KELT-6b: A P ∼ 7.9 DAY HOT SATURN TRANSITING A METAL-POOR STAR WITH A LONG-PERIOD COMPANION^*

KELT-6 is in KELT-North survey field 08, which is centered on ($\alpha =13^{{\rm h}}38^{{\rm m}}28\buildrel{\mathrm{s}}\over{.}25$, δ = +31°41'1267; J2000). We monitored field 08 from 2006 December to 2011 June, collecting a total of 7359 observations. We reduced the raw survey data using a custom implementation of the ISIS image subtraction package (Alard & Lupton 1998; Alard 2000), combined with point-spread fitting photometry using DAOPHOT (Stetson 1987). Using proper motions from the Tycho-2 catalog (Høg et al. 2000) and J and H magnitudes from Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006; Cutri et al. 2003), we implemented a reduced proper motion cut (Gould & Morgan 2003) based on the specific implementation of Collier Cameron et al. (2007b), in order to select likely dwarf and subgiant stars within the field for further post-processing and analysis. We applied the trend filtering algorithm (TFA; Kovács et al. 2005) to each remaining light curve to remove systematic noise, followed by a search for transit signals using the box-fitting least squares (BLS) algorithm (Kovács et al. 2002). For both TFA and BLS we used the versions found in the VARTOOLS package (Hartman et al. 2008).

One of the candidates from field 08 was star BD+31 2447/TYC 2532-556-1, located at ($\alpha =13^{{\rm h}}03^{{\rm m}}55\buildrel{\mathrm{s}}\over{.}65$, δ = +30°38'243; J2000). The star has Tycho magnitudes B_T = 10.736 ± 0.048 and V_T = 10.294 ± 0.050 (Høg et al. 2000), and passed our initial selection cuts. The discovery light curve of KELT-6 is shown in Figure 1. We observed a transit-like feature at a period of 7.8457 days, with a depth of about 5 mmag.

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After KELT-6 was selected as a candidate, we conducted RV observations to identify possible false-positive signatures and to determine the RV orbit. We obtained data using the Tillinghast Reflector Echelle Spectrograph²⁸ (TRES; Fűrész 2008), on the 1.5 m Tillinghast Reflector at the Fred L. Whipple Observatory (FLWO) at Mt. Hopkins, Arizona. We observed KELT-6 three times with TRES over three months, from UT 2012 April 12 to UT 2012 July 9. The spectra have a resolving power of R = 44,000, and were extracted following the procedures described by Buchhave et al. (2010). These three initial TRES single-order absolute RVs are listed in Table 1 and are consistent with no RV variations to within the errors, ruling out some classes of astrophysical false positives. However, the TRES RV uncertainties are large enough to still allow for a low-mass companion at the ∼7.8 day period of the KELT-North candidate signal, and on that basis we chose to continue with photometric follow-up. Note that due to the relatively large uncertainties, we chose not to include these TRES velocities in the final global analysis described in Section 4.

On UT 2012 June 26, we obtained high precision KELT-6 follow-up photometry of the final third of a predicted transit and detected an apparent shallow egress (see Section 2.3). Based on that detection and the lack of RV variations in the TRES data, we decided to pursue higher precision RV data.

Using the High Resolution Echelle Spectrometer (HIRES) instrument (Vogt et al. 1994) on the Keck I telescope located on Mauna Kea, Hawaii, we obtained 16 exposures between UT 2012 August 24 and UT 2013 February 21 with an iodine cell, plus a single iodine-free template spectrum. The absolute and precise relative RV measurements are listed in Table 1, and Figure 2 shows the HIRES relative RV data phased to the orbit fit with a linear trend of $\dot{\gamma }=-0.239$ m s⁻¹ day⁻¹ (see Section 4) removed, along with the residuals to the model fit.

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The HIRES RV observations were made using the standard setup of the California Planet Search program (Johnson et al. 2010; Howard et al. 2011). A pyrex cell containing gaseous iodine is placed in front of the spectrometer entrance slit, which imprints a dense set of molecular iodine lines on each stellar spectrum. The iodine lines provide a calibration of the instrumental profile as well as a precise measure of the wavelength scale at the time of observation (Marcy & Butler 1992). We measured the relative stellar RVs using the forward-modeling scheme of Butler et al. (1996) with improvements made over the years. We measured the absolute RVs using the methods of Chubak et al. (2012).

The point-spread function (PSF) varies quite dramatically in the slit-fed HIRES instrument simply from guiding and spectrometer focus variations. Since line asymmetries due to instrumental and stellar sources cannot be easily distinguished, we do not attempt to measure bisector spans for the HIRES observations.

We also obtained five RV measurements between UT 2013 February 1 and UT 2013 February 15 using the Hobby–Eberly Telescope. However, these data were taken without an iodine cell for wavelength reference, and as a result the uncertainties are >6 km s⁻¹, so we do not list them in the RV table or use them in the global fit analysis in Section 4.

Finally, 21 additional TRES RVs were obtained and reduced using multi-order analysis after most of the global analysis had been completed. The full TRES RV data set is listed in Table 1 and contains measurements from 24 different nights between UT 2012 April 12 and UT 2013 July 31, with typical relative uncertainties of 20 m s⁻¹. Although we do not use the TRES RV data in our global fit analysis (see Section 4.2), we note that these data independently confirm both the amplitude of the KELT-6b RV variations (see Figure 2) and the linear trend of the fiducial global fit (see Section 5), albeit with larger uncertainties due to the somewhat worse precision than the Keck data. Bisector spans were calculated from the TRES spectra following Torres et al. (2007) and are used in Section 6 as part of the false-positive analysis. The bisector spans are listed in Table 1, and shown in the bottom panel of Figure 2 phased to the orbital fit.

We acquired follow-up time-series photometry of KELT-6 to check for other types of false positives and to better determine the transit shape. To schedule follow-up photometry, we used the Tapir software package (Jensen 2013). We obtained 16 partial or full primary transits in multiple bands between 2012 June and 2013 June. The transit duration (>5.5 hr) and orbital period (>7.8 days) are long, so opportunities to observe full transits are rare. Figure 3 shows all the primary transit follow-up light curves assembled. A summary of the follow-up photometric observations is shown in Table 2. The transit times are shown in Table 3. We find consistent R_P/R_⋆ ratios in all light curves, which include observations in the g, r, i, z, V, I, and CBB filters,²⁹ helping to rule out false positives due to blended eclipsing binaries. Figure 4 shows all primary transit follow-up light curves from Figure 3 (except the Westminster College Observatory (WCO) light curve which contains significant residual systematics after detrending), combined and binned in 5 minute intervals. This combined and binned light curve is not used for analysis, but rather to show the best combined behavior of the transit. We also observed KELT-6 near the uncertain time of secondary transit on five different epochs (see Section 6).

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Table 3. KELT-6 Transit Times

Epoch	TC	$\sigma _{T_{\rm C}}$	O − C	O − C	Observatory/
	BJDTDB	(s)	(s)	$\sigma _{T_{\rm C}}$	Telescope
−31	2456104.581654	190	−45.17	−0.24	MORC
−8	2456285.030078	104	−145.43	−1.40	MORC
−6	2456300.723507	115	46.31	0.40	PvdKO
−1	2456339.949428	151	−151.18	−1.00	SPOT
0	2456347.797243	118	39.38	0.33	MOCDK
0	2456347.796609	79	−15.31	−0.19	MORC
0	2456347.797368	104	50.44	0.48	SPOT
0	2456347.795916	120	−77.26	−0.64	KEPCAM
0	2456347.795513	213	−112.42	−0.53	CROW
1	2456355.649675	179	625.66	3.48	MORC
1	2456355.648134	220	493.04	2.24	MBA
7	2456402.718026	82	155.28	1.89	MORC
7	2456402.715318	151	−77.39	−0.51	SPOT
8	2456410.554740	381	−618.29	−1.62	CROW
8	2456410.550639	298	−898.14	−3.01	WCO
13	2456449.788514	95	−128.47	−1.35	KEPCAM

Notes. The observatory/telescope abbreviations are the same as in Table 2.

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Unless otherwise noted, all photometric follow-up observations were reduced with the AstroImageJ (AIJ) package³⁰ (K. A. Collins & J. F. Kielkopf 2014, in preparation). AIJ is a general purpose image processing package, but is optimized for processing time-series astronomical image sequences. It is open source software written in Java and is compatible with all computing platforms commonly used to process astronomical data. AIJ is a graphical user interface driven package that provides an interactive multi-image display interface, CCD image calibration (bias, dark, flat-field, and nonlinearity correction), astronomical time and coordinate calculations, multi-aperture differential photometry, multi-data set plotting, and interactive light curve detrending. It can be operated in combination with any camera control software to reduce data and plot differential light curves in real time, or can be used in standard mode to post process data.

Also unless otherwise noted, calibration of all photometric follow-up observations included bias and dark subtraction followed by flat-field correction. Calibration of the MORC data also included a correction for CCD nonlinearity. Differential photometry was performed on the calibrated images using a circular aperture.

We observed three complete and three partial transits of KELT-6 using two telescopes at Moore Observatory, operated by the University of Louisville. The 0.6 m RCOS Telescope with an Apogee U16M 4K × 4K CCD, giving a 26' × 26' field of view and 0.39 arcsec pixel⁻¹, was used to observe the r egress on UT 2012 June 26, the r ingress on UT 2012 December 23, the full r transit on UT 2013 February 24, the z egress on UT 2013 March 4, and the full r transit on UT 2013 April 20. The 0.6 m was also used to observe near the time of secondary transit on UT 2013 April 16 in z. The Planewave Instruments 0.5 m CDK telescope with an Apogee U16M 4K × 4K CCD, giving a 37' × 37' field of view and 0.54 arcsec pixel⁻¹, was used to observe most of a transit in g on UT 2013 February 24. The gap in the data is due to a meridian flip.

We observed an egress in g at Swarthmore College's Peter van de Kamp Observatory on UT 2013 January 8. The observatory uses a 0.6 m RCOS Telescope with an Apogee U16M 4K × 4K CCD, giving a 26' × 26' field of view. Using 2 × 2 binning, it has 0.76 arcsec pixel⁻¹.

We observed one partial and two full transits at Spot Observatory. The observatory uses a 0.6 m RCOS Telescope with an SBIG STX 16803 4K × 4K CCD, giving a 26' × 26' field of view and 0.39 arcsec pixel⁻¹. An ingress in i was observed on UT 2013 February 16, and full transits were observed on UT 2013 February 24 in i and UT 2013 April 20 in z. We also observed near the time of secondary transit on UT 2013 February 20 in z.

We observed an egress in z on UT 2013 February 24 and an ingress in i on UT 2013 June 6 with KeplerCam on the 1.2 m telescope at FLWO. KeplerCam has a single 4K × 4K Fairchild CCD with 0.366 arcsec pixel⁻¹, and a field of view of 231 × 231. We also observed near the time of secondary transit on UT 2013 February 28, UT 2013 April 8, and UT 2013 April 24 in z.

We observed one full and one partial transit at Montgomery Bell Academy (MBA) Long Mountain Observatory. The observatory uses a PlaneWave Instruments 0.6 m CDK telescope with an SBIG STL 11002 4008 × 2672 CCD, giving a 30' × 20' field of view and 0.45 arcsec pixel⁻¹. A full transit was observed in V on UT 2013 February 24. However, the resulting light curve had large systematics that we were unable to adequately remove. Since the same transit epoch was observed by both Moore Observatory telescopes in overlapping filter bands, these data added no new information to the analysis and were not included in the global fit described in Section 4. An egress in I was observed on UT 2013 March 4, and observations near the time of secondary transit were collected in z on UT 2013 February 20.

We observed two partial transits at Canela's Robotic Observatory (CROW) in Portugal. The observations were obtained using a 0.3 m LX200 telescope with an SBIG ST-8XME 1530 × 1020 CCD, giving a 28' × 19' field of view and 1.11 arcsec pixel⁻¹. An ingress was observed in I_c on UT 2013 February 24, and an ingress was observed in V on UT 2013 April 28.

We observed a partial transit at WCO in Pennsylvania. The observations were obtained using a Celestron 0.35 m C14 telescope with an SBIG STL-6303E 3072 × 2048 CCD, giving a 24' × 16' field of view and 1.4 arcsec pixel⁻¹ at 3 × 3 pixel binning. An egress was observed using an Astrodon Clear with Blue Blocking (CBB) filter on UT 2013 April 28.

We observed near the time of secondary transit on UT 2013 April 8 and UT 2013 April 24 using the 1.0 m telescope at the ELP node of the Las Cumbres Observatory Global Telescope (LCOGT) network at McDonald observatory in Texas (Brown et al. 2013). The observations were obtained in the Pan-STARRS-Z band with an SBIG STX-16803 4096 × 4096 CCD, giving a 158 × 158 field of view and 0.464 arcsec pixel⁻¹ (2 × 2 binning). The ELP data were processed using the pipeline discussed in Brown et al. (2013).

We obtained adaptive optics (AO) imaging using NIRC2 (instrument PI: Keith Matthews) at Keck on UT 2012 December 7. The AO imaging places limits on the existence of nearby eclipsing binaries that could be blended with the primary star KELT-6 at the resolution of the KELT and follow-up data, thereby causing a false-positive planet detection. In addition, it places limits on any nearby blended source that could contribute to the total flux, and thereby result in an underestimate of the transit depth and thus planet radius in the global fit presented in Section 4. Our observations consist of dithered frames taken with the K' filter. We used the narrow camera setting to provide fine spatial sampling of the stellar PSF, and used KELT-6 as its own on-axis natural guide star. The total on-source integration time was 225 s. The resulting image is shown in Figure 5.

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We find no significant detection of off-axis sources in the immediate vicinity of KELT-6. We note that there are some conspicuous sources at the threshold of detection. However, without an image in a different filter, we are unable to determine if the positions of these sources are wavelength dependent, which would indicate that they are speckles rather than real sources. Nevertheless, we can still place a conservative upper limit on any real sources based on the contrast sensitivity. Figure 6 shows the 10σ contrast sensitivity (in Δmagnitude) versus angular separation computed from Figure 5 using a three-point dither pattern to build signal and subtract sky background (see Crepp et al. 2012). The top scale in Figure 6 shows projected separation in AU for a distance of 222 pc (see Section 3.4). The scale on the right side of the plot estimates the mass in units of M_☉ at a given contrast, estimated using the Baraffe et al. (1998) models. We can exclude companions beyond a distance of 0.5 arcsec (111 AU) from KELT-6 down to a magnitude difference of 6.0 mag at 10σ.

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Table 4 lists various properties and measurements of KELT-6 collected from the literature and derived in this work. The data from the literature include FUV and NUV fluxes from Galaxy Evolution Explorer (GALEX; Martin et al. 2005), B − V color from Harris & Upgren (1964), optical fluxes in the B_T and V_T passbands from the Tycho-2 catalog (Høg et al. 2000), V and I_C from The Amateur Sky Survey (TASS; Richmond et al. 2000), near-infrared (NIR) fluxes in the J, H, and K_S passbands from the 2MASS Point Source Catalog (Skrutskie et al. 2006; Cutri et al. 2003), near- and mid-infrared fluxes in three Wide-field Infrared Survey Explorer (WISE) passbands (Wright et al. 2010; Cutri et al. 2012), and proper motions from the NOMAD catalog (Zacharias et al. 2004).

We use both the TRES and HIRES spectra to derive the stellar properties of KELT-6. To analyze the TRES spectra, we use the Spectral Parameter Classification (SPC) procedure version 2.2 (Buchhave et al. 2012) with T_eff, log g_⋆, [m/H], and vsin i_⋆ as free parameters. Since each of the 24 TRES spectra yielded similar results, we took the mean value for each stellar parameter. The uncertainties are dominated by systematic rather than statistical errors, so we adopt the mean error for each parameter. The results are: T_eff = 6098 ± 50 K, log g_⋆ = 3.83 ± 0.10, [m/H] = −0.34 ± 0.08, and vsin i_⋆ = 6.7 ± 0.5 km s⁻¹, giving the star an inferred spectral type of F8.

To analyze the HIRES spectra, we use spectral synthesis modeling with Spectroscopy Made Easy (SME; Valenti & Piskunov 1996; Valenti & Fischer 2005). The free parameters for the model included T_eff, vsin i_⋆, log g_⋆, and [Fe/H]. The microturbulent velocity was fixed to 0.85 km s⁻¹ in this model and the macroturbulent velocity was specified as a function of effective temperature (Valenti & Fischer 2005). After the first model was generated, two other iterations were run with temperature offsets of ±100 K from the model temperature to evaluate degeneracy between the model parameters. If the rms for these new fit parameters relative to the original model values exceeds the uncertainties on the original model values estimated using the error analysis of Valenti & Fischer (2005), then these larger uncertainties are adopted. However, in this case, the fits starting with the temperature offsets settled on values very close to those found using the original model, differing by much less than the estimated uncertainties on the original model values. Therefore, we adopted these original uncertainties, which include systematic error sources as described in Valenti & Fischer (2005). Based on this analysis, KELT-6 appears to be a main sequence or very slightly evolved subgiant with T_eff = 6100 ± 44 K, log g_⋆ = 3.961 ± 0.060, and sub-solar metallicity, [Fe/H] = −0.277. The star has a projected rotational velocity vsin i_⋆ = 5.0 ± 0.5 km s⁻¹.

Comparing the parameter values determined from the TRES spectra using SPC version 2.2 to those determined from the HIRES spectra using SME, we generally find agreement to ∼1σ or better, except for vsin i_⋆, which differs by ∼3σ. We do not have a good explanation for the vsin i_⋆ discrepancy. However, we do not use vsin i_⋆ in our global fits, so this discrepancy is unimportant for the present analysis. The individual TRES spectra have a signal-to-noise ratio (S/N) of ∼40 while the HIRES spectrum used to derive the stellar parameters has a S/N of ∼180. We therefore adopt the higher S/N HIRES stellar parameters for the analyses in this paper, although we note that the uncertainties in both determinations are likely to be dominated by systematic errors.

We evaluate the motion of KELT-6 through the Galaxy to place it among standard stellar populations. We adopt an absolute RV of +1.1 ± 0.2 km s⁻¹, based on the mean of the TRES and HIRES absolute RVs listed in Table 1, where the uncertainty is due to the systematic uncertainties in the absolute velocities of the RV standard stars. Combining the adopted absolute RV with distance estimated from fitting the spectral energy distribution (SED, Section 3.4) and proper motion information from the NOMAD catalog (Zacharias et al. 2004), we find that KELT-6 has U, V, W space motion (where positive U is in the direction of the Galactic Center) of −6.3 ± 0.9, 23.2 ± 0.8, 6.9 ± 0.2, all in units of km s⁻¹, making it unambiguously a thin disk star.

We construct an empirical, broadband SED of KELT-6, shown in Figure 7. We use the FUV and NUV fluxes from GALEX (Martin et al. 2005), the B_T and V_T colors from the Tycho-2 catalog (Høg et al. 2000), V and I_C from TASS (Richmond et al. 2000), NIR fluxes in the J, H, and K_S passbands from the 2MASS Point Source Catalog (Cutri et al. 2003; Skrutskie et al. 2006), and the near- and mid-infrared fluxes in three WISE passbands (Wright et al. 2010). 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 fiducial model fit to the light curve, RV, and spectroscopic data as described in Section 4, and then finding the values of the visual extinction A_V and distance d that minimize χ². The best-fit model has a reduced χ² of 1.61 for 10 degrees of freedom. We find A_V = 0.01 ± 0.02 and d = 222 ± 8 pc. 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.

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Because KELT-6b's transits have an unusually long duration and relatively shallow depth (by ground-based observing standards), treatment of light curve systematics plays an important role in the accuracy of parameters determined by the EXOFAST global fit. The inclusion of detrending parameters into the global fit can often mitigate the effect of light curve systematics, but sometimes at the expense of introducing extra local minima in χ² space, which may cause other complications in the analysis. Therefore, it is important to maximize the detrending improvements to the fit of each light curve while minimizing the number of detrending parameters.

Systematically fitting each light curve using all combinations of ∼15 possible detrending parameters and comparing all of the resulting χ² values using the Δχ² statistic would be prohibitive. Instead, we opted to use the interactive detrending capabilities of the AIJ package (see Section 2.3) to search for up to three parameters that appeared to reduce the systematics in each light curve. We then individually fit each of the full transit light curves using EXOFAST, and repeated the fit using various combinations of the detrending parameters selected for that light curve. Finally, we compared χ² from before and after the inclusion of an additional detrending parameter to determine if the probability of a chance improvement was more than a few percent. If so, we did not include the additional detrending parameter in the global fit.

It is important to emphasize that the light curves fitted in EXOFAST were the raw light curves (i.e., not the detrended light curves from AIJ). The only way in which the results of the AIJ analysis entered into the final analysis was in the choice of detrending parameters and the initial conditions adopted. Specifically, the detrend parameter coefficients determined in AIJ were used as starting points for the EXOFAST fits. However these parameter coefficients were otherwise allowed to vary freely in order to minimize χ².

One detrending parameter we included that warrants additional discussion is an offset in the zero point of the photometry arising from a change in placement of the target and/or comparison star(s) on the CCD pixel array during time-series observations. These positional changes typically result in a zero point shift in the photometry at that epoch in the light curve due to interpixel response differences and imperfect flat-field corrections. We found such positional changes due to a meridian flip in the MOCDK light curve on UT 2013 February 24, as well as an equipment failure in the SPOT UT 2013 February 24 light curve (see Table 2 and Figure 3). We therefore included a detrending parameter that accounts for a change in the zero point of the relative photometry before and after the specified time.

In addition, fits to individual partial light curves often resulted in obviously incorrect models. We therefore chose detrending parameters for such ingress- or egress-only data by hand using AIJ without a rigorous Δχ² analysis.

Light curves from near the time of predicted secondary eclipse were treated somewhat differently. In particular, these were airmass detrended directly in AIJ, and when abrupt changes in the light curve were correlated with a change in position of the target star on the detector, x and y pixel positions of the target star centroid were also used as detrending parameters.

The final detrending parameters adopted for all of the light curves are shown in Table 2.

Using the KELT-6b primary transit light curves, the detrending parameters and priors determined in the previous section, and the results from the HIRES RV and spectroscopic analyses, we computed a series of 12 global fits using our custom version of EXOFAST. The results of six illustrative global fits are shown in Table 5. The table lists four global fit parameter choices (as detailed in the remainder of this subsection) for each of the six fits, along with the values of several key system parameters computed as part of each fit.

Table 5. Median Values and 68% Confidence Intervals for Selected Physical and Orbital Parameters of the KELT-6 System from Six Global Fits Described in Section 4.2

Parameter	Units	Fit 1 (Adopted)	Fit 2	Fit 3	Fit 4	Fit 5	Fit 6
Global fit parameters
Number of transits	5 or 16	5	5	5	5	5	16
M⋆ and R⋆ constraint	Torres or Yonsei–Yale	Yonsei–Yale	Yonsei–Yale	Yonsei–Yale	Yonsei–Yale	Torres	Yonsei–Yale
Orbital constraint	Circular or eccentric	Eccentric	Circular	Circular	Eccentric	Eccentric	Eccentric
log g⋆ Prior	Prior or no prior	No prior	Prior	No prior	Prior	No prior	No prior
Stellar parameters
Teff	Effective temp (K)	6102 ± 43	6101 ± 43	6103 ± 43	6102 ± 44	6105 ± 44	6109 ± 44
[Fe/H]	Metallicity	$-0.281_{-0.038}^{+0.039}$	$-0.285_{-0.038}^{+0.040}$	$-0.282_{-0.037}^{+0.039}$	$-0.284_{-0.039}^{+0.040}$	$-0.280_{-0.039}^{+0.039}$	$-0.284_{-0.038}^{+0.039}$
log g⋆	Surface gravity (cgs)	$4.074_{-0.070}^{+0.045}$	$4.057_{-0.037}^{+0.036}$	$4.083_{-0.042}^{+0.022}$	$4.012_{-0.054}^{+0.049}$	$4.085_{-0.073}^{+0.046}$	$4.064_{-0.068}^{+0.049}$
M⋆	Mass (M☉)	$1.085_{-0.040}^{+0.043}$	$1.086_{-0.036}^{+0.033}$	$1.081_{-0.034}^{+0.032}$	$1.110_{-0.041}^{+0.041}$	$1.199_{-0.060}^{+0.066}$	$1.090_{-0.040}^{+0.042}$
R⋆	Radius (R☉)	$1.580_{-0.094}^{+0.160}$	$1.615_{-0.078}^{+0.086}$	$1.562_{-0.046}^{+0.091}$	$1.720_{-0.110}^{+0.140}$	$1.640_{-0.100}^{+0.170}$	$1.600_{-0.100}^{+0.160}$
Planetary parameters
MP	Mass (MJ)	$0.430_{-0.046}^{+0.045}$	$0.438_{-0.037}^{+0.038}$	$0.436_{-0.037}^{+0.037}$	$0.446_{-0.043}^{+0.044}$	$0.461_{-0.048}^{+0.049}$	$0.431_{-0.046}^{+0.046}$
RP	Radius (RJ)	$1.193_{-0.077}^{+0.130}$	$1.228_{-0.070}^{+0.080}$	$1.178_{-0.043}^{+0.083}$	$1.304_{-0.093}^{+0.110}$	$1.240_{-0.085}^{+0.140}$	$1.206_{-0.085}^{+0.120}$
log gP	Surface gravity	$2.868_{-0.081}^{+0.063}$	$2.855_{-0.061}^{+0.057}$	$2.885_{-0.061}^{+0.049}$	$2.810_{-0.068}^{+0.065}$	$2.865_{-0.083}^{+0.064}$	$2.862_{-0.080}^{+0.064}$
e	Eccentricity	$0.22_{-0.10}^{+0.12}$	−	−	$0.27_{-0.12}^{+0.11}$	$0.22_{-0.10}^{+0.12}$	$0.22_{-0.10}^{+0.12}$
a	Semimajor axis (AU)	$0.079_{-0.00099}^{+0.00100}$	$0.079_{-0.00087}^{+0.00080}$	$0.079_{-0.00085}^{+0.00078}$	$0.080_{-0.00099}^{+0.00098}$	$0.082_{-0.00140}^{+0.00150}$	$0.080_{-0.001}^{+0.001}$
Teq	Equilibrium temp (K)	$1313_{-38}^{+59}$	$1327_{-30}^{+33}$	$1307_{-20}^{+34}$	$1364_{-43}^{+48}$	$1317_{-38}^{+61}$	$1323_{-41}^{+58}$

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All global fits included a prior on orbital period P = 7.8457 ± 0.0002 days from the KELT-North data and priors on host-star effective temperature T_eff = 6100 ± 44 K and metallicity [Fe/H] = −0.277 ± 0.04 from the HIRES spectroscopy. The priors were implemented as a χ² penalty in EXOFAST (see Eastman et al. 2013 for details). For some of the global fits we also included a prior on stellar surface gravity log g_⋆ = 3.961 ± 0.060 from the HIRES spectroscopy. For the others, log g_⋆ was constrained only by the transit data through the well-known direct constraint on ρ_⋆ from the light curve and RV data, combined with a constraint on the stellar mass–radius relation through either the Torres relations or the Yonsei–Yale evolutionary models. Fitting the HIRES RV data independently to a Keplerian model, we found an acceleration ("RV slope") of −0.239 m s⁻¹ day⁻¹, which is highly significant at the ∼7σ level. Therefore, we proceeded with RV slope as a free parameter for all global fits.

In addition to the slope, there were four additional choices that had to be considered when performing the global fit. First, we needed to decide which transits to include in the global fit. We defined two alternative sets of light curve data to consider: (1) the 5 "full" transits with both an ingress and egress and (2) all 16 full and partial transits. Second, as mentioned previously, we had the option to either include a prior on stellar surface gravity log g_⋆ = 3.961 ± 0.060 based on the HIRES spectroscopy, or to fit for stellar surface gravity without a prior. Third, we had the option to fit the orbital eccentricity and argument of periastron as free parameters or fix them to zero to force a circular orbit. Fourth, we had the option to break the degeneracy between M_⋆ and R_⋆ by imposing external constraints either from the relations of Torres et al. (2010; Torres constraints) or by imposing constraints from the Yonsei–Yale stellar models (Demarque et al. 2004; Yonsei–Yale constraints).

We first computed the four combinations of global fits using the five full transits with the Torres constraints. The four global fits are defined by the different combinations of eccentric versus circular orbits, and log g_⋆ with a spectroscopic prior versus log g_⋆ free. The column labeled "Fit 5" in Table 5 shows the results for the Torres constrained, eccentric global fit, with no log g_⋆ prior. As discussed in Section 7.1, we plotted Yonsei–Yale stellar evolution tracks corresponding to the stellar mass and metallicity results from these global fits and found that the intersection of log g_⋆ and T_eff values from EXOFAST did not fall within 1σ of the evolutionary tracks. We then computed the four combinations of global fits using the five full transits with the Yonsei–Yale constraints and found that for these fits the resulting log g_⋆ and T_eff values were consistent with the corresponding Yonsei–Yale stellar evolution tracks within 1σ error. Parameter values from these four fits are listed in the columns of Table 5 labeled "Fit 1," "Fit 2," "Fit 3," and "Fit 4." The Torres constrained planet mass and radius are larger than the Yonsei–Yale constrained mass and radius by ∼4}–7%, and although we cannot determine if the Torres relations or the Yonsei–Yale models best represent low metallicity systems, we prefer the Yonsei–Yale constrained global fits for self-consistency with the stellar evolution tracks in Section 7.1.

We next considered the 16 full and partial transit global fits. We computed only the four combinations corresponding to the adopted Yonsei–Yale constrained global fits. Although we computed very long Markov chains with 10⁶ links, three of the four global fits resulted in some parameters (mostly detrending parameters corresponding to partial light curves) that did not fully converge. Converged parameters have greater than 1000 independent draws and a Gelman–Rubin statistic less than 1.01 (see Eastman et al. 2013 and Ford 2006). The column labeled "Fit 6" in Table 5 lists the results for the Yonsei–Yale constrained, eccentric global fit, with no log g_⋆ prior. The system parameters resulting from the 16 transit global fits are nearly identical to the parameters from the 5 transit global fits. This is to be expected since detrended partial light curves will not add significant constraints to transit depth and shape when jointly fit with full transits. Given the partial transit minor convergence issues, concerns about the ability to properly remove systematics from these light curves, and the lack of significant additional constraints on transit depth and shape from the partial transits, we adopted the global fits based on the five full transits. We did however use the 16 transit global fits for the transit timing analysis in Section 4.3.

Next we examined the adopted Yonsei–Yale constrained global fits that use only the five full transits. These four global fits are defined by the different combinations of eccentric versus circular orbits, and log g_⋆ prior versus log g_⋆ free. Since it is typically difficult to measure log g_⋆ to the same precision spectroscopically that can be measured from a transit, we choose not to impose a prior on log g_⋆ from the HIRES spectroscopy. However, we are wary of measurements of log g_⋆ from the transits in this case, since the duration is very long for a ground-based transit observation. Comparing parameter values in column "Fit 4" of Table 5 with column "Fit 1," and comparing column "Fit 2" with column "Fit 3," we found that imposing a spectroscopic prior on log g_⋆ increased the stellar and planetary radii by ∼3% in the circular case and by ∼7% in the eccentric case. However, all of the system parameters are within ∼1σ of the results from the global fits without a prior on log g_⋆.

Since we had no strong prior expectation of tidal circularization of KELT-6b's relatively long ∼8 day orbit, we adopted the more conservative eccentric orbit global fits which have higher parameter errors. The eccentricity resulting from a fit without a spectroscopic prior on log g_⋆ is $e=0.22_{-0.10}^{+0.12}$. The eccentricity resulting from a fit with the HIRES spectroscopic prior on log g_⋆ is $e=0.27_{-0.12}^{+0.11}$. As pointed out by Lucy & Sweeney (1971), there is a bias for inferred values of eccentricity with low significance, due to the fact that e is a positive definite quantity. Although we adopt an eccentric orbit global fit, we cannot exclude the hypothesis that the orbit of KELT-6b is, in fact, circular.

Our final adopted fiducial stellar and planetary parameters were derived from the five full transit, Yonsei–Yale constrained, eccentric orbit global fit with no prior on log g_⋆. Table 6 lists the full set of system parameters for the fiducial fit.

Table 6. Adopted Median Values and 68% Confidence Intervals for the Physical and Orbital Parameters of the KELT-6 System from the Fiducial Global Fit Described in Section 4.2

Parameter	Units	Value (Adopted)
Stellar parameters
M⋆	Mass (M☉)	$1.085_{-0.040}^{+0.043}$
R⋆	Radius (R☉)	$1.580_{-0.094}^{+0.16}$
L⋆	Luminosity (L☉)	$3.11_{-0.39}^{+0.68}$
ρ⋆	Density (cgs)	$0.387_{-0.088}^{+0.068}$
log g⋆	Surface gravity (cgs)	$4.074_{-0.070}^{+0.045}$
Teff	Effective temperature (K)	6102 ± 43
[Fe/H]	Metallicity	$-0.281_{-0.038}^{+0.039}$
Planetary parameters
e	Eccentricity	$0.22_{-0.10}^{+0.12}$
ω⋆	Argument of periastron (°)	$80_{-120}^{+110}$
P	Period (days)	7.8457 ± 0.0002
a	Semimajor axis (AU)	$0.07939_{-0.00099}^{+0.0010}$
MP	Mass (MJ)	$0.430_{-0.046}^{+0.045}$
RP	Radius (RJ)	$1.193_{-0.077}^{+0.13}$
ρP	Density (cgs)	$0.311_{-0.076}^{+0.069}$
log gP	Surface gravity	$2.868_{-0.081}^{+0.063}$
Teq	Equilibrium temperature (K)	$1313_{-38}^{+59}$
Θ	Safronov number	$0.0521_{-0.0061}^{+0.0059}$
〈F〉	Incident flux (109 erg s−1 cm−2)	$0.653_{-0.076}^{+0.092}$
RV parameters
TC	Time of inferior conjunction (BJDTDB)	$2456269.3399_{-0.0072}^{+0.0071}$
TP	Time of periastron (BJDTDB)	$2456269.2_{-2.5}^{+1.7}$
K	RV semi-amplitude (m s−1)	$42.8_{-4.2}^{+4.5}$
MPsin i	Minimum mass (MJ)	$0.430_{-0.046}^{+0.045}$
MP/M⋆	Mass ratio	$0.000378_{-0.000037}^{+0.000036}$
u	RM linear limb darkening	$0.6035_{-0.0039}^{+0.0040}$
γHIRES	m s−1	−3.1 ± 3.2
$\dot{\gamma }_{\rm HIRES}$	RV slope (m s−1 day−1)	−0.239 ± 0.037
ecos ω⋆		$0.02_{-0.14}^{+0.13}$
esin ω⋆		$0.05_{-0.22}^{+0.23}$
f(m1, m2)	Mass function (MJ)	$0.000000061_{-0.000000017}^{+0.000000020}$
Primary transit parameters
RP/R⋆	Radius of the planet in stellar radii	$0.07761_{-0.00092}^{+0.0010}$
a/R⋆	Semimajor axis in stellar radii	$10.79_{-0.89}^{+0.60}$
i	Inclination (°)	$88.81_{-0.91}^{+0.79}$
b	Impact parameter	$0.20_{-0.13}^{+0.14}$
δ	Transit depth	$0.00602_{-0.00014}^{+0.00016}$
T0	Best-fit linear ephemeris from transits (BJDTDB)	2456347.796793 ± 0.000364
PTransit	Best-fit linear ephemeris period from transits (days)	7.8456314 ± 0.0000459
TFWHM	FWHM duration (days)	$0.212_{-0.029}^{+0.039}$
τ	Ingress/egress duration (days)	$0.0175_{-0.0028}^{+0.0039}$
T14	Total duration (days)	$0.230_{-0.032}^{+0.043}$
PT	A priori non-grazing transit probability	$0.091_{-0.021}^{+0.038}$
PT, G	A priori transit probability	$0.107_{-0.024}^{+0.044}$
Secondary eclipse parameters:
TS	Time of eclipse (BJDTDB)	$2456265.51_{-0.70}^{+0.66}$
bS	Impact parameter	$0.22_{-0.14}^{+0.18}$
TS, FWHM	FWHM duration (days)	$0.231_{-0.051}^{+0.073}$
τS	Ingress/egress duration (days)	$0.0194_{-0.0048}^{+0.0083}$
TS, 14	Total duration (days)	$0.251_{-0.056}^{+0.081}$
PS	A priori non-grazing eclipse probability	$0.084_{-0.010}^{+0.018}$
PS, G	A priori eclipse probability	$0.098_{-0.012}^{+0.020}$

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Comparing the fiducial system parameters with those from the other 11 global fits, we note differences in planetary mass ΔM_P ∼ 10% (∼1σ), planetary radius ΔR_P ∼ 10% (∼1σ), orbital radius Δa ∼ 5% (∼4σ), planetary equivalent temperature ΔT_eq ∼ 5% (∼1σ), stellar mass ΔM_⋆ ∼ 15% (∼3σ), and stellar radius ΔR_⋆ ∼ 15% (∼1.5σ). Clearly, the choice of global fit input parameters, priors, and external constraints significantly affects some of the inferred system parameters. Thus, it is important to note that other plausible global fits yield significantly different values for some system parameters.

The HIRES RV uncertainty scaling for the fiducial global fit is 2.808, which is fairly high and is suggestive of substantial stellar jitter in the RV data. The rms of the RV residuals of the fit to these scaled data is 8.0 m s⁻¹, which is somewhat high (∼2σ) compared to what we would expect based on Wright (2005). We do not have a compelling explanation for the high RV residuals. As noted in Section 2.2, we did not attempt to measure line bisectors for the HIRES data.

We investigated the transit center times of the 16 full and partial transits adopted from the 16 transit, Yonsei–Yale constrained, eccentric orbit global fit with no prior on log g_⋆ for any signs of transit time variations (TTVs). We were careful to ensure that all quoted times had been properly reported in BJD_TDB (e.g., Eastman et al. 2010). When we performed the global fit, we allowed for transit time T_{C, i} for each of the transits shown in Table 3 to be a free parameter. Therefore, the individual follow-up transit light curves do not constrain the KELT-6b ephemeris (global epoch T_C and period P). Rather, the constraints on these parameters in the global fit come only from the RV data, and the prior imposed from the KELT discovery data. Using the follow-up transit light curves to constrain the ephemeris in the global fit would artificially reduce any observed TTV signal.

Subsequent to the global fit, we then derived a separate ephemeris from only the transit timing data by fitting a straight line to all inferred transit center times from the global fit. These times are listed in Table 3 and plotted in Figure 8. We find T₀ = 2456347.796793 ± 0.000364, P_Transit = 7.8456314 ± 0.0000459, with a χ² of 38.70 and 14 degrees of freedom. While the χ² is larger than one might expect, this is often the case in ground-based TTV studies, likely due to systematics in the transit data. There are ∼3σ deviations from the linear ephemeris on epochs 1 and 8. However, although there are consistent TTV measurements from two independent observatories on both of those epochs, we note that these data are all from ingress- or egress-only observations. Given the likely difficulty with properly removing systematics in partial transit data, we are unwilling to claim convincing evidence for TTVs. Further study of KELT-6b transit timing is required to rule out TTVs.

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We use global fit values for T_eff, log g_⋆, stellar mass, and metallicity (Section 4 and Table 5 columns "Fit 1" and "Fit 5"), in combination with the theoretical evolutionary tracks of the Yonsei–Yale stellar models (Demarque et al. 2004), to estimate the age of the KELT-6 system. We have not directly applied a prior on the age, but rather have assumed uniform priors on [Fe/H], log g_⋆, and T_eff, which translates into non-uniform priors on the age. The standard version of EXOFAST uses the Torres et al. (2010) relations to estimate stellar mass and radius at each step of the MCMC chains. The top panel of Figure 12 shows the theoretical H-R diagram (log g_⋆ versus T_eff) corresponding to Table 5 column "Fit 5." We also show evolutionary tracks for masses corresponding to the ±1σ extrema in the estimated uncertainty. The Torres constrained global fit values for T_eff and log g_⋆ are inconsistent by more than 1σ with the Yonsei–Yale track corresponding to the stellar mass and metallicity preferred by this global fit. To investigate the inconsistency, we modified EXOFAST to use the Yonsei–Yale models rather than the Torres et al. (2010) relations to estimate stellar mass and radius at each MCMC step. The bottom panel of Figure 12 is the same as the top panel, but for the fiducial Yonsei–Yale constrained global fit corresponding to Table 5 column "Fit 1." The intersection of global fit values for T_eff and log g_⋆ now fall near the Yonsei–Yale track at 6.1 ± 0.2 Gyr, where the uncertainty does not include possible systematic errors in the adopted evolutionary tracks. The Torres constrained global fit yields an age that is about 25% younger, and planet mass and radius that are larger by ∼4}–7%. Although we cannot explain the inconsistency between the Torres constrained global fit and the Yonsei–Yale track, we expect that it may be due to slight inaccuracies in the Yonsei–Yale models and/or the Torres et al. (2010) relations for metal-poor stars. We adopt the Yonsei–Yale constrained global fit for the analyses in this paper.

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KELT-6 is evidently a late-F star that is just entering the subgiant stage of evolution. To check that the isochrone age is consistent with other parameters of KELT-6, we use the gyrochronology relations of Barnes (2007) to compute the age based on the rotation period of the star and its B − V color. We checked the KELT light curve for periodic variability associated with spot modulation as an indicator of P_rot, but we were unable to detect any significant sinusoidal variability beyond the photometric noise. Lacking a direct measurement, we estimated P_rot using the projected rotational velocity from Section 3.2 and the stellar radius from the adopted global fit in Section 4 to be P_rot/sin i_rot = 16.2 ± 3.8 days. Harris & Upgren (1964) photoelectrically measured magnitudes and colors of KELT-6 and found B − V = 0.49 ± 0.008. Tycho (Høg et al. 2000) measured B_T and V_T (Table 4), and through the filter transformations described in ESA (1997), the Tycho-based color is B − V = 0.415 ± 0.069. Because the Harris & Upgren (1964) precision is much higher than Tycho's, and since the Tycho color is consistent with the Harris & Upgren (1964) color at nearly 1σ, we adopt the Harris & Upgren (1964) color for this analysis. In particular, we are worried about inaccuracies in the Tycho-to-Johnson filter-band transformations, especially for metal-poor stars; Høg et al. (2000) state that these filter-band transformations are approximate. Based on the adopted rotation period and B − V color of the star, we calculate the maximum predicted age (subject to the inclination of the rotation axis to our line of sight) to be 5.7 ± 1.3 Gyr, which is fully consistent with the isochrone age. We note that if the Tycho fiducial color is used with the adopted rotation period, the Barnes (2007) relations yield an unrealistically large age of 46 Gyr, due to the fact that these relations break down for stars with B − V ≲ 0.4, which generally have small or non-existent convective envelopes.

In an investigation of transiting giant exoplanets, Demory & Seager (2011) found that for planets insolated beyond the threshold of 2 × 10⁸ erg s⁻¹ cm⁻² the radii are inflated compared to those planets with lower levels of insolation. KELT-6b currently has incident flux well above that threshold, and is a mildly inflated hot Saturn with a density of $0.248_{-0.050}^{+0.059}$ g cm⁻³. It follows the insolation–inflation trend displayed in Figure 1 of Demory & Seager (2011). However, it is worth investigating whether KELT-6b has always been insolated above the Demory & Seager (2011) threshold. If it turns out that KELT-6b only recently began receiving enhanced irradiation, this could provide an empirical probe of the timescale of inflation mechanisms (see Assef et al. 2009 and Spiegel & Madhusudhan 2012).

To answer that question, we simulate the reverse and forward evolution of the star–planet system, using the fiducial global fit parameters listed in Table 6 as the present boundary conditions. This analysis is not intended to examine circularization of the planet's orbit, tidal locking to the star, or any type of planet–planet or planet–disk interaction or migration. Rather, it is a way to infer the insolation of the planet over time due to the changing luminosity of the star and changing star–planet separation.

We include the evolution of the star, which is assumed to follow the YREC stellar model corresponding to M = 1.1 M_☉ and Z = 0.0162 (Siess et al. 2000). We also assume that the stellar rotation was influenced only by tidal torques due to the planet, with no magnetic wind and treating the star like a solid body. Although the fiducial model from Section 4.2 has an eccentric orbit, we assume a circular orbit throughout the full insolation analysis. The results of our simulations are shown in Figure 13. We tested a range of values for the tidal quality factor of the star Q_⋆, from logQ_⋆ = 5 to logQ_⋆ = 9. We find that this system is highly insensitive to the value of Q_⋆, because tides are not important for this system for the parameter ranges we analyzed. In all cases, KELT-6b has always received more than enough flux from its host to keep the planet irradiated beyond the Demory & Seager (2011) insolation threshold required for inflation.

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