Three Statistically Validated K2 Transiting Warm Jupiter Exoplanets Confirmed as Low-mass Stars

The three targets were observed by K2 during Campaign 2 (EPIC 202900527) and Campaign 3 (EPIC 206155547 and EPIC 206432863), in long cadence (29.4 minute integration time). We reduced the K2 light curves following Vanderburg & Johnson (2014) and Vanderburg et al. (2016). Upon identifying the transits we re-processed the light curves by simultaneously fitting for the transits, K2 thruster systematics, and low-frequency variations as described by Vanderburg et al. (2016). The phase-folded light curves are plotted in Figure 1.

Zoom In Zoom Out Reset image size

The Keck/HIRES data analyzed and presented here include 20 spectra at a resolution of R ∼ 60,000. We obtained 7 spectra of EPIC 206155547 and 13 of EPIC 206432863, during 18 nights from 2015 August 1 UT to 2017 June 28 UT. We have also obtained a Keck/HIRES spectrum of EPIC 202900527, used only for spectroscopic characterization of the primary star and not for radial velocity (RV) measurement (see Sections 2.3 and 3.1).

We used the Keck/HIRES instrumental setup of the California Planet Search (Howard et al. 2009). Since we can tolerate a medium RV precision of ∼0.1 km s⁻¹, we used the so-called telluric lines method where the iodine cell is removed from the light path (see, e.g. Shporer et al. 2016, their Section 2.2). Briefly, a wavelength solution is obtained through a nightly exposure of a Thorium–Argon lamp and the RVs are derived by measuring the offset in the position of the telluric absorption bands in the target spectra and that of a reference B-type star (Chubak et al. 2012). The RV due to Earth's barycentric motion is then removed, resulting in the target's absolute systemic velocity (Nidever et al. 2002; Chubak et al. 2012).

We used exposure times of 1.5–20 minutes, depending on target brightness, and the spectra we obtained have a signal-to-noise ratio (S/N) of 20–40 per pixel. Keck/HIRES RV measurements are listed in Table 1, and the phase-folded RV curves of EPIC 206155547 and EPIC 206432863 are shown in Figure 2.

Zoom In Zoom Out Reset image size

We obtained 11 spectra of EPIC 202900527 using the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész 2008) at the FLWO 1.5 m telescope on Mount Hopkins, Arizona. The TRES spectra have a resolution of R ∼ 44,000 and were collected between 2015 May 26 UT and 2017 June 10 UT. We used exposure times between 22 and 34 minutes, which resulted in an S/N per resolution element of 17–29.

We reduced and extracted the TRES spectra as described by Buchhave et al. (2010). We derived the RVs by cross correlating each spectrum order by order against the observed spectrum with the highest S/N in the wavelength range of 4520–6280 Å. EPIC 202900527 11 TRES RVs are listed in Table 1, and the phase-folded RV curve is shown in Figure 2.

The reference (or template) spectrum is at BJD = 2457854.95084 and its RV is listed as 0.0 km s⁻¹ in Table 1. To allow putting the TRES RVs on an absolute scale, we determined the template spectrum absolute RV by cross correlating it with a synthetic spectrum to be −57.87 ± 0.10 km s⁻¹. This RV offset is not added to the RVs in Table 1 to avoid inflating their uncertainties.

We derived the spectroscopic stellar parameters using the SpecMatch package (Petigura 2015; Petigura et al. 2017) and the iodine-free HIRES spectra of each star. Those include the effective temperature ${T}_{\mathrm{eff}}$, surface gravity $\mathrm{log}g$, metallicity [Fe/H], and stellar rotation projected on the line of sight $V\sin (I)$, where V is the equatorial rotation and I is the stellar rotation inclination angle. We averaged the parameters extracted from all of the individual observations. The observation-to-observation parameter variance was smaller than the quoted $1\sigma$ uncertainties in all cases. The SpecMatch results are listed in Table 2.

Table 2.  Fitted and Derived Parameters

Parameter	EPIC 202900527 (K2-51)			EPIC 206155547 (K2-67)			EPIC 206432863 (K2-76)
	Value	+$1\sigma$	−$1\sigma$	Value	+$1\sigma$	−$1\sigma$	Value	+$1\sigma$	−$1\sigma$
Spectroscopic parametersa
${T}_{\mathrm{eff}}$ (K)	5548	60	60	5907	60	60	5762	60	60
$\mathrm{log}g$ (cgs)	4.17	0.07	0.07	4.13	0.07	0.07	4.20	0.07	0.07
[Fe/H]	+0.32	0.04	0.04	−0.32	0.04	0.04	+0.01	0.04	0.04
$V\sin (I)$ (km s−1)	11.4	0.5	0.5	<2	⋯	⋯	5.3	1.8	1.8
Fitted parametersb
P (day)	13.00847	0.00027	0.00018	24.38752	0.00072	0.00067	11.98980	0.00017	0.00018
${T}_{0}-$2456900 (BJD)	5.75715	0.00069	0.00090	85.88408	0.00094	0.00086	83.82617	0.00055	0.00054
M1 (${M}_{\odot }$)	1.068	0.029	0.032	0.916	0.031	0.029	0.964	0.026	0.026
R1 (${R}_{\odot }$)	1.695	0.049	0.037	1.399	0.079	0.056	1.171	0.060	0.033
M2 (${M}_{\odot }$)	0.1459	0.0029	0.0032	0.1612	0.0072	0.0067	0.0942	0.0019	0.0019
${R}_{2}/{R}_{1}$	0.10047	0.00066	0.00065	0.14261	0.00130	0.00087	0.07843	0.00081	0.00046
i (deg)	89.98	1.08	0.97	89.37	0.43	0.52	89.35	0.43	0.42
$\sqrt{e}\cos \omega$	0.403	0.010	0.016	0.452	0.016	0.017	−0.4081	0.0104	0.0098
$\sqrt{e}\sin \omega$	0.4656	0.0078	0.0106	0.397	0.040	0.044	−0.2971	0.0104	0.0098
γc (km s−1)	−8.945	0.082	0.081	42.09	0.36	0.36	−6.506	0.050	0.053
Jitter s (km s−1)	0.170	0.150	0.090	0.81	0.40	0.36	0.107	0.070	0.056
[Fe/H]	+0.325	0.045	0.042	−0.318	0.043	0.044	+0.010	0.041	0.038
u1 d	0.4714	⋯	⋯	0.3272	⋯	⋯	0.3921	⋯	⋯
u2 d	0.2185	⋯	⋯	0.2971	⋯	⋯	0.2630	⋯	⋯
${F}_{2}/{F}_{1}$ e (ppm)	<190	⋯	⋯	560	160	180	<97	⋯	⋯
Derived parameters
R2 (${R}_{\odot }$)	0.1702	0.0046	0.0032	0.1996	0.0119	0.0067	0.0913	0.0048	0.0026
K (km s−1)	12.53	0.10	0.10	12.00	0.14	0.14	8.720	0.069	0.074
$a/{R}_{1}$	14.66	0.23	0.33	25.80	0.98	1.06	19.17	0.52	0.89
${T}_{\mathrm{eff}}$ (K)	5579	77	78	5908	64	63	5747	70	64
$\mathrm{log}g$ (cgs)	4.01	0.011	0.015	4.104	0.024	0.038	4.288	0.033	0.020
${L}_{1}\,({L}_{\odot })$	2.52	0.39	0.22	2.17	0.31	0.22	1.36	0.13	0.12
${L}_{2}\,({L}_{\odot })$ e	<0.00010	⋯	⋯	0.00114	0.00037	0.00043	<0.00011	⋯	⋯
Age (Gyr)	8.49	0.97	1.35	10.4	1.2	1.0	9.16	0.93	0.91
a (au)	0.11545	0.00091	0.00087	0.1687	0.0017	0.0017	0.10439	0.00093	0.00090
b	0.118	0.119	0.082	0.20	0.15	0.14	0.24	0.14	0.16
T14 (day)	0.2222	0.0016	0.0014	0.2533	0.0031	0.0022	0.2380	0.0020	0.0013
T12 (day)	0.02051	0.00102	0.00034	0.03276	0.0034	0.0013	0.0183	0.0021	0.0010
e	0.3797	0.0058	0.0090	0.360	0.016	0.018	0.2545	0.0065	0.0070
ω (deg)	40.7	1.1	1.7	48.6	3.9	3.6	−126.1	1.5	1.5
Occultation Phasef	0.6579	0.0048	0.0076	0.6764	0.0015	0.0021	0.3692	0.0046	0.0047
bocc	0.20	0.22	0.14	0.33	0.24	0.22	0.18	0.10	0.12

Notes.

^aDerived using SpecMatch analysis of the spectra. ^bModel fit parameters, fitted to the K2 light curve, RVs, and stellar isochrones. Gaussian priors are applied to [Fe/H] using the values derived from the SpecMatch spectroscopic analysis. See Section 3 for more information. ^cFor EPIC 206155547 and EPIC 206432863 γ is the binary system's center of mass RV since the HIRES RVs are on an absolute scale. For EPIC 202900527 the RV of the template spectrum (−57.87 ± 0.10 km s⁻¹; see Section 2.3) needs to be added to γ to get the center of mass RV. ^dParameter fixed during the model fitting process. ^e $3\sigma$ upper limit given when no eclipse was detected. ^fThe transit, or primary eclipse, is at phase zero.

Download table as:  ASCIITypeset image

We performed a global modeling of the available photometric and RV measurements, along with the spectroscopic atmospheric properties of the primary star, to derive the parameters for each system. For stellar binaries, the transit-derived orbital semimajor axis normalized by the primary stellar radius $a/{R}_{1}$ is dependent on the sum of the two components' masses ${M}_{1}+{M}_{2}$ and the volume of the primary star, as per Sozzetti et al. (2007):

$$\begin{eqnarray}&&{\left(\displaystyle \frac{a}{{R}_{1}}\right)}^{3}=\displaystyle \frac{G}{4{\pi }^{2}}{P}^{2}\displaystyle \frac{{M}_{1}+{M}_{2}}{{R}_{1}^{3}},\end{eqnarray} \tag{ 1 }$$

where P is the orbital period and G the gravitational constant. To take advantage of this relation, we fit directly for the masses of the two stars, the primary radius, and the secondary-to-primary radii ratio ${R}_{2}/{R}_{1}$, as well as the standard transit and RV orbital parameters including the orbital period P, mid-transit time T₀, line-of-sight orbital inclination i, orbital eccentricity parameters $\sqrt{e}\cos \omega$ and $\sqrt{e}\sin \omega$ (where e is the orbital eccentricity and ω the argument of periastron), RV zero-point γ, RV jitter s, and the primary metallicity [Fe/H]. We include the secondary eclipse in our model, where the eclipse depth is the secondary-to-primary flux ratio in the Kepler band $({F}_{2}/{F}_{1})$. We used the model of Mandel & Agol (2002) for the transit and secondary eclipse light curves.

At each iteration we use the trial masses and eccentricity to calculate the normalized orbital semimajor axis a/R₁, as per Equation (1), and an orbital RV semi-amplitude K. To constrain the stellar masses and radii we interpolate the Dartmouth isochrones (Dotter et al. 2008) at each step over the parameters M₁, R₁, and [Fe/H], to derive an expected ${T}_{\mathrm{eff}}$ value. We then compare the isochrone-derived ${T}_{\mathrm{eff}}$ with that measured spectroscopically and add the difference as a penalty term to the likelihood function. We apply a similar penalty in the likelihood function for the primary star's $\mathrm{log}g$ value, calculated from the tested M₁ and R₁ values, by comparing it to that measured spectroscopically. The stellar metallicity [Fe/H] is constrained by a Gaussian prior over its spectroscopically measured value. The remaining parameters are assumed to have uniform priors. The RV jitter s is calculated as per Haywood et al. (2016).

Quadratic limb-darkening coefficients, u₁ and u₂, are interpolated from Claret (2004) to the atmospheric parameters of each star and are held fixed during the fitting process.

We explore the posterior probability distributions via a Markov Chain Monte Carlo analysis, using the affine invariant ensemble sampler emcee (Foreman-Mackey et al. 2013). The 68.3% confidence regions for the MCMC free parameters, as well as several inferred parameters, are listed in Table 2. The inferred parameters include, in addition to parameters mentioned above, Kepler band luminosity of the primary L₁, and the secondary L₂, system age, impact parameter of the transit b, and of the secondary eclipse (occultation) b_occ, transit duration T₁₄, ingress duration T₁₂, and secondary eclipse phase where primary eclipse (transit) phase is taken as phase zero. The best-fit transit and secondary eclipse light curve models are shown in Figure 1 and the orbital RV curve models in Figure 2.

For the most part the transit parameters we derive are similar to those reported by Crossfield et al. (2016). One notable exception is the orbital period of EPIC 206432863. We find that the true orbital period is exactly half the one reported by those authors. Another difference is our detection of a secondary eclipse for EPIC 206155547, at a depth of ${560}_{-180}^{+160}$ ppm. For EPIC 202900527 and EPIC 206432863 we find no detectable secondary eclipses, and we place $3\sigma$ upper limits on their depths of 190 and 97 ppm, respectively.

The three systems discussed here were validated as planets by Crossfield et al. (2016) based on a statistical procedure that considered possible false-positive scenarios. That statistical validation procedure results in the relative likelihoods of the transit signals being due to a false positive or a true planet. The reported false-positive probabilities (FPPs) were ∼10⁻³ for the EPIC 202900527 and EPIC 206155547 systems and ∼10⁻⁴ for EPIC 206432863. Our identification of these objects as stellar binaries raises the question of why they were initially misclassified as planets.

For EPIC 202900527 and EPIC 206155547 the stellar companions' radii derived by Crossfield et al. (2016) are smaller than derived here by 30% and 20%, respectively. This is clearly one of the primary reasons for the low FPP estimated by Crossfield et al. (2016) for these two systems. The smaller companions' radii followed from a smaller estimate of the host star radius by 20% for both systems and a measured secondary-to-primary radii ratio that is 15% smaller for EPIC 202900527.

To investigate the origin of the smaller host star radii derived by Crossfield et al. (2016), we looked into their stellar characterization calculations (I. Crossfield 2017, private communication) using the isochrones package (Morton 2015a), which are then used by the vespa package (Morton 2015b) to calculate the FPPs. These calculations use optical spectra and broadband photometry, when available, from APASS, 2MASS, and WISE. We noticed that in these two cases the fitted stellar model is a poor fit to the data and is inconsistent with at least some of the input measurements. We believe this resulted from poor-quality broadband photometric measurements with underestimated uncertainties. Therefore, we conclude it is the host stars' poor characterization that led to the underestimated companion radii and the underestimated FPPs. Similar cases of poor stellar characterization can be identified by visually examining the isochrone output diagnostic plots or by calculating a goodness-of-fit metric.

The success of validation methods often relies on the ability to rule out the presence of secondary eclipses, which for systems with eccentric orbits, as those studied here, does not necessarily occur half an orbit away from the transit. While the procedure of Crossfield et al. (2016) did include a search for secondary eclipses throughout the entire orbital phase, it assumed an eclipse duration equal to that of the transit, which is usually not the case in eccentric systems. For EPIC 202900527, EPIC 206155547, and EPIC 206432863 the expected secondary eclipse durations are a factor of 1.66, 1.69, and 0.67 times the primary eclipse duration, respectively. As described in Section 3.2 we have searched for secondary eclipses as part of the global modeling. While we do not detect a secondary eclipse for EPIC 202900527 and EPIC 206432863, we do detect an eclipse for EPIC 206155547, the largest and most massive of the three objects, at close to $3\sigma$ significance. The measured eclipse depth of ${560}_{-180}^{+160}$ ppm is consistent with a stellar secondary and is at least an order of magnitude larger than the expected depth in case the secondary is substellar. The nondetection of this secondary eclipse by Crossfield et al. (2016) might be related to the fact that it is 1.69 times longer than the transit. Although, as noted earlier, the misclassification of EPIC 206155547 resulted from poor host star characterization, a detection of the secondary eclipse would have immediately led to classifying the companion as stellar.

We note that the radius distributions of large planets and small stars overlap, making it difficult for validation procedures to distinguish between the two kinds of objects. For EPIC 206432863 B this becomes especially difficult, since its mass of 0.0942 ± 0.0019 ${M}_{\odot }$ (=98.7 ± 2.0 ${M}_{{\rm{J}}}$) is close to the theoretical minimal stellar mass required for burning hydrogen, and its radius of ${0.0913}_{-0.0026}^{+0.0048}$ ${R}_{\odot }$ (=${0.888}_{-0.025}^{+0.047}$ ${R}_{{\rm{J}}}$) is fully consistent with radii of non-inflated planets. As shown in Figure 3 it is smaller than theoretically expected for its mass, making it further difficult to be identified as a stellar object through statistical validation. In addition, for EPIC 206432863 B Crossfield et al. (2016) report an orbital period that is twice the true value, which may have also affected the validation calculations.