EDP Sciences
Free Access
Issue
A&A
Volume 594, October 2016
Article Number A50
Number of page(s) 7
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201628204
Published online 10 October 2016

© ESO, 2016

1. Introduction

The extension of the Kepler mission (K2; Howell et al. 2014) is photometrically monitoring different fields along the ecliptic over ~80-day time spans. Despite the shorter time span and the slightly lower photometric precision with respect to the prime mission, several tens of extrasolar planets have been detected and characterized so far. These planets cover a wide range of properties, from disintegrating Neptune-sized objects (Sanchis-Ojeda et al. 2015) through validated Earth-sized planets (e.g., Crossfield et al. 2015; Petigura et al. 2015) to resonant multi-planetary systems (Armstrong et al. 2015b; Barros et al. 2015).

Several works have provided planet candidates based on independent analysis of the light curves (e.g., Foreman-Mackey et al. 2015). However, as in the prime part of the mission, any candidate requires follow-up observations to unveil its nature. Owing to the large Kepler pixel size (around 4 × 4 arcsec), contaminant sources can lie within the photometric aperture. Several high spatial resolution follow-up surveys were carried out for the prime mission (e.g., Lillo-Box et al. 2012, 2014b; Adams et al. 2012; Law et al. 2014) concluding that 2040% of the candidates have stellar companions closer than 3 arcsec. Thus, both high-resolution images and radial velocity (RV) data are needed.

The currently known extrasolar planets show an interesting population of close-in (a< 0.1 au) gaseous planets, known as hot Jupiters (HJ), with a maximum frequency at a 5-day period (Santerne et al. 2016). The detection and full characterization of these systems has become crucial to understanding early migration processes and also planet-star and planet-planet interactions. These are the best targets to study these processes because their consequences are easily detectable from the ground. For instance, HJs were found to be mostly solitary (Steffen et al. 2012), with no other planets in the system. This was explained by the possible suppression of rocky planet formation owing to the inward migration of the HJ early in the evolution of the system (e.g., Armitage 2003). However, the detection of inner and outer planets to the HJ WASP-47 b using K2 (Becker et al. 2015) has challenged this scenario. Also, measuring the spin-orbit angle provides hints about the migration history of the system (Morton & Johnson 2011) and this angle has already been determined for many HJs (e.g., Winn et al. 2005). Additionally, many HJs are found to be bloated. The source of this inflation is still not well understood; several mechanisms have been proposed (e.g., Batygin & Stevenson 2010; Showman & Guillot 2002), but none can explain the inflation by itself. In addition, transiting HJs currently represent the best chance to study exoplanet atmospheres with high-precision light curves, which allow phase curve studies.

Hence, a full characterization of a large population of HJs is necessary to analyze the migration and formation history of these systems and to study the planet-planet and planet-star interactions. We have used data from different facilities to identify and characterize the extrasolar planets K2-34 b and K2-30 b, two inflated hot Jupiters around solar-like stars. In this paper we detail the observations, data reduction, analysis, and conclusions regarding these systems.

2. Observations and data handling

2.1. K2 photometry

The star K2-30 (EPIC210957318, 03:29:22.07 +22:17:57.9) was observed by K2 during its campaign 4, between February 7th and April 23rd, 2015. K2-34 (EPIC212110888, 08:30:18.91 +22:14:09.3) belongs to field-of-view 5, photometrically monitored by K2 between April 27th and July 10th, 2015. The data was reduced using both the Warwick (Armstrong et al. 2015a) and the LAM- K2 (Barros et al. 2015) pipelines. The detrended data (see Tables 1 and 2) show 1.9% and 0.8% dimmings every 4.099 and 2.996 days for K2-30 and K2-34, respectively (see Figs. 1 and 2).

Table 1

Normalized detrended K2 light curve of K2-30 (see Sect. 2.1).

Table 2

Normalized detrended K2 light curve of K2-34 (see Sect. 2.1).

thumbnail Fig. 1

Results of the joint analysis with PASTIS for K2-30, including the primary transit (top panel) and radial velocity (bottom panels). The final models are shown with solid lines and the residuals of the data are presented in the lower part of each panel.

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2.2. High spatial resolution imaging

We obtained a high spatial resolution image of K2-34 and K2-30 with the instrument AstraLux at the 2.2m telescope in Calar Alto Observatory (Spain). We used the lucky-imaging technique, obtaining 90 000 frames (45 000 frames), each with an exposure time of 0.040 s (0.080 s) for K2-34 (K2-30). using the maximum gain setting. The images were reduced with the observatory pipeline, which performs basic reduction of the individual frames, selects the frames with the best Strehl ratios (Strehl 1902), aligns those frames, and combines them to provide a final near-diffraction limited image. In this case, we selected the best 10% of the frames, which translates into an effective exposure time of 360 s. No companion is detected within the sensitivity limits of the images. The sensitivity curve in each case was obtained by following the prescriptions in Lillo-Box et al. (2014a), simulating artificial stars at different positions in the reduced image and different contrast magnitudes and counting how many of them are recovered with a 5σ signal-to-noise ratio. In summary, the image would allow us to detect companions with contrast magnitudes brighter than 3.5 mag (3.7 mag) at 0.5 arcsec, 5.3 mag (5.0 mag) at 1 arcsec, and 8 mag (6.0 mag) at 2 arcsec for K2-34 (K2-30). Since no companion is detected within these limits, we assume that K2-34 and K2-30 are isolated and that their light curves are not polluted by other sources. In Hirano et al. (2016), the authors found a faint companion to K2-34 at 361.3 ± 3.5 mas with ΔmH = 6.19 ± 0.11. This source is below our detection limits, but owing to its faintness it has a negligible impact on the photometric analysis. The maximum contrast for a blended eclipsing binary to be able to mimic the detected transit of K2-34 in the Kepler band would be mag. Consequently, it is not possible that the close companion is the source of the eclipse. Hence, in practice, we can treat the system as being isolated.

thumbnail Fig. 2

Results of the joint analysis with PASTIS for K2-34. Same symbols as in Fig. 1.

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2.3. High-resolution spectroscopy

We observed the two transited stars with HARPS-N (Cosentino et al. 2012) at the Telescopio Nazionale Galileo (TNG), Spain, and SOPHIE (Bouchy et al. 2013) at the Observatoire de Haute-Provence (OHP), France. Two additional epochs for K2-34 were obtained with CAFE (Aceituno et al. 2013) at the 2.2m telescope of the Calar Alto Observatory (CAHA), Spain. The three instruments are fiber-fed high-resolution echelle spectrographs with resolving powers of R ~ 40 000 (SOPHIE in the high-efficiency mode), R = 110 000 (HARPS-N), and R = 63 000 (CAFE) and with no movable pieces. They are located in isolated chambers to improve their stability. SOPHIE and HARPS-N are stabilized in temperature and pressure, while these ambient conditions are simply monitored in the case of CAFE to check for possible RV drifts. In the three cases, the data was reduced with the corresponding online pipelines1. The RV is subsequently computed by determining the weighted cross-correlation function (CCF) between the spectra and a G2V binary mask2 (Baranne et al. 1996; Pepe et al. 2002). The SOPHIE data were corrected for the charge transfer inefficiency present in the charge-couple device of the instrument (Santerne et al. 2012). The RVs were also corrected for instrumental drifts using the RV standard star HD 56124 observed during the same nights and following the prescriptions in Santerne et al. (2014). CAFE RVs were also corrected using observations of the same standard star during the nights.

Table 3

Radial velocity data for K2-30.

Table 4

Radial velocity data for K2-34.

Table 5

List of free parameters used in the PASTIS analysis of the light curves, radial velocities and SED with their associated prior.

For K2-30, seven epochs were obtained with HARPS-N during four consecutive nights (January 47, 2016) having a signal-to-noise ratio (S/N) per pixel at 550 nm at the level of 1530, and five epochs were obtained with SOPHIE in the subsequent seven nights (January 813, 2016) with S/N of 1025. This provides a time span of ten days for this ~4-day period planet. For K2-34, we obtained three epochs with HARPS-N on January 47 2016 (S/N of 1650), four epochs with SOPHIE on January 1015 2016 (S/N of 2740), and two epochs with CAFE on December 2425 2015 (S/N of 1113). This encompasses a 22-day time span for this ~3-day period planet. The derived RV values are shown in Tables 3 and 4. In both cases, the radial velocity variations show no significant correlation with the bisector values, indicating that they do not originate from blended (undetected) stars. We calculated the projected rotational velocity of the star using the corresponding CCF following Boisse et al. (2010) (see Table 7).

3. Results

3.1. Stellar properties

The spectral analysis was performed on the HARPS-N data. For K2-30 the seven spectra were combined with the final spectrum reaching a S/N of 56. In the case ofK2-34, we used a single spectrum with S/N of 50. The spectroscopic parameters were derived with the ARES+MOOG method (see Sousa 2014, for details) which is based on the measurement of 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., Santos et al. 2013). The derived properties (Teff, log g, and [Fe/H]) for these G8V (K2-30) and F9V (K2-34) stars were used as priors for the joint analysis of the data (see Sect. 3.2) and are provided in Table 5. We also determined the lithium abundance for these host stars. We found an abundance of A(Li) = 2.16 ± 0.2 dex for K2-34 (Teff = 6130 ± 50 K) and an upper limit of A(Li)< 0.9 dex for K2-30 (Teff = 5585 ± 38 K). These abundances provide an estimated lower limit for the age of both targets of 2 Gyr when compared to the abundances of members of the NGC 752 (Sestito et al. 2004) or M67 cluster (Pasquini et al. 2008).

3.2. Joint analysis of the data

We used the PASTIS software (Díaz et al. 2014; Santerne et al. 2015) to perform a joint analysis of the K2 light curve, radial velocities, and magnitudes of the two targets. The transit signals were modeled3 using a modified version of the JKTEBOP code (Southworth 2011, and references therein) and a Keplerian orbit was fitted to the RV data. The spectral energy distribution (SED, Table 6) was modeled with the BT-SETTL library (Allard 2014) and the stellar parameters were derived using the Dartmouth stellar evolution tracks (Dotter et al. 2008).

We performed a statistical analysis using Markov chain Monte Carlo (MCMC) algorithms. The model is described by six free parameters for the host star (Teff, log g, [Fe/H], systemic radial velocity Vsys, interstellar extinction E(BV), and distance d) and seven free parameters for the transit (period P, epoch of first transit T0, radial velocity amplitude K, radius ratio Rp/R, orbital eccentricity e, inclination i, and argument of periastron ω). For the light curve, we also fit for an additional source of white noise, the out-of-transit flux level, and the level of contamination. For the RV, we additionally fit for a jitter term for each instrument and a RV offset between SOPHIE and the other instruments used. A jitter is also added for the SED analysis. For K2-34, owing to the low number of RV data points, we assumed a circular orbit4. This assumption is justified by the short period and circularization mechanisms. In total, 20 free parameters are fitted for both systems. Uniform priors are used for all free parameters except for the stellar values that were constrained to the results of the spectral analysis (see Sect. 3.1). The list of priors is shown in Table 5. We ran 20 chains of 3 × 105 iterations randomly drawn from the joint prior distribution. All chains converged toward the same solution, which is assumed to be the global maximum. In order to obtain the final solution and its uncertainties, we removed the burn-in phase of each chain and thinned them by computing their maximum correlation length. At this point we merged all of them to compute a well-sampled and clean posterior distribution having more than 2000 independent samples. The median values are presented in Table 7 together with the 15.7th and 84.3th percentiles of the marginalized distributions. In the table we also present other parameters derived from those fitted by the model (planet mass, planet radius, stellar mass, etc.). The data and best fit models are presented in Figs. 1, 2, and 4.

Table 6

Photometry used for the spectral energy distribution analysis of K2-30 and K2-34.

Table 7

Host star, planet, and orbital parameters inferred from the joint analysis of the data.

4. Discussion

The combination of different datasets for K2-30 b and K2-34 b establishes the planetary nature of the transiting objects around two main-sequence stars (G8V and F9V, respectively) observed by K2. The analysis of the data indicates that both systems are composed of single giant planets (1.197 ± 0.052 RJup for K2-30 and 1.217 ± 0.053 RJup for K2-34) in close-in orbits around their main-sequence stars.

In the case of K2-30, the insolation flux received by the planet is F = 4.24 ± 0.37 × 108 erg s-1 cm-2. This is significantly larger than the empirical cut-off limit derived by Demory & Seager (2011) for a planet to have an inflated radius (F> 2.08 × 108 erg s-1 cm-2). Assuming a Bond albedo A = 0 and a complete redistribution of the tidal heating along the planet, its expected radius according to Eq. (9) in Enoch et al. (2012) would be 0.777 ± 0.014RJup5. According to Weiss et al. (2013) the mass-radius-insolation flux relation provides an expected radius for this planet of 1.151 ± 0.010RJup. In the case of K2-34 b, the planet receives an insolation flux of F = 1.768 ± 0.14 × 109 erg s-1 cm-2. This is one order of magnitude larger than the above-mentioned cut-off limit derived by Demory & Seager (2011). The expected radius according to Enoch et al. (2012) would be 0.993 ± 0.016RJup and the expected radius from Weiss et al. (2013) is 1.267 ± 0.010RJup.

In both cases, the planets have comparable radii to those predicted by empirical calibrations (see Fig. 3). Although compared to the values predicted by Weiss et al. (2013) they are compatible within 1σ with being inflated due to the high stellar insolation flux, both are clearly larger (>3σ) than the predicted value by Enoch et al. (2012). It is known that high stellar irradiance can explain the inflation of the close-in Jupiter planets with radii up to ~1.2RJup (Guillot & Showman 2002). However, this cannot explain larger radii, and so other mechanisms must play a role (e.g., Bodenheimer et al. 2001; Batygin & Stevenson 2010; Chabrier & Baraffe 2007). The small eccentricity found in K2-30 (but statistically not significant) could possibly indicate some tidal heating, but other mechanisms cannot be rejected.

In this paper, we have characterized two HJs. They show bloated radii possibly due to the large stellar insolation that they are receiving from their host. However, other possible mechanisms such as tidal heating may be playing a role. Since the hosts are bright (V = 11.5 for K2-34 and V = 13.5 for K2-30) and the planets are inflated, they are amenable for atmospheric characterization either from the ground or from space. As they transit, they are also good candidates for the detection of the Rossiter-MacLaughlin effect used to infer the spin-orbit angle and to study the evolutionary history of these systems. From the derived parameters, the amplitude of this effect should be around 60 m/s and 40 m/s for K2-30 and K2-34, respectively. Future searches for additional bodies will be interesting in order to unveil planet-planet interactions during the onset of the planetary systems.

thumbnail Fig. 3

Insolation flux and planet radius for all extrasolar planets with known radius, Teff, and semi-major axis. Data taken from the The Extrasolar Planet Encyclopedia. The two hot Jupiters found in this work are marked as filled circles (K2-34 in red and K2-30 in blue). The expected radius-insolation flux dependencies according to Weiss et al. (2013) are shown as dashed red (K2-34) and dash-dotted blue (K2-30) lines.

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The K2-34 system was also analyzed by Hirano et al. (2016), with good agreement in the parameters directly derived from modeling the observations. Owing to small differences in the determined stellar properties, some absolute physical and orbital parameters disagree by a small percentage. Johnson et al. (2016) also analyzed K2-30 and their results are mainly in agreement with ours. Some parameters are different by a small percentage, but this could be due to their assumption of a circular orbit and to their use of a different approach for the calculation of the stellar parameters.

thumbnail Fig. 4

Results of the SED fitting in the joint analysis of the data with PASTIS for K2-30 (top panel) and K2-34 (bottom panel). The final models are shown with solid lines and the residuals of the data are presented in the lower part of each panel.

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1

For details on the CAFE pipeline see http://www.caha.es/CAHA/Instruments/CAFE/softw.html

2

In the case of CAFE, see Sect. 2.3 in Lillo-Box et al. (2015).

3

Models are numerically integrated over the Kepler exposure time with an oversampling factor of 10.

4

We tested the non-circular hypothesis and compared the Bayesian information criterion (BIC; see, e.g., Schwarz 1978; Smith et al. 2009) of the two models. As expected, the results provide strong evidence for the circular model given the current data, with a BIC difference of 2 in favor of the circular (i.e., simpler) hypothesis.

5

Larger albedos would imply smaller expected planetary radius, so this can be considered as an upper limit.

Acknowledgments

J.L.-B. acknowledges financial support from the Marie Curie Actions of the European Commission (FP7-COFUND) and the Spanish grant AYA2012- 38897-C02-01. O.D. acknowledges support by CNES through contract 567133. A.S. is supported by the European Union under a Marie Curie Intra-European Fellowship for Career Development with reference FP7-PEOPLE-2013-IEF, number 627202. D.J.A. and D.P. acknowledge funding from the European Union Seventh Framework programme (FP7/2007- 2013) under grant agreement No. 313014 (ETAEARTH). J.-M.A. acknowledges funding from the European Research Council under the ERC Grant Agreement n. 337591-ExTrA. P.A.W acknowledges the support of the French Agence Nationale de la Recherche (ANR), under program ANR-12-BS05-0012 “Exo-Atmos”. A.S., S.C.C.B., E.D.M., N.C.S., S.S., and M.T. acknowledge support by Fundação para a Ciência e a Tecnologia (FCT) through the research grants UID/FIS/04434/2013 (POCI-01-0145-FEDER-007672) and project PTDC/FIS-AST/1526/2014. N.C.S., S.G.S., and S.C.C.B. acknowledge the support from FCT through Investigador FCT contracts of reference IF/00169/2012, IF/00028/2014, and IF/01312/2014, respectively, and POPH/FSE (EC) by FEDER funding through the program “Programa Operacional de Factores de Competitividade COMPETE”. E.D.M. acknowledges the support from FCT in the form of the grant SFRH/BPD/76606/2011. This publication is based on observations collected with the NASA satellite Kepler, with the SOPHIE spectrograph at OHP (CNRS, France), HARPS-N (La Palma, Spain), and CAFE and AstraLux at Calar Alto Observatory (Spain). This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project (UCLA/JPL) funded by NASA. This research made use of the AAVSO Photometric All-Sky Survey, funded by the Robert Martin Ayers Sciences Fund.

References

All Tables

Table 1

Normalized detrended K2 light curve of K2-30 (see Sect. 2.1).

Table 2

Normalized detrended K2 light curve of K2-34 (see Sect. 2.1).

Table 3

Radial velocity data for K2-30.

Table 4

Radial velocity data for K2-34.

Table 5

List of free parameters used in the PASTIS analysis of the light curves, radial velocities and SED with their associated prior.

Table 6

Photometry used for the spectral energy distribution analysis of K2-30 and K2-34.

Table 7

Host star, planet, and orbital parameters inferred from the joint analysis of the data.

All Figures

thumbnail Fig. 1

Results of the joint analysis with PASTIS for K2-30, including the primary transit (top panel) and radial velocity (bottom panels). The final models are shown with solid lines and the residuals of the data are presented in the lower part of each panel.

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In the text
thumbnail Fig. 2

Results of the joint analysis with PASTIS for K2-34. Same symbols as in Fig. 1.

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In the text
thumbnail Fig. 3

Insolation flux and planet radius for all extrasolar planets with known radius, Teff, and semi-major axis. Data taken from the The Extrasolar Planet Encyclopedia. The two hot Jupiters found in this work are marked as filled circles (K2-34 in red and K2-30 in blue). The expected radius-insolation flux dependencies according to Weiss et al. (2013) are shown as dashed red (K2-34) and dash-dotted blue (K2-30) lines.

Open with DEXTER
In the text
thumbnail Fig. 4

Results of the SED fitting in the joint analysis of the data with PASTIS for K2-30 (top panel) and K2-34 (bottom panel). The final models are shown with solid lines and the residuals of the data are presented in the lower part of each panel.

Open with DEXTER
In the text

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