K2-29 b/WASP-152 b: AN ALIGNED AND INFLATED HOT JUPITER IN A YOUNG VISUAL BINARY

2.1.1. K2 Data

The target star K2-29³⁴ was observed by the Kepler telescope from 2015 February 07 to April 23. Basic information about this target is provided in Table 1. We reduced the K2 raw pixel data using both the Warwick (Armstrong et al. 2015a, 2015b) and the LAM-K2 (Barros et al. 2015) pipelines which gave similar results, except that the Warwick light curve has more noise. We therefore adopted the light curve produced by the LAM-K2 pipeline. A transiting candidate was easily detected by both pipelines as it presents a 2%-deep transit-like event with a periodicity of about 3.258 days. This period is close to 153.5 times the integration time of the long-cadence mode of Kepler. This means that the orbital phases covered by K2 coincide every two periods. As a consequence the transit is poorly sampled by the K2 data, hence the transit parameters are degenerated and thus they are not precisely determined. To correct for instrumental effects and stellar variability, we normalized the transits by fitting a parabola to 5 hr of out-of-transit data each side of the transit. This reduced light curve is the one used for the analysis described in Section 3. The star also exhibits a clear variability at the level of 1% with a rotation period of about 11 days (see Figure 1). Following the work of McQuillan et al. (2013, 2014), we computed the autocorrelation function of the light curve. We find that the host star has a rotation period of 10.79 ± 0.02 days, which is close to three times the orbit of the planet.

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Table 1.  Various Identification (IDs), Magnitudes, and Coordinates of the Target Star

	Value	Reference
EPIC ID	211089792	Huber et al. (2015)
TYC ID	1818-1428-1	Høg et al. (2000)
WASP ID	152	⋯
K2 ID	29	⋯
R.A.	04:10:40.955	Huber et al. (2015)
Decl.	+24:24:07.35	Huber et al. (2015)
pmR.A. (mas yr−1)	4.99	Fedorov et al. (2011)
pmDecl. (mas yr−1)	−39.73	Fedorov et al. (2011)
Kepler Kp	12.91	Huber et al. (2015)
Johnson B	13.597 ± 0.062	this work
Johnson V	12.526 ± 0.044	this work
2MASS J	10.622 ± 0.035	Cutri et al. (2013)
2MASS H	10.168 ± 0.041	Cutri et al. (2013)
2MASS Ks	10.062 ± 0.034	Cutri et al. (2013)
WISE 3.4 μm	10.095 ± 0.037	Cutri et al. (2013)
WISE 4.6 μm	10.142 ± 0.037	Cutri et al. (2013)
WISE 12 μm	9.991 ± 0.082	Cutri et al. (2013)

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2.1.2. Archival Super-WASP Data

2.1.3. Professional and Amateur Ground-based Photometry

2.2.1. FTN Seeing-limited Imaging

The SDSS DR9 (Ahn et al. 2012) images of the star K2-29 revealed the presence of a close companion. To characterize this companion further, we obtained seeing-limited images with the Faulkes Telescope North (FTN), operated by the LCOGT network (Brown et al. 2013). We collected three exposures of 20 s each in the B, V, and R bands. We clearly detected a stellar companion located at about 43 and ≈35° north-to-east (see Figure 2).

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We searched for archival data in the Digitalized Sky Survey. Images taken in 1949 and 1993 do not resolve this stellar companion but one can clearly see an elongated point-spread function. The angular separation is about 3'' and 45, with angles of ≈35° and 37° (north-to-east) in the 1949 and 1993 images, respectively. This suggests that star B is a physical companion of star A. In the rest of this paper, we refer to components A and B as the brightest and faintest stars in the system, respectively. Using aperture photometry, we find that component B is fainter than star A by 2.40 ± 0.03 mag, 2.14 ± 0.02 mag, and 1.78 ± 0.01 mag in the B, V, and R bands, respectively. We then used the contaminated magnitudes from the APASS catalog (Munari et al. 2014) to derive the B and V magnitudes of star A, which are reported in Table 1.

2.2.2. AstraLux Lucky-imaging Observations

2.3.1. CAFE

2.3.2. SOPHIE

2.3.3. HARPS-N

The spectral analysis was performed on the co-added HARPS-N spectra of star A. The spectroscopic parameters were derived with the ARES+MOOG method (see Sousa 2014, for details) which is based on the measurement of the equivalent widths of iron lines with ARES (Sousa et al. 2015). This method has been used to derive homogeneous parameters for planet-host stars (e.g., Sousa et al. 2011; Santos et al. 2013). We corrected the log g using the asteroseismic calibration of Mortier et al. (2014). We find that star A has a T_eff of 5363 ± 43 K, a log g of 4.49 ± 0.20 g cm⁻², a micro-turbulence velocity υ_micro of 1.05 ± 0.08 km s⁻¹, and an iron abundance [Fe/H] of 0.16 ± 0.03 dex. Using the method described in Boisse et al. (2010) on the CCF, we find a $\upsilon \mathrm{sin}{i}_{\star }$ of 4 ± 1 km s⁻¹. We find evidence of lithium in the co-added spectrum with an abundance of A(Li) = 1.05 ± 0.2 dex.

We attempted to take a spectrum of star B with HARPS-N but the automatic guiding of the telescope was moving to star A. Therefore, to characterize star B, we used the magnitude differences measured by the FTN and AstraLux facilities (see Section 2). We modeled the spectral energy distribution (SED) of both stars using the BT-SETTL atmosphere models (Allard 2014) which we integrated in the B, V, R, i', and z' bands. We used the result from the spectral analysis to estimate the magnitudes of star A and we derived the spectroscopic parameters of star B by fitting the observed differences of magnitude through a Markov chain Monte Carlo algorithm (MCMC). We assumed that both stars are at the same distance, and hence have the same interstellar extinction, and that they have the same iron abundance. At each step of the MCMC we checked that the stellar parameters did not correspond to unphysical stars or stars older than the universe, according to the Dartmouth evolution tracks of Dotter et al. (2008). We find that star B has a T_eff of 4400 ± 66 K and a log g of 4.60 ± 0.04 g cm⁻². This corresponds to a spectral type of K5V according to Cox (2000).

This allows us to determine precisely the contamination of the star B in the light curves of star A. The contaminant fully contributes to the flux measured either by K2, WASP, or the other professional and amateur facilities. By integrating the SED models in the Kepler, r', and V bands, we find that the contamination is 15.3 ± 0.4%, 15.4 ± 0.4%, and 12.8 ± 0.4%, respectively.

We analyzed all the light curves, radial velocities³⁸ , and the magnitudes (listed in Table 1) of the target star using PASTIS software (Díaz et al. 2014; Santerne et al. 2015). It models the transit light curves using a modified version of the JKTEBOP code (Southworth 2011, and references therein) that we oversampled by a factor of 10 to compensate the long integration time of the Kepler data (Kipping 2010). Radial velocities are modeled with a Keplerian orbit and the SED is modeled with the BT-SETTL library (Allard 2014). Stellar parameters are determined with the Dartmouth stellar evolution tracks and limb darkening coefficients are taken from the theoretical values of Claret & Bloemen (2011).

The statistical analysis of the data was performed with a MCMC algorithm which is fully described in Díaz et al. (2014). The model is described by six free parameters for the star (T_eff, log g, [Fe/H], the systemic radial velocity υ₀, the distance d, and the interstellar extinction E(B − V)), seven free parameters for the transiting planet (period P, epoch of first transit T₀, radial velocity amplitude K, the radius ratio k_r, the orbital eccentricity e, inclination i, and the angle of periastron ω). We added to the model an extra source of white noise (jitter), an out-of-transit flux, and the contamination level for each of the 21 light curves listed in Table 2 which are left free in the analysis. Finally, we also added a jitter term for each of the radial velocity instruments, a radial velocity offset between them, and a jitter term for the SED. In total, the model is composed of 82 free parameters.

We choose uninformative priors as much as possible, except for the stellar parameters that we constrained using on the results of the spectral analysis and the orbital ephemeris to speed up the convergence. We choose a Beta distribution as the prior for the orbital eccentricity (Kipping 2013). The exhaustive list of free parameters and their priors is provided in Table 4.

Table 4.  List of Free Parameters Used in the PASTIS Analysis of the Light Curves, Radial Velocities, and SED with their Associated Prior and Posterior Distributions

Parameter	Priora	Posterior
Orbital parameters
Orbital period P (day)	${ \mathcal N }(3.25883;1\times {10}^{-5})$	3.2588321 ± 1.9 × 10−6
Epoch of first transit T0 (BJDTDB)—2450000	${ \mathcal N }(3219.0128;0.001)$	3219.0095 ± 2.2 × 10−3
Orbital eccentricity e	β(0.867; 3.03)	0.066 ± 0.022
Argument of periastron ω (°)	${ \mathcal U }(0;360)$	132 ± 21
Inclination i (°)	${ \mathcal S }(70;90)$	${86.66}_{{}^{-0.08}}^{{}_{+0.11}}$
Planetary parameters
Radial velocity amplitude K (m s−1)	${ \mathcal U }(0;1000)$	103.5 ± 5.4
Planet-to-star radius ratio kr	${ \mathcal U }(0;0.5)$	0.14188 ± 6.2 × 10−4
Stellar parameters
Effective temperature Teff (K)	${ \mathcal N }(5363;43)$	5358 ± 38
Surface gravity log g (g cm−2)	${ \mathcal N }(4.49;0.20)$	4.540 ± 0.012
Iron abundance [Fe/H] (dex)	${ \mathcal N }(0.16;0.03)$	0.16 ± 0.03
Reddening $E(B-V)$ (mag)	${ \mathcal U }(0;1)$	0.19 ± 0.02
Systemic radial velocity υ0 (km s−1)	${ \mathcal U }(-100,100)$	32.8786 ± 0.0044
Distance to Earth d (pc)	${ \mathcal P }(2;10;1000)$	185 ± 3
Instrumental parametersb
CAFE radial velocity jitter (m s−1)	${ \mathcal U }(0;100)$	35 ± 32
SOPHIE radial velocity jitter (m s−1)	${ \mathcal U }(0;100)$	12 ± 4
HARPS-N radial velocity jitter (m s−1)	${ \mathcal U }(0;100)$	${11}_{{}^{-8}}^{{}_{+15}}$
CAFE—SOPHIE radial velocity offset (m s−1)	${ \mathcal U }(-1000;1000)$	77 ± 30
HARPS-N—SOPHIE radial velocity offset (m s−1)	${ \mathcal U }(-1000;1000)$	−71 ± 10
SED jitter (mag)	${ \mathcal U }(0;1)$	0.027 ± 0.025

Notes. The choice of prior for the orbital eccentricity is described in Kipping (2013).

^a ${ \mathcal N }(\mu ;{\sigma }^{2})$ is a normal distribution with mean μ and width σ², ${ \mathcal U }(a;b)$ is a uniform distribution between a and b, ${ \mathcal S }(a,b)$ is a sine distribution between a and b, β(a; b) is a Beta distribution with parameters a and b, and ${ \mathcal P }(n;a;b)$ is a power-law distribution of exponent n between a and b. ^bWe did not report in this table the out-of-transit flux, jitter, and contamination for each of the 21 light curves we analyzed, as they are not really meaningful. We choose uninformative priors for the two first ones and a normal prior for the latter one, to correspond with the estimated contamination and its uncertainty (see Section 2.2). Note that for ground-based light curves, we assumed a larger prior width (enlarged by a factor of 10 compared with the estimated error), to account for possible under/over-correction of the sky background.

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We ran five exploratory MCMC chains of 10⁵ iterations with an initial guess randomly drawn from the joint prior distribution. We then ran 20 MCMC chains of 3 × 10⁵ iterations starting from the best solution found in the exploratory MCMC, to further explore the posterior distribution in the vicinity of the global maximum. All chains converged toward the same solution which is assumed to be the global maximum. We then removed the burn-in phase of each chain before thinning (keep only one sample per maximum correlation length among all the parameters of each chain) and merging them to obtain more than 1000 independent samples of the posterior distribution. We finally determined the median and 68.3% confidence interval for each of the free parameters that we report in Table 4. Note that the uncertainties reported in this table are only the statistical ones and do not take into account the unknown uncertainties on the models.

We display in Figure 3 the phase-folded transit light curves from the 21 different instruments with the best-fit model. In Figure 4, we plot the phase-folded radial velocity data together with the best-fit model and the residuals. The rms of the radial velocity data are 23 m s⁻¹, 12 m s⁻¹, and 10 m s⁻¹, for CAFE, SOPHIE, and HARPS-N, respectively. We find no significant drift in the radial velocity data, with an upper limit of ±40 m s⁻¹ yr⁻¹ at the 99% confidence interval.

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We analyzed the radial velocity data obtained during the transit nights of 2016 January 6 and 15 with HARPS-N and SOPHIE, respectively. To model the Rossiter–McLaughlin effect, we used the formalism developed by Boué et al. (2013). We are neglecting here the effects of convective blueshift and macro-turbulence. We fit the data using the MCMC procedure as described above. We used the results of the combined analysis, listed in Table 4, as the priors for the orbital and transit parameters. We used a uniform prior for the spin–orbit angle λ and assumed a prior for the $\upsilon \mathrm{sin}{i}_{\star }$ which follows a normal distribution with a mean of 4 km s⁻¹and a width of 1 km s⁻¹. To account for the different integration times between HARPS-N (10 minutes) and SOPHIE (20 minutes) data, we oversampled the Rossiter–McLaughlin model to 1 minute before binning it back to the actual HARPS-N or SOPHIE cadence. This is similar to what was proposed for photometric transits by Kipping (2010).

We ran 20 chains of 3 × 10⁵ iteration each started randomly from the joint prior distribution. We analyzed the chains as previously and found that the planet is aligned relative to the stellar spin with a value of λ = 15 ± 87. The derived $\upsilon \mathrm{sin}{i}_{\star }$ is 3.7 ± 0.5 km s⁻¹. The HARPS-N and SOPHIE data are displayed in Figure 5 together with the best-fit model.

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The detection of both the reflex motion and the Rossiter–McLaughlin effect is not enough to firmly assess the planetary nature of a candidate (e.g., Santos et al. 2002; Torres et al. 2005; A. Santerne et al. 2016, in preparation). The radial velocity variation is detected on star A, thus we can exclude star B from being the transit host. Even if it is quite unlikely, the system might still be a triple system located within the detection limits of AstraLux. According to Santerne et al. (2015), this triple system would imprint a significant variation in the bisector and/or FHWM.

We find no variation in the bisector with rms of 20 m s⁻¹, 42 m s⁻¹, and 15 m s⁻¹ on SOPHIE, HARPS-N, and CAFE, respectively, which is compatible with the uncertainties (see Table 3). The FWHM has rms of 73 m s⁻¹, 63 m s⁻¹, and 50 m s⁻¹ (respectively). This is larger than the typical uncertainties (see Table 3). This variability is, however, not correlated with the observed radial velocity variation. We concluded that this FWHM scatter is caused by the variability of the star highlighted in the K2 light curve (see Figure 1).

We also derived the radial velocity amplitude for each instrument. As explained in Santerne et al. (2015), the difference of spectral resolution between SOPHIE (R ≈ 40,000), CAFE (R ≈ 63,000), and HARPS-N (R ≈ 110,000) should lead to different radial velocity amplitudes in the case of a blend. We find that K_SOPHIE = 99.4 ± 6.1 m s⁻¹, ${K}_{{\rm{CAFE}}}={260}_{{}^{-150}}^{{}_{+240}}$ m s⁻¹, and ${K}_{\mathrm{HARPS}-{\rm{N}}}={120}_{{}^{-19}}^{{}_{+45}}$ m s⁻¹. The three values are compatible within 1σ.

Finally, we reduced the SOPHIE and HARPS-N data using a binary mask corresponding to a K5 dwarf. Even if this mask does not correspond to the spectral type of the host star, it might reveal the presence of an unresolved colder stellar companion (Santerne et al. 2015). The radial velocity amplitude derived with the K5V mask is consistent within the uncertainties with the one derived with a G2V mask.

From the absence of evidence of a blend in the spectroscopic and high-resolution imaging, we conclude that this candidate is a bona-fide planet.

Based on the results of the combined and Rossiter–McLaughlin analyses, we derived the physical parameters for the K2-29 system and present the results in Table 5.

Table 5.  Physical Parameters of the K2-29 System

Parameter	Value and Uncertainty
Orbital parameters
Period P (day)	3.2588321 ± 1.9 × 10−6
Transit epoch T0 (BJD—2.45 × 106)	3219.0095 ± 2.2 × 10−3
Orbital eccentricity e	0.066 ± 0.022
Argument of periastron ω (°)	132 ± 21
Inclination i (°)	${86.656}_{{}^{-0.08}}^{{}_{+0.11}}$
Semimajor axis a (AU)	0.04217 ± 2.4×10−4
Spin–orbit angle λ (°)	1.5 ± 8.7
Transit and Keplerian parameters
System scale a/R⋆	10.51 ± 0.15
Impact parameter bprim	0.58 ± 0.02
Transit duration T14 (hr)	2.22 ± 0.01
Planet-to-star radius ratio kr	0.14188 ± 6.2 × 10−4
RV amplitude K (m s−1)	103.5 ± 5.4
Planet parameters
Planet mass Mp (M♃)	0.73 ± 0.04
Planet radius Rp (R♃)	1.19 ± 0.02
Planet density ρp (g cm−3)	0.53 ± 0.04
Equilibrium temperature Teq (K)	1171 ± 10
Stellar parameters
Stellar mass M⋆ (M⊙)	0.94 ± 0.02
Stellar radius R⋆ (R⊙)	0.86 ± 0.01
Stellar agea τ (Gyr)	2.6 ± 1.2
Stellar ageb τ (Gyr)	0.45 ± 0.25
Distance d (pc)	185 ± 3
Reddening $E(B-V)$ (mag)	0.19 ± 0.02
Systemic RV υ0 (km s−1)	32.8786 ± 0.0044
Effective temperature Teff (K)	5358 ± 38
Surface gravity log g (g cm−2)	4.540 ± 0.012
Iron abundance [Fe/H] (dex)	0.16 ± 0.03
Rotational velocity $\upsilon \mathrm{sin}{i}_{\star }$(km s−1)	3.7 ± 0.5
Rotation period Prot (day)	10.79 ± 0.02
Spectral type	G7V

Notes. All the uncertainties provided here are only the statistical ones. Errors on the models are not considered, as they are unknown. Stellar parameters are derived from the combined analysis of the data and not from the spectral analysis. We assumed 1 R_⊙ = 695,508 km, 1 M_⊙ = 1.98842 × 10³⁰ kg, 1 R_♃ = 71,492 km, 1 M_♃ = 1.89852 × 10²⁷ kg, and 1 AUau = 149,597,870.7 km.

^aBased on the Dartmouth stellar evolution tracks. ^bBased on lithium abundance and stellar rotation.

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The host star has a mass of 0.94 ± 0.02 M_⊙ and a radius of 0.86 ± 0.01 R_⊙. The age derived using the Dartmouth stellar tracks (Dotter et al. 2008) indicates that the system is 2.6 ± 1.2 Gyr old. The age can, however, be estimated as 450 ± 200 Myr based on both A(Li) and P_rot. Both values correspond to an age older than the M34 cluster (250 Myr). The star might be younger than the Hyades cluster (or Praesepe) but few members of this 625 Myr association display either lithium abundances or rotations similar to our estimates (Barrado y Navascues & Stauffer 1996; Jones et al. 1997; James et al. 2010; Barnes et al. 2015). We cannot use the activity index measured in the Ca ii lines as the signal-to-noise at these wavelengths is at the order of unity and thus too low for reliable measurements. A combined analysis of both stellar and planet models as done in Guillot & Havel (2011) could provide further constraints on the age of this system.

Several theoretical works have shown, however, that episodic accretion in the early ages can destroy lithium (Baraffe & Chabrier 2010) as well as the accretion of planetary material to fingering convection (Théado & Vauclair 2012). Considering these effects would give an even younger age for this system. Depending on the rotational evolution this star has experienced, the lithium depletion could be stronger or weaker, hence increasing the uncertainty on the age of this system.

The system is located at 185 ± 3 pc. With a separation of ∼43, the stellar companion (star B) has a current sky-projected separation of about 800 AU.

We find that the transiting planet has a mass of 0.73 ± 0.04 M_♃ and a radius of 1.19 ± 0.02 R_♃. This gives a bulk density of 0.53 ± 0.04 g cm⁻³. K2-29 b is therefore an inflated hot Jupiter. The orbit of the planet shows a 3σ detection of an eccentricity of 0.066 ± 0.022, but this might be caused by the effects of the stellar variability, clearly seen in the K2 light curve, affecting the radial velocity measurements. We find a sky-projected spin–orbit angle of 15 ± 87. With a stellar radius of 0.86 ± 0.01 R_⊙ and a rotational period of 10.79 ± 0.02 days, the rotational velocity of the star is 4.06 ± 0.05 km s⁻¹, which is consistent with the $\upsilon \mathrm{sin}{i}_{\star }$ measured with the Rossiter–McLaughlin effect of 3.7 ± 0.5 km s⁻¹. The star is therefore seen nearly equator-on and the transiting planet is well aligned with the stellar spin. With a central star T_eff < 6250 K, this aligned system is in agreement with the other systems of this kind reported in Albrecht et al. (2012).