KELT-11b: A Highly Inflated Sub-Saturn Exoplanet Transiting the V = 8 Subgiant HD 93396

KELT-11b is located in the KELT-South field 23, which is centered at J2000 α =10^h43^m48^s, δ = −20°00'00''. This field was monitored from UT 2010 March 12 to UT 2014 July 9, resulting in 3910 images after post-processing and removal of bad images. Following the same strategy as described in Kuhn et al. (2016), we reduced the raw images, extracted the light curves, and searched for transit candidates. One candidate from this processing, KS23C00790 (HD 93396, TYC 5499-1085-1, 2MASS J10464974-0923563), located at α = 10^h46^m 497, δ = −9°23'565 J2000, was rated as a top candidate from the field. The host star properties can be seen in Table 1. We use the Box-fitting Least-squares algorithm (Kovács et al. 2002) as implemented in the VARTOOLS software package (Hartman & Bakos 2016) to identify transit candidates, making use of statistics that come from the VARTOOLS package, as well as from Pont et al. (2006) and Burke et al. (2006). The associated selection criteria and the corresponding values for KELT-11b are shown in Table 2. For the choices of the particular selection criteria, refer to Siverd et al. (2012). The discovery light curve itself is shown in Figure 1, and the data are provided in Table 3.

Zoom In Zoom Out Reset image size

Table 1.  Stellar Properties of KELT-11

Parameter	Description	KELT-11 Value	Source	Reference(s)
Names		HD 93396
		TYC 5499-1085-1
		2MASS J10464974-0923563
αJ2000	Right ascension (R.A.)	10:46:49.741	Tycho-2	Høg et al. (2000)
δJ2000	Declination (decl.)	−09:23:56.48	Tycho-2	Høg et al. (2000)
BT	Tycho BT magnitude	9.072 ± 0.018	Tycho-2	Høg et al. (2000)
VT	Tycho VT magnitude	8.130 ± 0.013	Tycho-2	Høg et al. (2000)
V	Johnson V magnitude	8.03	Hipparcos	Perryman et al (1997)
J	2MASS magnitude	6.616 ± 0.024	2MASS	Cutri et al. (2003), Skrutskie et al. (2006)
H	2MASS magnitude	6.251 ± 0.042	2MASS	Cutri et al. (2003), Skrutskie et al. (2006)
KS	2MASS magnitude	6.122 ± 0.018	2MASS	Cutri et al. (2003), Skrutskie et al. (2006)
W1	WISE passband	6.152 ± 0.1	WISE	Wright et al. (2010), Cutri et al. (2014)
W2	WISE passband	6.068 ± 0.036	WISE	Wright et al. (2010), Cutri et al. (2014)
W3	WISE passband	6.157 ± 0.015	WISE	Wright et al. (2010), Cutri et al. (2014)
W4	WISE passband	6.088 ± 0.048	WISE	Wright et al. (2010), Cutri et al. (2014)
μα	Proper motion in R.A. (mas yr−1)	−78.30 ± 0.95	Tycho-2	van Leeuwen (2007)
μδ	Proper motion in decl. (mas yr−1)	−77.61 ± 0.68	Tycho-2	van Leeuwen (2007)
Ua	Space motion (km s−1)	−9.6 ± 1.2	⋯	This work
V	Space motion (km s−1)	−46.2 ± 3.0	⋯	This work
W	Space motion (km s−1)	−8.4 ± 3.4	⋯	This work
Distance	Distance (pc)	98 ± 5	⋯	This work
RV	Absolute RV (km s−1)	35.0 ± 0.1	⋯	This work
$v\sin {i}_{* }$	Stellar rotational velocity (km s−1)	2.66 ± 0.50	⋯	This work

Note.

^aU is positive in the direction of the Galactic center.

Download table as:  ASCIITypeset image

Table 2.  KELT-South Selection Criteria for Candidate KS23C00790

Statistic	Selection	Value for
	Criteria	KS23C00790/KELT-11
Signal detection efficiency	SDE > 7.0	9.91663
Signal to pink-noise	SPN > 7.0	8.16926
Transit depth	δ < 0.05	0.00344
χ2 ratio	$\tfrac{{\rm{\Delta }}{\chi }^{2}}{{\rm{\Delta }}{\chi }_{-}^{2}}\gt 1.5$	1.808
Duty cycle	q < 0.1	0.05333

Download table as:  ASCIITypeset image

We obtained follow-up time-series photometry of KELT-11b to check for false positives such as eclipsing binary stars, and to better determine the transit shape, depth, and duration. We used the TAPIR software package (Jensen 2013) to predict transit events, and we obtained nine full or partial transits in multiple bands between 2015 January and 2016 February. All data were calibrated and processed using the AstroImageJ package (AIJ;³⁴ Collins & Kielkopf 2013; Collins et al. 2017) unless otherwise stated. The follow-up light curves are displayed in Figure 2, and Table 4 lists the details of the observations. A binned combination of all of the follow-up light curves is shown in the bottom panel of Figure 2, though that combination is for display purposes and is not used for analysis.

Zoom In Zoom Out Reset image size

Table 4.  Record of the Photometric Follow-up Observations and Detrending Parameters Used by AIJ for the Global Fit

Observatory	Date (UT)	Filter	FOV	Pixel Scale	Exposure (s)	Detrending Parameters for Global Fit
WCO	UT 2015 Jan 01	I	24' × 16'	14	binned 4 × 10	Airmass, Time
MORC	UT 2015 Feb 08	g'	266 × 266	039	20	Airmass, Time
MORC	UT 2015 Feb 08	i'	266 × 266	039	20	Airmass, Time
MINERVA	UT 2015 Feb 08	i'	209 × 209	06	6	Airmass, Time
PEST	UT 2015 Mar 08	I	31' × 21'	12	binned 8 × 15	Airmass, Time
ICO	UT 2015 Mar 13	R	166 × 123	062	20	Airmass, Time
PvdK	UT 2015 Mar 18	z'	26' × 26'	076	45	Airmass, Time
LCOGT (CPT)	UT 2015 May 04	i'	158 × 158	023	12	Airmass, Time
MVRC	UT 2016 Feb 22	r'	266 × 266	039	binned 6 × 30	Airmass

Download table as:  ASCIITypeset image

It was extremely difficult to obtain reliable ground-based photometry, due to the combination of the shallow transit depth (about 2.5 mmag) and long duration (7.3 hr). Any given observatory will have difficulty observing a full transit including out-of-transit baseline observations within a single night. In fact, KELT-11b is the longest-duration transiting planet discovered using the transit method from a ground-based facility, and the one with the shallowest transit as well. We managed to obtain one full transit, and a number of partial transits that covered ingresses and egresses. The discovery light curve can be accessed in the online journal in a machine-readable table linked to Table 3. All follow-up photometric observations are provided in the online journal in a combined machine-readable table linked to Figure 2.

2.2.1. Westminster College Observatory (WCO)

2.2.2. MORC

2.2.3. MINERVA

2.2.4. Perth Exoplanet Survey Telescope (PEST) Observatory

2.2.5. Ivan Curtis Observatory (ICO)

2.2.6. Peter van de Kamp Observatory

2.2.7. Las Cumbres Observatory Global Telescope (LCOGT)-CPT

2.2.8. Manner-Vanderbilt Ritchey–Chrétien (MVRC)

We obtained spectroscopic observations of KELT-11 to measure the RV orbit of the planet, and to measure the parameters of the host star. The observations that were used to derive stellar parameters are listed in Table 5. The observations that provide RV measurements are listed in Table 6 and are displayed in Figure 3.

Zoom In Zoom Out Reset image size

Table 6.  KELT-11 RV Observations with HIRES and APF

${\mathrm{BJD}}_{\mathrm{TDB}}$	RV	RV Error	Bisector	Bisector Error	Instrument
	(m s−1)	(m s−1)	(m s−1)	(m s−1)
2454216.875149	4.4	1.5	⋯	⋯	HIRES
2454429.129861	4.5	1.3	⋯	⋯	HIRES
2454543.964648	2.7	1.4	⋯	⋯	HIRES
2454847.046979	6.9	1.5	⋯	⋯	HIRES
2455173.107559	−13.3	1.5	⋯	⋯	HIRES
2455232.144465	25.0	1.4	⋯	⋯	HIRES
2455319.783317	−19.2	1.6	⋯	⋯	HIRES
2455557.098633	−8.7	1.5	⋯	⋯	HIRES
2455634.925941	15.5	1.4	⋯	⋯	HIRES
2455945.177177	−20.9	1.6	⋯	⋯	HIRES
2456101.742516	−15.8	1.5	⋯	⋯	HIRES
2456477.738143	18.0	1.7	⋯	⋯	HIRES
2456641.045559	−15.6	1.4	⋯	⋯	HIRES
2457057.922673	−14.8	1.5	⋯	⋯	HIRES
2457058.902596	−11.6	1.5	⋯	⋯	HIRES
2457061.010742	15.6	1.4	⋯	⋯	HIRES
2457061.974167	−1.4	1.5	⋯	⋯	HIRES
2457034.993517	−24.0	2.9	2.5	2.6	APF
2457035.833572	−12.5	3.7	−4.8	6.7	APF
2457035.957552	0.8	3.7	−9.6	6.8	APF
2457038.956627	−23.8	3.5	−4.8	4.8	APF
2457044.920751	2.2	2.9	2.5	2.2	APF
2457044.941030	−4.6	2.7	3.1	4.7	APF
2457046.859494	35.6	2.9	13.4	8.8	APF
2457046.881613	18.9	3.0	−1.3	7.3	APF
2457048.072907	−10.7	3.1	−5.8	5.2	APF
2457051.020767	16.1	2.6	5.8	4.7	APF
2457051.041243	24.1	2.7	−1.1	2.8	APF
2457052.825840	−11.8	2.9	7.1	7.1	APF
2457054.832772	−0.9	3.2	4.7	4.3	APF
2457322.043143	19.4	2.9	4.8	1.7	APF
2457331.064594	12.9	3.4	−20.7	6.7	APF

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

2.3.1. Tillinghast Reflector Echelle Spectrograph (TRES)

2.3.2. KECK High Resolution Echelle Spectrometer (HIRES)

2.3.3. Automated Planet Finder (APF)

2.3.4. Bisector Spans (BSs)

We calculate BSs for each APF spectra following the prescription of Fulton et al. (2015a). We cross-correlate each spectrum with a synthetic stellar template interpolated from the Coelho (2014) grid of stellar atmosphere models to match the adopted stellar parameters. We restrict the BS analysis to the 15 echelle orders spanning 4260–5000 Å in order to avoid iodine contamination and telluric lines, and to reduce the effect of telescope guiding errors on the instrumental PSF. The blue orders were used where the seeing is generally worse and the slit is more uniformly illuminated. This reduces false bisector variations caused by changes in the slit illumination. The BS is a measure of the line asymmetry calculated as the difference in the midpoint of line segments drawn between the 65th and 95th percentile levels of the CCF. The reported BSs and uncertainties are the mean and standard deviation on the mean over the 15 spectral orders analyzed. The BS values are included in Table 6, and are plotted against the RV values in Figure 4.

Zoom In Zoom Out Reset image size

Table 7.  Stellar Parameters from the Spectral Analysis

Parameter	TRES	KECK HIRES	APF
${T}_{\mathrm{eff}}$ (K)	5390 ± 50	5413 ± 60	5444 ± 60
$\mathrm{log}{g}_{* }$	3.79 ± 0.10	3.87 ± 0.08	3.86 ± 0.08
$[\mathrm{Fe}/{\rm{H}}]$	0.19 ± 0.08a	0.31 ± 0.04	0.37 ± 0.04

Note.

^aThe SME analysis used for the TRES spectra yields a value for bulk metallicity [m/H] rather than $[\mathrm{Fe}/{\rm{H}}]$.

Download table as:  ASCIITypeset image

We observed KELT-11 with Adaptive Optics (AO) imaging to identify any faint, nearby companions to the host star. The observations were performed at Palomar Observatory's Hale telescope on 2015 February 7 using the Stellar Double Coronagraph (Bottom et al. 2015) operating with a ring-apodized vortex. Observations were taken in the K-short band, obtaining 60 exposures at 29.7 s each. Figure 5 shows the image of the star, and Figure 6 shows the associated contrast curve. No astrophysical sources are seen near KELT-11. At separations of 1.5–4 arcsec, which at the distance of KELT-11 corresponds to a projected separation of about 14–98 au, we can exclude companions with flux ratios of 4 × 10⁻⁴ compared to KELT-11, which includes stars down to mid-M-type dwarfs.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To obtain a thorough picture of the stellar parameters, we used multiple parameter extraction techniques with different spectra to obtain consistent and robust results.

We applied the spectral parameter classification (SPC; Buchhave et al. 2012) technique to the spectrum from TRES, with ${T}_{\mathrm{eff}}$, $\mathrm{log}{g}_{* }$, [m/H], and $v\sin {I}_{* }$ as free parameters. SPC cross-correlates an observed spectrum against a grid of synthetic spectra based on Kurucz atmospheric models (Kurucz 1992). The resulting parameters are ${T}_{\mathrm{eff}}=5390\pm 50$ K, $\mathrm{log}{g}_{* }$ = 3.789 ± 0.100, [m/H] = 0.189 ± 0.080, and $v\sin {I}_{* }=2.66\pm 0.50$ km s⁻¹. These parameters match the identification of KELT-11 from Houk & Swift (1999) as a G8/K0 IV spectral type.

We then independently analyzed the Keck and APF template spectra using a modified version of the SpecMatch pipeline (Petigura et al. 2015) as described in Fulton et al. (2015b). SpecMatch fits a grid of model stellar atmospheres (Coelho 2014) to large regions of the observed spectrum to measure ${T}_{\mathrm{eff}}$, $\mathrm{log}{g}_{* }$, and [Fe/H]. Our only modification to the code is to employ the ExoPy differential-evolution Markov Chain Monte Carlo (MCMC) fitting engine (Fulton et al. 2013) in place of χ² minimization to find the optimal solution. We calibrate the ${T}_{\mathrm{eff}}$ and $\mathrm{log}{g}_{* }$ values produced by SpecMatch to show good agreement with the values of Valenti & Fischer (2005) for the 353 stars in their sample that were observed on Keck. Values of $\mathrm{log}{g}_{* }$ are calibrated against the stars from the Huber et al. (2012) sample with asteroseismically measured $\mathrm{log}{g}_{* }$. This calibration is done separately for both APF and Keck spectra using our modified version of the pipeline. However, the faint Kepler stars from the (Huber et al. 2012) sample have not been observed on APF so the $\mathrm{log}{g}_{* }$ calibration is bootstrapped from stars that have been observed at both Keck and APF. Parameter uncertainties are determined by measuring the scatter of our calibrated parameters against the values form Valenti & Fischer (2005) and Huber et al. (2012).

Zoom In Zoom Out Reset image size

The best-fit spectroscopic parameters measured from all three reductions are listed in Table 7.

We estimate the distance and reddening to KELT-11 by fitting Kurucz (1979) stellar atmosphere models to the SED from catalog broadband photometry. The available catalog photometry spans the range from the GALEX FUV band at 0.16 μm to the WISE 22.8 μm band (see Table 1).

We fix T_eff, $\mathrm{log}{g}_{* }$, and [Fe/H] to the TRES-derived values from Section 3.1, and leave the distance (d) and reddening (A_V) as free parameters. We restricted A_V to be at most 0.11 mag, as determined from the maximum line-of-sight extinction from the dust maps of Schlegel et al. (1998). The catalog photometric and associated model fit are displayed in Figure 7. We find best-fit parameters of ${A}_{V}={0.09}_{-0.05}^{+0.02}$ mag and d = 98 ± 5 pc. This agrees quite well with, and is consistent with, the distance of 102 ± 9 pc from the Hipparcos parallax. The reduced χ² of the fit is 7.0 when including the GALEX FUV and NUV photometry, but 1.9 when excluding the GALEX photometry. This reflects the apparent excess in the GALEX bands, suggestive of chromospheric activity. While it may be surprising to see such activity, similarly chromospherically active subgiants are rare but are seen in previous surveys of activity among subgiants (Jenkins et al. 2011). We looked for evidence of chromospheric activity in the Ca H and K lines of the APF spectra and did not find any. Since the UV excess apparent in the SED is not corroborated by the Ca ii H and K spectroscopy, we do not use the UV flux excess for any other aspects of our analysis or interpretations.

One possible cause of excess chromospheric activity can be spin-up of the host star from a dynamically interacting planet. We can explore that possibility in this case since we have a spectroscopic $v\sin {I}_{* }$ measurement. Assuming the star and planet are not highly misaligned, and therefore that $\sin {I}_{* }\sim 1$, we have a rotational period for the star of roughly 52 days. This is much longer than the orbital period of the planet, and so we do not find evidence for an unusually high rotational velocity due to planet spin-up of the star.

Using the Hipparcos distance and the spectroscopic T_eff, we can measure the stellar radius independently by summing the SED flux and solving the Stefan–Boltzmann relation. The summed bolometric flux received at Earth is 1.85 ± 0.06 × 10⁻⁸ erg s⁻¹ cm⁻², and the resulting stellar radius is 2.84 ± 0.28 R_⊙, which we use as a prior on the global analysis of the transit (see Section 3.5).

We estimate the age of KELT-11 by fitting Yonsei–Yale isochrones to the values of T_eff, $\mathrm{log}{g}_{* }$, and [Fe/H] given in Table 8. We fix the stellar mass to the value of 1.438 M_⊙ as listed in Table 8 (see Section 3.8 for a detailed discussion of the determination of that mass value). Our best-fit stellar parameters indicate that the star happens to fall on a rapid part of the evolutionary track, namely, the so-called "Hertzsprung gap" prior to the star's ascent up the red giant branch (see Figure 8). This permits a relatively precise, though model-dependent, age estimate, and we quote an age range of 3.52–3.54 Gyr that spans the uncertainty in T_eff and $\mathrm{log}{g}_{* }$.

Zoom In Zoom Out Reset image size

Table 8.  Median Values and 68% Confidence Interval for the Physical and Orbital Parameters of the KELT-11 System

Parameter	Units	Adopted Value	Value	Value	Value
		(YY Circular; e = 0 Fixed)	(YY Eccentric)	(Torres Circular; e = 0 Fixed)	(Torres Eccentric)
Stellar Parameters
M*	Mass (M⊙)	${1.438}_{-0.052}^{+0.061}$	${1.463}_{-0.056}^{+0.064}$	${1.347}_{-0.068}^{+0.072}$	${1.364}_{-0.068}^{+0.070}$
R*	Radius (R⊙)	${2.72}_{-0.17}^{+0.21}$	${2.81}_{-0.19}^{+0.21}$	${2.78}_{-0.22}^{+0.24}$	2.89 ± 0.22
L*	Luminosity (L⊙)	${5.55}_{-0.69}^{+0.85}$	${5.90}_{-0.79}^{+0.86}$	${5.86}_{-0.90}^{+1.1}$	${6.28}_{-0.92}^{+1.0}$
ρ*	Density (cgs)	0.101 ± 0.017	${0.093}_{-0.015}^{+0.018}$	${0.088}_{-0.017}^{+0.022}$	${0.080}_{-0.014}^{+0.018}$
$\mathrm{log}{g}_{* }$	Surface gravity (cgs)	${3.727}_{-0.046}^{+0.040}$	3.706 ± 0.044	${3.678}_{-0.058}^{+0.060}$	${3.653}_{-0.053}^{+0.056}$
${T}_{\mathrm{eff}}$	Effective temperature (K)	${5370}_{-50}^{+51}$	5367 ± 50	5386 ± 49	${5385}_{-50}^{+49}$
$[\mathrm{Fe}/{\rm{H}}]$	Metallicity	0.180 ± 0.075	${0.173}_{-0.077}^{+0.076}$	0.194 ± 0.079	0.191 ± 0.079
Planet Parameters
e	Eccentricity	⋯	${0.066}_{-0.046}^{+0.059}$	⋯	${0.087}_{-0.058}^{+0.076}$
ω*	Argument of periastron (°)	⋯	${97}_{-65}^{+82}$	⋯	${86}_{-46}^{+69}$
P	Period (days)	${4.736529}_{-0.000059}^{+0.000068}$	${4.736525}_{-0.000057}^{+0.000067}$	${4.736528}_{-0.000062}^{+0.000069}$	${4.736519}_{-0.000058}^{+0.000063}$
a	Semimajor axis (au)	${0.06229}_{-0.00076}^{+0.00088}$	${0.06264}_{-0.00081}^{+0.00089}$	${0.0609}_{-0.0010}^{+0.0011}$	0.0612 ± 0.0010
MP	Mass (MJ)	${0.195}_{-0.018}^{+0.019}$	0.199 ± 0.021	0.187 ± 0.018	${0.190}_{-0.020}^{+0.021}$
RP	Radius (RJ)	${1.37}_{-0.12}^{+0.15}$	${1.41}_{-0.12}^{+0.14}$	${1.42}_{-0.15}^{+0.17}$	${1.46}_{-0.14}^{+0.15}$
ρP	Density(cgs)	${0.093}_{-0.024}^{+0.028}$	${0.088}_{-0.021}^{+0.027}$	${0.081}_{-0.022}^{+0.030}$	${0.076}_{-0.019}^{+0.025}$
$\mathrm{log}{g}_{P}$	Surface gravity	${2.407}_{-0.086}^{+0.080}$	${2.392}_{-0.083}^{+0.081}$	${2.360}_{-0.096}^{+0.093}$	${2.347}_{-0.087}^{+0.085}$
Teq	Equilibrium temperature (K)	${1712}_{-46}^{+51}$	${1733}_{-50}^{+49}$	1755 ± 64	1782 ± 60
Θa	Safronov number	${0.0123}_{-0.0015}^{+0.0016}$	${0.0120}_{-0.0016}^{+0.0017}$	${0.0119}_{-0.0016}^{+0.0017}$	${0.0117}_{-0.0015}^{+0.0017}$
$\langle F\rangle$	Incident flux (109 erg s−1 cm−2)	${1.95}_{-0.20}^{+0.24}$	${2.04}_{-0.22}^{+0.23}$	${2.15}_{-0.30}^{+0.33}$	${2.26}_{-0.28}^{+0.30}$
RV Parameters
TC	Time of inferior conjunction (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457061.9098}_{-0.0024}^{+0.0026}$	${2457061.9098}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0024}^{+0.0026}$
TP	Time of periastron (${\mathrm{BJD}}_{\mathrm{TDB}}$)	⋯	${2457061.99}_{-0.74}^{+1.0}$	⋯	${2457061.89}_{-0.48}^{+0.84}$
K	RV semi-amplitude (m s−1)	18.5 ± 1.7	18.7 ± 1.9	${18.5}_{-1.6}^{+1.7}$	${18.8}_{-1.9}^{+2.0}$
${M}_{P}\sin i$	Minimum mass (MJ)	0.195 ± 0.018	0.198 ± 0.021	${0.186}_{-0.017}^{+0.018}$	${0.190}_{-0.020}^{+0.021}$
MP/M*	Mass ratio	0.000129 ± 0.000012	0.000130 ± 0.000013	0.000133 ± 0.000012	${0.000133}_{-0.000013}^{+0.000014}$
u	RM linear limb darkening	${0.7061}_{-0.0073}^{+0.0071}$	0.7058 ± 0.0072	${0.7046}_{-0.0073}^{+0.0072}$	${0.7044}_{-0.0074}^{+0.0072}$
γAPF	m s−1	1.9 ± 2.4	${1.8}_{-2.7}^{+2.6}$	1.9 ± 2.3	${1.8}_{-2.6}^{+2.7}$
γKECK	m s−1	−1.8 ± 2.4	−1.6 ± 2.7	−1.9 ± 2.4	−1.7 ± 2.7
$\dot{\gamma }$	RV slope (m s−1 day−1)	−0.0060 ± 0.0015	−0.0059 ± 0.0017	−0.0060 ± 0.0015	−0.0060 ± 0.0017
$e\cos {\omega }_{* }$		⋯	$-{0.004}_{-0.051}^{+0.049}$	⋯	${0.000}_{-0.050}^{+0.064}$
$e\sin {\omega }_{* }$		⋯	${0.031}_{-0.042}^{+0.068}$	⋯	${0.058}_{-0.060}^{+0.084}$

Note.

^aHansen & Barman (2007).

Download table as:  ASCIITypeset image

We examined the three-dimensional space motion of KELT-11 to determine whether its kinematics match that of one of the main stellar populations of the Galaxy. The proper motion is −78.30 ± 0.95 mas yr⁻¹ in right ascension, and −77.61 ± 0.68 mas yr⁻¹ in declination (van Leeuwen 2007). The values for the absolute heliocentric RV as measured by the spectroscopic observations from Keck and APF (see Sections 2.3.2 and 2.3.3) are mutually consistent, and we adopt the value from the Keck results, which is 35.0 ± 0.1 km s⁻¹. The distance to the system as derived in Section 3.2 is 98 ± 5 pc. These values transform to U, V, W space motions with respect to the local standard of rest (LSR) of −9.6 ± 1.2, −46.2 ± 3.0, and −8.4 ± 3.4 km s⁻¹, respectively. When calculating the UVW motion, we have accounted for the peculiar velocity of the Sun with respect to the LSR, using U = 8.5 km s⁻¹, V = 13.38 km s⁻¹, and W = 6.49 km s⁻¹ from Coşkunoǧlu et al. (2011). These values are consistent with that of a fast-moving thin disk star (Bensby et al. 2003).

Using a modified version of the IDL exoplanet fitting package, EXOFAST (Eastman et al. 2013), we perform a simulataneous MCMC analysis on the KECK HIRES and APF RV measurements, and the follow-up photometric observations by the KELT Follow-up Network. See Siverd et al. (2012) for a more complete description of the global modeling. For KELT-11b, we use either the Yonsei–Yale stellar evolution models (Demarque et al. 2004) or the Torres relations (Torres et al. 2010) to constrain M_⋆ and R_⋆. Our SED analysis (Section 3.2) of the catalog photometry of KELT-11 yielded an observed bolometric flux from the star of 1.82 × 10⁻⁸ erg s⁻¹ cm⁻². We use the resulting stellar radius of R_* = 2.8 ± 0.3 ${R}_{\odot }$ as a prior in the global fit. From the KELT discovery data and follow-up photometric and spectroscopic observations, we set a prior on the host star's effective temperature (${T}_{\mathrm{eff}}$ = 5391 ± 50 K) and metallicity ($[\mathrm{Fe}/{\rm{H}}]$ = 0.189 ± 0.08). All priors have Gaussian distributions.

The raw light curve and detrending parameters (see Table 4 for detrending parameters of each data set) are inputs into the final global fit using EXOFAST. For KELT-11b, we ran four separate EXOFAST fits using either the Torres relations or Yonsei–Yale stellar evolution models. For each stellar constraint, we ran one fit where the eccentricity of the planet's orbit was a free parameter and another where it was fixed at an eccentricity of zero. The results of these fits are shown in Tables 8 and 9. In Table 9, the quantities T_C,1, T_C,2, etc., refer to the determination of the transit center time for each of the follow-up light curves used in the model, shown in Figure 2. Because all but one of our follow-up photometry light curves are partial transits, we do not fit for transit timing variations as part of the global fit. The secondary eclipse parameters in all cases are not directly measured, but are rather based on the global fit. All four global fits are consistent with each other to within 2σ. For our overall analysis and discussion, we adopt the Yonsei–Yale circular fit parameters. We select Yonsei–Yale mainly because there are no stars in the sample from which the Torres relations were derived with the combination of ${T}_{\mathrm{eff}}$ and $\mathrm{log}{g}_{* }$ that KELT-11 has, and with the short orbital period, there is a strong prior of zero eccentricity. However, since all fits yield similar results, we do not believe the particular choice significantly affects the overall system parameters.

Table 9.  Median Values and 68% Confidence Interval for the Physical and Orbital Parameters of the KELT-11 System

Parameter	Units	Adopted Value	Value	Value	Value
		(YY Circular; e = 0 Fixed)	(YY Eccentric)	(Torres Circular; e = 0 Fixed)	(Torres Eccentric)
Primary Transit
RP/R*	Radius of the planet in stellar radii	0.0519 ± 0.0026	0.0516 ± 0.0026	0.0526 ± 0.0027	0.0520 ± 0.0026
$a/{R}_{* }$	Semimajor axis in stellar radii	${4.93}_{-0.29}^{+0.26}$	${4.80}_{-0.27}^{+0.28}$	${4.71}_{-0.32}^{+0.36}$	${4.56}_{-0.29}^{+0.32}$
i	Inclination (°)	${85.8}_{-1.8}^{+2.4}$	${86.4}_{-2.2}^{+2.3}$	${84.4}_{-1.8}^{+2.6}$	${85.4}_{-2.3}^{+2.9}$
b	Impact parameter	${0.36}_{-0.20}^{+0.13}$	${0.29}_{-0.19}^{+0.17}$	${0.46}_{-0.19}^{+0.11}$	${0.34}_{-0.22}^{+0.17}$
δ	Transit depth	${0.00269}_{-0.00026}^{+0.00028}$	${0.00267}_{-0.00026}^{+0.00027}$	${0.00276}_{-0.00028}^{+0.00029}$	${0.00271}_{-0.00027}^{+0.00028}$
TFWHM	FWHM duration (days)	0.2874 ± 0.0048	0.2873 ± 0.0047	${0.2876}_{-0.0048}^{+0.0049}$	${0.2877}_{-0.0045}^{+0.0048}$
τ	Ingress/egress duration (days)	${0.0173}_{-0.0021}^{+0.0029}$	${0.0164}_{-0.0016}^{+0.0029}$	${0.0193}_{-0.0032}^{+0.0038}$	${0.0172}_{-0.0021}^{+0.0039}$
T14	Total duration (days)	${0.3051}_{-0.0051}^{+0.0053}$	${0.3043}_{-0.0052}^{+0.0053}$	${0.3072}_{-0.0053}^{+0.0059}$	${0.3056}_{-0.0052}^{+0.0058}$
PT	A priori non-grazing transit probability	${0.1925}_{-0.0096}^{+0.012}$	${0.205}_{-0.018}^{+0.024}$	0.201 ± 0.014	${0.221}_{-0.024}^{+0.033}$
${P}_{T,G}$	A priori transit probability	${0.214}_{-0.011}^{+0.013}$	${0.228}_{-0.020}^{+0.027}$	${0.224}_{-0.016}^{+0.017}$	${0.246}_{-0.027}^{+0.037}$
${T}_{C,0}$	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457024.0176}_{-0.0028}^{+0.0030}$	${2457024.0175}_{-0.0029}^{+0.0030}$	${2457024.0179}_{-0.0029}^{+0.0031}$	${2457024.0179}_{-0.0027}^{+0.0030}$
TC,1	Mid- transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457061.9098}_{-0.0024}^{+0.0026}$	${2457061.9098}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0024}^{+0.0026}$
TC,2	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457061.9098}_{-0.0024}^{+0.0026}$	${2457061.9098}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0024}^{+0.0026}$
TC,3	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457061.9098}_{-0.0024}^{+0.0026}$	${2457061.9098}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0025}^{+0.0027}$	${2457061.9101}_{-0.0024}^{+0.0026}$
TC,4	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457090.3290}_{-0.0022}^{+0.0024}$	${2457090.3289}_{-0.0022}^{+0.0024}$	${2457090.3293}_{-0.0023}^{+0.0025}$	${2457090.3292}_{-0.0022}^{+0.0024}$
TC,5	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457095.0655}_{-0.0022}^{+0.0024}$	${2457095.0655}_{-0.0022}^{+0.0024}$	${2457095.0658}_{-0.0022}^{+0.0024}$	${2457095.0657}_{-0.0022}^{+0.0024}$
TC,6	Mid- transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457099.8021}_{-0.0021}^{+0.0024}$	${2457099.8020}_{-0.0022}^{+0.0024}$	${2457099.8024}_{-0.0022}^{+0.0024}$	${2457099.8023}_{-0.0021}^{+0.0024}$
TC,7	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457147.1674}_{-0.0019}^{+0.0021}$	${2457147.1673}_{-0.0020}^{+0.0021}$	${2457147.1677}_{-0.0019}^{+0.0021}$	${2457147.1675}_{-0.0019}^{+0.0021}$
TC,8	Mid-transit time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457440.8323}_{-0.0036}^{+0.0042}$	${2457440.8319}_{-0.0036}^{+0.0041}$	${2457440.8325}_{-0.0038}^{+0.0043}$	${2457440.8318}_{-0.0037}^{+0.0040}$
u1I	Linear Limb-darkening	${0.3466}_{-0.0093}^{+0.0094}$	${0.3462}_{-0.0092}^{+0.0094}$	0.3437 ± 0.0094	0.3434 ± 0.0094
u2I	Quadratic Limb-darkening	0.2510 ± 0.0050	0.2511 ± 0.0049	0.2533 ± 0.0050	0.2536 ± 0.0050
u1R	Linear Limb-darkening	0.446 ± 0.012	0.446 ± 0.012	0.443 ± 0.012	0.443 ± 0.012
u2R	Quadratic Limb-darkening	${0.2374}_{-0.0071}^{+0.0070}$	0.2376 ± 0.0070	${0.2398}_{-0.0071}^{+0.0070}$	${0.2401}_{-0.0070}^{+0.0071}$
${u}_{1\mathrm{Sloang}}$	Linear Limb-darkening	0.695 ± 0.017	0.695 ± 0.017	0.692 ± 0.017	0.692 ± 0.017
${u}_{2\mathrm{Sloang}}$	Quadratic Limb-darkening	0.117 ± 0.013	0.117 ± 0.013	0.120 ± 0.013	0.120 ± 0.013
${u}_{1\mathrm{Sloani}}$	Linear Limb-darkening	0.371 ± 0.010	${0.3702}_{-0.0100}^{+0.010}$	0.368 ± 0.010	0.367 ± 0.010
${u}_{2\mathrm{Sloani}}$	Quadratic Limb-darkening	${0.2485}_{-0.0055}^{+0.0054}$	0.2486 ± 0.0054	0.2508 ± 0.0055	${0.2511}_{-0.0055}^{+0.0054}$
${u}_{1\mathrm{Sloanr}}$	Linear Limb-darkening	0.476 ± 0.013	0.475 ± 0.013	0.472 ± 0.013	0.472 ± 0.013
${u}_{2\mathrm{Sloanr}}$	Quadratic Limb-darkening	${0.2316}_{-0.0078}^{+0.0077}$	${0.2318}_{-0.0077}^{+0.0076}$	0.2340 ± 0.0077	0.2343 ± 0.0077
${u}_{1\mathrm{Sloanz}}$	Linear Limb-darkening	0.2976 ± 0.0075	0.2974 ± 0.0074	${0.2952}_{-0.0075}^{+0.0074}$	0.2949 ± 0.0075
${u}_{2\mathrm{Sloanz}}$	Quadratic Limb-darkening	${0.2549}_{-0.0036}^{+0.0037}$	${0.2549}_{-0.0036}^{+0.0035}$	0.2568 ± 0.0036	0.2570 ± 0.0036
Secondary Eclipse
TS	Time of eclipse (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2457059.5415}_{-0.0025}^{+0.0027}$	${2457064.27}_{-0.16}^{+0.15}$	${2457059.5418}_{-0.0025}^{+0.0027}$	${2457064.28}_{-0.15}^{+0.19}$
bS	Impact parameter	⋯	${0.31}_{-0.20}^{+0.16}$	⋯	${0.39}_{-0.24}^{+0.15}$
${T}_{S,\mathrm{FWHM}}$	FWHM duration (days)	⋯	${0.303}_{-0.022}^{+0.042}$	⋯	${0.315}_{-0.029}^{+0.057}$
τS	Ingress/egress duration (days)	⋯	${0.0183}_{-0.0024}^{+0.0029}$	⋯	${0.0205}_{-0.0031}^{+0.0039}$
TS,14	Total duration (days)	⋯	${0.322}_{-0.023}^{+0.043}$	⋯	${0.336}_{-0.030}^{+0.058}$
PS	A priori non-grazing eclipse probability	⋯	${0.1890}_{-0.0069}^{+0.013}$	⋯	${0.1934}_{-0.0093}^{+0.016}$
${P}_{S,G}$	A priori eclipse probability	⋯	${0.2095}_{-0.0079}^{+0.014}$	⋯	${0.215}_{-0.011}^{+0.018}$

Download table as:  ASCIITypeset image

Our stellar parameter priors strongly favor young, pre-main sequence stars, and also imply a mass prior strongly peaked at 1 M_⊙ with a long tail toward higher masses. However, our global fit, due to the stellar density constraint from the transit, excludes the peak of this prior with high confidence, enhancing the importance of the high mass tail. The prior around the value of the ultimately inferred mass is biased slightly toward lower-mass stars relative to a flat, "uninformative" prior. We believe this is justified because generally lower-mass stars with temperatures and surface gravities consistent with those measured for KELT-11 are favored both because higher-mass stars are rarer and because they spend less time in this region of the HR diagram.

We find a negative slope in the RV observations of −0.006 ± 0.0015 m s⁻¹ day⁻¹. That is most likely a result of an outer massive companion in orbit around KELT-11. Since there is no evidence of significant curvature in the slope, the companion must have an orbital period longer than about 20 years. The companion could be a large planet or a brown dwarf, but it likely cannot be stellar mass, since there are no signs of an additional object in the spectral analysis. As noted in Section 2.4, there are no indications of a companion in the AO observations, though those observations are most sensitive at wide separations from the star.

We find that KELT-11b is a highly inflated planet, joining the ranks of other gas giant planets that manifest radii much larger than predicted by standard models of irradiated objects with Jovian masses, which do not invoke additional sources of energy deposition in the interior of the planet. Several authors (e.g., Demory & Seager 2011) have suggested an empirical insolation threshold (≈2 × 10⁸ erg s⁻¹ cm⁻²) above which gas giants exhibit increasing amounts of radius inflation. KELT-11b clearly lies above this threshold, with a current estimated insolation of ${1.95}_{-0.20}^{+0.24}\times {10}^{9}$ erg s⁻¹ cm⁻² and therefore its currently large inflated radius is not surprising. At the same time, the KELT-11 host star is found to currently be in a very rapid state of evolution, such that its radius is rapidly expanding as the star crosses the Hertzsprung gap toward the red giant branch. This means that the star's surface is rapidly encroaching on the planet, which presumably is rapidly driving up the planet's insolation and also the rate of any tidal interactions between the planet and the star.

Therefore it is interesting to consider whether KELT-11b's incident radiation from its host star has been below the empirical radius inflation threshold in the past. If KELT-11b's insolation only recently exceeded the inflation threshold, the system could then serve as an empirical testbed for the different timescales predicted by different inflation mechanisms (see, e.g., Assef et al. 2009; Spiegel & Madhusudhan 2012).

To investigate this, we follow Penev et al. (2014) to simulate the past and future evolution of the star–planet system, using the measured parameters listed in Tables 8 and 9 as the present-day boundary conditions. This analysis is not intended to examine any type of planet–planet or planet–disk migration effects. Rather, it is a way to investigate the change in 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, assumed to follow the Yonsei–Yale stellar model with mass and metallicity as in Table 8. For simplicity, we assume that the stellar rotation is negligible and treat the star as a solid body. We also assume a circular orbit aligned with the stellar equator throughout the full analysis. The results of our simulations are shown in Figure 9. We tested a range of values for the tidal quality factor of the star ${Q}_{\star }^{\prime }$, from $\mathrm{log}{Q}_{\star }^{\prime }=6$ to $\mathrm{log}{Q}_{\star }^{\prime }=8$ (assuming a constant phase lag between the tidal bulge and the star–planet direction). ${Q}_{\star }^{\prime }$ is defined as the tidal quality factor divided by the Love number (i.e., ${Q}_{\star }^{\prime }={Q}_{\star }/{k}_{2}$).

Zoom In Zoom Out Reset image size

We find that in all cases the planet has always received more than enough flux from its host to keep the planet irradiated beyond the insolation threshold identified by Demory & Seager (2011).

We examine several lines of evidence to explore whether the combination of observations of this system are caused by a false positive, such as a blended eclipsing binary. First, we verify that all photometric observations of the transit are consistent with achromatic transit depths (see Section 2.2), since wavelength-dependent transit depths at the level detectable by our photometry would indicate that this is a blended eclipsing binary. We then check that in the KELT-11 spectra there are no signs of a second stellar spectrum blended with the spectrum of the host star (see Section 2.3), and we also see no faint companions blended with KELT-11b in the AO observations (Section 2.4). We also find no correlation between the BSs and the measured RVs (see Figure 4). The stellar surface gravity ($\mathrm{log}(g)={3.727}_{-0.046}^{+0.040}$) derived from the transits in the global fit, with no spectroscopic $\mathrm{log}{g}_{* }$ prior imposed, is consistent with the three spectroscopically derived $\mathrm{log}{g}_{* }$ values (see Table 7) within ≈1σ. We therefore conclude that KELT-11b is a bona fide planet.

We find that the KELT-11 host star is located in a relatively sparsely populated part of the Hertzsprung–Russell (H–R) diagram, namely the "Hertzsprung gap." This is the part of the H–R diagram, where relatively massive stars (M_* ≳ 1.5 M_⊙) have finished core hydrogen fusion, but have yet to initiate hydrogen shell fusion, i.e., they have yet to reach the giant branch. In other words, this region is typically populated by relatively massive subgiants. This part of the diagram is sparsely populated because massive stars spend a very small amount of time in this phase of their evolution relative to the duration of their hydrogen main sequence or giant branch evolutionary states, and because massive stars are intrinsically more rare than less massive stars. It is precisely the short duration of this massive star's subgiant phase that allows us to put such a precise (albeit model-dependent) constraint on the age of the star.

However, the rapid evolution through this part of the H–R diagram and the relative paucity of massive stars also implies that it is a priori unlikely that we would have found a transiting planet orbiting such a star. We therefore must be more diligent than usual in justifying our claims of the estimated parameters of the host star. The parameter that most strongly controls the duration of the star's time during the subgiant phase is the stellar mass. Therefore, we concentrate our subsequent discussion on our confidence in the accuracy of our estimate of the stellar mass, and in particular our inference that the star is relatively massive (M_* ≳ 1.3 M_⊙).

The fiducal parameters (including mass) we adopt for KELT-11 are obtained using a global fit as described in Section 3.5. Along with the photometric and RV data, this fit used priors on the stellar effective temperature and metallicity from high-resolution spectroscopy, and stellar radius as determined from the SED and Hipparcos parallax (see Section 3.2). For our fiducial adopted values, we also used constraints from the YY evolutionary models and assumed zero eccentricity. We also explored the parameters inferred assuming eccentric orbits, as well as using the Torres et al. (2010) empirical relations for the mass and radius of the host star as a function of the stellar effective temperature, surface gravity, and metallicity.

Our procedure, or similar procedures (see Holman et al. 2007; Sozzetti et al. 2007), are commonly used to estimate the masses and radii of transiting planet hosts and their planets. However, it is worth recalling that a single-lined spectroscopic binary with only a primary eclipse does not yield a complete solution to the system. Indeed, as pointed out by Seager & Mallén-Ornelas (2003), the only parameter that is directly measured from the photometry and RVs of such a system is the parameter a/R_*, which can be related to the stellar density with the (typically reasonable) assumption that R_p ≪ R_* and M_p ≪ M_* (and a measurement or constraint on the eccentricity). Therefore, there is a one-parameter degeneracy between M_* and R_* for such systems, unless one includes additional direct observables of the system, or invokes model isochrones or empirical relations based on other stars. Using the latter may have some pitfalls, as described below.

For stars with properties that are not too different from the Sun, we can expect that both the YY isochrones and Torres et al. (2010) relations should be fairly reliable. However, it is worth pointing out that it is known that sometimes these do not agree. In particular, Collins et al. (2014) demonstrated that the parameters inferred for the host star of KELT-6b, which happens to be relatively metal-poor ($[\mathrm{Fe}/{\rm{H}}]$ ∼ −0.3), are significantly different when obtained using the YY constraints relative to those obtained using the Torres et al. (2010) relations. This is likely because the YY isochrones and/or the Torres et al. (2010) relations are not very accurate at low metallicity. It is also worth noting that only a small subset of the stars used to calibrate the Torres et al. (2010) relations have metallicity measurements.

In the case of KELT-11, we are fortunate to have another constraint on the property of the host star, specifically the host star radius. However, there are also some unusual difficulties with this system. Because the parallax measurement is relatively imprecise (∼10%), this radius constraint is relatively poor. Furthermore, the constraint on the stellar density measured directly from the light curve and the radial velocities is also relatively poor, due to the shallow depth and long duration, and the relatively weak constraint on the eccentricity. Therefore, our final estimate of the mass and radius of KELT-11 is strongly influenced by our prior from the YY models or the Torres et al. (2010) relations. This is problematic because the YY models have not been well-calibrated for massive subdwarfs (because there are so few of them with direct mass measurements), and because there are no stars in the Torres et al. (2010) sample with the parameters we infer for KELT-11. Thus by invoking the Torres et al. (2010) relations, we are essentially extrapolating them from where they were calibrated.

Thus, given our relatively a priori unlikely inference that this is a relatively massive star (in a short phase of its lifetime), it is worth exploring what "model-independent" estimates of the stellar mass we can infer. There are two essentially direct (but not entirely independent) methods we can use to estimate the mass of the star without invoking the YY isochrones or the Torres et al. (2010) relations.

First, we can use the estimate of the surface gravity of the star from high-resolution spectra, combined with the measurement of R_* from the parallax and SED, to break the ${M}_{* }-{R}_{* }$ degeneracy. This is problematic on its own because the surface gravities derived from spectra can have relatively large systemic errors, even with high S/N spectra (Torres et al. 2012), and furthermore spectroscopic surface gravities are also notoriously inaccurate for stars on the subgiant branch (Holtzman et al. 2015). Nevertheless, we can employ this process to provide a "direct" method of estimating the mass of KELT-11. Adopting the surface gravity from the TRES spectra of $\mathrm{log}{g}_{* }$ = 3.79 ± 0.10, we find M_* = 1.81 ± 0.44 ${M}_{\odot }$. Adopting instead $\mathrm{log}{g}_{* }$ = 3.86 ± 0.10 from the APF or Keck spectra, we find M_* = 2.13 ± 0.57 ${M}_{\odot }$. Thus, this procedure leads us to infer that KELT-11 is a relatively massive star. The mass we infer is significantly higher and less precise than the global fit results, but formally does not rely on any models or empirical relations (though it does rely on the spectroscopic surface gravity).

Second, if we wish to avoid using the spectroscopic $\mathrm{log}{g}_{* }$ as well as any stellar models or empirical relations, we could in principle determine the stellar mass purely through the transit light curve and the stellar radius determined from the parallax and SED. The relation between the stellar mass and the direct observables is

$$\begin{eqnarray}&&{M}_{* }=\left(\displaystyle \frac{4{{PR}}_{* }^{3}}{\pi {{GT}}_{\mathrm{FWMH}}^{3}}\right){\left(\displaystyle \frac{\sqrt{1-{e}^{2}}}{1+e\sin \omega }\right)}^{3}{(1-{b}^{2})}^{3/2},\end{eqnarray} \tag{ 1 }$$

assuming R_p ≪ R_* and M_p ≪ M_*. The first factor in parentheses is reasonably well measured, and is ∼1.82 M_⊙. This depends on our estimate of T_FWHM from the global fit, but this is fairly well constrained from the follow-up photometry alone. We are also in the process of analyzing Spitzer observations (Spitzer ID 12096) of the primary eclipse of this target, and a preliminary analysis verifies the value of T_FWHM derived in this paper. The second factor in parentheses depends on the eccentricity, which is not well constrained. We find that the orbit is consistent with circular, but the eccentricity could be as high as 0.16 at 1σ. Thus this factor may vary from ∼0.5 to ∼1.3. Finally, the impact parameter is also poorly constrained by our data due the shallowness and duration of the transit, but is constrained to be <0.5 at 1σ. In fact, visual inspect of our preliminary Spitzer reduction indicates that the transit is unlikely to have an impact parameter as high as ∼0.5. Nevertheless, allowing for this full range, we find that the last term can be anywhere between 1 and 0.65. Thus the full range of allowed masses is 0.6–2.4 M_⊙, although we strongly favor values of ≳1.6 M_⊙ based on our preliminary Spitzer data that are consistent with a nearly central transit and our strong prior that the orbit is likely to be circular.

Thus we have four methods of estimating the mass of the primary: (1) using YY isochrones, (2) using the Torres empirical relations, (3) using the spectroscopic $\mathrm{log}{g}_{* }$ combined with an estimate of the stellar radius from the SED and parallax, and (4) using the density of the star from the transit period and duration, impact parameter, and a constraint on the eccentricity combined with the radius from the SED and parallax. These four methods demonstrate that KELT-11 has a mass around ≳1.3 M_⊙, and potentially larger. In particular, the global modeling using the YY isochrones and the Torres et al. (2010) relations finds good agreement, deriving masses of ${M}_{* }={1.438}_{-0.052}^{+0.061}\,{M}_{\odot }$ and ${M}_{* }={1.347}_{-0.068}^{+0.072}\,{M}_{\odot }$, respectively (assuming a circular orbit). The model-independent or quasi-model-independent methods described above yield larger mass estimates but with significantly larger errors, and thus all four estimates are nominally consistent. Although it is possible (and perhaps even likely) that there are significant systematic errors in all four of these estimates, we believe it is unlikely that those sytematics would all collude to lead us to the interpretation that this star is significantly more massive than the Sun, if, in fact, it is not.

The fact that KELT-11 hosts a transiting planet makes it a particularly valuable member of the "Retired A-star" sample of Johnson et al. (2007). Stars with transiting planets allow an additional constraint on the properties of the host star, namely a direct measurement of a/R_*, and, given the (reasonable) assumption of R_p ≪ R_* and M_p ≪ M_*, and a measurement or constraint on the eccentricity, and an estimate of the host star density ρ_*. Currently, the constraint on the density of KELT-11 is relatively poor because of the imprecise measurement of transit duration and ingress/egress time (T_FWHM and τ) due to the relatively shallow and long duration of the transit. Nevertheless, when combined with an independent estimate of its radius derived from the fact that it has a direct distance measurement via the Hipparcos parallax, this provides a second, purely empirical estimate of the mass of the host star. The fact that this estimate agrees with our more model-dependent estimate of the host star mass via global fitting using isochrones, and the fact that these further agree with our estimate of the host star using the empirical relations of Torres et al. (2010), gives us confidence that the host star mass is indeed significantly more massive than ∼1.2 M_⊙, and thus the host star really is a "Retired A (or early F) star."

Once we have fully analyzed the above-mentioned Spitzer follow-up photometry of a primary transit of KELT-11b, we will have a much more precise measurement of T_FWHM and τ, and thus ρ_*. When combined with an exquisite measurement of the stellar parallax with Gaia (Perryman et al. 2001) and thus stellar radius, we will be able to provide much more accurate, precise, and essentially direct empirical constraint on the host star mass, using the methods described previously.