K2-287 b: An Eccentric Warm Saturn Transiting a G-dwarf

Observations of campaign 15 (field centered at R.A. =15:34:28 and decl. = −20:04:44) of the K2 mission (Howell et al. 2014) took place between 2017 August 23 and November 20. The data of K2 campaign 15 was released on 2018 March. We followed the steps described in previous K2CL discoveries to process the light curves and identify transiting planet candidates. Briefly, the K2 light curves for Campaign 15 were detrended using our implementation of the EVEREST algorithm (Luger et al. 2016), and a Box-Least-Squares (Kovács et al. 2002) algorithm was used to find candidate box-shaped signals. The candidates that showed power above the noise level were then visually inspected to reject evident eclipsing binary systems and/or variable stars. We identified 23 candidates in this field. Among those candidates, K2-287 (EPIC 24945186) stood out as a high priority candidate for follow-up due to its relatively long period, deep flat-bottomed transits, and bright host star (V = 11.4 mag). The detrended light curves of the six transits observed for K2-287 by K2 are displayed in Figure 1.

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We obtained 52 R = 48,000 spectra between March and July of 2018 using the FEROS spectrograph (Kaufer et al. 1999) mounted on the 2.2 MPG telescope in the La Silla observatory. Each spectrum achieved a signal-to-noise ratio of ≈90 per spectral resolution element. The instrumental drift was determined via comparison with a simultaneous fiber illuminated with a ThAr+Ne lamp. We additionally obtained 25 R = 115,000 spectra between March and August of 2018 using the HARPS spectrograph (Mayor et al. 2003). Typical signal-to-noise ratio for these spectra ranged between 30 and 50 per spectral resolution element. Both FEROS and HARPS data were processed with the CERES suite of echelle pipelines (Brahm et al. 2017a), which produce radial velocities and bisector spans in addition to reduced spectra.

Radial velocities and bisector spans are presented in Table 1 with their corresponding uncertainties, and the radial velocities are displayed as a function of time in Figure 2. No large amplitude variations were identified, which could be associated with eclipsing binary scenarios for the K2-287 system, and no additional stellar components were evident in the spectra. The radial velocities present a time correlated variation in phase with the photometric ephemeris, with an amplitude consistent with the one expected to be produced by a giant planet. We find no correlation between the radial velocities and the bisector spans (95% confidence intervals for the Pearson coefficient are [−0.19, 0.21], see Figure 3).

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On July 14 of 2018 we observed the primary transit of K2-287 with the Chilean-Hungarian Automated Telescope (CHAT), installed at Las Campanas Observatory, Chile. CHAT is a newly commissioned 0.7 m telescope, built by members of the HATSouth (Bakos et al. 2013) team, and dedicated to the follow-up of transiting exoplanets. A more detailed account of the CHAT facility will be published at a future date (A. Jordán et al. 2018, in preparation¹⁷ ). Observations were obtained in the Sloan i band and the adopted exposure time was of 53 s per image, resulting in a peak pixel flux for K2-287 of ≈45,000 ADU during the whole sequence. The observations covered a fraction of the bottom part of the transit and the egress (see Figure 6). The same event was also monitored by one telescope of the Las Cumbres Observatory 1 m network (Brown et al. 2013) at Cerro Tololo Inter-American Observatory, Chile. Observations were obtained with the Sinistro camera with 2 mm of defocus in the Sloan i band. The adopted exposure time for the 88 observations taken was 60 s, and reduced images were obtained with the standard Las Cumbres Observatory pipeline (BANZAI pipeline). The light curves for CHAT and the Las Cumbres 1 m telescope were produced from the reduced images using a dedicated pipeline (N. Espinoza et al. 2018, in preparation).

The light curves were detrended by describing the systematic trends as a Gaussian Process with an exponential squared kernel depending on time, airmass, and centroid position and whose parameters are estimated simultaneously with those of the transit. A photometric jitter term is also included; this parameter is passed on as a fixed parameter in the final global analysis that determines the planetary parameters (Section 3.2). In more detail, the magnitude time series is modeled as

$$\begin{eqnarray}&&{m}_{i}=Z+{x}_{1}{c}_{1,i}+{x}_{2}{c}_{i,2}+{\delta }_{i}+{\epsilon }_{i},\end{eqnarray} \tag{ 1 }$$

where Z is a zero-point, c₁ and c₂ are comparison light curves, x₁ and x₂ are parameters weighting the light curves, δ is the transit model, and is a Gaussian Process to model the noise. The subscript i denotes evaluation at the time t = t_i of the time series. For the Gaussian process, we assume a kernel given by

$$\begin{eqnarray}&&{k}_{{ij}}=A\exp \left[-\displaystyle \sum _{m}{\alpha }_{m}{\left({x}_{m,i}-{x}_{m,j}\right)}^{2}\right]+{\sigma }^{2}{\delta }_{{ij}}.\end{eqnarray} \tag{ 2 }$$

The variables x_m are normalized time (m = 0), flux centroid in x (m = 1), and flux centroid in y (m = 2); δ_ij is the Kronecker delta. The normalization is carried out by setting the mean to 0 and the variance to 1. The priors on the kernel hyper parameters were taken to be the same as the ones defined in Gibson (2014), the priors for the photometric jitter term σ and A were taken to be uniform in the logarithm between 0.01 and 100, with σ and A expressed in mmag. In Figure 4 we show the CHAT and LCOGT light curves with the weighted comparison stars subtracted along with the Gaussian process posterior model for the systematics.

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Observations of K2-287 by GAIA were reported in DR2 (Gaia Collaboration et al. 2016, 2018). From GAIA DR2, K2-287 has a parallax of 6.29 ± 0.05 mas, an effective temperature of ${T}_{\mathrm{eff}}=4994\pm 80$ K and a radius of ${R}_{\star }\,=1.18\pm 0.04\,{R}_{\odot }$. We used the observed parallax for K2-287 measured by GAIA for estimating a more precise value of ${R}_{\star }$ by combining it with the atmospheric parameters obtained from the spectra as described in Section 3. We corrected the GAIA DR2 parallax for the systematic offset of −82 μas reported in Stassun & Torres (2018).

Two additional sources to K2-287 are identified by GAIA inside the adopted K2 aperture ($\approx 12^{\prime\prime}$). However, both stars are too faint (ΔG > 7.8 mag) to produce any significant effect on the planetary and stellar parameters found in Section 3. The RV variations in-phase with the transit signal, which are caused by K2-287, confirm that the transit is not caused by a blended stellar eclipsing binary on one of the companions.

As in previous K2CL discoveries we estimated the atmospheric parameters of the host star by comparing the coadded high resolution spectrum to a grid of synthetic models through the ZASPE code (Brahm et al. 2017b). In particular, for K2-287 we used the coadded FEROS spectra, because they provide the higher signal-to-noise ratio spectra, and because the synthetic grid of models used by ZASPE was empirically calibrated using FEROS spectra of standard stars. Briefly, ZASPE performs an iterative search of the optimal model through χ² minimization on the spectral zones that are most sensitive to changes in the atmospheric parameters. The models with specific values of atmospheric parameters are generated via trilinear interpolation of a precomputed grid generated using the ATLAS9 models (Castelli & Kurucz 2004). The interpolated model is then degraded to match the spectrograph resolution by convolving it with a Gaussian kernel that includes the instrumental resolution of the observed spectrum and an assumed macroturbulence value given by the relation presented in Valenti & Fischer (2005). The spectrum is also convolved with a rotational kernel that depends on $v\sin i$, which is considered as a free parameter. The uncertainties in the estimated parameters are obtained from Monte Carlo simulations that consider that the principal source of error comes from the systematic mismatch between the optimal model and the data, which in turn arises from poorly constrained parameters of the atomic transitions and possible deviations from solar abundances. We obtained the following stellar atmospheric parameters for K2-287: ${T}_{\mathrm{eff}}$ = 5695 ± 58 K, $\mathrm{log}g$ = 4.4 ±0.15 dex, $[\mathrm{Fe}/{\rm{H}}]$ = 0.20 ± 0.04 dex, and $v\sin i$ = 3.2 ±0.2 km s⁻¹. The ${T}_{\mathrm{eff}}$ value obtained with ZASPE is significantly different to that reported by GAIA DR2, but is consistent that of the K2 input catalog (Huber et al. 2016).

The stellar radius is computed from the GAIA parallax measurement, the available photometry, and the atmospheric parameters. As in Brahm et al. (2019), we used a BT-Settl-CIFIST spectral energy distribution model (Baraffe et al. 2015) with the atmospheric parameters derived with ZASPE to generate a set of synthetic magnitudes at the distance computed from the GAIA parallax. These magnitudes are compared to those presented in Table 2 for a given value of ${R}_{\star }$. We also consider an extinction coefficient A_V in our modeling that affects the synthetic magnitudes by using the prescription of Cardelli et al. (1989). We explore the parameter space for ${R}_{\star }$ and A_V using the emcee package Foreman-Mackey et al. (2013), using uniform priors in both parameters. We found that K2-287 has a radius of ${R}_{\star }=1.07\pm 0.01$ ${R}_{\odot }$ and has a reddening of A_V = 0.56 ± 0.03 mag, which is consistent with what is reported by GAIA DR2.

Table 2 .  Stellar Properties of K2-287

Parameter	Value	References
Names	EPIC 249451861	EPIC
	2MASS J15321784-2221297	2MASS
	TYC 6196-185-1	TYCHO
	WISE J153217.84-222129.9	WISE
R.A. (J2000)	15h32m1784	EPIC
Decl. (J2000)	−22d21m2974	EPIC
pmR.A. (mas yr−1)	−4.59 ± 0.11	GAIA
pmdecl. (mas yr−1)	−17.899 ± 0.074	GAIA
π (mas)	6.288 ± 0.051	GAIA
Kp (mag)	11.058	EPIC
B (mag)	12.009 ± 0.169	APASS
g' (mag)	11.727 ± 0.010	APASS
V (mag)	11.410 ± 0.129	APASS
r' (mag)	11.029 ± 0.010	APASS
i' (mag)	10.772 ± 0.020	APASS
J (mag)	9.677 ± 0.023	2MASS
H (mag)	9.283 ± 0.025	2MASS
Ks (mag)	9.188 ± 0.021	2MASS
WISE1 (mag)	9.114 ± 0.022	WISE
WISE2 (mag)	9.148 ± 0.019	WISE
WISE3 (mag)	9.089 ± 0.034	WISE
${T}_{\mathrm{eff}}$ (K)	5695 ± 58	zaspe
$\mathrm{log}g$ (dex)	4.398 ± 0.015	zaspe
$[\mathrm{Fe}/{\rm{H}}]$ (dex)	+0.20 ± 0.04	zaspe
$v\sin i$ (km s−1)	3.2 ± 0.2	zaspe
${M}_{\star }$ (${M}_{\odot }$)	1.056 ± 0.022	YY + GAIA
${R}_{\star }$ (${R}_{\odot }$)	1.07 ± 0.01	GAIA + this work
Age (Gyr)	4.5 ± 1	YY + GAIA
${\rho }_{\star }$ (g cm−3)	1.217 ± 0.045	YY + GAIA

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Finally, the stellar mass and evolutionary stage for K2-287 are obtained by comparing the estimation of ${R}_{\star }$ and the spectroscopic ${T}_{\mathrm{eff}}$ with the predictions of the Yonsei-Yale evolutionary models (Yi et al. 2001). We use the interpolator provided with the isochrones to generate a model with specific values of ${M}_{\star }$, age, and $[\mathrm{Fe}/{\rm{H}}]$, where $[\mathrm{Fe}/{\rm{H}}]$ is fixed to the value found in the spectroscopic analysis. We explore the parameter space for ${M}_{\star }$ and stellar age using the emcee package, using uniform priors in both parameters. We find that the mass and age of K2-287 are ${M}_{\star }=1.036\pm 0.033$ ${M}_{\odot }$ and 5.6 ± 1.6 Gyr (see Figure 5), similar to those of the Sun. The stellar parameters we adopted for K2-287 are summarized in Table 2.

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In order to determine the orbital and transit parameters of the K2-287b system we performed a joint analysis of the detrended K2 photometry, the follow-up photometry, and the radial velocities. As in previous planet discoveries of the K2CL collaboration, we used the exonailer code, which is described in detail in Espinoza et al. (2016). Briefly, we model the transit light curves using the batman package (Kreidberg 2015) by taking into account the effect on the transit shape produced by the long integration time of the long-cadence K2 data (Kipping 2010). To avoid systematic biases in the determination of the transit parameters we considered the limb-darkening coefficients as additional free parameters in the transit modeling (Espinoza & Jordán 2015), with the complexity of limb-darkening law chosen following the criteria presented in Espinoza & Jordán (2016). In our case, we select the quadratic limb-darkening law, whose coefficients were fit using the uninformative sampling technique of Kipping (2013). We also include a photometric jitter parameter for the K2 data, which allows us to have an estimation of the level of stellar noise in the light curve. The radial velocities are modeled with the radvel package (Fulton et al. 2018), where we considered systemic velocity and jitter factors for the data of each spectrograph. We use the stellar density estimated in our stellar modeling as an extra "data point" in our global fit as described in Brahm et al. (2018). Briefly, there is a term in the likelihood of the form

$$\begin{eqnarray*}&&p({{\boldsymbol{y}}}_{{\rho }_{\ast }}| \theta )=\displaystyle \frac{1}{\sqrt{2\pi {\sigma }_{{\rho }_{\ast }}^{2}}}\exp \,-\,\left[\displaystyle \frac{{\left({\rho }_{\ast }-{\rho }_{\ast }^{m}\right)}^{2}}{2{\sigma }_{{\rho }_{\ast }}^{2}}\right],\end{eqnarray*}$$

where

$$\begin{eqnarray*}&&{\rho }_{* }^{m}=\displaystyle \frac{3\pi }{{{GP}}^{2}}{\left(\displaystyle \frac{a}{{R}_{* }}\right)}^{3}\end{eqnarray*}$$

by Newton's version of Kepler's law, and ρ_* and ${\sigma }_{{\rho }_{* }}$ are the mean stellar density and its standard deviation, respectively, derived from our stellar analysis. In essence, because the period P is tightly constrained by the observed periodic transits, this extra term puts a strong constraint on a/R_*, which in turn helps to extract information about the eccentricity e and argument of periastron ω from the duration of the transit. Resulting planet parameters are set out in Table 3, the best-fit light curves in Figure 6, and the best-fit orbit solutions in Figures 2 and 7.

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Table 3 .  Planetary Properties of the K2-287 System

Parameter	Prior	Value
P (days)	N(14.893, 0.01)	14.893291 ± 0.000025
T0 (BJD)	N(2458001.722, 0.01)	2458001.72138 ± 0.00016
a/R${}_{\star }$	U(1,300)	${23.87}_{-0.31}^{+0.30}$
${R}_{{\rm{P}}}$/${R}_{\star }$	U(0.001,0.5)	${0.08014}_{-0.00098}^{+0.00086}$
${\sigma }_{w}^{K2}$ (ppm)	J(10, 50000)	${47.7}_{0.54}^{+0.54}$
${q}_{1}^{K2}$	U(0, 1)	${0.32}_{-0.05}^{+0.06}$
${q}_{2}^{K2}$	U(0, 1)	${0.57}_{-0.11}^{+0.13}$
${q}_{1}^{\mathrm{CHAT}}$	U(0, 1)	${0.83}_{-0.17}^{+0.12}$
${q}_{2}^{\mathrm{CHAT}}$	U(0, 1)	${0.15}_{-0.11}^{+0.16}$
${q}_{1}^{\mathrm{LCO}}$	U(0, 1)	${0.62}_{-0.19}^{+0.20}$
${q}_{2}^{\mathrm{LCO}}$	U(0, 1)	${0.08}_{-0.06}^{+0.11}$
K (m s−1)	N(0, 100)	${28.8}_{-2.2}^{+2.3}$
e	U(0, 1)	${0.478}_{-0.026}^{+0.025}$
i (deg)	U(0, 90)	${88.13}_{-0.08}^{+0.1}$
ω(deg)	U(0, 360)	${10.1}_{-4.2}^{+4.6}$
γFEROS (m s−1)	N(32963.2, 0.1)	${32930.41}_{-0.10}^{+0.10}$
γHARPS (m s−1)	N(32930.4, 0.1)	${32963.19}_{-0.10}^{+0.10}$
σFEROS (m s−1)	J(0.1, 100)	${16.0}_{-1.8}^{+2.1}$
σHARPS (m s−1)	J(0.1, 100)	${4.8}_{-1.6}^{+1.8}$
${M}_{{\rm{P}}}$ ( ${M}_{{\rm{J}}}$)		0.315 ± 0.027
${R}_{{\rm{P}}}$ (${R}_{{\rm{J}}}$)		0.847 ± 0.013
a (au)		${0.1206}_{-0.0008}^{+0.0008}$
${T}_{\mathrm{eq}}$ a (K)		${804}_{-7}^{+8}$

Note. For the priors, $N(\mu ,\sigma )$ stands for a normal distribution with mean μ and standard deviation σ, U(a, b) stands for a uniform distribution between a and b, and J(a, b) stands for a Jeffrey's prior defined between a and b.

^aTime-averaged equilibrium temperature computed according to Equation (16) of Méndez & Rivera-Valentín (2017).

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