EDP Sciences
Free Access
Issue
A&A
Volume 558, October 2013
Article Number L6
Number of page(s) 5
Section Letters
DOI https://doi.org/10.1051/0004-6361/201322201
Published online 25 October 2013

© ESO, 2013

1. Introduction

Transiting brown dwarfs (BD) are much less common than transiting giant planets. Above 20 MJup , only eight such objects are known: CoRoT-3 b (Deleuil et al., 2008), KELT-1 b (Siverd et al., 2012), KOI-205 b (Díaz et al., 2013), the young pair of eclipsing brown dwarfs 2M0535-05 (Stassun et al., 2007), WASP-30 b (Triaud et al., 2013), LHS 6343 C (Johnson et al., 2011), and CoRoT-15 b (Bouchy et al., 2011). The precise measurement of their mass and radius offers important constraints for the transition region between giant planets and low-mass stars, to be compared with theoretical predictions as given by, for instance, Burrows et al. (1997), Chabrier et al. (2000) and Baraffe et al. (2003). If CoRoT-15 b appears to be inflated, WASP-30 b, LHS 6343 C and KOI-205 b have a radius compatible with their age, as predicted by models. 2M0535-05 A and B may have smaller radii than predicted because of their activity (Stassun et al., 2012).

In this paper, we report the discovery and characterization of a new transiting brown dwarf in a long-period and highly-eccentric orbit: KOI-415 b is one the ~2300 transiting candidates identified by Kepler  (Batalha et al., 2013). The host star is a 14.11 magnitude star identified as KIC 6289650 or 2MASS-19331345+4136229. The transiting companion has been established as a brown dwarf by complementary observations with the SOPHIE radial-velocity instrument. KOI-415 b is one of the few known Kepler objects of interest (KOI) that lie in the brown dwarf domain and not in the planet domain (as KOI-205 b), a type of false-positive scenario whose low-occurrence is favored by the “brown-dwarf desert”, however.

2. Data

2.1. Kepler photometry

KOI-415 was observed by Kepler with a temporal sampling of 29.4 min (long-cadence data) for 1239.8 days; short-cadence data (one point per minute) are not available for this target. The ~59   000 raw simple-aperture-photometry measurements, which cover fourteen quarters, from Q1 to Q14, were downloaded from the MAST archive1. The flux excess caused by background stars that contaminate the photometric mask, as estimated by the Kepler team for each quarter2, does not exceed 5% of the total flux collected by Kepler and was subtracted from the raw data.

The light curve exhibits seven transits with a period of 166.8 d, a depth of ~0.5%, and a duration of ~6 h. The median of the errors of the individual measurements is 185 ppm. Figure 1 displays the phase-folded transit of KOI-415 b.

No variations attributable to starspots and faculae on the stellar photosphere are noticed, which indicates that the star is magnetically quiet.

2.2. SOPHIE spectroscopy and velocimetry

We have secured 14 measurements of KOI-415 from July 2012 to June 2013 with the SOPHIE spectrograph at Observatoire de Haute-Provence. SOPHIE is an echelle optical spectrograph in a thermally controlled room, fed by a fiber link from the Coudé focus of the 1.93-m telescope. It covers the range 390–687 nm at a resolving power of 40 000 in high-efficiency (HE) mode; the acceptance on the sky is 3′′ diameter. The radial velocities (RV) were extracted with the SOPHIE pipeline by measuring the cross-correlation function (CCF) of the spectra with a numerical mask of a G2 star, following the method described in Baranne et al. (1996). The CCF was measured without the seven bluest orders, which are dominated by noise. The G2 mask is preferred above the other F0 and K5 masks because it gives lower-noise measurements. The average RV uncertainty of the 14 measurements of KOI-415 is 31 m s-1.

When the background was bright, the CCF in the neighboring sky fiber was subtracted from the stellar CCF before the stellar CCF was fitted by a Gaussian model. In four spectra out of the 14, the background was detected and the RV were corrected for the contamination, with offsets varying from 13 m s-1 to 100 m s-1. The final measurements are listed in Table 1 together with the exposure time, signal-to-noise ratio (S/N) per spectrum, and the bisector span of the CCF.

The radial velocities exhibit a scatter of 2 km s-1. Their variations are in phase with the Kepler photometric transit event and compatible with the highly eccentric orbit of a massive object, as plotted in Fig. 2.

The bisector spans were used to check that the stellar CCF was not blended by an additional stellar spectrum, as is commonly done in transit-validation processes (Torres et al, 2004; Bouchy et al., 2009). The bisector spans of KOI-415  do not vary significantly in our data set, and show a dispersion of 75 ± 60 m s-1.

thumbnail Fig. 1

Top panel: phase-folded transit light curve of KOI-415. The red solid line shows the transit model rebinned at the Kepler sampling rate (see text for explanation). Bottom panel: residuals between the observations and the best-fit model.

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3. Host star

After RV corrections, all spectra that were only weakly affected by the moon reflected light were co-added. This resulted in a final spectrum with a S/N of 120 per pixel at 5500 Å. The effective temperature Teff, surface gravity log g, and metallicity [Fe/H] were estimated by using the versatile wavelength analysis package (VWA; Bruntt et al. 2004, 2010). We selected 242 spectral lines of FeI and FeII and fitted them iteratively, until the derived abundances minimized the correlation with the respective equivalent width and excitation potential and the mean FeI and FeII abundances coincided. vmacro was fixed according to Teff following Bruntt et al. (2010) to the value 2.4 km s-1. vmicro was fixed to 1.6 km s-1.

thumbnail Fig. 2

Radial velocities of KOI-415 obtained by SOPHIE as a function of time. The bottom plot shows the residuals after subtracting the model.

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KOI-415 appears to be a slightly evolved solar-type star with Teff = 5810 ± 80 K, log g = 4.5 ± 0.2 and [Fe/H]  = −0.24 ± 0.11. We derived log   g from the pressure-sensitive lines of Ca at 6122, 6162 and 6439 Å and from the MgIb line at 5172 Å, as well. The best fit was obtained from the Ca6122 and the Ca6162 lines (4.34 ± 0.26 dex) and agrees with the result from the Fe lines. Abundances of elements presenting isolated lines were calculated. Using an estimated B − V value of 0.58, the CCF parameters correspond to a projected rotational velocity of 2.8 ± 1.5 km s-1. The spectroscopic vsini was derived by fitting a set of isolated spectral lines to the corresponding synthetic profiles, which were convolved with different rotational profiles. Its low value (1 ± 1   km   s-1) is compatible within 1.2σ with the CCF estimate. The low vsini confirms the hypothesis that KOI-415 is an evolved star. Furthermore, no activity was observed through the CaII H and K lines. Using the spectroscopically determined v sin i and the stellar radius, the projected spin period of the star is 30 to 60 days. The final parameters of the host star are derived after the transit modeling in the next section.

4. Modeling the data and parameter estimation

Before starting the combined analysis of Kepler and SOPHIE data, a preliminary fit of the radial-velocity data was performed with a Keplerian model by using the downhill simplex algorithm (Press et al., 1992) and fixing the transit epoch and the orbital period to the values determined from the photometry. From the best solution, the uncertainties of SOPHIE data were scaled to derive a reduced χ2 = 1. The scaling factor corresponds to an RV jitter of 39   m   s-1.

The transits were normalized by locally fitting a parabola to the 10 h intervals of the light curve before the ingress and after the egress of each transit. The seventh transit, which occured at 2456078.870  BJDTBD, was not considered for our analysis because a gap taking place before its ingress prevented us from properly normalizing it. Photometrically correlated noise was estimated following Pont et al. (2006) and Bonomo et al. (2012), but its contribution was found to be negligible.

The eleven free parameters of our combined fit are the transit epoch T0, the orbital period P, the systemic RV Vr, the RV semi-amplitude K, and , where e is the eccentricity and ω the argument of periastron, the transit duration T14, the ratio of the brown dwarf to stellar radii Rb/R, the inclination i between the orbital plane and the plane of the sky, and the two limb-darkening coefficients u+ = ua + ub and u = ua − ub.

The transit fitting was carried out using the model of Giménez (2006, 2009) and a denser temporal sampling δtmodel = δt/5, to overcome the problem of the coarse long-cadence sampling that distorts the transit shape (Kipping, 2010). The χ2 of each trial model was then computed by binning the model samples at the Kepler sampling rate δt. An initial combined fit was performed by using the algorithm AMOEBA (Press et al., 1992) and changing the initial values of the parameters with a Monte Carlo method to properly explore the parameter space.

Table 2

KOI-415 system parameters.

The posterior distributions of our free parameters were determined by means of a differential evolution Markov chain Monte Carlo (DE-MCMC) method which is an MCMC version of the genetic algorithm (Ter Braak, 2006; Eastman et al., 2013). Twenty-two chains, which is twice the number of the fitted parameters, were simultaneously run after starting at different positions in the parameter space but reasonably close to the best solution previously found with AMOEBA. The jumps for a current chain in the parameter space were determined from the other chains according to the prescriptions given by Ter Braak (2006). The Metropolis-Hastings algorithm was used to accept or reject a proposal step for each chain. Uniform priors were implicitly imposed for all parameters except for the limb-darkening coefficients, for which Gaussian priors were considered, that is, Nu+(0.7,0.07) and Nu(0.15,0.14), where the most probable values were determined by the exploratory fit with AMOEBA.

Our DE-MCMC stopped when the convergence of the chains was achieved according to Ford (2006), that is, when the Gelman-Rubin statistics was lower than 1.01 (Gelman et al., 2004) and the number of independent draws was greater than 1000. Steps belonging to the “burn-in” phase, which were identified following Knutson et al. (2009) and Eastman et al. (2013), were discarded.

The medians of the posterior distributions of the fitted and derived parameters and their 34% intervals are quoted in Table 2 as the final values and their 1σ uncertainties, respectively.

The RV observations carried out with SOPHIE and the solution of the Keplerian fit derived from our combined fit are shown in Fig. 2. The scatter of the residuals is 71 m/s. Figure 1 displays the phase-folded transit of KOI-415 b and the transit model. The photometric residuals show an rms of 177 ppm, consistent with the median error of the data points (185 ppm). The rms over 3 h is 72 ppm, in agreement with the combined differential photometric precision of ~85  ppm (Gilliland et al., 2011) provided by the Kepler team.

The stellar density derived from the transit fitting and the Yonsey-Yale evolutionary tracks (Demarque et al., 2004) for the effective temperature and metallicity of KOI-415 indicate that with a mass M = 0.94 ± 0.06  M, a radius , and age of 10.5 ± 2.2 Gyr at 1σ, this star is slightly evolved. This is compatible with the absence of activity-related features in the Kepler light curve. The photometric log  dex agrees with the spectroscopic value, which is more uncertain.

The derived coefficients of the quadratic limb-darkening law ua = 0.42 ± 0.05 and ub = 0.28 ± 0.07 agree very well with the values determined by Sing (2010) using Kurucz stellar models (Kurucz, 1993) and the Kepler bandpass3, after linearly interpolating at the Teff, log g and metallicity of the star, that is, ua = 0.36 ± 0.02 and ub = 0.28 ± 0.01.

According to the determined stellar parameters, the mass and radius of the brown dwarf KOI-415 b are Mb = 62.14 ± 2.69  MJup and . The corresponding density is . Its very large error is dominated by the uncertainty on the brown dwarf radius.

thumbnail Fig. 3

Top panel: mass-radius diagram in the transition domain between brown dwarfs and stars. Isochrones for 10, 5, 1, and 0.1 Gyr are shown for comparison. Bottom panel: radius as a function of system’s age for objects from 15 to 100 Jupiter masses. BT-SETTL isochrones are shown for 0.02 to 0.09 M. Color symbols indicate the mass range: 15–25 MJup (green), 37−40 MJup (blue), 59−65 MJup (black), and 89−97 MJup (pink).

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5. Discussion

Figure 3 (top) shows the mass and radius of KOI-415 b and other similar objects in the transition domain between giant planets and low-mass stars. They are compared with values predicted by isochrones4 for models of isolated BDs developed by Chabrier et al. (2000), Allard et al. (2001), and Baraffe et al. (2003). With its long period (166.8 days), KOI-415 b more closely resembles the isolated BD as modeled in the tracks than the short-period companions more easily found by transiting surveys. The radius of KOI-415 b perfectly fits the predicted radius for a system age of 10 Gy and a non-metallic system with a cloud-free atmosphere (Burrows et al., 1997; Baraffe et al., 2003; Burrows et al., 2011). It shows that long-period BDs are adequately supported by partial electron degeneracy physics with a quantitatively correct equation of state. Brown dwarfs such as KOI-415 b are among the smallest ones in size, corresponding to the evolved state of its system, its low metallicity and low irradiation. It is also the oldest characterized BD (Fig. 3 (bottom)).

The models predict an effective temperature of 950 K for KOI-415 b. With an eccentricity of about 0.7 and period of 166.8 days, the temperature of the dayside of the brown dwarf likely increases by as much as 400 K along its orbit, from periastron to apastron due to changing stellar irradiation. It could be interesting to investigate, with dedicated modeling, the impact on the internal structure this seasonal effect may have.

Finally, the speckle imaging of the field around KOI-415 shows the existence of a nearby companion with a magnitude difference 2.9 in the optical, at 1.93′′ from the main target5. If it were bound to the main star, this companion would be an M1 dwarf at about 1600 AU orbital distance. The existence of such a stellar companion could then explain the high eccentricity of the brown dwarf KOI-415 b. Doppler measurements collected over a few years timescale could be sufficient to unveil their relationship; a background star is also a possibility.


Acknowledgments

A.S.B. gratefully acknowledges support through INAF/HARPS-N fellowship. We thank the staff at Haute-Provence Observatory. We acknowledge the PNP of CNRS/INSU, and the French ANR for their support. R.F.D. is supported by CNES. AS acknowledges the support by the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953.

References

Online material

Table 1

Radial velocity measurements for KOI-415.

All Tables

Table 2

KOI-415 system parameters.

Table 1

Radial velocity measurements for KOI-415.

All Figures

thumbnail Fig. 1

Top panel: phase-folded transit light curve of KOI-415. The red solid line shows the transit model rebinned at the Kepler sampling rate (see text for explanation). Bottom panel: residuals between the observations and the best-fit model.

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In the text
thumbnail Fig. 2

Radial velocities of KOI-415 obtained by SOPHIE as a function of time. The bottom plot shows the residuals after subtracting the model.

Open with DEXTER
In the text
thumbnail Fig. 3

Top panel: mass-radius diagram in the transition domain between brown dwarfs and stars. Isochrones for 10, 5, 1, and 0.1 Gyr are shown for comparison. Bottom panel: radius as a function of system’s age for objects from 15 to 100 Jupiter masses. BT-SETTL isochrones are shown for 0.02 to 0.09 M. Color symbols indicate the mass range: 15–25 MJup (green), 37−40 MJup (blue), 59−65 MJup (black), and 89−97 MJup (pink).

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In the text

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