Transit analysis of the CoRoT-5, CoRoT-8, CoRoT-12, CoRoT-18, CoRoT-20, and CoRoT-27 systems with combined ground- and space-based photometry

ABSTRACT

1 INTRODUCTION

The study of transiting extrasolar planets was revolutionized by the data obtained by space telescopes like CoRoT and Kepler, as they provide high-precision, high-cadence, continuous light curves (LCs) of a very high number of stars. Thanks to these extraordinary capabilities, the first rocky super-Earths were detected (CoRoT-7b, Kepler-10b, Queloz et al. 2009; Batalha et al. 2011), starting a new era of exoplanet discoveries.

CoRoT (convection, rotation, and planetary transits) was the first space mission dedicated to the detection of transiting planets. The mission was launched in 2006 December and started its first science observation in 2007 January. The spacecraft was equipped with a 27-cm telescope and a 4-CCD wide-field camera. Each pair of CCDs was designed for one of the two main goals of the mission, asteroseismology, or exoplanets. A complete overview on the CoRoT mission can be found in ‘The CoRoT Legacy Book: The adventure of the ultra high precision photometry from space’ (CoRot Team 2016). Because of its low-earth orbit, CoRoT could point in one direction for not longer than 6 months per year to avoid the Sun entering in its field of view (FoV). The ∼6 month observing time in one direction was divided into two separate runs lasting ∼30 d (short run, SR) and ∼150 d (long run, LR). CoRoT observed the fields with two cadence modes, a short cadence of 32 s exposure time and a long cadence with 16 exposures of 32 s stacked together resulting in 512 s cadence (Ollivier et al. 2016). While most stars were observed in long cadence mode, the 32 s exposures were only downloaded for selected targets i.e. after the detection of transit like events.

In 2009 March, the satellite suffered a loss of communication with one of the data processing units (DPU), which reduced the FoV by 50 per cent. In 2012 November, the second and last DPU failed resulting in the end of the mission in 2013 June. So far 34 confirmed exoplanets have been published and ∼500 candidate exoplanets are awaiting evaluation (CoRot Team 2016).

To truly benefit from CoRoT’s planet findings, the planet and orbit parameters need to be accurately determined. Since CoRoT could observe transiting planets only for a maximum duration of 150 d, ground-based follow-up is mandatory to extend the observational baseline. We have therefore initiated a dedicated project to combine the unprecedented precision of CoRoT LCs with ground-based follow-up photometry, in order to refine the planets orbital elements, constrain their physical parameters and search for additional bodies in the system. We selected 12 suitable targets that fulfilled the following criteria:

• The brightness of the host star is V < 16 mag and the transit depth is at least 8 mmag, to ensure sufficient photometric and timing precision at 1–2 m class ground-based telescopes.

• The orbit of the known transiting planet is not well constrained through radial velocity (RV) observations or shows non-zero eccentricity (though the circularization time-scale is much shorter than the system age) and/or the data presents deviant RV points, possibly indicating a perturber.

• Timing errors are critically large, which would impede the planetary transit observations within a few years.

A short description and first results of this study were published in Raetz et al. (2015). Here, we report on our observations of six of these targets, CoRoT-5, CoRoT-8, CoRoT-12, CoRoT-18, CoRoT-20, and CoRoT-27. Table 1 summarizes the literature values of the physical properties of these systems. Fig. 1 gives the propagation of the original published ephemeris uncertainties for these targets to the present. In particular, CoRoT-20 and CoRoT-27 are of special interest as they have the largest uncertainties in our sample. Moreover, both targets are massive hot Jupiters and, hence, very interesting systems to study formation, migration, and evolution of gas giant planets.

Figure 1.

Propagation of the uncertainties on the original published ephemeris for our targets from the start of CoRoT’s first science run in 2007 January to our last observation in 2016 December. The change points of the lines (close to zero) denotes the transit time at epoch zero (transit discovery).

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2 OBSERVATION, DATA REDUCTION, AND PHOTOMETRY

We started our follow-up campaign in 2013 October after first test observations that were carried out in 2012 September. In total, we collected 16 high-precision LCs of the six selected targets, CoRoT-5, CoRoT-8, CoRoT-12, CoRoT-18, CoRoT-20, and CoRoT-27, from 2012 September to 2016 December. Our ground-based observations were performed with three 1-m class telescopes located in Germany and Spain. Summaries of the participating observatories and observations are given in Tables 2 and 3, respectively. We have also re-analysed the CoRoT observations for these targets. The details are given in the following sections.

2.1 CoRoT observations

We downloaded the fully reduced LCs (N2 – the primary scientific, Version 2.1 or 2.2) produced by the CoRoT pipeline (Auvergne et al. 2009) from the CoRoT archive mirror at the ‘NASA Exoplanet Archive’ (Akeson et al. 2013, http://exoplanetarchive.ipac.caltech.edu/). In all cases we used the white-light LCs. For most of the targets, the LCs consist of the long cadence data at the beginning of the observations as well as short cadence data for the rest.

In preparation for the LC analysis we applied several steps to clean the LCs. First, we removed all flagged measurements (flagged e.g. because of energetic particles, South Atlantic Anomaly crossings, Earth eclipses; Chaintreuil et al. 2016). Then we extracted the transits from the LC by using all data points ±0.2 d around the expected transit time calculated with the published ephemeris. In the same step, we corrected the time stamp, which is given in heliocentric julian date at the end of the measurements in the original LCs, to the middle of the exposure. In step three, we normalized the LCs. After the division by the average out-of-transit flux, additional light (‘third’ light) L₃ induced by contaminants in the aperture around the target star was subtracted from the normalized flux before re-normalizing. In a last step we cleaned the LCs from outliers. By using a moving average of the time-series we created a smoothed LC. Finally, we removed all data points that deviated more than 3σ from this smoothed LC.

2.2 Ground-based observations

One observation in 2012 was carried out using the ‘Schmidt Teleskop Kamera’ (STK, Mugrauer & Berthold 2010) mounted at the 90 cm Schmidt telescope (60 cm in Schmidt mode) at the University Observatory Jena. With 2048 × 2048 pixels and a pixel scale of 1.55 arcsec/pixel, we could observe a large FoV of 53 x 53 arcmin.

Most of the LCs (12 out of 16) were collected with the 1.5-m reflector at the Observatorio de Sierra Nevada (OSN), which is operated by the Instituto de Astrofísica de Andalucía, CSIC, Spain. Using a VersArray:2048B CCD camera (2048 × 2048 pixels, pixel scale 0.23 arcsec/pixel) we covered a FoV of |$7.85\, \times \, 7.85\,\mathrm{ arcmin}$|⁠.

From 2015 November to 2016 June, we obtained three additional LCs at ESA’s Optical Ground Station (OGS), a 1-m telescope located at the Observatorio del Teide on Tenerife. The mounted spectrograph (Schulz et al. 2014) was used in imaging mode for the observations. The Roper Spec Camera provides 2048 × 2048 pixels with a pixel scale of 0.403 arcsec/pixel. The initial FoV of |$13.8\, \times \, 13.8\,{ \mathrm{ arcmin}}$| was windowed to shorten read-out time.

Since the CoRoT targets are relatively faint (⁠|$V\sim 14-15.5\,$|mag, see Table 1) all observations were carried out either in R-band or without any filter, with exposure times between 90 and 180 s.

Data reduction and photometry were performed following the procedures described by us in e.g. Raetz et al. (2014, 2016). In short, we subtracted a bias (as overscan for the data of the STK) and a dark frame (only for STK) and divided by a sky flat field using the iraf¹ routines zerocombine, darkcombine, flatcombine, and ccdproc. For the aperture photometry with 10 different aperture radii we used a script based on the standard iraf routine phot. Finally, we derived differential magnitudes using an optimized artificial comparison star (Broeg, Fernández & Neuhäuser 2005). We chose the aperture radius that produced the lowest LC scatter (lowest standard deviation) for a sample of constant stars.

As preparation for the LC analysis we applied part of the LC treatment as explained for the CoRoT LCs. In particular, steps three and four were performed to transform the differential magnitudes into fluxes, normalize the LCs, and remove outliers.

3 LIGHT CURVE ANALYSIS

The LC analysis was performed by fitting the transit model of Mandel & Agol (2002) to the LCs using the Transit Analysis Package² (tap v2.1, Gazak et al. 2012). tap fits the LCs using exofast (Eastman, Gaudi & Agol 2013) and estimates parameter uncertainties with the wavelet-based technique of Carter & Winn (2009).

All CoRoT and ground-based LCs of a given target were simultaneously fitted using 10 Markov Chain Monte Carlo (MCMC) chains with 10⁵ steps each. The wavelength independent parameters (orbital inclination i and the semimajor-axis scaled by stellar radius |$\frac{a}{R_{\mathrm{A}}}$|⁠) and the wavelength dependent parameters (planetary to stellar radii ratio |$\frac{R_{\mathrm{b}}}{R_{\mathrm{A}}}$| and the limb darkening coefficients) were connected for all LCs and for LCs in the same filter, respectively. The signal-to-noise ratio of the individual LCs was not sufficient (between ∼2 and 16) to derive the limb darkening coefficients from the LC analysis (Csizmadia et al. 2013). When the coefficients were allowed to vary in a wide range, the fitting procedure sometimes gave unphysical results. However, to not underestimate the parameter uncertainties by using limb darkening coefficients that were held fixed (see e.g. Maciejewski et al. 2013), they were allowed to vary ±0.1 around the theoretical values for the quadratic limb darkening law (used by tap). The limb darkening coefficients were inferred from the tables by Claret (2000) and Sing (2010) for the ground-based and the CoRoT observations, respectively. Photometric trends in the LCs were fitted simultaneously with the transit. The system parameters resulting from the LC modelling are given in Table 4.

4 PHYSICAL PROPERTIES

From the system parameters we obtained from the LC modelling, we calculated the physical properties for each of the observed systems. As explained by us in detail in e.g. Raetz et al. (2015), we followed the procedures of Southworth (2009). In a first step, we determined the stellar parameters mass M_A, luminosity L_A, and age by employing PARSEC isochrones (version 1.2S, Bressan et al. 2012). For transiting planetary systems, a modified version of the Hertzsprung–Russel diagram (HRD) can be drawn by using the mean stellar density ρ_A, which can accurately be determined from the LC modelling as shown by Winn (2010). The improved orbital period P necessary to calculate ρ_A was derived from all available transit times (see the next section). In addition, we deduced the stellar radius R_A and the surface gravity g_A from the fitted parameters a/R_A and R_b/R_A and the simplified formulas given in Southworth (2009), respectively. The planetary parameters R_b and g_b were derived along with the stellar ones. In the next step, we re-determined the planetary mass M_b and computed the planetary density ρ_b. We then calculated the planet’s equilibrium temperature, T_eq, assuming the effective temperature of the host star from the literature and the Safronov number Θ (a measure of the efficiency with which a planet gravitationally scatters other bodies, Safronov 1972). Finally, we calculated the geometrical parameters, semimajor axis a using Kepler’s third law, and the impact parameter b.

5 TRANSIT TIMING

The mid-transit times of each transit were obtained by the simultaneous modelling with tap where T_c was always a free parameter. The transit times, which are given in heliocentric julian date and julian date for the CoRoT and the ground-based observations, respectively, were converted into the barycentric Julian Date based on the barycentric dynamic time (BJD_TDB) using the online converter³ by Eastman, Siverd & Gaudi (2010). Our observations were carried out 5–9 yr, 7 yr on average, after the CoRoT planet discovery. We used the ephemeris that are available in the literature to compute ‘observed minus calculated’ (O–C) residuals for all transit times. As expected from the uncertainties of the published ephemeris, in most cases the observed transit times deviate significantly from the predicted ones. Hence, a re-calculation of the transit ephemeris was necessary for all observed targets. For an exact determination of the ephemeris, we plotted the mid-transit times over the epoch and performed a weighted linear fit.

Finally, we computed the generalized Lomb–Scargle periodogram (gls; Zechmeister & Kürster 2009) to search for a periodicity in the transit timing residuals.

6 COROT-5

CoRoT-5 b was discovered during the first LR on the galactic anti-centre direction (LRa01) that started on 2007 October 24 and lasted 112 d (Rauer et al. 2009). The observations started with a cadence of 512s that was changed to the 32s-mode after seven transit events. In total, 31 transits were found. One event was lost in a larger data gap caused by a DPU reset (Rauer et al. 2009). Photometric and spectroscopic follow-up observations were scheduled right after the ‘alarm mode’ was triggered. Radial velocity measurement with SOPHIE and HARPS confirmed that CoRoT-5 b is a hot Jupiter-type planet orbiting a 14 mag F9V star. The spectroscopic observations also yielded a slight eccentricity of the planetary orbit. The published physical properties of the CoRoT-5 system are summarized in Table 1. CoRoT-5 b belongs to the planets with the lowest mean density. It was found to be larger by 20 per cent compared to standard evolutionary models (Rauer et al. 2009).

We observed three ground-based LCs between 2014 January and 2016 December at OSN. The exposure times of the R-band observations were chosen between 120 and 150 s.

We also re-analysed the CoRoT data that initially consisted of 269 390 data points. After removing all flagged data the number of data points reduced to 236 774. We extracted 31 transit events with a depth of ∼1.4 per cent and a duration of ∼2.7 h. The contribution of L₃ was estimated to be 8.4 per cent by Rauer et al. (2009).

Figure 2.

Light curves of CoRoT-5 b with best-fitting model resulting from the simultaneous fit of all CoRoT and ground-based LCs. The dates of observation, observatory, filter, and the rms of the fit are indicated in each individual panel.

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Figure 3.

The O–C diagram of CoRoT-5 b. The grey squares and the black circles denote the CoRoT and the OSN transits, respectively. The dashed line represents the updated ephemeris given in equation (1).

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The results of the LC analysis is given in Table 4 and shown in Fig. 4, the obtained physical properties are summarized in Table 6. We found the geometrical parameters in excellent agreement with the ones of Rauer et al. (2009). Also most of the stellar and planetary values agree with each other within their error bars on a 2σ level. Only the surface gravity of the star that was determined spectroscopically in Rauer et al. (2009) slightly differs. These authors also give the photometrically obtained value of log g_A = 4.311 ± 0.033, which agrees with the result of our LC analysis.

Figure 4.

Phase-folded LCs of all 31 CoRoT transits as well as of all three OSN R-band transits of CoRoT-5. The trend was removed before phase-folding. Overlaid are the best-fitting models obtained with tap.

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Fig. 5 shows the position of CoRoT-5 in a modified version of the HRD, together with the PARSEC isochrones. CoRoT-5 is in an area of the HRD with overlapping isochrones of young (∼ 20 Myr) and old (∼ 6 Gyr) ages. However, as Rauer et al. (2009) have already shown, the very low level of stellar variability in the global LC as well as the missing signs of the Ca ii or a strong Li I absorption line hints to the older age.

Figure 5.

Position of CoRoT-5 in the |$\rho _{\mathrm{A}}^{-1/3}\, -\, T_{\mathrm{eff}}$| plane. The PARSEC isochrones of metallicity [M/H]= -0.25 for log(age) = 7.29 − 7.34 with steps of 0.01 and log(age)  =  9.71 − 9.89 with steps of 0.03 for the young and the old age, respectively, are also shown.

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7 COROT-8

CoRoT-8b, which was observed by CoRoT during the first LR in constellation Aquila (LRc01) from 2007 May 16 to October 5, orbits a K1 dwarf in ∼6.2 d (Bordé et al. 2010). It was detected by the ‘alarm mode’-pipeline which switched the observation mode to the short cadence after ∼68 d and triggered follow-up observations. L₃ is given as 1.55 per cent in the Exo-dat data base (Deleuil et al. 2009). RV follow-up observations that confirmed the planetary nature of CoRoT-8 b were carried out with SOPHIE and HARPS. With its measured radius and mass, CoRoT-8 b appears to be somewhat between Saturn and Neptune (Bordé et al. 2010).

We observed two transits of CoRoT-8 separated by ∼4 yr. One transit was observed in 2012 September 6 at the University Observatory Jena and the other one in 2016 June 16 at ESA’s OGS. Unfortunately, in both cases we could only observe a partial transit event. Our LCs are shown in Fig. 6.

Figure 6.

Same as Fig. 2 but for CoRoT-8. The date of observation, observatory, filter, and the rms of the fit are indicated in each individual panel.

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We extracted 23 transits, 11 of them in long cadence mode, from the CoRoT-LC that consist in total of 182 380 unflagged data points. The altogether 25 transits were simultaneously modelled. The phase-folded LCs including all transits are shown in Fig. 7. The resulting system parameters are given in Table 4.

Figure 7.

Phase-folded LCs of all 23 CoRoT transits as well as our own transits of CoRoT-8. The trend was removed before phase-folding. Overlaid are the best-fitting models obtained with tap.

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Computing the physical properties of the system from these system parameters resulted in significant deviations from the values given in Bordé et al. (2010). In particular, the stellar radius |$R_{\mathrm{A}}=1.048\pm ^{0.082}_{0.067}$| R_⊙, the stellar density |$\rho _{\mathrm{A}}=0.89\pm ^{0.20}_{0.15}$| ρ_⊙ and the impact parameter |$b=0.75\pm ^{0.11}_{0.09}$| differ by more than 3-σ. The much lower density results in a higher stellar mass and a very low pre-main-sequence age of log(age)  =  7.38 ± 0.13 when plotting it into the modified HRD with the PARSEC isochrones. Consequently, also the planetary parameters deviate. The discrepancies originate in the best-fitting values of i, a/R_A, and R_b/R_A obtained with tap, which we found to be strongly correlated. The analysis of relations between the parameters reveals significant correlation or anti-correlations (with the Pearson correlation coefficients r ranging from 0.873 to 0.995) between i and a/R_A, i and R_b/R_A, and a/R_A and R_b/R_A. An example for the correlation between i and a/R_A is shown in Fig. 8.

Figure 8.

Example of a significant correlation between a/R_A and the orbital inclination i (correlation coefficients r = 0.995) of CoRoT-8 b for one MCMC chain.

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CoRoT-8 was found to be a K1 main-sequence star by (Bordé et al. 2010). They excluded very young ages because of its slow rotation and the absence of detectable Ca ii or Li i absorption lines. Hence, a radius of ∼1 R_⊙ is very unlikely. A cross-check with Gaia DR2 yielded a radius of 0.8 (0.71 − 0.87) R_⊙ (Gaia Collaboration et al. 2016, 2018, note: this value has to be taken with caution). Because of the strong parameter correlations a smaller radius (a higher a/R_A) can be accounted for with a higher inclination i without degrading the quality of the fit. Therefore, we placed a prior before we re-fit our data. Bordé et al. (2010) determined a projected stellar rotational velocity of |$v$| sin i = 2 ± 1 km s⁻¹. Using the gyrochronology relation by Angus et al. (2015) and assuming spin-orbit alignment (i ∼ 90°), we estimated a stellar age of 1.7|$\pm ^{2.3}_{1.4}$| Gyr. The PARSEC isochrones of our age estimate were used to constrain the stellar density to |$\rho _{\mathrm{A}}=\, 1.73\, \pm \, 0.26\, \mathrm{\rho }_{\mathrm{\odot }}$|⁠. The resulting value of a/R_A = 17.07 ± 0.84 (calculated by using the formula of Winn 2010) was finally used as prior for the LC modelling with tap. The results of our re-analysis using a prior on the stellar density are given in Table 7, and the corresponding physical properties of the system in comparison to the literature values are summarized in Table 8. By applying gyrochronology to constrain the stellar density we found the physical properties in good agreement (on a 2-σ level) with the values of Bordé et al. (2010). However, using a prior in the fitting process may result in our uncertainties being underestimated.

Figure 9.

Same as Fig. 3 but for CoRoT-8 b. The dashed line represents the updated ephemeris given in equation (2).

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8 COROT-12

CoRoT-12 b is a hot Jupiter that orbits its V = 15.5 mag, quiet and slowly rotating star in 2.83 d. It was discovered by the CoRoT satellite in field LRa01 which was monitored from 2007 October 24 to 2008 March 3. The transits were noticed by the ‘alarm mode’-pipeline after 29 d of observations. L₃ was determined through ground based photometric follow-up observations as 3.3 ± 0.5  per cent. RV measurements were obtained with HARPS and with HIRES. CoRoT-12 b appears to be a very low-density, inflated hot Jupiter. The slightly non-zero eccentricity was measured to be between 0.06 and 0.08. The CoRoT-LC consist of 245 780 unflagged measurements and contains 47 transits, 36 of them in the short cadence mode.

We observed three transits of CoRoT-12 b from 2014 December to 2016 February, one at OSN and two at ESA’s OGS. All three LCs together with the best-fitting model are shown in Fig. 10.

Figure 10.

Same as Fig. 2 but for CoRoT-12. The date of observation, observatory, filter and the rms of the fit are indicated in each individual panel.

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The simultaneous fit of all CoRoT and ground-based LCs (see Fig. 11) resulted in the system parameters given in Table 4. We calculated the stellar density and plotted CoRoT-12 in the |$\rho _{\mathrm{A}}^{-1/3}\, -\, T_{\mathrm{eff}}$| plane together with the PARSEC isochrones (Fig. 12). As already mentioned by Gillon et al. (2010) the age is poorly constrained. The modified HR-diagram shows overlapping isochrones of young and an old age. But since CoRoT-12 appears to be very quiet and does not show chromospheric activity or a Li absorption line, a young age seems to be unlikely. Our derived old age of log(Age)  =  9.79 ± 0.26 is in agreement with the age given in Gillon et al. (2010).

Figure 11.

Phase-folded LCs of all 47 CoRoT transits as well as our own transits of CoRoT-12. The trend was removed before phase-folding. Overlaid are the best-fitting models obtained with tap.

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Figure 12.

Position of CoRoT-12 in the |$\rho _{\mathrm{A}}^{-1/3}\, -\, T_{\mathrm{eff}}$| plane. The PARSEC isochrones of metallicity [M/H]= 0.16 for log(age) = 7.41 − 7.48 with steps of 0.01 and log(age)  =  9.73 − 9.97 with steps of 0.03 for the young and the old age, respectively, are also shown.

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Figure 13.

Same as Fig. 3 but for CoRoT-12 b. The dashed line represents the updated ephemeris given in equation (3).

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