KELT-4Ab: AN INFLATED HOT JUPITER TRANSITING THE BRIGHT (V ∼ 10) COMPONENT OF A HIERARCHICAL TRIPLE

As part of the by-eye object selection, we inspect the corresponding public SuperWASP data, if available (Butters et al. 2010). While SuperWASP achieved roughly the same photometric precision with almost as many observations as KELT did, due to the near-integer period of KELT-4Ab (Period = $2.9895936\pm 0.0000048$) and the relatively short span of the SuperWASP observations, SuperWASP did not observe the ingress of the planet, as shown in Figure 2.

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While HAT and SuperWASP adopt a strategy to change fields often, likely because of the shallow dependence of the detectability with the duration of observations (Beatty & Gaudi 2008), KELT has generally opted to monitor the same fields for much longer, increasing its sensitivity to longer and near-integer periods, as demonstrated by this find.

We have amassed an extensive follow-up network consisting of around 30 telescopes from amateurs, universities, and professional observatories. Coordinating with the KELT team, collaborators obtained 19 high-quality transits in six bands with six different telescopes, shown in Figure 3. All transits are combined and binned in 5-minute intervals in Figure 4 to demonstrate the statistical power of the combined fit to the entire data set, as well as the level of systematics present in this combined fit, though this combined light curve was not used directly for analysis.

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We used KeplerCam on the 1.2 m Fred Lawrence Whipple Observatory (FLWO) telescope at Mount Hopkins to observe 10 transits of KELT-4Ab in the Sloan i, g, and z bands. These are labeled "FLWO" in Figure 3. In the end, only eight of these transits were used in the final fit. We excluded one transit on the night of UT 2013 January 15. Cloudy weather forced the dome to close twice during the first half of the observations. Thin clouds continued throughout egress. When analyzed, these data produced a 7σ significant outlier in the transit time, hinting at large systematics in this light curve. We include it with our electronic tables for completeness, but due to the cloudy weather, we do not include it in our analysis. We also excluded another transit observed on the night of UT 2012 May 11. While there is no obvious fault with the light curve, our Markov Chain Monte Carlo (MCMC) analysis found two widely separated, comparably likely regions of parameter space by exploiting a degeneracy in the baseline flux and the airmass detrending parameter, which significantly degraded the quality of the global analysis. Again, we include this observation in the electronic tables for completeness, but do not use it for our analysis. The change in the best-fit parameters of KELT-4Ab is negligible whether this transit is included or not.

We observed four transits, two in the Sloan g, one in Sloan r, and one in Sloan i, at the Moore Observatory using the 0.6 m RCOS telescope, operated by the University of Louisville in Kentucky (labeled "ULMO") and reduced with the AstroImageJ package (Collins & Kielkopf 2013; Collins 2015). See Collins et al. (2014) for additional observatory information.

We observed two transits at the Westminster College Observatory in Pennsylvania (labeled "WCO") with a Celestron C14 telescope in the CBB (blue blocking) filter. As there are no limb darkening tables for this filter in Claret & Bloemen (2011), we modeled it as the closest analog available—the COnvection ROtation and planetary Transits (CoRoT) bandpass (Baglin et al. 2006).

The Las Cumbres Observatory Global Telescope (LCOGT) consists of a 0.8 m prototype telescope and nine 1 m telescopes spread around the world (Brown et al. 2013). We used the prototype telescope (labeled "BOS") to observe transits in the Sloan i band and the Sloan g band. Additionally, we used the 1 m telescope at McDonald Observatory in Texas (labeled "ELP") to observe two partial transits in the Sloan g band and Pan Starrs z band. As there are no limb darkening tables for Pan-Starrs z in Claret & Bloemen (2011), we modeled it as the closest analog available—the Sloan z filter.

We observed one partial transit in the I band at Canela's Robotic Observatory (labeled "CROW") in Portugal on UT 2013 April 17. 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 per pixel.

We obtained RV measurements of KELT-4A from four different telescopes/instruments, shown in Figures 5 and 6, and summarized in Table 1. The table expresses the radial velocities as relative velocities, using the raw velocities and subtracting the best-fit instrumental velocities from each. For the HIRES velocities, absolute RVs were measured with respect to the telluric lines separately, using the method described by Chubak et al. (2012) with a mean offset of −23.5 ± 0.1 km s⁻¹.

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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 2012 July 01 and 2013 February 21 with an iodine cell, plus a single iodine-free template spectrum. One of these points fell within the transit window and therefore provides a weak constraint on the Rossiter–McLaughlin effect (see Figure 7). We followed standard procedures of the California Planet Survey (CPS) to set up and use HIRES, reduce the spectra, and compute relative RVs (Howard et al. 2010). We used the "C2" decker (086 wide) and oriented the slit with an image rotator to avoid contamination from KELT-4B, C.

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We obtained five spectra with the FIbre-fed Echelle Spectrograph (FIES) on the 2.5 m Nordic Optical Telescope (NOT) in La Palma, Spain (Djupvik & Andersen 2010) between 2012 March 13 and 17 with the high-resolution fiber (13 projected diameter) with resolving power R ≈ 67,000. We discarded one observation which the observer marked as bad and had large quoted uncertainites. We used standard procedures to reduce these data, as described in Buchhave et al. (2010, 2012).

Eight spectra were taken with the EXPERT spectrograph (Ge et al. 2010) at the 2.1 m telescope at Kitt Peak National Observatory between 2012 December 21 and 2013 January 23 and reduced using a modified pipeline described by Wang & Sharon (2012). EXPERT has a resolution of R = 30,000, 0.39–1.0 μm coverage, and a 12 fiber. Two of these spectra were taken during transit and therefore provide a weak constraint on the RM effect.

We took 16 RV observations with the TRES spectrograph (Fűrész 2008), which has a resolving power of 44,000, a fiber diameter of 23, and a typical seeing of 15. Because of the typical seeing, the fiber diameter, and the nearby companion, we initially excluded all of the TRES data, but when we found the fit to be consistent (albeit with slightly higher scatter than is typical for TRES), we included it in the global fit. The higher scatter was taken into account by scaling the errors such that the probability of ${\chi }^{2}$ we got was 0.5, as we do for all data sets.

Stellar parameters ($\mathrm{log}g$, ${T}_{{\rm{eff}}}$, $[{\rm{Fe}}/{\rm{H}}]$, and $v\mathrm{sin}{I}_{*}$) were derived from the FIES and TRES using the Stellar Parameter Classification (SPC) tool (Buchhave et al. 2014), and the HIRES spectra using SpecMatch (E. Petigura et al. 2015, in preparation). It is well known that the transit light curve alone can constrain the stellar density (Seager & Mallén-Ornelas 2003). Coupled with the Yonsie Yale (YY) isochrones (Yi et al. 2001) and a measured ${T}_{{\rm{eff}}}$, the transit light curve provides a tight constraint on the $\mathrm{log}g$ (Torres et al. 2012). Alternatively, we have discovered that the limb darkening of the transit itself is sufficient to loosely constrain the ${T}_{{\rm{eff}}}$ and therefore the $\mathrm{log}g$ without spectroscopy during a global fit, which we use as another check on the stellar parameters. Finally, we iterated on the HIRES spectroscopic parameters using a prior on the $\mathrm{log}g$ from the global fit. That is, we used the HIRES spectroscopic parameters to seed a global fit, found the $\mathrm{log}g$ using the more precise transit constraint, fed that back into SpecMatch to derive new stellar parameters that are consistent with the transit, and then ran the final global fit.

All of these methods were marginally consistent (<1.7σ) with one another, as shown in Table 2. Since the uncertainties in the measured stellar parameters are typically dominated by the stellar atmospheric models, this marginal consistency is uncommon and may be indicative of a larger than usual systematic error. It is likely that the discrepancy is due to the blend with the neighbor 15 away. While the FIES $\mathrm{log}g$ agrees best with the $\mathrm{log}g$ derived from the transit photometry, we adopted the HIRES parameters derived with an iterative $\mathrm{log}g$ prior from the global analysis because of its higher spatial resolution and better median site seeing. However, to account for the inconsistency between methods, we inflated the uncertainties in ${T}_{{\rm{eff}}}$ and $[{\rm{Fe}}/{\rm{H}}]$ as shown in Table 2 so they were in good agreement with the values without the $\mathrm{log}g$ prior and did not include a spectroscopic prior on the $\mathrm{log}g$ during the global fit. Still, systematic errors in the stellar parameters (and therefore the derived planetary parameters) at the 1σ level would not be surprising. The slightly hotter star preferred by the other spectroscopic methods would make the star bigger and therefore the planet even more inflated. The cooler star preferred by the limb darkening would make the star and planet smaller.

Table 2.  Summary of Measured Stellar Parameters

	$\mathrm{log}g$	${T}_{{\rm{eff}}}$	$[{\rm{Fe}}/{\rm{H}}]$	$v\mathrm{sin}{I}_{*}$
Instrument	(cgs)	(K)		(km s−1)
FIES	4.11 ± 0.10	6360 ± 49	−0.12 ± 0.08	7.6 ± 0.5
TRES	4.05 ± 0.10	6249 ± 49	−0.12 ± 0.08	7.8 ± 0.5
HIRES	4.20 ± 0.08	6281 ± 70	−0.10 ± 0.05	7.6 ± 1.7
HIRESa	4.12 ± 0.08	6218 ± 70	−0.12 ± 0.05	6.2 ± 1.2
Global fitb	4.104 ± 0.019	${6090}_{-320}^{+390}$	⋯	⋯
Adopted priorsc	N/A	6218 ± 80	−0.12 ± 0.08	6.2 ± 1.2
Final valuesd	$4.108\pm 0.014$	$6206\pm 75$	$-{0.116}_{-0.069}^{+0.065}$	6.2 ± 1.2

Notes.

^aIncludes an iterative $\mathrm{log}g$ prior from the global transit fit. ^bValues from the global fit without a $\mathrm{log}g$ or ${T}_{{\rm{eff}}}$ prior, but with an $[{\rm{Fe}}/{\rm{H}}]=-0.12\pm 0.08$ prior and guided by the stellar limb darkening. ^cSpectroscopic priors used in the final iteration of the global fit. ^dThe values from the final iteration of the global fit with the adopted spectroscopic priors.

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As compiled by the Washington Double Star Catalog (Mason et al. 2001), KELT-4 was originally identified as a common proper motion binary with a separation of 15 by Couteau (1973), who named it COU 777. It was later observed in 1987 by Argue et al. (1992), Hipparcos in 1991 (Perryman et al. 1997; van Leeuwen 2007), and the Tycho Survey in 1991 (Fabricius et al. 2002). The magnitudes, position angles (degrees east of north), and separations (arcseconds) from these historical records are summarized in Table 3 at the observed epochs, in addition to our own measurement described in Section 2.5.

On 2012 May 07, we obtained adaptive optics (AO) imaging on the Keck II telescope located on Mauna Kea, Hawaii, using NIRC2 in both the J and K bands (Yelda et al. 2010), shown in Figure 8. We used the narrow camera, with a pixel scale of 0009942 pix⁻¹.

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The proper motions determined by Hipparcos of μ_α =11.79 ± 1.31 mas yr⁻¹ and μ_δ =  −12.63 ± 0.9 mas yr⁻¹ over the 40-year baseline between the original observations by Couteau (1973) and ours have amounted to over 05 of total motion. If the companion mentioned in Section 2.4 was not gravitationally bound, this motion would have significantly changed the separation, which would be trivial to detect in our AO images. However, the separations remain nearly identical. Therefore, we confirm this system as a common proper motion binary.

Interestingly, for the first time, our AO image further resolves the stellar companion as a binary itself, with a separation of 49.14 ± 0.39 mas and a position angle of 32523 ± 013 at epoch 2012.3464, as shown in Figure 8. The AO imaging shows the companion binary (which we now designate as KELT-4BC) to have J and K apparent magnitudes that are identical to within the photometric measurement uncertainties of ∼10%. Thus in our spectral energy distribution (SED) modeling of the full system and thus in our estimates of the flux contamination contributed to the KELT-4A light curves, we treat KELT-4BC as a single object with the total apparent magnitudes listed in Table 3.

From the relative magnitudes of KELT-4BC and KELT-4A, we use SED modeling (see Figure 10) to estimate the KELT-4BC pair to be twin K stars with ${T}_{{\rm{eff}}}\approx 4300$ K and ${R}_{*}=0.6\pm 0.1\;{R}_{\odot }$. Using Demory et al. (2009), we translate that to a mass of 0.65 ± 0.1 $\;{M}_{\odot }$. Therefore, KELT-4Ab is a companion to the brightest member of a hierarchical triple stellar system. That is, KELT-4A is orbited by KELT-4Ab, a ∼ 1 M_J mass planet with a period of 3 days and also by KELT-4BC, a twin K-star binary. In all of our follow-up light curves, this double, with a combined V magnitude of 13, was blended with KELT-4A, contributing ∼2%–7% to the baseline flux, depending on the observed bandpass.

At the distance of 210 pc determined from our SED modeling (Section 3.1), the projected separation between KELT-4A and KELT-4BC is 328 ± 16 AU, and the projected separation KELT-4B and KELT-4C is 10.30 ± 0.74 AU. Assuming the orbit is face on and circular, the period of the outer binary, P_A,BC, would be 3780 ± 290 years and the period of the twin stars, P_B,C, would be 29.4 ± 3.6 years.

While assuming the orbit is face on and circular is likely incorrect, it gives us a rough order of magnitude of the signal we might expect. If correct, in the 21 years between Hipparcos and Keck data, we would expect to see about 55 mas of motion of KELT-4BC relative to KELT-4A. This is roughly what we see, though it is worth noting that the clockwise trend between the Hipparcos position and our measurement is in contradiction to the 1σ counter-clockwise trend for the two Hipparcos values.

Extending the baseline to the full 40 years, we expect to see about 110 mas of motion. While the historical values are quoted without uncertainties, using the 200 mas discrepancy between the two 1972 data points as a guide, the data seem to confirm the clockwise trend and are consistent with a 110 mas magnitude (see Figure 9). Unfortunately, the data sample far too little of the orbit and are far too imprecise to provide meaningful constraints on any other orbital parameters.

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While we are unlikely to get a complete, precise orbit for the KELT-4A-BC system in our lifetimes, we should be able to place observational constraints on the eccentricity and inclination with additional data immediately, while simultaneously constraining the BC orbit. Even a lack of detectable motion would rule out a circular, face-on orbit for the KELT-4A-BC system.

We used the broadband photometry for the combined light for all three components, summarized in Table 4, the spectroscopic value of ${T}_{{\rm{eff}}}$, and an iterative solution for ${R}_{*}$ from EXOFAST to model the SED of KELT-4A and KELT-4BC, assuming the B and C components were twins.

Table 4.  Stellar Properties of KELT-4A and Combined Photometry for all Three Components Used for the SED Fit

Parameter	Description (Units)	Value	Source	Reference
Names	⋯	BD+26 2091	⋯	⋯
	⋯	HIP 51260	⋯	⋯
	⋯	GSC 01973–00954	⋯	⋯
	⋯	SAO 81366	⋯	⋯
	⋯	2MASS J10281500+2534236	⋯	⋯
	⋯	TYC 1973 954 1	⋯	⋯
	⋯	CCDM J10283+2534A	⋯	⋯
	⋯	WDS 10283+2534	⋯	⋯
	⋯	GALEX J102814.9+253423	⋯	⋯
	⋯	COU 777	⋯	⋯
${\alpha }_{J2000}$	R.A. (J2000)	10 28 15.011	Hipparcos	1
${\delta }_{J2000}$	Decl. (J2000)	+25 34 23.47	Hipparcos	1
FUVGALEX	Far UV Magnitude	20.39 ± 0.16	GALEX	2
NUVGALEX	Near UV Magnitude	14.49 ± 0.01	GALEX	2
B	Johnson B Magnitude	10.47 ± 0.03	APASS	3
V	Johnson V Magnitude	9.98 ± 0.03	APASS	3
J	J Magnitude	9.017 ± 0.021	2MASS	4
H	H Magnitude	8.790 ± 0.023	2MASS	4
K	K Magnitude	8.689 ± 0.020	2MASS	4
WISE1	WISE 3.6 μm	8.593 ± 0.022	WISE	5
WISE2	WISE 4.6 μm	8.642 ± 0.020	WISE	5
WISE3	WISE 11 μm	8.661 ± 0.023	WISE	5
WISE4	WISE 22 μm	8.608 ± 0.336	WISE	5
μα	Proper Motion in R.A. (mas yr−1)	11.79 ± 1.31	Hipparcos	1
μδ	Proper Motion in Decl. (mas yr−1)	−12.63 ± 0.90	Hipparcos	1
πa	Parallax (mas)	3.02 ± 1.41	Hipparcos	1
da	Distance (pc)	${211}_{-12}^{+13}$	This work (Eccentric)	⋯
da	Distance (pc)	$210.7\pm 9.0$	This work (Circular)	⋯
da	Distance (pc)	210 ± 10	This work (SED)	⋯
Ub	Galactic motion (km s−1)	33.2 ± 1.3	This work	⋯
V	Galactic motion (km s−1)	9.8 ± 1.0	This work	⋯
W	Galactic motion (km s−1)	−8.6 ± 0.7	This work	⋯
AV	Visual Extinction	${0.05}_{-0.03}^{+0.0}$	This work	⋯

Notes.

^aWe quote the parallax from Hipparcos, but derive a more precise distance from our SED modeling and semi-independently through both the eccentric and circular global EXOFAST models. While all are consistent, we adopt the SED distance as our preferred value. ^bPositive U is in the direction of the Galactic Center.

References. 1—Perryman et al. (1997), van Leeuwen (2007), 2—Martin et al. (2005), 3—Henden et al. (2012), 4—Cutri et al. (2003), Skrutskie et al. (2006), 5—Wright et al. (2010), Cutri et al. (2012).

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The SED of KELT-4 is shown in Figure 10, using the blended photometry from all 3 components summarized in Table 4. We fit for extinction, A_V, and the distance, d. A_V was limited to a maximum of 0.05 based on the Schlegel dust map value (Schlegel et al. 1998) for the full extinction through the Galaxy along the line of sight). From the SED analysis, we derive an extinction of 0.01 mag and a distance of 210 ± 10 pc—consistent with, but much more precise than the Hipparcos parallax (330 ± 150 pc).

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Because KELT-4A was blended with KELT-4BC in all of our transit photometry, the SED-modeled contributions from KELT-4B and KELT-4C were subtracted before modeling the transit. The contribution from the KELT-4BC component was 1.827% in Sloan g, 4.077% in Sloan r, 5.569% in Sloan i, 7.017% in Sloan z, and 3.670% in CBB.

We ran several iterations of the EXOFAST fit (see Section 3.3), first with a prior on the distance from the SED modeling, but without priors on ${T}_{{\rm{eff}}}$ or $\mathrm{log}g$. The ${R}_{*}$ from EXOFAST was fed back into the SED model, and we iterated until both methods produced consistent values for ${T}_{{\rm{eff}}}$ and $\mathrm{log}g$.

Because the distance derived from the SED modeling relies on the ${R}_{*}$ from EXOFAST, we removed the distance prior during the final iteration of the global fit so as not to double count the constraint. The only part of the SED modeling our global fit relies on is the extinction and the blending fractions in each bandpass that dilute the transit depth. The details of the iterative fit are described further in Section 3.3.

Using the distance, proper motion, the systemic velocity from Keck, and the Coşkunoǧlu et al. (2011) determination of the Sun's peculiar motion with respect to the local standard of rest, we calculate the 3-space motion of the KELT-4A system through the Galaxy, summarized in Table 4. According to the classification scheme of Bensby et al. (2003), this gives the system a 99% likelihood of being in the Galaxy's thin disk, which is consistent with the other known parameters of the system.

Similar to Beatty et al. (2012), after iterative SED modeling and transit modeling with the blend subtracted converged on the same stellar properties, we used a modified version of EXOFAST (Eastman et al. 2013) to model the unblended KELT-4A parameters, radial velocities, and deblended transits in a global solution.

We imposed Gaussian priors for ${T}_{{\rm{eff}}}=6218\pm 80$ K, $[{\rm{Fe}}/{\rm{H}}]=-0.12\pm 0.08$, and $V\mathrm{sin}{I}_{*}=6.2\pm 1.2\;\mathrm{km}\;{{\rm{s}}}^{-1}$ from the Keck high resolution spectra as measured by SpecMatch with an iterative solution on $\mathrm{log}g$ from the global fit. The uncertainties in $[{\rm{Fe}}/{\rm{H}}]$ and ${T}_{{\rm{eff}}}$ were inflated due to the marginal disagreement with the parameters measured by FIES and TRES, as discussed in Section 2.3.

We also imposed Gaussian priors from a linear fit to the transit times: P = 2.9895933 ± 0.0000049 and T_C = 2456190.30201 ± 0.00022. These priors do not affect the measured transit times since a separate TTV was fit to each transit without limit. These priors only impact the RV fit, the timing of the RM effect, and the shape of the transit slightly through the period. In addition, we fixed the extinction, A_V, to 0.01 and the deblending fractions for each band summarized in Section 3.1 from the SED analysis, and the V-band magnitude to 10.042 from Tycho in order to derive the distance.

The errors for each data set were scaled such that the probability of obtaining the ${\chi }^{2}$ we got from an independent fit was 0.5. For all the transit data, the scaled errors are reported in the online data sets. For the eccentric fit to the EXPERT data, which did not have enough data points for an independent fit, we iteratively found the residuals from the global fit and scaled the uncertainties based on that. The FIES data, with only four good data points, also did not have enough data points for independent fits for either the eccentric or circular fits. However, it had a scatter about the best-fit global model that was smaller than expected. We opted not to scale the FIES uncertainties at all, as enforcing a ${\chi }_{\nu }^{\;2}=1$ would result in uncertainties that were significantly smaller than HIRES, which is not justified based on our experience with both instruments. The scalings for each fit and RV data set are reported in Table 5. Note that a common jitter term for all data sets does not reproduce a ${\chi }_{\nu }^{\;2}=1$ for each data set, as one would expect if the stellar jitter were the sole cause of the additional scatter. We would require a 55 m s⁻¹ jitter term for the EXPERT and TRES data sets and a 23 m s⁻¹ jitter term for the HIRES RVs. The FIES ${\chi }_{\nu }^{\;2}$ is below 1, so no jitter term could compensate. We suppose that contamination is to blame for the higher scatter in the TRES and EXPERT data, while the limited number of data points makes it relatively likely to get a smaller-than-expected scatter by chance for the FIES data.

Table 5.  Median Values and 68% Confidence Interval for KELT-4Ab

Parameter	Units	Eccentric	Circular
Stellar Parameters:
M*	Mass ($\;{M}_{\odot }$)	${1.204}_{-0.063}^{+0.072}$	${1.201}_{-0.061}^{+0.067}$
R*	Radius ($\;{R}_{\odot }$)	${1.610}_{-0.068}^{+0.078}$	${1.603}_{-0.038}^{+0.039}$
L*	Luminosity ($\;{L}_{\odot }$)	${3.46}_{-0.38}^{+0.43}$	${3.43}_{-0.27}^{+0.28}$
ρ*	Density (cgs)	$0.407\pm 0.044$	${0.411}_{-0.017}^{+0.018}$
Age	Age (Gyr)	${4.38}_{-0.88}^{+0.81}$	${4.44}_{-0.89}^{+0.78}$
$\mathrm{log}{g}_{*}$	Surface gravity (cgs)	${4.105}_{-0.032}^{+0.029}$	$4.108\pm 0.014$
${T}_{{\rm{eff}}}$	Effective temperature (K)	${6207}_{-76}^{+75}$	$6206\pm 75$
$[{\rm{Fe}}/{\rm{H}}]$	Metallicity	$-{0.116}_{-0.071}^{+0.067}$	$-{0.116}_{-0.069}^{+0.065}$
$v\mathrm{sin}{I}_{*}$	Rotational velocity (m s−1)	$6000\pm 1200$	$6000\pm 1200$
λ	Spin-orbit alignment (degrees)	${30}_{-74}^{+85}$	${14}_{-64}^{+100}$
d	Distance (pc)	${211}_{-12}^{+13}$	$210.7\pm 9.0$
Planetary Parameters:
e	Eccentricity	${0.030}_{-0.021}^{+0.036}$	⋯
ω*	Argument of periastron (degrees)	${60}_{-120}^{+110}$	⋯
P	Period (days)	$2.9895933\pm 0.0000049$	$2.9895932\pm 0.0000049$
a	Semimajor axis (AU)	${0.04321}_{-0.00077}^{+0.00085}$	${0.04317}_{-0.00074}^{+0.00079}$
MP	Mass ($\;{M}_{{\rm{J}}}$)	${0.878}_{-0.067}^{+0.070}$	${0.902}_{-0.059}^{+0.060}$
RP	Radius ($\;{R}_{{\rm{J}}}$)	${1.706}_{-0.076}^{+0.085}$	${1.699}_{-0.045}^{+0.046}$
ρP	Density (cgs)	${0.219}_{-0.029}^{+0.031}$	${0.228}_{-0.018}^{+0.019}$
$\mathrm{log}{g}_{P}$	Surface gravity	${2.873}_{-0.045}^{+0.042}$	${2.889}_{-0.030}^{+0.029}$
Teq	Equilibrium temperature (K)	${1827}_{-42}^{+44}$	$1823\pm 27$
Θ	Safronov number	${0.0368}_{-0.0029}^{+0.0030}$	$0.0381\pm 0.0024$
$\langle F\rangle$	Incident flux (109 erg s−1 cm−2)	${2.53}_{-0.23}^{+0.25}$	$2.51\pm 0.15$
RV Parameters:
TC	Time of inferior conjunction (${\mathrm{BJD}}_{\mathrm{TDB}}$)	$2456190.30201\pm 0.00022$	$2456190.30201\pm 0.00022$
TP	Time of periastron (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2456190.09}_{-0.97}^{+0.85}$	$--$
K	RV semi-amplitude (m s−1)	$108.6\pm 7.4$	${111.8}_{-6.4}^{+6.3}$
KR	RM amplitude (m s−1)	$72\pm 14$	$71\pm 14$
${M}_{P}\mathrm{sin}i$	Minimum mass ($\;{M}_{{\rm{J}}}$)	${0.871}_{-0.066}^{+0.069}$	${0.896}_{-0.058}^{+0.060}$
MP/M*	Mass ratio	$0.000695\pm 0.000049$	$0.000717\pm 0.000042$
u	RM linear limb darkening	${0.6018}_{-0.0068}^{+0.0078}$	${0.6018}_{-0.0067}^{+0.0077}$
γEXPERT	m s−1	$317\pm 23$	$317\pm 16$
γFIES	m s−1	$-98\pm 13$	$-99\pm 12$
γHIRES	m s−1	$15.7\pm 7.4$	$15.9\pm 6.7$
γTRES	m s−1	$-11\pm 15$	$-10\pm 13$
$\dot{\gamma }$	RV slope (m s−1 day−1)	$-0.014\pm 0.044$	$-{0.013}_{-0.041}^{+0.040}$
$e\mathrm{cos}{\omega }_{*}$	⋯	${0.004}_{-0.017}^{+0.025}$	⋯
$e\mathrm{sin}{\omega }_{*}$	⋯	${0.002}_{-0.029}^{+0.039}$	⋯
$f(m1,m2)$	Mass function ($\;{M}_{{\rm{J}}}$)	${0.000000414}_{-0.000000079}^{+0.000000091}$	${0.000000454}_{-0.000000073}^{+0.000000081}$
σEXPERT	Error scaling for EXPERT	2.00	1.37
σFIES	Error scaling for FIES	1.00	1.00
σHIRES	Error scaling for HIRES	7.48	6.85
σTRES	Error scaling for TRES	2.32	2.09
Primary Transit Parameters:
RP/R*	Radius of the planet in stellar radii	${0.10892}_{-0.00055}^{+0.00054}$	$0.10893\pm 0.00054$
a/R*	Semimajor axis in stellar radii	${5.77}_{-0.22}^{+0.20}$	${5.792}_{-0.082}^{+0.086}$
i	Inclination (degrees)	${83.11}_{-0.57}^{+0.48}$	${83.16}_{-0.21}^{+0.22}$
b	Impact parameter	${0.689}_{-0.012}^{+0.011}$	${0.689}_{-0.012}^{+0.011}$
δ	Transit depth	$0.01186\pm 0.00012$	$0.01187\pm 0.00012$
TFWHM	FWHM duration (days)	$0.11893\pm 0.00045$	$0.11892\pm 0.00044$
τ	Ingress/egress duration (days)	${0.02535}_{-0.00089}^{+0.00090}$	${0.02536}_{-0.00088}^{+0.00089}$
T14	Total duration (days)	${0.14428}_{-0.00083}^{+0.00084}$	${0.14428}_{-0.00083}^{+0.00084}$
PT	A priori non-grazing transit probability	${0.1548}_{-0.0092}^{+0.012}$	$0.1539\pm 0.0022$
PT, G	A priori transit probability	${0.193}_{-0.011}^{+0.015}$	${0.1915}_{-0.0029}^{+0.0028}$
Secondary Eclipse Parameters:
TS	Time of eclipse (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2456188.815}_{-0.032}^{+0.047}$	$2456188.80721\pm 0.00022$
bS	Impact parameter	${0.693}_{-0.043}^{+0.055}$	⋯
TS, FWHM	FWHM duration (days)	${0.11840}_{-0.0027}^{+0.00073}$	⋯
τS	Ingress/egress duration (days)	${0.0256}_{-0.0029}^{+0.0046}$	⋯
TS,14	Total duration (days)	${0.1445}_{-0.0038}^{+0.0027}$	⋯
PS	A priori non-grazing eclipse probability	$0.1540\pm 0.0022$	⋯
PS, G	A priori eclipse probability	$0.1917\pm 0.0029$	⋯

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We replaced the Torres relation within EXOFAST with YY evolutionary tracks (Yi et al. 2001; Demarque et al. 2004) to derive the stellar properties more consistently with the SED analysis. At each step in the Markov chain, R_* was derived from the step parameters. That, along with the steps in $\mathrm{log}{M}_{*}$ and $[{\rm{Fe}}/{\rm{H}}]$, were used as inputs to the YY evolutionary tracks to derive a value for ${T}_{{\rm{eff}}}$. Since there is sometimes more than one value of ${T}_{{\rm{eff}}}$ for given values of $\mathrm{log}{M}_{*}$ and $[{\rm{Fe}}/{\rm{H}}]$, we use the YY ${T}_{{\rm{eff}}}$ closest to the step value for ${T}_{{\rm{eff}}}$. The global model is penalized by the difference between the YY-derived ${T}_{{\rm{eff}}}$ and the MCMC step value for ${T}_{{\rm{eff}}}$, assuming a YY model uncertainty of 50 K, effectively imposing a prior that the host star lie along the YY evolutionary tracks. The step in ${T}_{{\rm{eff}}}$ was further penalized by the difference between it and spectroscopic prior in ${T}_{{\rm{eff}}}$ to impose the spectroscopic constraint. This same method was used in all KELT discoveries including and after KELT-6b, as well as HD 97658b (Dragomir et al. 2013).

The distance derived in Table 5 does not come from an explicit prior from the SED analysis. Rather, the value quoted in the table is derived through the transit $\mathrm{log}g$ and the $[{\rm{Fe}}/{\rm{H}}]$ and ${T}_{{\rm{eff}}}$ priors coupled with the YY evolutionary tracks (i.e., the stellar luminosity), the extinction, the magnitude, and the bolometric correction from Flower (1996) (and M_bol,⊙ = 4.732, Torres et al. 2010). The agreement in the distances derived from EXOFAST and the SED analysis is therefore a confirmation that the two analyses were done self-consistently. We adopt the distance determination from the SED fit (210 ± 10 pc) as the preferred value.

The quadratic limb darkening parameters, summarized in Table 6, were derived by interpolating the Claret & Bloemen (2011) tables with each new step in $\mathrm{log}g$, ${T}_{{\rm{eff}}}$, and $[{\rm{Fe}}/{\rm{H}}]$ and not explicitly fit. Since this method ignores the systematic model uncertainty in the limb darkening tables, which likely dominate the true uncertainty, we do not quote the MCMC uncertainties. All light curves observed in the same filter used the same limb darkening parameters.

Table 6.  Median Values and 68% Confidence Interval for the Limb Darkening Parameters for KELT-4A

Parameter	Units	Eccentric	Circular
u1, CoRoT	Linear Limb-darkening	$0.3216$	$0.3217$
u2, CoRoT	Quadratic Limb-darkening	$0.2970$	$0.2969$
u1,g'	Linear Limb-darkening	$0.472$	$0.472$
u2,g'	Quadratic Limb-darkening	$0.2697$	$0.2697$
u1,r'	Linear Limb-darkening	$0.3126$	$0.3127$
u2,r'	Quadratic Limb-darkening	$0.3144$	$0.3143$
u1,i'	Linear Limb-darkening	$0.2395$	$0.2396$
u2,i'	Quadratic Limb-darkening	$0.3045$	$0.3044$
u1,I	Linear Limb-darkening	$0.2216$	$0.2217$
u2,I	Quadratic Limb-darkening	$0.3022$	$0.3022$
u1,z'	Linear Limb-darkening	$0.1892$	$0.1893$
u2, z'	Quadratic Limb-darkening	$0.2949$	$0.2948$

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We modeled the system allowing a non-zero eccentricity of KELT-4Ab, but found it perfectly consistent with a circular orbit. This is generally expected because the tidal circularization timescales of such Hot Jupiters are much much smaller than the age of the system (Adams & Laughlin 2006). Therefore, we reran the analysis fixing KELT-4Ab's eccentricity to zero. The results of both the circular and eccentric global analyses are summarized in Table 5, though we generally favor the circular fit due to our expectation that the planet is tidally circularized and the smaller uncertainties. All figures and numbers shown outside of this table are derived from the circular fit.

While we only had three serendipitous RV data points during transit, we allowed λ, the spin–orbit alignment, to be free during the fit. The most likely model is plotted in Figure 6 and a zoom in on the RM effect in Figure 7, showing the data slightly favor an aligned geometry. However, the median value and 68% confidence interval ($\lambda ={14}_{-64}^{+100}$) show this constraint is extremely weak. In reality, the posterior for λ is bimodal with peaks at −30° and 120°, has a non-negligible probability everywhere, and is strongly influenced by the $v\mathrm{sin}{I}_{*}$ prior. In fact, the distribution of likely values is not far from uniform which would have a 68% confidence interval of 0° ± 123°. Therefore, we consider λ to be essentially unconstrained. Note that in our quoted (median) values for angles, we first center the distribution about the mode to prevent boundary effects from skewing the inferred value to the middle of the arbitrary range.

Finally, we fit a separate transit time, baseline flux, and detrend with airmass to each of the 19 transits during the global fit, a separate zero point for each of the 4 RV data sets, and a slope to detect an RV trend, for a total of 75 free parameters (73 for the circular fit).

Great care was taken to translate each of our timestamps to a common system, ${\mathrm{BJD}}_{\mathrm{TDB}}$ (Eastman et al. 2010). All observers report ${\mathrm{JD}}_{\mathrm{UTC}}$ at mid exposure and the translation to ${\mathrm{BJD}}_{\mathrm{TDB}}$ is done uniformly for all observations prior to the fit. In addition, we have double checked the values quoted directly from an example image header for each observer. During the global fit, the transit time for each of the 19 transits were allowed to vary freely, as shown in Figure 11 and summarized in Table 7. While most epochs were consistent with a linear ephemeris,

$$\begin{eqnarray}{T}_{0} & = & 2456193.29157\pm 0.00021,\\ P & = & 2.9895936\pm 0.0000048,\end{eqnarray} \tag{ 1 }$$

there are a few large outliers. However, given the TTV results for Hot Jupiters from the Kepler mission (Steffen et al. 2012), the heterogeneity of our clocks, observatories, and observing procedures, and the potential for atmospheric and astrophysical sources of red noise to skew our transit times by amounts larger than our naive error estimates imply (Carter & Winn 2009), we do not view these outliers as significant. In particular, our experience with KELT-3b (Pepper et al. 2013), where we observed the same epoch with three different telescopes and found that the observation from FLWO differed by 5-sigma (7 minutes) from the other two with no discernible cause has led us to be skeptical of all ground-based TTV detections. Curiously, the two most significant outliers are also from FLWO, possibly pointing to a problem with the stability of its observatory clock (at the 5–10 minute level). We have set up monitoring of this clock and are watching it closely both for drifts and short-term glitches. While we feel our skepticism of these nominally significant TTVs is warranted, the recent results for WASP-47b (Becker et al. 2015) is a counter-example to the observation that Hot Jupiters tend not to have companions, so these outliers may be worth additional follow-up with a more homogeneous setup.

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Table 7.  Median Values and 68% Confidence Interval for the Transit Times of All 19 Follow-up Light Curves of KELT-4Ab from the Global Circular Fit, along with Residuals from the Best-fit Linear Ephemeris: ${T}_{C,N}({\mathrm{BJD}}_{\mathrm{TDB}})=2456193.29157\pm 0.00021+N(2.9895936\pm 0.0000048)$

Parameter	UT Date	Telescope	Filter	Epoch	TC (${\mathrm{BJD}}_{\mathrm{TDB}}$)	$O-C$ (s)	$O-C$ (${\sigma }_{{T}_{C}}$)
TC,0	2012 Mar 30	FLWO	i	−59	$2456016.9045\pm 0.0011$	−94.08	−1.01
TC,1	2012 Apr 08	FLWO	g	−56	$2456025.8724\pm 0.0015$	−166.03	−1.25
TC,2	2012 Apr 20	BOS	i	−52	$2456037.8371\pm 0.0013$	377.05	3.46
TC,3	2012 Apr 29	FLWO	z	−49	$2456046.80185\pm 0.00092$	31.30	0.39
TC,4	2012 May 08	BOS	g	−46	${2456055.7703}_{-0.0013}^{+0.0014}$	0.14	0.00
TC,5	2012 May 14	FLWO	g	−44	$2456061.7511\pm 0.0012$	143.37	1.42
TC,6	2012 May 23	ELP	g	−41	$2456070.7183\pm 0.0013$	2.65	0.02
TC,7	2012 Jun 10	ULMO	r	−35	$2456088.6563\pm 0.0012$	41.23	0.39
TC,8	2012 Dec 18	FLWO	i	29	$2456279.98810\pm 0.00038$	−145.14	−4.44
TC,9	2012 Dec 27	FLWO	i	32	${2456288.95246}_{-0.00089}^{+0.00087}$	−527.01	−6.92
TC,10	2013 Jan 08	ULMO	g	36	${2456300.91808}_{-0.00063}^{+0.00064}$	98.93	1.80
TC,11	2013 Jan 20	ULMO	g	40	$2456312.87644\pm 0.00036$	97.52	3.14
TC,12	2013 Feb 01	ELP	z	44	${2456324.8362}_{-0.0013}^{+0.0012}$	213.79	1.93
TC,13	2013 Feb 04	ULMO	g	45	$2456327.82297\pm 0.00037$	−27.14	−0.85
TC,14	2013 Feb 10	WCO	CBB	47	${2456333.80597}_{-0.00098}^{+0.00096}$	302.63	3.61
TC,15	2013 Feb 13	WCO	CBB	48	${2456336.79097}_{-0.00099}^{+0.0010}$	−94.51	−1.10
TC,16	2013 Feb 13	FLWO	z	48	${2456336.79221}_{-0.00058}^{+0.00057}$	13.23	0.26
TC,17	2013 Mar 12	FLWO	i	57	$2456363.69882\pm 0.00041$	35.76	1.01
TC,18	2013 Apr 17	CROW	I	69	${2456399.5754}_{-0.0024}^{+0.0025}$	162.86	0.77

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