion of a star as

$$\begin{equation} H_{J} = J + 5\log (\mu /{\rm{mas\ yr^{-1}}}) \end{equation} \tag{ 1 }$$

and determine the star to be a giant if it fails to satisfy

$$\begin{eqnarray} H_J &{>}& {-}141.25(J-H)^4 + 473.18(J-H)^3\nonumber \\ && - 583.6(J-H)^2 + 313.42(J-H) - 43.0. \end{eqnarray} \tag{ 2 }$$

This process leaves us with anywhere from 10,000 to 30,000 catalog-matched putative dwarf stars and subgiants (hereafter dwarfs) per field, depending primarily on the location of the field relative to the Galactic plane.

The dwarfs are then run through the Trend Filtering Algorithm (TFA; Kovács et al. 2005)²⁰ to reduce systematic noise. We select a new set of detrending stars for each light curve by taking the 150 closest stars—outside of a 20 pixel exclusion zone centered on the star being detrended—that are within two instrumental magnitudes of the star being detrended.

KELT's Paramount ME is a German Equatorial mount, which requires a "flip" as it tracks stars past the meridian. Therefore, the optics and detector are rotated 180 deg with respect to the stars between observations in the Eastern and Western hemispheres, and detector defects, optical distortions, PSF shape, flat-fielding errors, etc., for a given star can be completely different. This requires us to treat observations in the East and West essentially as two separate instruments. Thus, the preceding steps (magnitude conversion, error scaling, dwarf identification, TFA) are each performed separately on the East and West images of each field. After the dwarf stars in the East and West have been run through TFA, we then combine the two light curves of each target into one East+West light curve. We first match stars from the East and the West pointings by their Tycho IDs, and then determine the error-weighted scaling factor of the Western light curve needed to match the error-weighted mean instrumental magnitude of the East light curve.

All of the light curves from the matched Tycho dwarf stars in a field are given an internal ID. We next search the combined East+West light curves of the dwarfs for transit-like signals using the box-fitting least-squares algorithm (BLS; Kovács et al. 2002). We use a custom version of BLS modified to skip over integer and half-integer multiples of the sidereal day to reduce the effect of spurious signals due to diurnal systematics and their aliases on the BLS statistics. We perform selection cuts along six of the statistics that are output by the vartools implementation of the BLS algorithm: signal detection efficiency SDE, signal to pink noise SPN,²¹ the fraction of transit points from one night f_1n, depth δ, the ratio of Δχ² for the best transit model to best inverse transit model Δχ²/Δχ²₋ (Burke et al. 2006), and the fraction of the orbit spent in transit or duty cycle q. In order to determine the appropriate threshold values for these statistics, we injected realistic transit signals with a range of properties into a large sample of light curves, and then attempted to recover these using the BLS algorithm. We then determined the values of these statistics that roughly maximize the overall detection efficiency while minimizing the number of spurious detections. The final adopted values are given in Table 1.

In addition to the cuts we make on the BLS statistics, we also impose restrictions on the effective temperature and inferred density of the candidate host stars. For the temperature, we require that T_eff < 7500 K. We calculate the stellar effective temperature of each candidate from its 2MASS J − K colors. We used the Yonsei-Yale isochrones (Demarque et al. 2004) at 5 Gyr with solar metallicity and no alpha enhancement to create a simple polynomial fit for T_eff as a function of J − K:

$$\begin{eqnarray} \nonumber \log T_{\rm eff}&=&3.94808\hbox{--}0.7353(J-K)\\ &&+1.0116(J-K)^2\hbox{--}0.8334(J-K)^3. \end{eqnarray} \tag{ 3 }$$

As we have conducted our follow-up spectroscopy, we have found that this relation generally predicts T_eff to within ∼100 K for T_eff ≲ 7000 K and to within ∼300 K for stars with T_eff = 7000–7500 K.

We also require that the stellar density, ρ_*, as inferred from the BLS transit fits to the KELT-North light curve, to be within 1.0 dex of the stellar density calculated for each star using its J − K colors, assuming the star is on the main sequence. A large disparity in the observed versus the calculated density is indicative of a blend or of a giant that made it through the reduced proper motion cuts (Seager & Mallén-Ornelas 2003). Again using the Yonsei-Yale isochrones at 5 Gyr with solar metallicity and no alpha enhancement, we made a fit for density as a function of J − K:

$$\begin{eqnarray} \nonumber \log (\rho _{*,\rm {calc}}/\rho _\odot)&=&{-}1.00972+2.82824(J-K)\\ &&{-}1.19772(J-K)^2. \end{eqnarray} \tag{ 4 }$$

We require that this value be within 1.0 dex of the stellar density we calculate from the KELT-North light curve

$$\begin{equation} \log \rho _{*,\rm obs}=\log \left[\frac{3}{G\pi ^2q^3P^2}\right], \end{equation} \tag{ 5 }$$

where P and q are the orbital period and duty cycle (transit duration relative to the period) as returned by BLS. This equation assumes circular orbits and that the companion mass is much smaller than the host star mass, M_P ≪ M_*. Also, because BLS does not attempt to fit for the ingress/egress duration, and furthermore KELT-North data typically do not resolve the ingress or egress well, we are not able to determine the transit impact parameter and thus the true stellar radius crossing time. Equation (5) therefore implicitly assumes an equatorial transit, and so formally provides only an upper limit to the true stellar density. For a transit with an impact parameter of b = 0.7, the true density is ∼0.5 dex smaller than that inferred from Equation (5).

All of the light curves that pass these selection criteria are designated as candidates, and a number of additional diagnostic tests are then performed on them, including Lomb–Scargle (LS, Lomb 1976; Scargle 1982) and AoV (Schwarzenberg-Czerny 1989; Devor 2005) periodograms. The results of these tests, the values of the BLS statistics, the light curves themselves, as well as a host of additional information, are all collected into a Web site for each candidate. Members of the team can then use this information to vote on the true nature of the candidate (probable planet, eclipsing binary, sinusoidal variable, spurious detection, blend, or other). All candidates with at least one vote for being a probable planet are then discussed, and the most promising are then passed along for follow-up photometry, reconnaissance spectroscopy, or both.

KC20C05168 emerged as a strong candidate from the analysis of the combined light curves from stars in the overlap area between fields 1 and 13. The KC20C05168 light curve contains 8185 epochs distributed over ∼4.2 years, between UT 2006 October 25 and UT 2010 December 28, with a weighted rms of 9.8 millimagnitudes (mmag). This rms is typical for KELT-North light curves of stars with this magnitude (V ∼ 10.7). A strong BLS signal was found at a period of P ≃ 1.2175 days, with a depth of δ ≃ 3.8 mmag, and detection statistics SPN = 8.53, SDE = 12.41, q = 0.09, Δχ²/Δχ²₋ = 2.06, and log (ρ_{*, obs}/ρ_{*, cal}) = −0.06. The phased KELT-North light curve is shown in Figure 1. A significant signal also appeared in SuperWASP data (Butters et al. 2010) of this star at the same period. The KELT-North data exhibit some evidence for out-of-transit variability at the mmag level and exhibit some relatively weak peaks in the LS and AoV periodograms, but we did not consider these signals to be strong enough to warrant rejection of the candidate. In addition, the depth of the photometric transit signal in the original KELT-North light curve is substantially smaller than we find in the high-precision follow-up data (see Section 3.4). Further analysis indicates that the out-of-transit variability and smaller depth were likely due to a minor problem with the original data reduction.

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Based on the strength of the K20C05168 signal, the estimated effective temperature of the host star of T_eff ∼ 6500 K, and the fact that the star was sufficiently isolated in a DSS image, we submitted the candidate for reconnaissance spectroscopy with the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész 2008) on the 1.5m Tillinghast Reflector at the Fred Lawrence Whipple Observatory (FLWO) on Mount Hopkins in Arizona. The first observation on UT 2011 November 9 at the predicted quadrature confirmed the T_eff estimate of the star, and also demonstrated that it was a slightly evolved dwarf with log g ∼ 4, and that it was rapidly rotating with  vsin I_* ∼ 55 km s⁻¹. A second observation was obtained on UT 2011 November 11 separated by ∼1.9 days or ∼1.54 in phase, from the first observation and thus sampled the opposite quadrature. The two observations exhibited a large and significant RV shift of ∼8 km s⁻¹, consistent with a BD companion.

Efforts to obtain photometric follow-up during the transit and secondary eclipse were then initiated. Concurrently, additional spectra with TRES were taken to characterize the spectroscopic orbit. In addition, we obtained adaptive optics imaging of the target to search for close companions. Finally, once we were fairly confident that the signals were due to a low-mass transiting companion, we obtained continuous spectroscopic time series with TRES during the transits on UT 2011 December 21 and UT 2012 January 7 for the purposes of measuring the Rossiter–McLaughlin (RM) effect. All of these observations are described in greater detail in the subsequent sections and summarized in Table 2.

KELT-1b was also recognized as a photometric transiting planet candidate by the HATNet project, based on observations obtained in 2006. In 2009 September the candidate HTR162-002 was forwarded to D. Latham's team for spectroscopic follow-up. An initial observation with TRES confirmed that the target was a late F main-sequence star, as expected from 2MASS color J − K_s = 0.245. The synthetic template with T_eff = 6250 K and log g = 4.0 and assumed solar metallicity gave the best match to the observed spectrum. However, that first TRES spectrum also revealed that the star was rotating rapidly, with  vsin I_* = 55 km s⁻¹. At that time, the D. Latham's team routinely put aside candidates rotating more rapidly than about  vsin I_* = 30 km s⁻¹, arguing that it would not be possible to determine velocities with a precision sufficient for an orbital solution for a planetary companion.

HTR162-002 remained on the HATNet "do not observe with TRES" list until it was independently rediscovered by the KELT-North team and was forwarded as candidate KC20C05168 to D. Latham's team in 2011 November for spectroscopic follow-up with TRES. During the intervening 26 months, there were two relevant developments in the procedures and tools used by Latham's team, both resulting from contributions by L. Buchhave. The first development, enabled by convenient tools in the observing Web site, was the practice of observing new candidates only near opposite quadratures, according to the discovery ephemeris and assuming circular orbits. The second development was a much improved procedure for deriving radial velocities for rapidly rotating stars, initially motivated by the Kepler discovery of hot white dwarfs transiting rapidly rotating A stars (Rowe et al. 2010). As it turned out, the second observation of KC20C05168 with TRES described above was taken before the first observation was reviewed, so the candidate was not relegated to the rejected list due to its rapid rotation before the opposite quadrature was observed. When the results were reviewed after the second observation, the evidence for a significant RV shift between the two observations was obvious, despite the rapid rotation, therefore suggesting that the unseen companion was probably a BD, if not a giant planet.

It should also be recognized that over the 26 months since the first observation of HTR162-002, the attitude against pursuing rapidly rotating stars as possible hosts for transiting planets had gradually softened among the exoplanet community. An important development was the demonstration that slowly rotating subgiants that have evolved from rapidly rotating main-sequence A stars do occasionally show the RV signatures of orbiting planetary companion (e.g., Johnson et al. 2007). A second insight came from the demonstration that the companion that transits the rapidly rotating A star WASP-33 must be a planet, using Doppler imaging (Collier Cameron et al. 2010). Finally, the discovery of transiting BD companions suggested the possibility of detecting their large amplitude RV signals even when they orbit stars with large  vsin I_* and thus poor RV precision.

In the early days of wide-angle photometric surveys for transiting planets, Latham's team had established procedures for handling candidates forwarded for spectroscopic follow-up by more than one team. Such duplications were fairly common, and the goal was to assign credit to the initial discovery team, which was especially important in an era when few transiting planets had been confirmed. By the time it was noticed in mid 2011 December that KC20C05168 was the same as HTR162-002, the KELT-North team already had in hand a convincing orbital solution from TRES and high-quality light curves from several sources, confirming that KELT-1b was indeed a substellar companion.

A total of 81 spectra of KELT-1 were taken using the TRES spectrograph on the 1.5 m Tillinghast Reflector at FLWO. These were used to determine the Keplerian parameters of the spectroscopic orbit, measure bisector variations in order to exclude false positive scenarios, measure the spectroscopic parameters of the primary, and measure anomalous RV shift of the stellar spectral lines as the companion transits in front of the rapidly rotating host star, i.e., the RM effect (Rossiter 1924; McLaughlin 1924). The TRES spectrograph provides high resolution, fiber-fed echelle spectroscopy over a bandpass of 3900–8900 Å (Fűrész 2008). The observations obtained here employed the medium fiber for a resolution of R ∼44,000. The data were reduced and analyzed using the methods described in Quinn et al. (2012) and Buchhave et al. (2010).

A subset of six spectra were combined in order to determine the spectroscopic parameters of the host star using the Spectral Parameter Classification (SPC) fitting program (L. A. Buchhave et al., in preparation). SPC cross-correlates the observed spectrum against a grid of synthetic Kurucz (Kurucz 1979) spectra. This analysis yielded T_eff = 6512  ±  50 K, log g = 4.20  ±  0.10, [Fe/H] =0.06  ±  0.08, and  vsin I_* = 55.2  ±  2.0 km s⁻¹. These parameters were used as priors for the joint global fit to the RV, RM, and photometric data as described in Section 5.2.

Spectra were taken at a range of phases in order to characterize the spectroscopic orbit and search for bisector span variations indicative of a blend. One of these spectra happened to be taken during a transit on UT 2011 November 18, and so was not used in the analysis because it is likely to be affected by the RM effect. The RV and bisector data for the remaining 23 spectra are listed in Table 7. These observations span ∼88 days from UT 2011 November 9 through UT 2012 February 5. The uncertainties on the listed radial velocities have been scaled by a factor of 1.214 based on an independent fit to these data, as described in Section 5.2. The scaled median RV uncertainty is ∼230 m s⁻¹. The uncertainties in the bisector measurements have not been scaled. The median bisector uncertainty is ∼110 m s⁻¹.

Time series spectroscopy was obtained with TRES on two different nights of transits in order to measure the spin–orbit alignment of the companion via the RM effect. On UT 2011 December 21 15 observations were obtained and 42 observations on UT 2012 January 7. Conditions were relatively poor for the first run, resulting in a factor ∼2 larger uncertainties and incomplete coverage of the transit. We therefore decided not to include these data in our final analysis, although we confirmed that this has no effect on our final inferred parameters. The RV and bisector data for the RM run on UT 2012 January 7 are listed in Table 8. The RV uncertainties have been scaled by a factor of 0.731, also based on the global model fit described in Section 5.2. We note that the majority of the χ² for these data are due to a few outliers. The median scaled RV uncertainty is ∼160 m s⁻¹. The bisector uncertainties were not scaled.

All of the RV measurements used in the subsequent analysis are shown as a function of epoch of observation in BJD_TDB in Figure 2. The RV and bisector measurements phased to the best-fit companion period from the joint fit to photometric and RV data are shown in Figure 3, demonstrating the very high signal-to-noise ratio with which the RV signal of the companion was detected, and the good phase coverage of the orbit. A detail of the RV data near the time transit with the orbital (Doppler) RV signal removed is shown in Figure 4, showing the clear detection of the RM effect and a suggestion that the orbit normal is well aligned with the projected stellar spin axis.

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Finally, we determined the absolute RV of the system barycenter using a simple circular orbit fit to radial velocities determined from the full set of spectra, which were determined using a single order near the Mg b line. (Note that the relative RVs used for determining the orbit were determined using the full, multi-order analysis of the spectra.) The zero point correction to these velocities was determined using contemporaneous monitoring of five RV standard stars. The final value we obtain is γ_obs = −14.2  ±  0.2 km s⁻¹, where the uncertainty is dominated by the systematic uncertainties in the absolute velocities of the standard stars. This zero point, along with the global fit to the data in Section 5.2, was used to place the instrumental relative radial velocities on an absolute scale. Therefore, the RVs listed in Tables 7 and 8 are on an absolute scale.

We obtained high-precision follow-up photometry of KELT-1 in order to confirm the K20C05168 transit signal, search for evidence of a strongly wavelength-dependent transit depth indicative of a stellar blend, and search for evidence of a secondary eclipse. Also, these data enable precision measurements of the transit depth, ingress/egress duration, and total duration, in order to determine the detailed parameters of the KELT-1 system. In all, we obtained coverage of nine complete and four partial transits, and two complete and one partial secondary eclipse, using six different telescopes in all. Many of these data were taken under relatively poor conditions and/or suffer from strong systematics. We therefore chose to include only a subset for the final analysis, including six of the transits and the three secondary eclipses. In the following subsections, we detail the observatories and data reduction methods used to obtain these data. The dates, observatories, and filters for these data sets are summarized in Table 2. The light curves for the transits are displayed in Figure 5 and the data are listed in Tables 9–14, whereas the light curves for the secondary eclipse are displayed in Figure 6 and the data are listed in Tables 15–17. The combined and binned transit light curve is shown in Figure 7.

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3.4.1. Peter van de Kamp Observatory (PvdKO)

3.4.2. University of Louisville Moore Observatory (ULMO)

3.4.3. Hereford Arizona Observatory (HAO)

3.4.4. FLWO/KeplerCam

3.4.5. Las Cumbres Observatory Global Telescope Network (LCOGT)

To further assess the multiplicity of KELT-1, we acquired adaptive optics images using NIRC2 (PI: Keith Matthews) at Keck on UT 2012 January 7. Our observations consist of dithered frames taken with the K' (λ_c = 2.12 μm) and H (λ_c = 1.65 μm) filters. We used the narrow camera setting to provide fine spatial sampling of the stellar PSF. The total on-source integration time was 81 s in each bandpass.

Images were processed by replacing hot pixel values, flat-fielding, and subtracting thermal background noise. No companions were identified in individual raw frames during the observations; however, upon stacking the images we noticed a point source (8σ) to the southeast of KELT-1. Figure 8 shows the final processed K' image. Inspection of the companion location showed that its separation from the star does not change with wavelength, demonstrating that it is not a speckle. This object is too faint and close to the primary to be detected with seeing-limited images.

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We performed aperture photometry to estimate the relative brightness of the candidate tertiary, finding ΔH = 5.90  ±  0.10 and ΔK' = 5.59  ±  0.12. An H − K' = 0.4  ±  0.2 color is consistent with spectral-types M1–L0 (Leggett et al. 2002; Kraus & Hillenbrand 2007). If the candidate is bound to KELT-1 and thus at the same distance of 263  ±  14 pc and suffers the same extinction of A_V = 0.18  ±  0.10 (see Section 5.1), then we estimate its absolute H magnitude to be M_H = 8.31  ±  0.15, corresponding to an M4–5 spectral type, consistent with its color (see, e.g., the compilation of Kirkpatrick et al. 2012).

We also measured an accurate position of the companion relative to the star by fitting a Gaussian model to each of the PSF cores. After correcting for distortion in the NIRC2 focal plane,²³ and adopting a plate scale value of 9.963  ±  0.006 mas pixel⁻¹ and instrument orientation relative to the sky of 013  ±  002 (Ghez et al. 2008), we find a separation of ρ = 588  ±  1 mas and position angle P.A. = 1574  ±  02 east of north. If it is bound to KELT-1, it has a projected physical separation of ∼154  ±  8 AU, and a period of ∼1700 years assuming a circular, face-on orbit.

We used the Galactic model from Dhital et al. (2010) to assess the probability that the companion is an unrelated star (i.e., a chance alignment). The model uses empirical number density distributions to simulate the surface density of stars along a given line of sight and thus determine probability of finding a star within a given angular separation from KELT-1. We estimate an a priori probability of ∼0.05% of finding a star separated by ≲ 059 from KELT-1b. We therefore conclude that the companion is likely to be a bona fide, physically associated binary system. With a total proper motion of ∼20 mas yr⁻¹, it will be possible to definitively determine whether the candidate tertiary is physically associated with KELT-1 within 1 year.

We note that the companion is unresolved in our follow-up transit photometry, and thus in principle leads to a dilution of the transit signal and a bias in the parameters we infer from a fit to the photometry described in Section 5.2. However, the effect is negligible. As we discuss in the next section, we are confident that the primary is being eclipsed. Thus, the fractional effect on the transit depth is of the same order as the fractional contribution of the companion flux to the total flux. For the photometric bands where we have transit photometry, and assuming the companion is an M1 star or later, we estimate that it contributes ≲ 0.2% to the flux from the primary.

Table 3 lists various collected properties and measurements of the KELT-1 host star. Many of these have been culled from the literature, and the remainder are derived in this section. In summary, KELT-1 is a mildly evolved, solar-metallicity, mid-F star with an age of ∼1.5–2 Gyr located at a distance of ∼260 pc, with kinematics consistent with membership in the thin disk.

We constructed an empirical spectral energy distribution (SED) of KELT-1 using optical fluxes in the B_T and V_T passbands from the Tycho-2 catalog (Høg et al. 2000), near-infrared (IR) fluxes in the J, H, and Ks passbands from the 2MASS Point Source Catalog (Skrutskie et al. 2006; Cutri et al. 2003), and near- and mid-IR fluxes in three of the WISE passbands (Wright et al. 2010; Cutri et al. 2012). This SED is shown in Figure 11. We fit this SED to NextGen models from Hauschildt et al. (1999) by fixing the values of T_eff, log g, and [Fe/H] inferred from the global fit to the light curve and RV data as described in Section 5.2 and listed in Table 4, and then finding the values of the visual extinction A_V and distance d that minimizes χ². We find A_V = 0.18 ± 0.10 and d = 263 ± 14pc, with a χ² = 10.5 for 6 degrees of freedom, indicating a reasonable fit (P(> χ²) ∼ 10%). We also performed a fit to the SED without priors, finding T_eff = 6500 ± 400 K, A_V = 0.20 ± 0.15, log g = 4.25 ± 0.75, and [Fe/H] =−0.5 ± 0.5, consistent with the constrained fit. There is no evidence for an IR excess.

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We note that the quoted statistical uncertainties on A_V and d are likely to be underestimated, because we have not accounted for the uncertainties in values of T_eff, log g, and [Fe/H] used to derive the model SED. Furthermore, it is likely that alternate model atmospheres would predict somewhat different SEDs and thus values of the extinction and distance.

In Figure 12, we plot the predicted evolutionary track of KELT-1 on a theoretical H-R diagram (log g versus T_eff), from the Yonsei-Yale stellar models (Demarque et al. 2004). Here, again we have used the values of M_* and [Fe/H] derived from the global fit (Section 5.2 and Table 4). We also show evolutionary tracks for masses corresponding to the ±1σ extrema in the estimated uncertainty. In order to estimate the age of the KELT-1 system, we compare these tracks to the values of T_eff and log g and associated uncertainties as determined from the global fit. These intersect the evolutionary track for a fairly narrow range of ages near ∼2 Gyr. The agreement between the prediction from the evolutionary track at this age and the inferred temperature and surface gravity for KELT-1 is remarkably good, but perhaps not entirely surprising. The values of T_eff, log g, [Fe/H], and M_* were all determined in the global fit to the light curve and RV data in Section 5.2, which uses the empirical relations between both M_* and R_* and (T_eff, log g, [Fe/H]) inferred by Torres et al. (2010) as priors on the fit, in order to break the well-known degeneracy between M_* and R_* for single-lined spectroscopic eclipsing systems. These empirical relations are known to reproduce the constraints between these parameters imposed by the physics of stellar evolution quite well (see, e.g., Section 8 in Torres et al. 2010).

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Based on its T_eff and J − K and the empirical table of spectral type versus color and T_eff for main sequence from Kenyon & Hartmann (1995), we infer the spectral type of KELT-1 to be F5 with an uncertainty of roughly ±1 spectral type.

We determined the Galactic U, V, W space velocities of the KELT-1 system using the proper motion of (μ_α, μ_δ) = (− 10.1 ± 0.7, −9.4 ± 0.7) mas yr⁻¹ from the NOMAD catalog (Zacharias et al. 2004), the distance of d = 263 ± 14 pc from our SED fit described above, and the barycentric RV of the system as determined from the TRES observations (Section 3.3) of γ_abs = −14.2 ± 0.2 km s⁻¹. We used a modification of the IDL routine GAL_UVW, which is itself based on the method of Johnson & Soderblom (1987). We adopt the correction for the Sun's motion with respect to the Local Standard of Rest from Coşkunoǧlu et al. (2011), and choose a right-handed coordinate system such that positive U is toward the Galactic Center. We find (U, V, W) = (19.9 ± 1.1, −9.6 ± 0.5, −2.6 ± 0.9) km s⁻¹, consistent with membership in the thin disk (Bensby et al. 2003). We note also that the distance of KELT-1 from the Galactic plane is ∼80 pc.

Finally, we use the solar evolutionary models of Guenther et al. (1992), updated with input physics from van Saders & Pinsonneault (2012), to gain some insight into the detailed structure of the host star. Fixing the mass and metallicity at the values determined from the global fit (Section 5.2 and Table 4), we evolved the model forward until the model log g and T_eff approximately matched the values inferred for KELT-1. We found that an age of ∼1.75 Gyr best matched the available constraints, and thus this model prefers a somewhat younger age than the Yale-Yonsei model of Demarque et al. (2004, Figure 12). We therefore decided to adopt an age of 1.75 ± 0.25 Gyr, consistent with both estimates. For this range of ages, the models of Guenther et al. (1992) predict a radius of the base of the convective zone of R_cz = 1.31 ± 0.03 R_☉ and a very small mass for the convective zone of M_cz = [2.8 ± 0.4] × 10⁻⁴ M_☉, as expected given the effective temperature of T_eff ∼ 6500 K. In addition, the moment of inertia for the star and convective zone are C_* = [1.18 ± 0.04] × 10⁵⁴ g cm² and C_cz = [3.2 ± 0.7] × 10⁵¹ g cm², respectively. We can also write the moment of inertia of the star as C_* = α_*M_*R²_* with α_* = 0.042 (Guenther et al. 1992). We will use these to estimate the angular momenta of the star, companion, and orbit in Section 6.2.

It is well known that a joint fit to high-quality RVs and transit photometry of a transiting planet system allows one to determine the mass and radius of the star and planet, as well as the semimajor axis of the orbit, in principle to very high precision, up to a perfect one-parameter degeneracy (Seager & Mallén-Ornelas 2003). This degeneracy arises because the duration, depth, and shape of the transit, when combined with the eccentricity, longitude of periastron, and period of the planet from RV data, allow one to precisely estimate the density of the primary star ρ_*, but not M_* or R_* separately. Breaking this M_* − R_* degeneracy generally requires imposing some external constraint, such as a theoretical mass–radius relation (Cody & Sasselov 2002; Seager & Mallén-Ornelas 2003) or constraints from theoretical isochrones (e.g., Bakos et al. 2012). In principle, a measurement of log g from a high-resolution spectrum can be used to break the degeneracy, but in practice these measurements are generally not competitive with the constraint on ρ_* and often have systematic uncertainties that are comparable to the statistical uncertainties.

We fitted the RV and transit data using a modified version of the IDL fitting package EXOFAST (Eastman et al. 2012). The approach of EXOFAST to breaking the M_* − R_* degeneracy is similar to the method described in, e.g., Anderson et al. (2012), but with significant differences. We will review it briefly here, but direct the reader to Eastman et al. (2012) for more details. We fitted the RV and transit data simultaneously with a transit photometric model (Mandel & Agol 2002) and a standard Keplerian RV model using a modified MCMC method (described in more detail below). In addition to the standard fitting parameters, we also included T_eff, log g, and [Fe/H] as proposal parameters. We then included priors on the measured values of T_eff, log g, and [Fe/H] as determined from analysis of the TRES spectra and given in Section 3.3. In addition, we included separate priors on both M_* and R_*, each of which are based on the empirical relations between M_* and R_* and (T_eff, log g, [Fe/H]) determined by Torres et al. (2010). These priors essentially break the M_* − R_* degeneracy, as they provide similar constraints as isochrones, i.e., they encode the mapping between the M_*, [Fe/H], and age of a star to its T_eff and log g as dictated by stellar physics.

We fitted the six transits, Doppler RV, stellar parameters, and RM effect simultaneously using EXOFAST, which employs a Differential Evolution Markov Chain Monte Carlo (DE-MC) method (ter Braak 2006). We converted all times to the BJD_TDB standard (Eastman et al. 2010), and then at each step in the Markov Chain, we converted them to the target's barycentric coordinate system (ignoring relativistic effects). Note that the final times were converted back to BJD_TDB for ease of use. This transformation accurately and transparently handles the light travel time difference between the RVs and the transits.

First, we fitted the Doppler RV data independently to a simple Keplerian model, ignoring the RM data taken on UT 2012 January 7. At this stage, we did not include any priors on the stellar parameters, as they do not affect the RV-only fit. We scaled the uncertainties such that the probability P(> χ²) of finding a value of χ² equal to or larger than the value we measured was 0.5, in order to ensure that the resulting parameter uncertainties were roughly accurate. For a uniform prior in eccentricity, we found the orbit is consistent with circular, with a 3σ upper limit of e < 0.04. Nevertheless, in order to provide conservative estimates for the fit parameters, we allowed for a non-zero eccentricity in our final fit. However, to test the effect of this assumption, we repeated the final fit forcing e = 0. We also investigated the possibility of a slope in the RVs, but found it to be consistent with zero, so we did not include this in the final fit.

Next, we fitted each of the four transits individually, including a zero point, F_{0, i} and air-mass detrending variable, C_{0, i} for each of the i transits. The air-mass detrending coefficient was significant (>1σ) for all but one transit, so for consistency, we included it for all. After finding the best fit with AMOEBA (Nelder & Mead 1965), we scaled the errors for each transit such that P(> χ²) = 0.5. At this stage, we included the priors on the stellar parameters as described above.

Next, we performed a combined fit to all the data, including a prior on the projected stellar rotation velocity ( vsin I_* = 55.2 ± 2.0 km s⁻¹) from the spectra,²⁴ and a prior on the period from the KELT-North discovery light curve (P = 1.217513 ± 0.000015 days). Because it is usually systematics in the RV data that vary over long timescales (due to a combination of instrumental drift and stellar jitter) that ultimately set the error floor to the RVs, we expect the uncertainties of densely packed observations to be smaller than the rms of all observations, but with a systematic offset relative to the rest of the orbit. Therefore, we fitted a separate zero point during the RM run, and also scaled the errors on the RVs during transit to force P(> χ²) = 0.5 for those subsets of points. P(> χ²) depends on the number of degrees of freedom, but it is not obvious how many degrees of freedom there are in the RM run—technically, the entire orbit and the transit affect the χ² of the RM (13 parameters), but the freedom of the RM measurements to influence most of those parameters is very limited, when fit simultaneously with the transits. Indeed, even  vsin I_* is constrained more by the spectroscopic prior than the RM in this case, which means there are only two parameters (the projected spin–orbit alignment, λ, and the zero point, γ) that are truly free. To be conservative, we subtracted another degree of freedom to encompass all the other parameters on which the RM data have a slight influence, before scaling the errors.

The RM data were modeled using the Ohta et al. (2005) analytic approximation with linear limb darkening.²⁵ At each step in the Markov Chain, we interpolated the linear limb-darkening tables of Claret & Bloemen (2011) based on the chain's value for log g, T_eff, and [Fe/H] to derive the linear limb-darkening coefficient, u. We assumed the V-band parameters to approximate the bandpass of TRES, though we repeated the exercise in the B band with no appreciable difference in any of the final parameters. Note that we do not fit for the limb-darkening parameters, as the data are not sufficient to constrain them directly. The uncertainties in all the limb-darkening parameters provided in Table 5 arise solely from the scatter in log g, T_eff, and [Fe/H]. We assume no error in the interpolation of the limb-darkening tables.

In order to search for Transit Timing Variations (TTVs), during the combined fit, we fitted a new time of transit, T_{C, i} for each of the i transits. Therefore, the constraint on T_C and P (quoted in Tables 5 and 4, respectively) comes from the prior imposed from the KELT-North light curve and the RV data, not the follow-up light curves. Using these times to constrain the period during the fit would artificially reduce any observed TTV signal. A separate constraint on T_C and P follows from fitting a linear ephemeris to the transit times, as discussed in Section 5.3. It is the result from this fit that we quote as our final adopted ephemeris.

The results from this global fit are summarized in Tables 4 and 5. We also show the results for the physical parameters assuming e = 0 in Table 4; the differences between the fixed and free eccentricity fits are always smaller than their uncertainties, and generally negligible for most of these parameters. The values of T_eff, log g, and [Fe/H] we infer from the global fit are in agreement with the values measured directly from the TRES spectra to within the uncertainties. Since the spectroscopic values were used as priors in the global fit, this generally indicates that there is no tension between the value of ρ_* inferred from the light curve and RV data, and the spectroscopic values. The median value and uncertainty for T_eff and [Fe/H] are nearly unaffected by the global fit. On the other hand, the uncertainty in log g from the global fit is a factor of ∼5 smaller than the uncertainty from the spectroscopic measurement. This is not surprising, since the constraint on ρ_* from the RV and light curve data provides a strong constraint on log g via the relations of Torres et al. (2010).

We also present in Table 4 our estimates of the median values and uncertainties for a number of derived physical parameters of the system that may be of interest, including the planet equilibrium temperature assuming zero albedo and perfect redistribution T_eq, the average amount of stellar flux at the orbit of the companion <F >, and the Safronov number Θ = (a/R_p)(M_P/M_*) (e.g., Hansen & Barman 2007). In addition, in Table 5 we quote our estimates of various fit parameters and intermediate derived quantities for the Keplerian RV fit, the transits, and the secondary eclipse.

We note that the final uncertainties we derive for M_*, R_*, log g, and ρ_* are relatively small, ∼3%–6%. These uncertainties are of the same order as those found for other transiting planet systems using methods similar to the one used here (e.g., Anderson et al. 2012). Specifically, these methods derive physical parameters from a fit to the light curve and RV data, which simultaneously impose empirically determined relations between M_* and R_* and (T_eff, log g, [Fe/H]), which are ultimately derived from Torres et al. (2010). These constraints help to break the M_* − R_* degeneracy pointed out by Seager & Mallén-Ornelas (2003) and discussed above. These Torres et al. (2010) relations, including the scatter about these relations, in concert with the constraint on ρ_* from the transit light curves, largely determine the final uncertainty on M_* and R_* (and thus M_P and R_P). In particular, we find that our spectroscopic measurement of log g provides a much weaker constraint. Given that our results rely so heavily on the Torres et al. (2010) relations, it is worthwhile to ask to what extent our parameters and uncertainties might be affected should these relations be systematically in error. First, as already noted, these empirical relations are known to agree well with stellar isochrones in general (Torres et al. 2010), and for KELT-1 in particular (Figure 12). Second, analyses using stellar isochrones rather than empirical relations produce similar uncertainties on M_* and R_* (e.g., Bakos et al. 2011), suggesting that the small uncertainties we derive are not a by-product of our specific methodology. Finally, Southworth (2009) demonstrated that the results of the analysis of 14 transiting systems with several different sets of isochrones generally agree to within ∼2%–5%. This suggests that the systematic errors caused by uncertainties in the isochrones (and so the Torres et al. 2010 relations) are of the same order as the statistical uncertainties we infer. We therefore conclude that our results are likely accurate, with systematic errors at the level of our statistical uncertainties (a few to several percent).

Table 6 lists the measured transit times for each of the six modeled transits, and Figure 13 shows the residuals of these times from a fit to a linear ephemeris. The best fit has

$$\begin{eqnarray} \nonumber T_C(\rm {BJD_{TDB}}) &=& 2455909.29280 \pm 0.00023\\ P &=& 1.217501 \pm 0.000018, \end{eqnarray} \tag{ 6 }$$

which is consistent with the ephemeris derived from the KELT-North light curve alone. The χ² = 45.5 for the linear fit with 4 degrees of freedom is formally quite poor. This is mostly driven by one nominally significant (5σ) outlier, specifically for the transit observed on UT 2011 December 16 from FLWO. We note that the faint companion to KELT-1, if indeed bound, is too distant to explain such large TTVs.

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We have taken great care to ensure the accuracy of our clocks and our conversion, and the fact that the residuals from different observatories roughly follow the same trend in time suggests that a catastrophic error in the observatory clock cannot be blamed. Since we fit the trend with air mass simultaneously with the transit, the potentially large covariance between it and the transit time should be accurately reflected in the quoted uncertainties (Eastman et al. 2012). Nevertheless, our MCMC analysis does not adequately take into account the effect of systematic uncertainties, and in particular we do not account for correlated uncertainties (Pont et al. 2006b; Carter & Winn 2009), which could skew the transit time of a given event substantially. And, given the results from Kepler which suggest the rarity of such TTVs (Steffen et al. 2012), we are reluctant to overinterpret this result. Nevertheless, this is an interesting target for future follow-up.

We observed the predicted secondary eclipses of KELT-1b assuming e = 0 on UT 2011 December 2, 2011 December 30, and 2012 January 4. In none of the three were we able to detect a secondary eclipse. The observations on 2011 December 2 and on 2012 January 4 were taken from the ULMO Observatory in i. On both nights we were able to observe through the predicted ingress and egress of the potential secondary. The two i-band light curves have a combined 236 data points, and show an rms scatter of 1.56 mmag. The observations on 2011 December 30 were taken with the FTN telescope in Pan-STARRS-Z. In this case, we were only able to begin observations half way through the predicted secondary eclipse. This Z-band light curve has 72 points, and an rms scatter of 0.75 mmag.

We used the system parameters derived from the joint fit (Section 5.2) to fit our three observations. Since we did not detect a secondary eclipse, we used these fits to explore the combination of heat redistribution efficiency and Bond albedo A_B that would give rise to a secondary eclipse depth that is inconsistent with our data. To do so, we calculated the secondary eclipse depths we would expect for a range of redistribution efficiencies and albedos, and then fit a secondary eclipse model with the predicted depth to all three of our observations simultaneously.

In calculating the expected secondary eclipse depths, we made the assumption that both the star and the planet were blackbodies. We also assumed that the planet was a gray Lambert sphere, so the geometric albedo A_g = (2/3)A_B, and the spherical albedo is constant as a function of wavelength. Following Seager (2010), we parameterized the heat redistribution efficiency as f', which is 1/4 in the case of uniform redistribution, and 2/3 in the case of no redistribution. We note that in between these two extremes, f' is not easily related to the amount of heat redistribution, i.e., f' = 0.45 does not imply that half of the incident stellar energy is redistributed around the planet.

To test these expected secondary eclipse depths against our observations, we fit simple trapezoidal eclipse curves with the expected depths to all three data sets simultaneously. Under our assumptions, the depth, timing, shape, and duration of the secondary eclipse are all determined by the parameters derived from the global fit and our specified values of A_B and f'. We then fit this model to our data, allowing for a normalization and a linear trend in the flux with time. We used the Δχ² between the best-fit eclipse model and the best constant fit, which itself was allowed a free slope and offset, to evaluate the detectability of each of the secondary eclipse depths. We used the χ² distribution to transform these Δχ² values into detection probabilities. Figure 6 shows an example light curve against a median binned version of our data. This particular curve is the secondary eclipse we would expect if KELT-1b had A_B = 0.1, and instantaneously re-radiated its incident stellar flux, i.e., f' = 2/3. We would have detected this event with more than 95% confidence.

Figure 14 shows the results of our exploration of the heat redistribution versus Bond albedo parameter space. Contours where the eclipse depths are detectable at the 68%, 90%, and 95% confidence level are indicated. The particular shapes of the contours on this plot come from the competing effects of reflection and blackbody emission from KELT-1b on the depth of the secondary eclipse. Along the very bottom of the figure the Bond albedo is zero, and thus there is only thermal emission. We see the strong change in eclipse depth as the amount of heat redistribution decreases, thus causing the temperature and eclipse depth for KELT-1b to increase. Along the top of the figure, where the Bond albedo is 0.75, the reflected starlight dominates the blackbody emission such that changing the redistribution efficiency has little effect on the eclipse depth.

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Slightly more than half of the allowed parameter space in Figure 14 would have caused secondary eclipses detectable in our data at greater than 90% confidence, while almost all would have been detected at more than 68% confidence. Since we did not see a secondary eclipse in our observations, we conclude that either KELT-1b has a non-zero albedo, or it must redistribute some heat from the day side, or both. Formally, the scenario that is most consistent with our data is that KELT-1b has both a low Bond albedo and is very efficient at redistributing heat away from its day side, however we are reluctant to draw any strong conclusions based on these data.

Is KELT-1b a BD or is it a suppermassive planet? By IAU convention, BDs are defined to have masses between the deuterium burning limit of ∼13 M_Jup (Spiegel et al. 2011) and the hydrogen burning limit of ∼80 M_Jup (e.g., Burrows et al. 1997). Less massive objects are defined to be planets, whereas more massive objects are stars. By this definition, KELT-1b is a low-mass BD. However, it is interesting to ask whether or not KELT-1b could have plausibly formed in a protoplanetary disk, and therefore might be more appropriately considered a "supermassive planet" (Schneider et al. 2011). More generally, it is interesting to consider what KELT-1b and systems like it may tell us about the formation mechanisms of close companions with masses in the range of 10–100 M_Jup.

One of the first results to emerge from precision Doppler searches for exoplanets is the existence of a BD desert, an apparent paucity BD companions to FGK stars with periods less than a few years, relative to the frequency of stellar companions in the same range of periods (Marcy & Butler 2000). Subsequent studies uncovered planetary companions to such stars in this range of periods in abundance (Cumming et al. 2008), indicating that the BD desert is a local nadir in the mass function of companions to FGK stars. The simplest interpretation is that this is the gap between the largest objects that can form in a protoplanetary disk, and the smallest objects that can directly collapse or fragment to form a self-gravitating object in the vicinity of a more massive protostar. Therefore, the location of KELT-1b with respect to the minimum of the BD mass function might plausibly provide a clue to its origin.

6.1.1. Comparison Sample of Transiting Exoplanets, Brown Dwarfs, and Low-mass Stellar Companions

In order to place the parameters of KELT-1b in context, we construct a sample of transiting exoplanets, BDs, and low-mass stellar companions to main-sequence stars. We focus only on transiting objects, which have the advantage that both the mass and radius of the companions are precisely known.²⁶ We collect the transiting exoplanet systems from the Exoplanet Data Explorer (exoplanets.org; Wright et al. 2011), discarding systems for which the planet mass is not measured. We supplement this list with known transiting BDs (Deleuil et al. 2008; Johnson et al. 2011; Bouchy et al. 2011a, 2011b; Anderson et al. 2011). We do not include the system discovered by Irwin et al. (2010), because a radius measurement for the BD was not possible. We also do not include 2M0535 − 05 (Stassun et al. 2007) because it is a young, double BD system. We add several transiting low-mass stars near the hydrogen burning limit (Pont et al. 2005, 2006a; Beatty et al. 2007). We adopt the mass of XO-3b from the discovery paper (Johns-Krull et al. 2008), which is M_P = 13.1 ± 0.4 M_Jup, which straddles the deuterium burning limit (Spiegel et al. 2011). However, later estimates revised the mass significantly lower to M_P = 11.8 ± 0.6 (Winn et al. 2008). We will therefore categorize XO-3b as an exoplanet.

The disadvantage of using samples culled from transit surveys is that the sample size is much smaller, and transit surveys have large and generally unquantified selection biases (e.g., Gaudi et al. 2005; Fressin et al. 2009), particularly ground-based transit surveys. We emphasize that such biases are almost certainly present in the sample we construct. We have therefore made no effort to be complete. The comparisons we make based on this sample should not be considered definitive, but rather suggestive.

Figure 15 places KELT-1b among the demographics of known transiting companions to main-sequence stars, focusing on massive exoplanets, BDs, and low-mass stars with short periods of ≲ 30 days. KELT-1b has the tenth shortest period of any transiting exoplanet or BD known. It has the sixth shortest period among giant (M_P ≳ 0.1 M_Jup) planets, with only WASP-19b, WASP-43b, WASP-18b, WASP-12b, OGLE-TR-56b, and HAT-P-23b having shorter periods. KELT-1b is more massive by a factor ∼3 than the most massive of these, WASP-18b (Hellier et al. 2009). KELT-1b has a significantly shorter period than any of the previously known transiting BDs, by a factor of ≳ 3. KELT-1b therefore appears to be located in a heretofore relatively unpopulated region of the M_P − P parameter space for transiting companions.

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Although the KELT-1 system is relatively unique, it is worth asking if there are any other known systems that bear some resemblance to it. The M_Psin i ≃ 18 M_Jup, P ≃ 1.3 day RV-discovered companion to the M dwarf HD 41004B (Zucker et al. 2003) has similar minimum mass and orbit as KELT-1b; however, the host star is obviously quite different. Considering the host star properties as well, perhaps the closest analogs are WASP-18b (Hellier et al. 2009), WASP-33b (Collier Cameron et al. 2010), and KOI-13b (Mazeh et al. 2012; Mislis & Hodgkin 2012). All three of these systems consist of relatively massive (M_p ≳ 3 M_Jup) planets in short (≲ 2 day) orbits around hot (T_eff ≳ 6500 K) stars.

The mass of KELT-1b (∼27 M_Jup) is close to the most arid part of the BD desert, estimated to be at a mass of 31⁺²⁵₋₁₈ M_Jup according to Grether & Lineweaver (2006). Thus, under the assumption that the BD desert reflects the difficulty of forming objects with this mass close to the parent star under any formation scenario, KELT-1b may provide an interesting case to test these various models. For disk scenarios, gravitational instability can likely form such massive objects, but likely only at much larger distances (Rafikov 2005; Dodson-Robinson et al. 2009; Kratter et al. 2010). The maximum mass possible from core accretion is poorly understood, but may be as large as ∼40 M_Jup (Mordasini et al. 2009). The possibility of significant migration of KELT-1b from its birth location to its present position must also be considered, particularly given the existence of a possible stellar companion to KELT-1 (Section 3.5). This possibility complicates the interpretation of the formation of KELT-1b significantly. For example, it has been suggested that BD companions are more common at larger separations (Metchev & Hillenbrand 2009); thus KELT-1b may have formed by collapse or fragmentation at a large separation, and subsequently migrated to its current position via the Kozai–Lidov mechanism (Kozai 1962; Lidov 1962).

One clue to the origin of KELT-1b and the BD desert may be found by studying the frequency of close BD companions to stars as a function of the stellar mass or temperature. Figure 15 shows the mass of known transiting short period companions as a function of the effective temperature of the host stars. As pointed out by Bouchy et al. (2011a), companions with M_P ≳ 5 M_Jup appear to be preferentially found around hot stars with T_eff ≳ 6000 K, and KELT-1b follows this trend. Although these hot stars are somewhat more massive, the most dramatic difference between stars hotter and cooler than 6000 K is the depth of their convection zones. This led Bouchy et al. (2011a) to suggest that tides may play an important role in shaping the frequency and distribution of massive exoplanet and BD companions to old stars. Some evidence for this has been reported by Winn et al. (2010), who argue that hot (T_eff ⩾ 6250 K) stars with close companions preferentially have high obliquities, suggesting that if the emplacement mechanisms are similar for all stars, tidal forces must later serve to preferentially bring cool host stars into alignment. Figure 16 shows the distribution of spin–orbit alignments for transiting planets versus the host star effective temperature. KELT-1b falls in the group of hot stars with small obliquities. Interestingly the other massive ≳ 5 M_Jup planets are also located in this group.

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We discuss the possible formation and evolutionary history of KELT-1b, and the likely role of tides in this history, in more detail below. We remain agnostic about the classification of KELT-1b as a BD or supermassive planet.

Given the relatively large mass and short orbital period of KELT-1b, it seems probable that tides have strongly influenced the past evolution of the system and may continue to be affecting its evolution. The literature on the influence of tides on exoplanet systems is vast (see, e.g., Rasio et al. 1996; Ogilvie & Lin 2004; Jackson et al. 2008; Leconte et al. 2010; Matsumura et al. 2010; Hansen 2010, for but a few examples), and there appears to be little consensus on the correct treatment of even the most basic physics of tidal dissipation, with the primary uncertainties related to where, how, and on what timescale the tidal energy is dissipated.

While we are interested in evaluating the importance of tides on the evolution of the orbit of KELT-1b and the spin of KELT-1, delving into the rich but difficult subject of tides is beyond the scope of this paper. We therefore take a somewhat heuristic approach. Specifically, we construct a few dimensionless quantities that likely incorporate the primary physical properties of binary systems that determine the scale of tidal evolution, but do not depend on the uncertain physics of energy dissipation. Specifically, we define,

$$\begin{eqnarray} {\cal T}_a & \equiv & \frac{M_*}{M_P} \left(\frac{a}{R_*}\right)^5,\qquad {\rm and} \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} {\cal T}_{\omega _*} & \equiv & \left(\frac{M_*}{M_P}\right)^2 \left(\frac{a}{R_*}\right)^3. \end{eqnarray} \tag{ 8 }$$

For some classes of theories of tidal dissipation and under some assumptions, ${\cal T}_a$ is proportional to the e-folding timescale for decay of the orbit, and ${\cal T}_{\omega _*}$ is proportional to the timescale for synchronization of the spin of the star with the companion orbital period. It is worthwhile to note that for transiting planet systems the combinations of parameters M_P/M_* and a/R_* are generally much better determined than the individual parameters. In particular, the ratio of the mass of the planet to that of the star is closely related to the RV semi-amplitude K, whereas a/R_* is closely related to the ratio of the duration of the transit to the period (Winn 2010). Figure 17 shows ${\cal T}_a$ and ${\cal T}_{\omega _*}$ as a function of orbital period for the sample of transiting exoplanets, BDs, and low-mass stars discussed previously. KELT-1b has shorter timescales than nearly the entire sample of systems, with the exception of a few of the low-mass stars. We therefore expect tidal effects to be quite important in this system.

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As a specific example, under the constant time lag model (Hut 1981; Matsumura et al. 2010), and assuming dissipation in the star, zero eccentricity, zero stellar obliquity, and a slowly rotating star, the characteristic timescale for orbital decay due to tides is $\tau _{{\rm decay}} \equiv a/|{\dot{a}}| = (12\pi)^{-1} Q_*^{\prime } {\cal T}_a P$, where Q'_* is related to the dimensionless tidal quality factor. For KELT-1b, ${\cal T}_a \sim 3 \times 10^{4}$, and so τ_decay ∼ 0.3 Gyr for Q'_* = 10⁸, clearly much shorter than the age of the system. Similarly, the timescale for spinning up the star by the companion is $\tau _{{\rm synch}} \equiv \omega _*/|\dot{\omega }_*| \propto Q_*^{\prime }{\cal T}_{\omega _*} P$ (Matsumura et al. 2010) and so is also expected to be short compared to the age of the system.

Given the expected short synchronization timescale and the fact that the expected timescale for tidal decay is shorter than the age of the system, it is interesting to ask whether or not the system has achieved full synchronization, thus ensuring the stability of KELT-1b. The measured projected rotation velocity of the star is  vsin I_* = 56 ± 2 km s⁻¹, which, given the inferred stellar radius, corresponds to a rotation period of P_* = 2πR_*sin I_*/ vsin I_* = [1.329 ± 0.060]sin I_* days, which differs from the orbital period of KELT-1b by ∼2σ for I_* = 90°. This is suggestive that the system is indeed synchronized. The small discrepancy could either be due to a slightly underestimated uncertainty on  vsin I_* or the host could be moderately inclined by I_* ∼ [66⁺⁸₋₅]°. However, one might expect the obliquity of the star to be realigned on roughly the same timescale as the synchronization of its spin (Matsumura et al. 2010). The stellar inclination can also be constrained by the precise shape of the transit light curve: lower inclinations imply higher rotation velocities, and thus increased oblateness and gravity brightening (Barnes 2009). Ultimately, the inclination is limited to I_* ≳ 10° in order to avoid break up.

We can also ask, given the known system parameters, if the system is theoretically expected to be able to achieve a stable synchronous state. A system is "Darwin stable" (Darwin 1879; Hut 1980) if its total angular momentum,

$$\begin{equation} L_{{\rm tot}} = L_{{\rm orb}} + L_{\omega ,*} + L_{\omega ,P}, \end{equation} \tag{ 9 }$$

is more than the critical angular momentum of

$$\begin{equation} L_{{\rm crit}} \equiv 4\left[\frac{G^2}{27}\frac{M_*^3M_P^3}{M_*+M_P}(C_*+C_P)\right]^{1/4}, \end{equation} \tag{ 10 }$$

where L_orb is the orbital angular momentum, $L_{\omega _*}$ is the spin angular momentum of the star, L_{ω, P} is the spin angular momentum of the planet, and C_* = α_*M_*R²_* and C_P = α_PM_PR²_P are the moments of inertia of the star and planet, respectively (Matsumura et al. 2010). Since C_P/C_* ∼ (M_P/M_*)(R_P/R_*)² ∼ 10⁻³, the contribution from the planet spin to the total angular momentum is negligible. We find L_tot/L_crit = 1.03 ± 0.03, consistent with the critical value for stability. In addition, we find (L_{ω, *} + L_{ω, P})/L_orb = 0.15 ± 0.01, which is smaller than the maximum value of 1/3 required for a stable equilibrium (Hut 1980). Curiously, if we assume the star is already tidally synchronized, we instead infer (L_{ω, *} + L_{ω, P})/L_orb = 0.17  ±  0.01, i.e., remarkably close to exactly one-half the critical value of 1/3.

Two additional pieces of information potentially provide clues to the evolutionary history of this system: the detection of a possible tertiary (Section 3.5; Figure 8) and the measurement of the RM effect (Figure 4), demonstrating that KELT-1 has small projected obliquity. If the nearby companion to KELT-1 is indeed bound, it could provide a way of emplacing KELT-1b in a small orbit via the Kozai–Lidov mechanism (Kozai 1962; Lidov 1962). If KELT-1b were originally formed much further from its host star, and on an orbit that was significantly misaligned with that of the putative tertiary, then its orbit might subsequently be driven to high eccentricity via secular perturbations from the tertiary (Holman et al. 1997; Lithwick & Naoz 2011; Katz et al. 2011). If it reached sufficiently high eccentricity such that tidal effects became important at periastron, the orbit would be subsequently circularized at a relatively short period (Fabrycky & Tremaine 2007; Wu et al. 2007; Socrates et al. 2012). Nominally, one might expect the orbit of KELT-1b to be then left with a relatively large obliquity (Naoz et al. 2011). The measured projected obliquity is ≲ 16 deg, implying that either the current true obliquity is small or the star is significantly inclined (i.e., I_* ∼ 0). However, if the star is significantly inclined, then the system cannot be synchronized. Perhaps a more likely alternative is that, after emplacement by the tertiary and circularization of the orbit, the system continued to evolve under tidal forces, with KELT-1b migrating inward to its current orbit while damping the obliquity of KELT-1 and synchronizing its spin period. Clearly, detailed simulations are needed to establish whether or not this scenario has any basis in physical reality.

Transiting BDs provide one of the only ways to test and calibrate models of BD structure and evolution, which are used to interpret observations of the hundreds of free floating BDs for which no direct measurement of mass and radius is possible. Given that only five transiting BDs with radius measurements were previously known, KELT-1b potentially provides another important test of these models. Figure 18 shows the mass–radius relation for the known transiting companions to main-sequence stars with companion masses in the range 10–100 M_J. Being close to the minimum in the BD desert, the mass of KELT-1b begins to fill in the dearth of know systems between ∼20 and 60 M_Jup. Furthermore, the formal uncertainty in its radius is only ∼3%, thereby allowing for a stringent test of models. In contrast, the two transiting BDs with similar masses, CoRoT-3b (Deleuil et al. 2008) and KOI-423b (Bouchy et al. 2011a), have much larger radius uncertainties, presumably due to the relative faintness of the host stars.

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Evolutionary models for isolated BDs generally predict that young (∼0.5 Gyr) objects in the mass range 10–100 M_Jup should have radii of ∼R_Jup (see the models of Baraffe et al. 2003 in Figure 18, and also models by Burrows et al. 2011). As these objects cool, however, their radii decrease, particularly for masses between 50 and 80  M_Jup. After ∼1 Gyr, all isolated objects with mass between 20 and 80 M_Jup are predicted to have radii <R_Jup. The radius we measure for KELT-1b is R_P = 1.116^+0.038_−0.029 R_Jup, which, at a mass of M_P = 27.38 ± 0.93  M_J, is ∼6σ and ∼8σ larger than the radius predicted by Baraffe et al. (2003) for ages of 1 Gyr and 5 Gyr, respectively. KELT-1b is strongly irradiated, which in principle can delay its cooling and contraction. However, Bouchy et al. (2011b) predict that the effect of insolation is small for BDs in this mass range, although their models were for a much more modest insolation corresponding to an equilibrium temperature of 1800 K (versus ∼2400 K for KELT-1b). Therefore, given the estimated 1.5–2 Gyr age of the system, KELT-1b is likely to be significantly inflated relative to predictions.

Using the benchmark double transiting BD 2M0535−05, Gómez Maqueo Chew et al. (2009) explore models in which brown dwarfs have large spots, which reduce the flux from their surface, thereby decreasing their effective temperatures and increasing their radii relative to those without spots (see also Bouchy et al. 2011b). They find that these can lead to significantly inflated radii, but only for large spot filling factors of ∼50% and for relatively young (∼0.5 Gyr) systems. However, a detailed spectroscopic analysis of that system by Mohanty et al. (2010) and Mohanty & Stassun (2012) shows that surface spots cannot be present with such a large filling factor, and thus favor global structural effects such as strong internal magnetic fields (e.g., Mullan & MacDonald 2010). Many other mechanisms have been invoked to explain the inflated radii of some giant exoplanets (see Fortney & Nettelmann 2010 for a review); however, it is not clear which, if any, of the many mechanisms that have proposed may also be applied to inflated brown dwarfs.

We would be remiss if we did not question whether we were erroneously inferring a large radius for the planet. In the past, such situations have arisen when there is a discrepancy between the constraint on the stellar density from the light curve and the constraint on the stellar surface gravity of the star from spectroscopy (e.g., Johns-Krull et al. 2008; Winn et al. 2008). In our case, we find no such tension. The parameters of the star inferred from the spectroscopic data alone are in nearly perfect agreement with the results from the global analysis of the light curve, RV data, and spectroscopic constraints. We note that the effect of allowing a non-zero eccentricity also has a negligible effect on the inferred planetary radius. Finally, we reiterate that the faint companion detected in AO imaging (Section 3.5), which is unresolved in our follow-up photometry, has a negligible effect on our global fit and inferred parameters. Therefore, we believe our estimate of R_P is likely robust.

We conclude by noting that there is a need for predictions of the radii of brown dwarfs for a range of ages and stellar insolations, and it would be worthwhile to explore whether or not the inflation mechanisms that have been invented to explain anomalously large giant planets might work for much more massive and dense objects as well.

Figure 19 compares the transit depth and apparent visual magnitude of the KELT-1 system (δ ∼ 0.6%, V = 10.7) to the sample of transiting systems collected in Section 6.1.1 with available V magnitudes. KELT-1 is not particularly bright compared to the bulk of the known transiting exoplanet hosts. However, it is significantly brighter than the hosts of all known transiting brown dwarfs; the next brightest is WASP-30 (Anderson et al. 2011), which is ∼1.2 mag fainter. On the other hand, the depth of the KELT-1b transit is similar to that of the other known brown dwarfs.

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The prospects for follow-up of KELT-1b are exciting, not only because of the brightness of the host, but also because of the extreme nature of the system parameters, in particular the relatively short orbital period, relatively large stellar radius, and relatively large amount of stellar irradiation received by the planet. Following Mazeh & Faigler (2010) and Faigler & Mazeh (2011), we can estimate the amplitudes of ellipsoidal variations A_ellip, Doppler beaming A_beam (see also Loeb & Gaudi 2003), reflected light eclipses and phase variations A_ref, and thermal light eclipses and phase variations A_therm:

$$\begin{eqnarray} A_{{\rm beam}} &=& \alpha _{{\rm beam}}4\left(\frac{K}{c}\right) \sim 5.7\alpha _{{\rm beam}}\times 10^{-5} \end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray} A_{{\rm ref}} &=& \alpha _{{\rm ref}} \left(\frac{R_P}{a}\right)^2\sim 4.7\alpha _{{\rm ref}}\times 10^{-4} \end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray} A_{{\rm ellip}} &=& \alpha _{{\rm ellip}}\frac{M_P}{M_*} \left(\frac{R_*}{a}\right)^3 \sim 4.1\alpha _{{\rm ellip}}\times 10^{-4} \end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray} A_{{\rm therm}} &=& \alpha _{{\rm therm}} \left(\frac{R_P}{R_*}\right)^2 \left(\frac{R_*}{a}\right)^{1/2} \sim 3.2 \alpha _{{\rm therm}}\times 10^{-3},\quad \end{eqnarray} \tag{ 14 }$$

where the expression for A_therm assumes observations in the Rayleigh–Jeans tail of both objects, and the expression for A_ellip assumes an edge-on orbit. The dimensionless constants α are defined in Mazeh & Faigler (2010), but to make contact with the secondary eclipse analysis in Section 5.4 we note that α_ref = A_g and α_therm = [f'(1 − A_B)]^1/4. All of these constants are expected to be of the order of unity, except for α_ref, which may be quite low for strongly irradiated planets, depending on wavelength (Burrows et al. 2008). Based on previous results, all of these effects with the possible exception of Doppler beaming are likely to be detectable with precision photometry (see, e.g., Cowan et al. 2012). For ellipsoidal variations in particular, we expect α_ellip ∼ 2 and thus a relatively large amplitude of A_ellip ∼ 10⁻³. Furthermore, the detection of all these signals is facilitated by the short orbital period for KELT-1b.

The prospects for transmission spectroscopy are probably poorer, given the relatively small planet/star radius ratio (∼0.078) and more importantly the large surface gravity for KELT-1b. For the optimistic case of T_eq ≃ 2400 K assuming zero albedo and perfect redistribution, the scale height is only H ∼ kT/(μm_Hg_P) ∼ 16km, and thus will only lead to changes in the transit depth of order ∼2H/R_P ∼ 0.04%.