Issue 
A&A
Volume 576, April 2015



Article Number  A11  
Number of page(s)  13  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/201425062  
Published online  13 March 2015 
Kepler423b: a halfJupiter mass planet transiting a very old solarlike star^{⋆,}^{⋆⋆}
^{1} Landessternwarte Königstuhl, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany
email: davide.gandolfi@lsw.uniheidelberg.de
^{2} INAF–Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123 Catania, Italy
^{3} Department of Physics, University of Oxford, Oxford, OX1 3RH, UK
^{4} Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Spain
^{5} Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Spain
^{6} Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany
^{7} Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, 439 92, Onsala, Sweden
^{8} Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA, Leiden, The Netherlands
^{9} Physics Department “E. Fermi”, University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
^{10} Istituto Nazionale di Fisica Nucleare, Largo B. Pontecorvo 3, 56127 Pisa, Italy
^{11} Nordic Optical Telescope, Apartado 474, 38700 Santa Cruz de La Palma, Spain
^{12} Thüringer Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany
^{13} School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
^{14} Tuorla Observatory, Department of Physics and Astronomy, University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland
^{15} Stellar Astrophysics Centre, Department of Physics and Astronomy, Århus Uni., Ny Munkegade 120, 8000 Århus C, Denmark
Received: 26 September 2014
Accepted: 17 November 2014
We report the spectroscopic confirmation of the Kepler object of interest KOI183.01 (Kepler423b), a halfJupiter mass planet transiting an old solarlike star every 2.7 days. Our analysis is the first to combine the full Kepler photometry (quarters 1−17) with highprecision radial velocity measurements taken with the FIES spectrograph at the Nordic Optical Telescope. We simultaneously modelled the photometric and spectroscopic datasets using Bayesian approach coupled with Markov chain Monte Carlo sampling. We found that the Kepler presearch data conditioned light curve of Kepler423 exhibits quartertoquarter systematic variations of the transit depth, with a peaktopeak amplitude of ~4.3% and seasonal trends reoccurring every four quarters. We attributed these systematics to an incorrect assessment of the quarterly variation of the crowding metric. The host star Kepler423 is a G4 dwarf with M_{⋆} = 0.85 ± 0.04 M_{⊙}, R_{⋆} = 0.95 ± 0.04 R_{⊙}, T_{eff}= 5560 ± 80 K, [M/H] = − 0.10 ± 0.05 dex, and with an age of 11 ± 2 Gyr. The planet Kepler423b has a mass of M_{p}= 0.595 ± 0.081M_{Jup} and a radius of R_{p}= 1.192 ± 0.052R_{Jup}, yielding a planetary bulk density of ρ_{p} = 0.459 ± 0.083 g cm^{3}. The radius of Kepler423b is consistent with both theoretical models for irradiated coreless giant planets and expectations based on empirical laws. The inclination of the stellar spin axis suggests that the system is aligned along the line of sight. We detected a tentative secondary eclipse of the planet at a 2σ confidence level (ΔF_{ec} = 14.2 ± 6.6 ppm) and found that the orbit might have asmall nonzero eccentricity of 0.019^{+0.028}_{0.014}. With a Bond albedo of A_{B} = 0.037 ± 0.019, Kepler423b is one of the gasgiant planets with the lowest albedo known so far.
Key words: planets and satellites: detection / planets and satellites: fundamental parameters / techniques: radial velocities / planets and satellites: individual: Kepler423b / stars: fundamental parameters / techniques: photometric
Based on observations obtained with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, in time allocated by OPTICON and the Spanish Time Allocation Committee (CAT).
© ESO, 2015
1. Introduction
We can rightfully argue that spacebased transit surveys such as CoRoT (Baglin et al. 2006) and Kepler (Borucki et al. 2010) have revolutionised the field of exoplanetary science. Their highprecision and nearly uninterrupted photometry has opened up the doors to planet parameter spaces that are not easily accessible from the ground, most notably, the Earthradius planet domain (e.g., Leger et al. 2009; SanchisOjeda et al. 2013; Quintana et al. 2014).
When combined with highresolution spectroscopy, spacebased photometry provides us with the most accurate planetary and stellar parameters, which in turn are essential to investigate planet’s internal structure, migration, and evolution (Rauer et al. 2014). The exquisite photometry from space allows us to detect the eclipse of hot Jupiters even in the visible (e.g., Coughlin & LópezMorales 2012; Parviainen et al. 2013). The eclipse of transiting exoplanets – also known as planet occultation, secondary eclipse, and secondary transit – is a powerful tool for probing their atmospheres, in particular their albedos and brightness temperatures (Winn 2010). The timing and duration of the secondary eclipse, coupled with the timing and duration of the transit, enable us to measure small nonzero eccentricities (e ≲ 0.1) that are not easily detectable with radial velocity (RV) measurements. The eccentricity is an important parameter for the investigation of the starplanet tidal interactions, planetplanet gravitational perturbations, and migration mechanisms of hot Jupiters.
Ever since June 2010 the Kepler team has been releasing and updating a list of transiting planet candidates, also known as Kepler Objects of Interest (KOI), which as of August 2014 amounts to 7305 objects^{1}. Whereas Kepler multitransiting system candidates have a low probability of being false positives (Lissauer et al. 2014; Rowe et al. 2014), the same does not apply for those where a single planet is observed to transit (Santerne et al. 2012; Sliski & Kipping 2014). These require groundbased followup observations for validation, such as highresolution spectroscopy and highprecision RV measurements. The aim of followup observations is thus twofold: a) to rule out falsepositive scenarios and confirm that the photometric signal is caused by a bona fide transiting planet; b) to characterise the system by exploiting simultaneously both the photometric and spectroscopic data.
In the present paper we report on the confirmation of the Kepler transiting planet Kepler423b (also known as KOI183.01). We combined the full Kepler photometry with highresolution spectroscopy from FIES at NOT to confirm the planetary nature of the transiting object and derive the system parameters.
This paper is organised as follows. Section 2 describes the available Kepler photometry of Kepler423, whereas Sect. 3 reports on our spectroscopic followup with FIES at NOT. In Sect. 4, we detail how the fundamental parameters of the host star were derived. In Sect. 5, we outline our global Bayesian analysis and report on the quartertoquarter instrumental systematics affecting the Kepler photometry. Results are discussed in Sect. 6 and conclusions are given in Sect. 7.
2. Kepler photometry
Kepler423 – whose main designations, equatorial coordinates, and optical and infrared photometry are listed in Table 2 – was previously identified as a Kepler planethosting star candidate by Borucki et al. (2011) and Batalha et al. (2013) and assigned the identifier KOI183.
The Kepler photometry^{2} of Kepler423 covers quarters 1−17 (Q_{1}–Q_{17}), offering four years of nearly continuous observations, from 13 May 2009 to 11 May 2013. The short cadence (SC; T_{exp} = 58.85 s) data are available for Q_{4}–Q_{8} and Q_{13}, and encompass 190 individual transits. The long cadence (LC; T_{exp} = 1765.46 s) photometry contains the SC transits and 311 additional LConly transits observed in Q_{1}–Q_{3}, Q_{9}–Q_{12}, and Q_{14}–Q_{17}.
In this work we used the Kepler simple aperture photometry (SAP; Jenkins et al. 2010), as well as the same data processed with the new version of the presearch data conditioning (PDC) pipeline (Stumpe et al. 2012), which uses a Bayesian maximum a posteriori (MAP) approach to remove the majority of instrumental artefacts and systematic trends (Smith et al. 2012). The iterative filtering procedure by Aigrain & Irwin (2004) with a 5σ clipping algorithm was applied to both the SAP and the PDCMAP light curves to identify and reject further outliers. We also performed a visual inspection of the Kepler light curves to remove photometric discontinuities across the data gaps that coincide with the quarterly rolls of the spacecraft. The pointtopoint scatter estimates for the PDCMAP SC and LC light curve are 1146 ppm (1.24 mmag) and 292 ppm (0.32 mmag), respectively (Table 5).
Fig. 1 Example section of mediannormalised long cadence light curve of Kepler423. Data are from Kepler quarter 13. 

Open with DEXTER 
Main identifiers, equatorial coordinates, and optical/infrared magnitudes of the planethosting star Kepler423.
Figure 1 shows the mediannormalised LC data of Kepler423 from Kepler quarter 13. The ~1.8%deep transit signals occurring every 2.7 days are clearly visible, along with a ~0.5% (peaktopeak) outoftransit modulation. Given the spectral type of the planet host star (G4 V; see Sect. 4.1), this variability is likely to be due to magnetic active regions carried around by stellar rotation. Using an algorithm based on the autocorrelation function of the Q_{3}–Q_{14} timeseries, McQuillan et al. (2013) found a stellar rotation period of P_{rot} = 22.047 ± 0.121 days.
FIES radial velocity measurements of Kepler423.
3. Highresolution spectroscopy
The spectroscopic followup of Kepler423 was performed with the FIbrefed Échelle Spectrograph (FIES; Frandsen & Lindberg 1999; Telting et al. 2014) mounted at the 2.56m Nordic Optical Telescope (NOT) of Roque de los Muchachos Observatory (La Palma, Spain). The observations were carried out between June and September 2013, under OPTICON and CAT observing programmes 2013A025 and 79NOT14/13A, respectively. We used the 1.3″highres fibre, which provides, in conjunction with a 50μm slit at the fibre exit, a resolving power of R = 67 000 in the spectral range 3600−7400 Å. Three consecutive exposures of 1200 s were taken per epoch observation to remove cosmic ray hits. Following the observing strategy described in Buchhave et al. (2010), we traced the RV drift of the instrument by acquiring longexposed (T_{exp} = 15 s) ThAr spectra right before and after each epoch observation. The data were reduced using a customised IDL software suite, which includes bias subtraction, flat fielding, order tracing and extraction, and wavelength calibration. RV measurements were derived via multiorder crosscorrelations technique with the RV standard star HD 182572 – observed with the same instrument setup as the target object – and for which we adopted an heliocentric RV of −100.350 km s^{1}, as measured by Udry et al. (1999).
The FIES RV measurements are listed in Table 2 along with the observation barycentric Julian dates in barycentric dynamical time (BJD_{TDB}, see Eastman et al. 2010), the crosscorrelation function (CCF) bisector spans, and the signaltonoise ratios (S/N) per pixel at 5500 Å. The upper panel of Fig. 2 shows the FIES RVs of Kepler423 and the Keplerian fit to the data – as obtained from the global analysis described in Sect. 5 – whereas the lower panel displays the CCF bisector spans plotted against the RV measurements, assuming that the error bars of the former are twice those of the latter. We followed the method described in Loyd & France (2014) to account for the uncertainties of our measurements and found that the probability that uncorrelated random datasets can reproduce the observed arrangement of points (null hypothesis) is about 50%. The lack of significant linear correlation between the CCF bisector spans and the RVs indicates that most likely the Doppler shifts observed in Kepler423 are induced by the orbital motion of the companion rather than stellar activity or a blended eclipsing binary (see, e.g., Queloz et al. 2001).
Fig. 2 Upper panel: FIES radial velocities of Kepler423 – after subtracting the systemic velocity V_{γ} – versus BJD_{TDB} and Keplerian fit to the data. Lower panel: bisector spans of the FIES crosscorrelation functions versus RV measurements, after subtracting the systemic velocity V_{γ}. Error bars in the CCF bisector spans are taken to be twice the uncertainties in the RV data. 

Open with DEXTER 
4. Properties of the host star
4.1. Photospheric parameters
We derived the fundamental photospheric parameters of the host star Kepler423 using the coadded FIES spectrum, which has a S/N of about 60 per pixel at 5500 Å. Two independent analyses were performed. The first method compares the coadded FIES spectrum with a grid of theoretical models from Castelli & Kurucz (2004), Coelho et al. (2005), and Gustafsson et al. (2008), using spectral features that are sensitive to different photospheric parameters. We adopted the calibration equations for Sunlike dwarf stars from Bruntt et al. (2010) and Doyle et al. (2014) to determine the microturbulent v_{micro} and macroturbulent v_{macro} velocities, respectively. The projected rotational velocity v sin i_{⋆} was measured by fitting the profile of several clean and unblended metal lines. The second method relies on the use of the spectral analysis package SME 2.1, which calculates synthetic spectra of stars and fits them to observed highresolution spectra (Valenti & Piskunov 1996; Valenti & Fischer 2005). It uses a nonlinear least squares algorithm to solve for the model atmosphere parameters. The two analysis provided consistent results well within the errors bars. The final adopted values are T_{eff}= 5560 ± 80 K, log g = 4.44 ± 0.10 (log_{10} cm s^{2}), [M/H] = − 0.10 ± 0.05 dex, v_{micro} = 1.0 ± 0.1 km s^{1}, v_{macro} = 2.8 ± 0.4 km s^{1}, and v sin i_{⋆} = 2.5 ± 0.5 km s^{1}. Using the Straizys & Kuriliene (1981) calibration scale for dwarf stars, the effective temperature of Kepler423 translates to a G4 V spectral type.
Fig. 3 Modified HertzsprungRussell diagram showing the stellar bulk density versus effective temperature. The position of Kepler423 is overplotted on theoretical evolutionary tracks and isochrones from the Pisa Stellar Evolution Data Base for lowmass stars. The blue hatched areas represent different masses (0.81, 0.85, and 0.89 M_{⊙} from right to left), while the greys represent the age isochrones (9, 11, and 13 Gyr from bottom to top), computed for an initial metal content between Z = 0.012 and Z = 0.014. 

Open with DEXTER 
4.2. Stellar mass, radius, and age
Stellar mass, radius, and age were determined using the effective temperature T_{eff} and metallicity [M/H], as derived from the spectral analysis (Sect. 4.1), along with the stellar bulk density ρ_{⋆}, as obtained from the modelling of the transit light curve (Sect. 5). We compared the position of Kepler423 on a ρ_{⋆}versusT_{eff} diagram with a grid of ad hoc evolutionary tracks (Fig. 3).
We generated stellar models using an updated version of the FRANEC code (Degl’Innocenti et al. 2008; Tognelli et al. 2011) and adopting the same input physics and parameters as those used in the Pisa Stellar Evolution Data Base for lowmass stars^{3} (see, e.g., Dell’Omodarme et al. 2012, for a detailed description). To account for the current surface metallicity of Kepler423 ([M/H] = − 0.10 ± 0.05 dex) and microscopic diffusion of heavy elements towards the centre of the star, we computed evolutionary tracks assuming an initial metal content of Z = 0.010, Z = 0.011,Z = 0.012,Z = 0.013,Z = 0.014, and Z = 0.015. The corresponding initial helium abundances, i.e., Y = 0.268, 0.271, 0.273, 0.275, 0.277, and 0.279, were determined assuming a heliumtometal enrichment ratio ΔY/ΔZ=2 (Jimenez et al. 2003; Casagrande 2007; Gennaro et al. 2010) and a cosmological ^{4}He abundance Y_{p} = 0.2485 (Cyburt 2004; Peimbert et al. 2007a,b). For each chemical composition, we generated a very fine grid of evolutionary tracks in the mass domain M_{⋆} = 0.70–1.10 M_{⊙}, with step of ΔM_{⋆} = 0.01 M_{⊙}, leading to a total of 246 stellar tracks.
We found that evolutionary tracks with initial metal content between Z = 0.012 and Z = 0.014 have to be used to reproduce the current photospheric metallicity of Kepler423. We derived a mass of M_{⋆} = 0.85 ± 0.04 M_{⊙} a radius of R_{⋆} = 0.95 ± 0.04 R_{⊙} and an age of t = 11 ± 2 Gyr (Table 5). Mass and radius imply a surface gravity of log g = 4.41 ± 0.04 (log_{10} cm s^{2}), which agrees with the spectroscopically derived value log g = 4.44 ± 0.10 (log_{10} cm s^{2}).
Using premain sequence (PMS) evolutionary tracks would lead to consistent results in terms of stellar mass and radius, but would also yield an age of 25 ± 5 Myr. Given the relatively rapid evolutionary timescale of PMS stars, we note that the likelihood of finding Kepler423 still contracting towards the zeroage main sequence (ZAMS) is about 600 times lower than the probability for the star to be found in the post ZAMS phase. Moreover, such a young scenario is at odds with: a) the distance from the galactic plane, which amounts to 166 ± 17 pc (given the spectroscopic distance of 725 ± 75 pc – see below – and galactic latitude of +12.92 °); b) the relatively long rotation period of the star (P_{rot} = 22.047 ± 0.121 days); c) the absence of high magnetic activity level (the peaktopeak photometric variation is ~0.5%); d) the lack of detectable Li i λ6708 Å absorption line in the coadded FIES spectrum. Short rotation period (P_{rot} ≲ 5 days), coupled with high magnetic activity and strong Li i λ6708 Å absorption line (EW_{Li} ≳ 300 mÅ), are usually regarded as youth indicators in PMS lowmass stars (see, e.g., Marilli et al. 2007; Gandolfi et al. 2008).
4.3. Interstellar extinction and distance
We followed the method described in Gandolfi et al. (2008) to derive the interstellar extinction A_{v} and spectroscopic distance d of the system. We simultaneously fitted the available optical and infrared colours listed in Table 2 with synthetic theoretical magnitudes obtained from the NextGen model spectrum with the same photospheric parameters as the star (Hauschildt et al. 1999). We excluded the W3 and W4 WISE magnitudes, owing to the poor photometry (Cutri et al. 2012). Assuming a normal extinction (R_{v} = 3.1) and a black body emission at the star’s effective temperature and radius, we found that Kepler423 suffers a negligible interstellar extinction of A_{v} = 0.044 ± 0.044 mag and that its distance is d = 725 ± 75 pc (Table 5).
5. Bayesian and MCMC global analysis
5.1. Approach
We estimated the system parameters, i.e., stellar, planetary, and orbital parameters for which inference can be made based on photometry and RVs, using a Bayesian approach where the photometric and RV data are modelled simultaneously, similarly to the work described in Gandolfi et al. (2013) and Parviainen et al. (2014). The model describes the primary transits, secondary eclipses, and RV variations. The significance of a possible secondary eclipse signal (Sect. 6.2) was assessed separately using a method based on Bayesian model comparison (Parviainen et al. 2013).
We obtained an estimate of the model posterior distribution using the Markov chain Monte Carlo (MCMC) technique. The sampling was carried out using emcee^{4} (ForemanMackey et al. 2012), a Python implementation of the Affine Invariant Markov chain Monte Carlo sampler (Goodman & Weare 2010). We used PyDE^{5}, a Python implementation of the differential evolution algorithm for global optimisation, to generate an initial population of parameter vectors clumped close to the global posterior maximum used to initialise the MCMC sampling. The sampling was carried out with 500 simultaneous walkers (chains). The sampler was first run iteratively through a burnin period consisting of 20 runs of 500 steps each, after which the walkers had converged to sample the posterior distribution. The chains were considered to have converged to sample the posterior distribution after the ensemble properties of the chains did not change during several sets of 500 iterations, and the results from different walker subsets agreed with each other. The final sample consists of 1500 iterations with a thinning factor of 50 (chosen based on the average parameter autocorrelation lengths to ensure that we had independent samples), leading to 15 000 independent posterior samples.
Fig. 4 Upper panel: average, observed−modelled (O − M) flux residual of the photometric points encompassing the second (T_{2}) and third transit contact (T_{3}) as a function of the transit numbers for the PDCMAP data, assuming that the Kepler contamination metric has been properly estimated. The light blue lines show the standard error of the mean for each transit. The beginning of each Kepler quarter is marked with dashed grey vertical lines. Middle panel: as in the upper panel, but for the SAP data. Lower panel: same as before, but for the PDCMAP cotrended data, following our quarterly crowding metric correction constrained by an informative prior (see text for more details). 

Open with DEXTER 
5.2. Dataset
The dataset consists of the 12 FIES RVs (Sect. 3), subsets of the SC and LC data for the transit modelling, and subsets of the LC data for the secondary eclipse modelling.
The photometric data for the transit modelling included 12 h of data around each transit, where each segment was detrended using a secondorder polynomial fitted to the outoftransit points. We preferred short time cadence light curves when available, and excluded the LC transits for which SC data was available. The final SC and LC transit light curves contain about 138 400 and 12 100 points, respectively. We chose not to use PDCMAP data because of the issues in the crowding metric correction applied by the pipeline, but used the PDCMAP cotrended fluxes instead (see Sect. 5.4).
The eclipse model was evaluated using LC data alone. We included about 18 h of data centred on halfphase from each individual orbit – enough to allow for eccentricities up to 0.2 – and did not detrend the individual data segments (we used Gaussian processes to model the baseline instead). We rejected 69 subsets of LC data because of clear systematics and performed the secondary eclipse modelling using 447 LC segments.
5.3. Logposterior probability density and parametrisation
The nonnormalised logposterior probability density is described as (1)where F_{SC} and F_{LC} are the short and longcadence photometric data for the primary transit, F_{EC} is the long cadence photometric data for the secondary eclipse, RV corresponds to the FIES RV data, θ is the parameter vector containing the parameters listed in Table 3, and D the combined dataset. The first term in the righthand side of Eq. (1), namely log P(θ), is the logarithm of the joint prior probability, i.e., the product of individual parameter prior probabilities, and the four remaining terms are the likelihoods for the RV and light curve data.
Model parametrisation used in the basic system characterisation.
The likelihoods for the combined RV and photometric dataset D follow the basic form for a likelihood assuming independent identically distributed errors from normal distribution (2)where D_{i} is the single observed data point i, M(t_{i},θ) the model explaining the data, t_{i} the centre time for a data point i, N_{D} the number of data points, and σ_{D} the standard deviation of the error distribution (see, e.g., Gregory 2005).
The likelihood for the secondary eclipse data was calculated using Gaussian processes (GPs) to reduce our sensitivity to systematic noise (Rasmussen & Williams 2006; Gibson et al. 2012). We modelled the residuals as a GP with an exponential kernel, with the kernel hyperparameters fixed to values optimised to the data.
The RV model follows from equation (3)where V_{γ} is the systemic velocity, K the RV semiamplitude, ω the argument of periastron, ν the true anomaly, and e the eccentricity.
The transit model used PyTransit, an optimised implementation of the (Giménez 2006) transit shape model^{6}. The longcadence and planetary eclipse models were supersampled using 8 subsamples per LC exposure to reduce the effects from the extended integration time (Kipping 2010).
We defined the planettostar surface brightness ratio f as the flux ratio per projected unit area (instead of as eclipse depth). The eclipse depth is thus .
Fig. 5 Upper panel: quarterly median transit depth residuals, as derived from the Kepler PDCMAP light curve of Kepler423, against Kepler crowding metrics. Error bars are the median absolute deviations. Quarters sharing the same Kepler observing season are plotted with the same symbol and colour: Q_{1}, Q_{5}, Q_{9}, Q_{13}, and Q_{17} (upward green triangles); Q_{2}, Q_{6}, Q_{10}, and Q_{14} (downward black triangles); Q_{3}, Q_{7}, Q_{11}, and Q_{15} (blue squares); Q_{4}, Q_{8}, Q_{12}, and Q_{16} (red circles). Lower panel: same as before, but for the PDCMAP cotrended data, following our quarterly crowding metric correction constrained by an informative prior. The xaxis reports our estimates of the quarterly crowding metrics (Table 4). 

Open with DEXTER 
5.4. Systematic effects in the Kepler photometric data: quarterly transit depth variation
Van Eylen et al. (2013) recently observed systematic depth variations in the Kepler transit light curves of HATP7, which were found to be related to the 90degree rolling of the spacecraft occurring every quarter (i.e., every ~90 days). They proposed four possible causes for the variations, i.e., unaccountedfor light contamination, too small aperture photometric masks, instrumental nonlinearities, and colourdependence in the pixel response function, but noted that it is not possible to choose the most likely cause based on Kepler data alone.
We searched for similar instrument systematics in the Kepler light curve of Kepler423 by subtracting, from each PDCMAP and SAP transit light curve, the corresponding bestfitting transit model obtained using simultaneously all the Kepler segments (Sect. 5.2). The upper panel of Fig. 4 displays the transit depth residual as a function of the transit number for the PDCMAP data. We found a significant (~16σ) quartertoquarter systematic variation of the transit depth, with a seasonal trend reoccurring every four quarters and with the Q_{4}, Q_{8}, Q_{12}, and Q_{16} data yielding the deepest transit light curves. The peaktopeak amplitude is about 800 parts per million (ppm), which corresponds to ~4.3% of the mean transit depth.
Intriguingly, there is no significant (~2σ) quartertoquarter variation of the transit depth in the SAP data, as shown in the middle panel of Fig. 4. The SAP residuals exhibit, however, intraquarter systematic trends that might result from the motion of the target within its photometric aperture due to telescope focus variation, differential velocity aberration, and spacecraft pointing (Kinemuchi et al. 2012). The PDCMAP data are corrected for these effects using cotrending basic vectors generated from a suitable ensemble of highlycorrelated light curves on the same channel (Stumpe et al. 2012). Because different behaviours of the Kepler detectors would most likely cause systematics visible in both PDCMAP and SAP data, we can safely exclude the channeltochannel nonlinearity difference as the source of the quartertoquarter transit depth variation. Moreover, the Kepler CCD nonlinearity is reported to be 3% over the whole dynamic range (Caldwell et al. 2010) and the systematic variations are at least one order of magnitude larger than the expected nonlinearity effect at the transit depth signal.
This leaves the crowding metric correction performed by the PDCMAP pipeline as the most plausible explanation. The crowding metric is defined as the fraction of light in the photometric aperture arising from the target star. Since apertures are defined for each quarter – to account for the redistribution of target flux over a new CCD occurring at each roll of the spacecraft – the crowding metrics are computed quarterly for each target. The excess flux due to crowding within the photometric aperture is automatically removed by the PDCMAP pipeline from the SAP light curve. The upper panel of Fig. 5 shows the quarterly median transit depth residuals – as derived from the PDCMAP light curve – plotted against the crowding metrics – as extracted from the header keyword CROWDSAP listed in the Kepler data (Table 4, second column). We found a significant correlation between the two quantities, with a null hypothesis probability of only 0.15%. The lack of significant quartertoquarter transit depth variation in the SAP data (Fig. 4, middle panel) suggests that the crowding metric variation among quarters is most likely overestimated, i.e., the excess flux arising from nearby contaminant sources is very likely to be almost constant from quarter to quarter.
Kinemuchi et al. (2012) quoted the completeness of the Kepler input catalogue (KIC) as possible source of contamination error. However, from a comparison with the POSS II image centred around Kepler423, we noted that all nearby faint stars up to Kepler magnitude K_{p}< 20 mag are included in the KIC. We therefore considered the Kepler crowding metric values to be generally correct, but not their variations among quarters. The crowding metric correction is the last data processing step performed by the PDCMAP pipeline on the cotrended Kepler light curve (Smith et al. 2012; Stumpe et al. 2012). To account for the quarterly systematics, we carried out the parameter estimation with the PDCMAP cotrended data. The latter were obtained by removing the Kepler crowding metric correction from the pipelinegenerated PDCMAP data. The parameter estimation was then performed including a perquarter contamination metric to the model with informative prior based on the average crowding metric derived by the Kepler team (Fig. 4, lower panel). Thus, our approach also yielded fitted estimates for the quarterly crowding factor.
Kepler quarterly crowding metrics (second column), and our estimates and uncertainties (last two columns).
Fig. 6 Quarterly crowding metric estimates rederived from our analysis and their 1σ uncertainties (Table 4) versus quarter numbers. The posterior crowding estimates are a product of transit modelling using the PDCMAP cotrended data and informative priors based on the Kepler crowding estimates. 

Open with DEXTER 
Kepler423 system parameters.
5.5. Priors
The final joint model has 31 free parameters, listed in Table 3. We used uninformative priors (uniform) on all parameters except the 17 crowding metrics, for which we used normal priors centred on 0.96 with a standard deviation of 0.01, based on the crowding metrics estimated by the Kepler team. While reducing the objectivity of the analysis, setting an informative prior on the quarterly crowding metrics was a necessary compromise, since the shape of the transit light curve alone cannot constrain totally free contamination.
Fig. 7 Phasefolded transit light curves of Kepler423, best fitting model, and residuals. LC data are shown on the left panel, SC on the right panel, both binned at ~1.9 min. The shaded area corresponds to the 3σ errors in the binned fluxes. The dashed lines mark the T_{14} limits, and the dotted lines the T_{23} limits. The blurring of the transit shape – due to the long integration time – is obvious in the LC plot (left panel). 

Open with DEXTER 
We considered two cases for the secondary eclipse. For model comparison purposes, we carried out the sampling for a model with a delta prior forcing the planettostar surface brightness ratio to zero (noeclipse model), and with a uniform prior based on simple modelling of expected flux ratios. We estimated the allowed range for the planettostar surface brightness ratio using a Monte Carlo approach by calculating the flux ratios for 50 000 samples of stellar effective temperature, semimajor axis, heat redistribution factor, and Bond albedo. The effective temperature and semimajor axis distributions are based on estimated values (Table 5), the heat distribution factor values are drawn from uniform distribution U(1/4,2/3) and the Bond albedo values from uniform distribution U(0,0.5). The resulting distribution is nearly uniform, and extends from 0.0 to 0.012 (99th percentile), and thus we decided to set a uniform prior U(0,0.012) on the surface brightness ratio.
Fig. 8 Radial velocity data with the median and 68% and 99% percentile limits of the posterior predictive distribution. 

Open with DEXTER 
6. Results and discussions
We list our results in Table 5. The system’s parameter estimates were taken to be the median values of the posterior probability distributions. Error bars were defined at the 68% confidence limit. We show the phasefolded transit and RV curves along with the fitted models in Figs. 7 and 8, respectively.
The quarterly correction estimates, along with their 1σ uncertainties, are listed in Table 4. For the sake of illustration, they are also plotted in Fig. 6. We found no significant correlation (51% null hypothesis probability) between the quarterly transit depth residuals – as derived from the PDCMAP cotrended light curve, following our correction for contamination factor – and our estimates of the quarterly crowding metrics, as displayed in the lower panel of Fig. 5. We note that neglecting the quartertoquarter transit depth variation leads to a significant (7σ) underestimate of the planettostar radius ratio by about 1.5% and doubles its uncertainty.
Fig. 9 Massradius diagram for transiting hot Jupiters (grey circles; P_{orb} < 10 days and 0.1 <M_{p}< 15M_{Jup}, from the Extrasolar Planet Encyclopedia at http://exoplanet.eu/, as of 15 September 2014). Kepler423b is marked with a thicker blue circle. The Fortney et al. (2007) isochrones for a planet core mass of 0, 25, 50 M_{⊕} – interpolated to the solar equivalent semimajor axis of Kepler423b and extrapolated to an age of 11 Gyr – are overplotted with thick green lines from top to bottom. Isodensity lines for density ρ_{p} = 0.25, 0.5, 1, 2, and 4 g cm^{3}are overlaid with dashed lines from left to right. 

Open with DEXTER 
6.1. Planet properties
The planet Kepler423b has a mass of M_{p}= 0.595 ± 0.081M_{Jup} and a radius of R_{p}= 1.192 ± 0.052R_{Jup}, yielding a planetary bulk density of ρ_{p} = 0.459 ± 0.083 g cm^{3}. We show in Fig. 9 how Kepler423b compares on a massradius diagram to all other known transiting hot Jupiters (P_{orb} < 10 days; 0.1 <M_{p}< 15M_{Jup}). With a system age of 11 Gyr, the radius of Kepler423b is consistent within 1.5σ with the expected theoretical value for an irradiated coreless gasgiant planet (Fortney et al. 2007). Alternatively, the planet might have a core and be inflated because of unaccountedfor heating source, atmospheric enhanced opacities, and reduced interior heat transport (Guillot 2008; Baraffe et al. 2014). It is worth noting that the radius of Kepler423b agrees within 1σ to the empirical radius relationship for Jupitermass planets from Enoch et al. (2012), which predicts a radius of 1.28 ± 0.14 R_{Jup}, given the planetary mass M_{p}, equilibrium temperature T_{eq}, and semimajor axis a_{p} listed in Table 5.
6.2. Secondary eclipse and planet albedo
We detected a tentative secondary eclipse of Kepler423b in the Kepler long cadence light curve and measured a depth of 14.2 ± 6.6 ppm (Fig. 10). The eclipse signal is relatively weak and could in theory be due to random instrumental or astrophysical events. We set to verify the eclipse signal and assessed its significance using a method based on Bayesian model selection, as described by Parviainen et al. (2013). We introduced some additional improvements that we briefly describe in the following paragraph^{7}. The Bayesian evidence integration could be carried out using simple Monte Carlo integration because of the low dimensionality of the effective parameter space.
Fig. 10 Secondary eclipse light curve of Kepler423, phasefolded to the orbital period of the planet. Kepler data are medianbinned in intervals of 0.015 cycles in phase (~1 h). The 1σ error bars are the median absolute deviations of the data points inside the bin, divided by the square root of the number of points. The best fitting transit model is overplotted with a red line. 

Open with DEXTER 
We considered two models, one without an eclipse signal (M_{0}) and one with an eclipse signal (M_{1}), and assigned equal prior weights on both models. We calculated the Bayes factor in favour of M_{1} cumulatively for each orbit, i.e., we calculated the Bayesian evidence for both models separately for every individual 18 hlong data segment. Since we assumed that the model global likelihoods – or Bayesian evidence – are independent from orbit to orbit, the final global likelihood is the product of the model likelihoods for each orbit – or a sum of the model loglikelihoods. A real eclipse signal that exists from orbit to orbit leads to a steadily increasing Bayes factor in favour of M_{1}^{8}. In contrast, a signal from an individual event mimicking an eclipse would be visible as a jump in the cumulative Bayes factor trace.
The Bayes factor in favour of the eclipse model was found to depend strongly on our choice of priors on eccentricity and surface brightness ratio. Assuming a uniform prior on eccentricity between 0 and 0.2 and a Jeffreys prior on surface brightness ratio encompassing all physically plausible values for planetary albedos up to 0.5 (i.e., flux ratios between 0 and 0.008) results in a Bayes factor only slightly higher than unity. Lowering the maximum eccentricity to 0.05 and maximum surface brightness ratio to 0.0015 (based on our MCMC posterior sampling, which is going to the grey area of Bayesian model selection) yielded a Bayes factor of ~2.6, corresponding to positive support for the eclipse model.
We show the log posteriors sample differences and the Bayes factor in favour of the eclipse model mapped as a function of eclipse centre – itself a function of the eccentricity and argument of periastron – in Fig. 11, and the cumulative Bayes factor in Fig. 12.
The Bayes factor map is used as an expository tool to probe the Bayesfactor space as a function of our prior assumptions, and in this case shows that a) the tentative eclipse found near 0.5 phase is the only eclipselike signal inside the sampling volume constrained by our priors; b) while the Bayes factor is only moderately in favour of the eclipse model, it is against the eclipse model for eclipse signals occurring away from the identified eclipse (with a peaktopeak log Bayes factor difference being ~4). However, the Bayes factor trace (Fig. 12) shows that the support for the eclipsemodel is mostly from a small continuous subset of orbits (but not from a single orbit that would indicate a jump in the data). Thus, we must consider the detected eclipse signal to be only tentative.
Fig. 11 Differences between the individual posterior samples for the eclipse model (M_{1}) and noeclipse model (M_{0}) plotted against the eclipse centre (light blue circles), mapped from the sampling space that uses eccentricity and argument of periastron. Only 447 LC segments are used for the modelling (see Sect. 5.2). A Bayes factor map produced by sliding a uniform prior with a width of 15 min along the transit centre is overlaid with a black thick line. 

Open with DEXTER 
Fig. 12 The cumulation of log B_{10} as a function of increasing data. The plot shows only the 447 orbits used for the secondary eclipse modelling (see Sect. 5.2). The upper plot shows the trace for the maximum log B_{10} case (identified as a slashed line in the lower plot), and the lower plot shows log B_{10} mapped as a function of a sliding prior on the eclipse centre (as in Fig. 11) on the yaxis, with the amount of data (number of orbits included) increasing on the xaxis. 

Open with DEXTER 
The depth of the planetary eclipse would imply a planettostar surface brightness ratio of f = (8.93 ± 4.13) × 10^{4}, allowing us to constrain the geometric A_{g} and Bond A_{b} albedo of the planet. From the effective stellar temperature, eccentricity, and scaled semimajor listed in Table 5, and assuming A_{g} = 1.5 × A_{B} and heat redistribution factor between 1/4 and 2/3, we found tentative values of A_{g} = 0.055 ± 0.028, A_{B} = 0.037 ± 0.019, and a planet brightness temperature of T_{br} = 1950 ± 250 K. This would make Kepler423b one of the gasgiant planets with lowest Bond albedo known so far (see, e.g., Angerhausen et al. 2014).
6.3. Tidal interaction and nonzero eccentricity
The RV data alone constrain the eccentricity to e< 0.16 (99th percentile of the posterior distribution). The inclusion of the photometric data and the tentative detection of the planet occultation give a small nonzero eccentricity of . We stress that ignoring the planet eclipse signal and imposing a circular orbit have a negligible effect on the values of the derived planetary parameters.
We estimated the tidal evolution timescales of the system using the model of Leconte et al. (2010), which is valid for arbitrary eccentricity and obliquity. However, instead of using a constant time lag Δt between the tidal bulge and the tidal potential, we recast their model equations using a constant modified tidal quality factor Q′, for an easy comparison with results for other planetary systems usually given in terms of Q′. Specifically, we assumed that Δt = 3/(2k_{2}nQ′), where k_{2} is the potential Love number of the second degree and n the mean orbital motion. This approximation is the same as, e.g., in Mardling & Lin (2002) and is justified for a first estimate of the timescales in view of our limited knowledge of tidal dissipation efficiency inside stars and planets.
The rotation period of the star is longer than the orbital period of the planet, therefore tides act to reduce the semimajor axis of the orbit a and to spin up the star. Assuming for the star, we obtained a tidal decay timescale  (1 /a)(da/ dt)^{1} ~ 4 Gyr, while the timescales for spin alignment and spin up are both  (1/Ω)(dΩ/dt)^{1} ~ 10 Gyr, all comparable to the age of the system. This suggests that a substantial orbital decay accompanied by a spin up of the star could have occurred during the mainsequence evolution of the system. Applying standard gyrochronology to the star (Barnes 2007), we estimated an age of ~3.7 Gyr for the observed rotation period of 22.046 days, which supports the conclusion that stellar magnetic braking is counteracted by the planet. The expected rotation period is ~40 days for an age of 11 Gyr, i.e., the star is rotating about 1.8 times faster than expected. The present orbital angular momentum is about 2.5 times the stellar spin angular momentum. If the angular momentum of excess rotation comes from the initial orbital angular momentum, its minimum value was ~1.25 the present orbital angular momentum, corresponding to an initial orbital period of at least 4.9 days for a planet of constant mass. If the stellar tidal quality factor , as suggested by Ogilvie & Lin (2007) for nonsynchronous systems as in the case of Kepler423, the orbital decay and the stellar spin up would have been negligible during the mainsequence evolution of the host and the excess rotation could be associated with a reduced efficiency of the stellar wind due to the magnetic perturbations induced by the planet (Lanza 2010; Cohen et al. 2010).
Separately, if the orbital eccentricity is indeed nonzero and equal to its most likely value , we estimated that this would require and . The latter is consistent with the tidal quality factor estimated by Goodman & Lackner (2009) for coreless planets.
6.4. Spinorbit alignment along the line of sight
The spinorbit angle, i.e., the angle between the stellar spin axis and the angular momentum vector of the orbit, is regarded as a key parameter to study planet migration mechanisms (see, e.g., Winn et al. 2010; Gandolfi et al. 2012; Crida & Batygin 2014). Assuming that a star rotates as a rigid body, one can infer the inclination i_{⋆} of the stellar spin with respect to the line of sight through (4)where P_{rot}, R_{⋆}, and v sin i_{⋆} are the stellar rotation period, radius, and projected rotational velocity, respectively. Since a transiting planet is seen nearly edgeon (i_{p} ≈ 90°), the inclination of the stellar spin axis can tell us whether the system is aligned along the line of sight or not. However, the method does not allow us to distinguish between prograde and retrograde systems, as i_{⋆} and π − i_{⋆} angles provide both the same sin i_{⋆}.
Using the values reported in Table 5, we found that sin i_{⋆} = 1.15 ± 0.23, which implies that i_{⋆} is between ~70 and 90° or ~160 and 180°. Given the fact that the measurements of the RossiterMcLaughlin effect have shown that retrograde systems around relatively cool stars (T_{eff}≲ 6250 K) are rare (see, e.g., Winn et al. 2010; Albrecht et al. 2012; Hirano et al. 2014), our findings are consistent with spinorbit alignment along the line of sight. Moreover, as seen in Sect. 6.3, the tidal interaction timescale for the evolution of the obliquity is comparable to the age of the system, implying that any primordial misalignment of the planet has most likely been damped down by tidal forces. This agrees with the general trend observed in systems with short tidal interaction timescales (Albrecht et al. 2012).
6.5. Search for transit timing variations
We carried out a search for additional perturbing objects in the system by looking for gravitationallyinduced variations in the transit centre times of Kepler423b, the socalled transit timing variations (TTVs). The TTV search was carried out using MCMC and exploiting – for the first time – the full Kepler light curve of Kepler423, from Q_{1} to Q_{17}. The transit centre posteriors were estimated by fitting a transit model to the individual transits with parameter posteriors from the main characterisation run used as priors for all the parameters except the transit centre. A wide uniform prior centred on the expected transit centre time, assuming no TTVs, was used for the transit centre.
Our results are shown in the upper panel of Fig. 13. The transit centres do not deviate significantly from the linear ephemeris and the results allow us to rule out TTVs with peaktopeak amplitude larger than about 2 min. Our finding agrees with those from Ford et al. (2011) and Mazeh et al. (2013), and further confirm the trend that stars hosting hot Jupiters are often observed to have no other closein planets (Steffen et al. 2012; Szabó et al. 2013).
The LombScargle periodogram of the Kepler423b TTV data shows no peaks with false alarm probability smaller than 1%. However, it is worth noting that there are peaks at the stellar rotation period and its first harmonic (Fig. 13, middle panel), which might be due to the passage of Kepler423b in front of active photospheric regions (see, e.g., Oshagh et al. 2013). The peak at half the stellar rotation period might be caused by the occultations of starspots at opposite stellar longitudes. As a matter of fact, the Kepler light curve shows also quasiperiodic variations recurring every ~11 days (i.e., half the stellar rotation period), which are visible in the second half of the Q_{13} data plotted in Fig. 1.
Fig. 13 Upper panel: differences between the observed and modelled transit centre times of Kepler423 (TTVs). Transit timing variations extracted from the short cadence data are plotted with red triangles, while long cadence TTVs are shown with blue circles. Middle panel: LombScargle periodogram of the TTV data in the 5–30 day period range. The two arrows mark the peak close to the stellar rotation period and its first harmonic. Lower panel: transit timing variation versus local transit slope. The straight blue line marks the linear fit to the data. 

Open with DEXTER 
As recently suggested by Mazeh et al. (2014), the anticorrelation (correlation) between the TTV and the slope of the light curve around each transit can be used to identify prograde (retrograde) planetary motion with respect to the stellar rotation. The lower panel of Fig. 13 shows that there is no significant correlation (anticorrelation) in our data between TTVs and local photometric slopes, the linear Pearson correlation coefficient and null hypothesis probability being −0.16 and 13%, respectively.
The lack of TTVversusslope correlation (anticorrelation) might imply that there are no detectable spotcrossing events in the TTV data, and that the photometric variation observed in the Kepler light curve is mainly dominated by active regions that are not occulted by the planet. Alternatively, there might be spotcrossing events whose signal in the TTV data is just below the noise. As a sanity check, we performed a visual inspection of the SC transits – the only ones in which a spotcrossing event can potentially be identified by eye – and found only one significant event. However, we believe that our data are mainly dominated by noise, because the TTVs are normally distributed around zero with a standard deviation (~22 s) comparable with the average uncertainty of our measurements (~19 s).
7. Conclusions
We spectroscopically confirmed the planetary nature of the Kepler transiting candidate Kepler423b. We derived the systems parameters exploiting – for the first time – the whole available Kepler photometry and combined it with highprecision RV measurements taken with FIES at NOT.
We found that the PDCMAP Kepler data are affected by seasonal systematic transit depth variations recurring every 4 quarters. We believe that these systematics are caused by an uncorrected estimate of the quarterly variation of the crowding metric, rather than different behaviours of the Kepler detectors (linearity), and treated them as such.
Kepler423b is a moderately inflated hot Jupiter with a mass of M_{p}= 0.595 ± 0.081M_{Jup} and a radius of R_{p}= 1.192 ± 0.052R_{Jup}, translating into a bulk density of ρ_{p} = 0.459 ± 0.083 g cm^{3}. The radius is consistent with both theoretical models for irradiated coreless giant planets and expectations based on empirical laws. Kepler423b transits every 2.7 days an old, G4 V star with an age of 11 ± 2 Gyr.
The stellar rotation period, projected equatorial rotational velocity v sin i_{⋆} and star radius R_{⋆} constrain the inclination i_{⋆} of the stellar spin axis to likely lie between ~70 and 90°, implying that the system is aligned along the line of sight.
We found no detectable TTVs at a level of ~22 s (1σ confidence level), confirming the lonely trend observed in hot Jupiter data. Our tentative detection of the planetary eclipse yields a small nonzero eccentricity of , and geometric and Bond albedo of A_{g} = 0.055 ± 0.028 and A_{b} = 0.037 ± 0.019, respectively, placing Kepler423b amongst the gasgiant planets with the lowest albedo known so far.
Note added in proof. Endl et al. (2014) presented an independent spectroscopic confirmation of the planetary nature of Kepler423b. While their estimate of the planet radius (R_{p}= 1.200 ± 0.065R_{Jup}) agrees very well with ours, their planetary mass of M_{p}= 0.72 ± 0.12M_{Jup} is slightly (~1σ) higher than our value. This is mainly due to their higher estimate of the stellar mass (M_{⋆} = 1.07 ± 0.05M_{⊙}), which in turn results from an hotter stellar effective temperature (T_{eff}= 5790 ± 116 K) and higher iron content ([Fe/H] = 0.26 ± 0.12 dex).
Available at http://archive.stsci.edu/kepler
Available at http://astro.df.unipi.it/stellarmodels/
Available at github.com/dfm/emcee
Available at github.com/hpparvi/PyDE
Available at github.com/hpparvi/PyTransit
Acknowledgments
We are infinitely grateful to the staff members at the Nordic Optical Telescope for their valuable and unique support during the observations. We thank the editor and the anonymous referee for their careful review and very positive feedback. Davide Gandolfi thanks Gabriele Cologna for the interesting conversations on the properties of the planetary system. Hannu Parviainen has received support from the Rocky Planets Around Cool Stars (RoPACS) project during this research, a Marie Curie Initial Training Network funded by the European Commission’s Seventh Framework Programme. He has also received funding from the Väisälä Foundation through the Finnish Academy of Science and Letters and from the Leverhulme Research Project grant RPG2012661. Financial supports from the Spanish Ministry of Economy and Competitiveness (MINECO) are acknowledged by Hans J. Deeg for the grant AYA201239346C0202, by Sergio Hoyer for the 2011 Severo Ochoa program SEV20110187, and Roi Alonso for the Ramón y Cajal program RYC201006519. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission Directorate. The Kepler data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS526555. Support for MAST for nonHST data is provided by the NASA Office of Space Science via grant NNX13AC07G and by other grants and contracts. This research has made an intensive use of the Simbad database and the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS, 143, 23.
References
 Aigrain, S., & Irwin, M. 2004, MNRAS, 350, 331 [NASA ADS] [CrossRef] [Google Scholar]
 Albrecht, S., Winn, J. N., Johnson, J. A., et al. 2012, ApJ, 757, 18 [NASA ADS] [CrossRef] [Google Scholar]
 Angerhausen, D., DeLarme, E., Morse, J. A. 2014 [arXiv:1404.4348] [Google Scholar]
 Baglin, A., Auvergne, M., Boisnard, L., et al. 2006, 36th COSPAR Scientific Assembly, 36, 3749 [Google Scholar]
 Baraffe, I., Chabrier, G., Fortney, J., et al. 2014, in Protostars and Planets VI, eds. H. Beuther, R. Klessen, C. Dullemond, & Th. Henning (Tucson: University of Arizona Press), 763 [Google Scholar]
 Barnes, S. A. 2007, ApJ, 669, 1167 [NASA ADS] [CrossRef] [Google Scholar]
 Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013, ApJS, 204, 24 [NASA ADS] [CrossRef] [Google Scholar]
 Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
 Borucki, W. J., Koch, D., Basri, G., et al. 2011, ApJ, 728, 117 [NASA ADS] [CrossRef] [Google Scholar]
 Bruntt, H., Bedding, T. R., Quirion, P.O., et al. 2010, MNRAS, 405, 1907 [NASA ADS] [Google Scholar]
 Buchhave, L. A., Bakos, G. A., Hartman, J. D., et al. 2010, ApJ, 720, 1118 [NASA ADS] [CrossRef] [Google Scholar]
 Caldwell, D. A., Kolodziejczak, J. J., van Cleve, J. E., et al. 2010, ApJ, 713, L92 [NASA ADS] [CrossRef] [Google Scholar]
 Casagrande, L. 2007, ASP Conf. Ser., 374, 71 [NASA ADS] [Google Scholar]
 Castelli, F., & Kurucz, R. L. 2004, Proc. IAU Symp. 210, poster A20 [arXiv:astroph/0405087] [Google Scholar]
 Coelho, P., Barbuy, B., Meléndez, J., et al. 2005, A&A, 443, 735 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Cohen, O., Drake, J. J., Kashyap, V. L., et al. 2010, ApJ, 723, L64 [NASA ADS] [CrossRef] [Google Scholar]
 Coughlin, J. L., & LópezMorales, M. 2012, AJ, 143, 39 [NASA ADS] [CrossRef] [Google Scholar]
 Crida, A., & Batygin, K. 2014, A&A, 567, A42 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, in 2MASS AllSky Catalog of Point Sources, NASA/IPAC Infrared Science Archive [Google Scholar]
 Cutri, R. M., et al. 2012, Vizier Online Catalog: II/311 [Google Scholar]
 Cyburt, R. H. 2004, Phys. Rev. D, 70, 023505 [NASA ADS] [CrossRef] [Google Scholar]
 Degl’Innocenti, S., Prada Moroni, P. G., Marconi, M., & Ruoppo, A. 2008, Ap&SS, 316, 25 [NASA ADS] [CrossRef] [Google Scholar]
 Dell’Omodarme, M., Valle, G., Degl’Innocenti, S., & Prada Moroni, P. G. 2012, A&A, 540, A26 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Doyle, A. P., Davies, G. R., Smalley, B., et al. 2014, MNRAS, 444, 3592 [NASA ADS] [CrossRef] [Google Scholar]
 Eastman, J., Siverd, R., & Gaudi, B. S. 2010, PASP, 122, 935 [NASA ADS] [CrossRef] [Google Scholar]
 Endl, M., Caldwell, D. A., Barclay, T., et al. 2014, ApJ, 795, 151 [NASA ADS] [CrossRef] [Google Scholar]
 Enoch, B., Collier Cameron, A., & Horne, K. 2012, A&A, 540, A99 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Ford, E. B., Rowe, J. F., Fabrycky, D. C., et al. 2011, ApJS, 197, 2 [NASA ADS] [CrossRef] [Google Scholar]
 ForemanMackey, D., Hogg, D. W., Lang, D., et al. 2013, PASP, 125, 306 [NASA ADS] [CrossRef] [Google Scholar]
 Fortney, J. J., Marley, M. S., & Barnes, J. W. 2007, ApJ, 659, 1661 [NASA ADS] [CrossRef] [Google Scholar]
 Frandsen, S., & Lindberg, B. 1999, in Astrophysics with the NOT, Proc. Conf., eds. H. Karttunen, & V. Piirola, 71 [Google Scholar]
 Gandolfi, D., Alcalá, J. M., Leccia, S., et al. 2008, ApJ, 687, 1303 [NASA ADS] [CrossRef] [Google Scholar]
 Gandolfi, D., Hébrard, G., Alonso, R., et al. 2010, A&A, 524, A55 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Gandolfi, D., Collier Cameron, A., Endl, M., et al. 2012, A&A, 543, L5 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Gandolfi, D., Parviainen, H., Fridlund, M., et al. 2013, A&A, 557, A74 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Gennaro, M., Prada Moroni, P. G., & Degl’Innocenti, S. 2010, A&A, 518, A13 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Gibson, N. P., Aigrain, S., Roberts, S., et al. 2012, MNRAS, 419, 2683 [NASA ADS] [CrossRef] [Google Scholar]
 Giménez, A. 2006, A&A, 450, 1231 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Goodman, J., & Lackner, C. 2009, ApJ, 696, 2054 [NASA ADS] [CrossRef] [Google Scholar]
 Goodman, J., & Weare, J. 2010, Comm. Appl. Math. Comput. Sci., 5, 65 [CrossRef] [MathSciNet] [Google Scholar]
 Gregory, P. C. 2005, in Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica Support (Cambridge University Press) [Google Scholar]
 Guillot, T. 2008, Phys. Scr., 130, 014023 [NASA ADS] [CrossRef] [Google Scholar]
 Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Hauschildt, P. H., Allard, F., & Baron, E. 1999, ApJ, 512, 377 [NASA ADS] [CrossRef] [Google Scholar]
 Hirano, T., SanchisOjeda, R., Takeda, Y., et al. 2014, ApJ, 783, 9 [NASA ADS] [CrossRef] [Google Scholar]
 Jenkins, J. M., Caldwell, D. A., Chandrasekaran, H., et al. 2010, ApJ, 713, L87 [NASA ADS] [CrossRef] [Google Scholar]
 Jimenez, R., Flynn, C., MacDonald, J., et al. 2003, Science, 299, 1552 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
 Kinemuchi, K., Barclay, T., Fanelli, M., et al. 2012, PASP, 124, 963 [NASA ADS] [CrossRef] [Google Scholar]
 Kipping, D. M. 2010, MNRAS, 408, 1758 [NASA ADS] [CrossRef] [Google Scholar]
 Lanza, A. F. 2010, A&A, 512, A77 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Leconte, J., Chabrier, G., Baraffe, I., & Levrard, B. 2010, A&A, 516, A64 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Léger, A., Rouan, D., Schneider, J., et al. 2009, A&A, 506, 287 [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
 Lissauer, J. J., Marcy, G. W., Bryson, S. T., et al. 2014, ApJ, 784, 44 [NASA ADS] [CrossRef] [Google Scholar]
 Loyd, R. O. P., & France, K. 2014, ApJS, 211, 9 [NASA ADS] [CrossRef] [Google Scholar]
 Mardling, R. A., & Lin, D. N. C. 2002, ApJ, 573, 829 [NASA ADS] [CrossRef] [Google Scholar]
 Marilli, E., Frasca, A., Covino, E., et al. 2007, A&A, 463, 1081 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Mazeh, T., Nachmani, G., Holczer, T., et al. 2013, ApJS, 208, 16 [NASA ADS] [CrossRef] [Google Scholar]
 Mazeh, T., Holczer, T., & Shporer, A. 2014, ApJ, submitted [arXiv:1407.1979] [Google Scholar]
 McQuillan, A., Mazeh, T., & Aigrain, S. 2013, ApJ, 775, L11 [NASA ADS] [CrossRef] [Google Scholar]
 Ogilvie, G. I., & Lin, D. N. C. 2007, ApJ, 661, 1180 [NASA ADS] [CrossRef] [Google Scholar]
 Oshagh, M., Santos, N. C., Boisse, I., et al. 2013, A&A, 556, A19 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Parviainen, H., Deeg, H. J., & Belmonte, J. A. 2013, A&A, 550, A67 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Parviainen, H., Gandolfi, D., Deleuil, M., et al. 2014, A&A, 562, A140 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Peimbert, M., Luridiana, V., Peimbert, A., & Carigi, L. 2007a, ASP Conf. Ser., 374, 81 [NASA ADS] [Google Scholar]
 Peimbert, M, Luridiana, V., & Peimbert, A. 2007b, ApJ, 666, 636 [NASA ADS] [CrossRef] [Google Scholar]
 Queloz, D., Henry, G. W., Sivan, J. P., et al. 2001, A&A, 379, 279 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Quintana, E. V., Barclay, T., Raymond, S. N., et al. 2014, Science, 344, 277 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
 Rasmussen, C. E., & Williams, C. K. I. 2006, in Gaussian processes for machine learning (The MIT Press) [Google Scholar]
 Rauer, H., Catala, C., Aerts, C., et al. 2014, Exp. Astron., 38, 249 [NASA ADS] [CrossRef] [Google Scholar]
 Rowe, J. F., Bryson, S. T., Marcy, G. W., et al. 2014, ApJ, 784, 45 [NASA ADS] [CrossRef] [Google Scholar]
 SanchisOjeda, R., Rappaport, S., Winn, J. N., et al. 2013, ApJ, 774, 54 [NASA ADS] [CrossRef] [Google Scholar]
 Santerne, A., Díaz, R. F., Moutou, C., et al. 2012, A&A, 545, A76 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Sliski, D. H., & Kipping, D. M. 2014, ApJ, 788, 148 [NASA ADS] [CrossRef] [Google Scholar]
 Smith, J. C., Stumpe, M. C., Van Cleve, J. E., et al. 2012, PASP, 124, 1000 [NASA ADS] [CrossRef] [Google Scholar]
 Steffen, J. H., Ragozzine, D., Fabrycky, D. C., et al. 2012, PNAS, 109, 7982 [NASA ADS] [CrossRef] [Google Scholar]
 Straizys, V., & Kuriliene, G. 1981, Ap&SS, 80, 353 [NASA ADS] [CrossRef] [Google Scholar]
 Stumpe, M. C., Smith, J. C., Van Cleve, J. E., et al. 2012, PASP, 124, 985 [NASA ADS] [CrossRef] [Google Scholar]
 Szabó, R., Szabó, Gy. M., Dálya, G., et al. 2013, A&A, 553, A17 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Telting, J. H., Avila, G., Buchhave, L., et al. 2014, Astron. Nachr., 335, 41 [NASA ADS] [CrossRef] [Google Scholar]
 Tognelli, E., Prada Moroni, P. G., & Degl’Innocenti, S. 2011, A&A, 533, A109 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Udry, S., Mayor, M., & Queloz, D. 1999, ASP Conf. Ser., 185, 367 [NASA ADS] [Google Scholar]
 Valenti, J. A., & Piskunov, N. 1996, A&AS, 118, 595 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Valenti, J. A., & Fischer, D. A. 2005, ApJS, 159, 141 [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
 Van Eylen, V., Lindholm Nielsen, M., Hinrup, B., et al. 2013, ApJ, 774, L19 [NASA ADS] [CrossRef] [Google Scholar]
 Winn, J. N. 2010, in Exoplanets, ed. S. Seager (Tucson, AZ: University of Arizona Press) [Google Scholar]
 Winn, J. N., Fabrycky, D. C., Albrecht, S., et al. 2010, ApJ, 718, L145 [NASA ADS] [CrossRef] [Google Scholar]
 Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868 [NASA ADS] [CrossRef] [Google Scholar]
All Tables
Main identifiers, equatorial coordinates, and optical/infrared magnitudes of the planethosting star Kepler423.
Kepler quarterly crowding metrics (second column), and our estimates and uncertainties (last two columns).
All Figures
Fig. 1 Example section of mediannormalised long cadence light curve of Kepler423. Data are from Kepler quarter 13. 

Open with DEXTER  
In the text 
Fig. 2 Upper panel: FIES radial velocities of Kepler423 – after subtracting the systemic velocity V_{γ} – versus BJD_{TDB} and Keplerian fit to the data. Lower panel: bisector spans of the FIES crosscorrelation functions versus RV measurements, after subtracting the systemic velocity V_{γ}. Error bars in the CCF bisector spans are taken to be twice the uncertainties in the RV data. 

Open with DEXTER  
In the text 
Fig. 3 Modified HertzsprungRussell diagram showing the stellar bulk density versus effective temperature. The position of Kepler423 is overplotted on theoretical evolutionary tracks and isochrones from the Pisa Stellar Evolution Data Base for lowmass stars. The blue hatched areas represent different masses (0.81, 0.85, and 0.89 M_{⊙} from right to left), while the greys represent the age isochrones (9, 11, and 13 Gyr from bottom to top), computed for an initial metal content between Z = 0.012 and Z = 0.014. 

Open with DEXTER  
In the text 
Fig. 4 Upper panel: average, observed−modelled (O − M) flux residual of the photometric points encompassing the second (T_{2}) and third transit contact (T_{3}) as a function of the transit numbers for the PDCMAP data, assuming that the Kepler contamination metric has been properly estimated. The light blue lines show the standard error of the mean for each transit. The beginning of each Kepler quarter is marked with dashed grey vertical lines. Middle panel: as in the upper panel, but for the SAP data. Lower panel: same as before, but for the PDCMAP cotrended data, following our quarterly crowding metric correction constrained by an informative prior (see text for more details). 

Open with DEXTER  
In the text 
Fig. 5 Upper panel: quarterly median transit depth residuals, as derived from the Kepler PDCMAP light curve of Kepler423, against Kepler crowding metrics. Error bars are the median absolute deviations. Quarters sharing the same Kepler observing season are plotted with the same symbol and colour: Q_{1}, Q_{5}, Q_{9}, Q_{13}, and Q_{17} (upward green triangles); Q_{2}, Q_{6}, Q_{10}, and Q_{14} (downward black triangles); Q_{3}, Q_{7}, Q_{11}, and Q_{15} (blue squares); Q_{4}, Q_{8}, Q_{12}, and Q_{16} (red circles). Lower panel: same as before, but for the PDCMAP cotrended data, following our quarterly crowding metric correction constrained by an informative prior. The xaxis reports our estimates of the quarterly crowding metrics (Table 4). 

Open with DEXTER  
In the text 
Fig. 6 Quarterly crowding metric estimates rederived from our analysis and their 1σ uncertainties (Table 4) versus quarter numbers. The posterior crowding estimates are a product of transit modelling using the PDCMAP cotrended data and informative priors based on the Kepler crowding estimates. 

Open with DEXTER  
In the text 
Fig. 7 Phasefolded transit light curves of Kepler423, best fitting model, and residuals. LC data are shown on the left panel, SC on the right panel, both binned at ~1.9 min. The shaded area corresponds to the 3σ errors in the binned fluxes. The dashed lines mark the T_{14} limits, and the dotted lines the T_{23} limits. The blurring of the transit shape – due to the long integration time – is obvious in the LC plot (left panel). 

Open with DEXTER  
In the text 
Fig. 8 Radial velocity data with the median and 68% and 99% percentile limits of the posterior predictive distribution. 

Open with DEXTER  
In the text 
Fig. 9 Massradius diagram for transiting hot Jupiters (grey circles; P_{orb} < 10 days and 0.1 <M_{p}< 15M_{Jup}, from the Extrasolar Planet Encyclopedia at http://exoplanet.eu/, as of 15 September 2014). Kepler423b is marked with a thicker blue circle. The Fortney et al. (2007) isochrones for a planet core mass of 0, 25, 50 M_{⊕} – interpolated to the solar equivalent semimajor axis of Kepler423b and extrapolated to an age of 11 Gyr – are overplotted with thick green lines from top to bottom. Isodensity lines for density ρ_{p} = 0.25, 0.5, 1, 2, and 4 g cm^{3}are overlaid with dashed lines from left to right. 

Open with DEXTER  
In the text 
Fig. 10 Secondary eclipse light curve of Kepler423, phasefolded to the orbital period of the planet. Kepler data are medianbinned in intervals of 0.015 cycles in phase (~1 h). The 1σ error bars are the median absolute deviations of the data points inside the bin, divided by the square root of the number of points. The best fitting transit model is overplotted with a red line. 

Open with DEXTER  
In the text 
Fig. 11 Differences between the individual posterior samples for the eclipse model (M_{1}) and noeclipse model (M_{0}) plotted against the eclipse centre (light blue circles), mapped from the sampling space that uses eccentricity and argument of periastron. Only 447 LC segments are used for the modelling (see Sect. 5.2). A Bayes factor map produced by sliding a uniform prior with a width of 15 min along the transit centre is overlaid with a black thick line. 

Open with DEXTER  
In the text 
Fig. 12 The cumulation of log B_{10} as a function of increasing data. The plot shows only the 447 orbits used for the secondary eclipse modelling (see Sect. 5.2). The upper plot shows the trace for the maximum log B_{10} case (identified as a slashed line in the lower plot), and the lower plot shows log B_{10} mapped as a function of a sliding prior on the eclipse centre (as in Fig. 11) on the yaxis, with the amount of data (number of orbits included) increasing on the xaxis. 

Open with DEXTER  
In the text 
Fig. 13 Upper panel: differences between the observed and modelled transit centre times of Kepler423 (TTVs). Transit timing variations extracted from the short cadence data are plotted with red triangles, while long cadence TTVs are shown with blue circles. Middle panel: LombScargle periodogram of the TTV data in the 5–30 day period range. The two arrows mark the peak close to the stellar rotation period and its first harmonic. Lower panel: transit timing variation versus local transit slope. The straight blue line marks the linear fit to the data. 

Open with DEXTER  
In the text 
Current usage metrics show cumulative count of Article Views (fulltext article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 4896 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.