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H. Parviainen

Publications and source records attributed to H. Parviainen.

At least 91 records · Page 5Linked to original sources

A feature-rich transmission spectrum for WASP-127b

WASP-127b is one of the lowest density planets discovered to date. With a sub-Saturn mass ($M_{\rm p}=0.18 \pm 0.02 M_J$) and super-Jupiter radius ($R_{\rm p}= 1.37 \pm 0.04 R_J$), it orbits a bright G5 star, which is about to leave the main-sequence. We aim to explore WASP-127b's atmosphere in order to retrieve its main atmospheric components, and to find hints for its intriguing inflation and evolutionary history. We used the ALFOSC spectrograph at the NOT telescope to observe a low resolution ($R\sim330$, seeing limited) long-slit spectroscopic time series during a planetary transit, and present here the first transmission spectrum for WASP-127b. We find the presence of a strong Rayleigh slope at blue wavelengths and a hint of Na absorption, although the quality of the data does not allow us to claim a detection. At redder wavelengths the absorption features of TiO and VO are the best explanation to fit the data. Although higher signal-to-noise ratio observations are needed to conclusively confirm the absorption features, WASP-127b seems to posses a cloud-free atmosphere and is one of the best targets to perform further characterization studies in the near future.

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The GTC exoplanet transit spectroscopy survey. VII. Detection of sodium in WASP-52b's cloudy atmosphere

We report the first detection of sodium absorption in the atmosphere of the hot Jupiter WASP-52b. We observed one transit of WASP-52b with the low-resolution Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at the 10.4 m Gran Telescopio Canarias (GTC). The resulting transmission spectrum, covering the wavelength range from 522 nm to 903 nm, is flat and featureless, except for the significant narrow absorption signature at the sodium doublet, which can be explained by an atmosphere in solar composition with clouds at 1 mbar. A cloud-free atmosphere is stringently ruled out. By assessing the absorption depths of sodium in various bin widths, we find that temperature increases towards lower atmospheric pressure levels, with a positive temperature gradient of 0.88 +/- 0.65 K/km, possibly indicative of upper atmospheric heating and a temperature inversion.

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The GTC exoplanet transit spectroscopy survey. VI. A spectrally-resolved Rayleigh scattering slope in GJ 3470b

Aims. As a sub-Uranus-mass low-density planet, GJ 3470b has been found to show a flat featureless transmission spectrum in the infrared and a tentative Rayleigh scattering slope in the optical. We conducted an optical transmission spectroscopy project to assess the impacts of stellar activity and to determine whether or not GJ 3470b hosts a hydrogen-rich gas envelop. Methods. We observed three transits with the low-resolution OSIRIS spectrograph at the 10.4 m Gran Telescopio Canarias, and one transit with the high-resolution UVES spectrograph at the 8.2 m Very Large Telescope. Results. From the high-resolution data, we find that the difference of the Ca II H+K lines in- and out-of-transit is only 0.67 +/- 0.22%, and determine a magnetic filling factor of about 10-15%. From the low-resolution data, we present the first optical transmission spectrum in the 435-755 nm band, which shows a slope consistent with Rayleigh scattering. Conclusions. After exploring the potential impacts of stellar activity in our observations, we confirm that Rayleigh scattering in an extended hydrogen/helium atmosphere is currently the best explanation. Further high-precision observations that simultaneously cover optical and infrared bands are required to answer whether or not clouds and hazes exist at high-altitude.

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K2-31b, a grazing transiting hot Jupiter on an 1.26-day orbit around a bright G7V star

We report the discovery of K2-31b, the first confirmed transiting hot Jupiter detected by the K2 space mission. We combined K2 photometry with FastCam lucky imaging and FIES and HARPS high-resolution spectroscopy to confirm the planetary nature of the transiting object and derived the system parameters. K2-31b is a 1.8-Jupiter-mass planet on an 1.26-day-orbit around a G7\,V star ($M_\star=0.91$~\Msun, $R_\star=0.78$~\Rsun). The planetary radius is poorly constrained (0.7$<$$R_\mathrm{p}$$<$1.4~\Rjup), owing to the grazing transit and the low sampling rate of the K2 photometry.

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The GTC exoplanet transit spectroscopy survey. IV.: No asymmetries in the transit of Corot-29b

Context. The launch of the exoplanet space missions obtaining exquisite photometry from space has resulted in the discovery of thousands of planetary systems with very different physical properties and architectures. Among them, the exoplanet CoRoT-29b was identified in the light curves the mission obtained in summer 2011, and presented an asymmetric transit light curve, which was tentatively explained via the effects of gravity darkening. Aims. Transits of CoRoT-29b are measured with precision photometry, to characterize the reported asymmetry in their transit shape. Methods. Using the OSIRIS spectrograph at the 10-m GTC telescope, we perform spectro-photometric differential observations, which allow us to both calculate a high-accuracy photometric light curve, and a study of the color-dependence of the transit. Results. After careful data analysis, we find that the previously reported asymmetry is not present in either of two transits, observed in July 2014 and July 2015 with high photometric precisions of 300ppm over 5 minutes. Due to the relative faintness of the star, we do not reach the precision necessary to perform transmission spectroscopy of its atmosphere, but we see no signs of color-dependency of the transit depth or duration. Conclusions. We conclude that the previously reported asymmetry may have been a time-dependent phenomenon, which did not occur in more recent epochs. Alternatively, instrumental effects in the discovery data may need to be reconsidered.

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Transiting exoplanets from the CoRoT space mission XXVIII. CoRoT-33b, an object in the brown dwarf desert with 2:3 commensurability with its host star

We report the detection of a rare transiting brown dwarf with a mass of 59 M_Jup and radius of 1.1 R_Jup around the metal-rich, [Fe/H] = +0.44, G9V star CoRoT-33. The orbit is eccentric (e = 0.07) with a period of 5.82 d. The companion, CoRoT-33b, is thus a new member in the so-called brown dwarf desert. The orbital period is within 3% to a 3:2 resonance with the rotational period of the star. CoRoT-33b may be an important test case for tidal evolution studies. The true frequency of brown dwarfs close to their host stars (P < 10 d) is estimated to be approximately 0.2% which is about six times smaller than the frequency of hot Jupiters in the same period range. We suspect that the frequency of brown dwarfs declines faster with decreasing period than that of giant planets.

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Transiting exoplanets from the CoRoT space mission XXVII. CoRoT-28b, a planet orbiting an evolved star, and CoRoT-29b, a planet showing an asymmetric transit

Context. We present the discovery of two transiting extrasolar planets by the satellite CoRoT. Aims. We aim at a characterization of the planetary bulk parameters, which allow us to further investigate the formation and evolution of the planetary systems and the main properties of the host stars. Methods. We used the transit light curve to characterize the planetary parameters relative to the stellar parameters. The analysis of HARPS spectra established the planetary nature of the detections, providing their masses. Further photometric and spectroscopic ground-based observations provided stellar parameters (log g,Teff,v sin i) to characterize the host stars. Our model takes the geometry of the transit to constrain the stellar density into account, which when linked to stellar evolutionary models, determines the bulk parameters of the star. Because of the asymmetric shape of the light curve of one of the planets, we had to include the possibility in our model that the stellar surface was not strictly spherical. Results. We present the planetary parameters of CoRoT-28b, a Jupiter-sized planet (mass 0.484+/-0.087MJup; radius 0.955+/-0.066RJup) orbiting an evolved star with an orbital period of 5.208 51 +/- 0.000 38 days, and CoRoT-29b, another Jupiter-sized planet (mass 0.85 +/- 0.20MJup; radius 0.90 +/- 0.16RJup) orbiting an oblate star with an orbital period of 2.850 570 +/- 0.000 006 days. The reason behind the asymmetry of the transit shape is not understood at this point. Conclusions. These two new planetary systems have very interesting properties and deserve further study, particularly in the case of the star CoRoT-29.

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Kepler423b: a half-Jupiter mass planet transiting a very old solar-like star

We report the spectroscopic confirmation of the Kepler object of interest KOI-183.01 (Kepler-423b), a half-Jupiter mass planet transiting an old solar-like star every 2.7 days. Our analysis is the first to combine the full Kepler photometry (quarters 1-17) with high-precision radial velocity measurements taken with the FIES spectrograph at the Nordic Optical Telescope. We simultaneously modelled the photometric and spectroscopic data-sets using Bayesian approach coupled with Markov chain Monte Carlo sampling. We found that the Kepler pre-search data conditioned (PDC) light curve of KOI-183 exhibits quarter-to-quarter systematic variations of the transit depth, with a peak-to-peak amplitude of about 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 KOI-183 is a G4 dwarf with $M_\star=0.85\pm0.04$ M$_\rm{Sun}$, $R_\star=0.95\pm0.04$ R$_\rm{Sun}$, $T_\mathrm{eff}=5560\pm80$ K, $[M/H]=-0.10\pm0.05$ dex, and with an age of $11\pm2$ Gyr. The planet KOI-183b has a mass of $M_\mathrm{p}=0.595\pm0.081$ M$_\mathrm{Jup}$ and a radius of $R_\mathrm{p}=1.192\pm0.052$ R$_\mathrm{Jup}$, yielding a planetary bulk density of $ρ_\mathrm{p}=0.459\pm0.083$ g/cm$^{3}$. The radius of KOI-183b 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 2-$σ$ confidence level ($ΔF_{\mathrm{ec}}=14.2\pm6.6$ ppm) and found that the orbit might have a small non-zero eccentricity of $e=0.019^{+0.028}_{-0.014}$. With a Bond albedo of $A_\mathrm{B}=0.037\pm0.019$, KOI-183b is one of the gas-giant planets with the lowest albedo known so far.

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Confirmation of an exoplanet using the transit color signature: Kepler-418b, a blended giant planet in a multiplanet system

We announce confirmation of Kepler-418b, one of two proposed planets in this system. This is the first confirmation of an exoplanet based primarily on the transit color signature technique. We used the Kepler public data archive combined with multicolor photometry from the Gran Telescopio de Canarias and radial velocity follow-up using FIES at the Nordic Optical Telescope for confirmation. We report a confident detection of a transit color signature that can only be explained by a compact occulting body, entirely ruling out a contaminating eclipsing binary, a hierarchical triple, or a grazing eclipsing binary. Those findings are corroborated by our radial velocity measurements, which put an upper limit of ~1 Mjup on the mass of Kepler-418b. We also report that the host star is significantly blended, confirming the ~10% light contamination suspected from the crowding metric in the Kepler light curve measured by the Kepler team. We report detection of an unresolved light source that contributes an additional ~40% to the target star, which would not have been detected without multicolor photometric analysis. The resulting planet-star radius ratio is 0.110 +/- 0.0025, more than 25% more than the 0.087 measured by Kepler, leading to a radius of 1.20 +/- 0.16 Rjup instead of the 0.94 Rjup measured by the Kepler team. This is the first confirmation of an exoplanet candidate based primarily on the transit color signature, demonstrating that this technique is viable from ground for giant planets. It is particularly useful for planets with long periods such as Kepler-418b, which tend to have long transit durations. Additionally, multicolor photometric analysis of transits can reveal unknown stellar neighbors and binary companions that do not affect the classification of the transiting object but can have a very significant effect on the perceived planetary radius.

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Transiting exoplanets from the CoRoT space mission XXV. CoRoT-27b: a massive and dense planet on a short-period orbit

We report the discovery of a massive and dense transiting planet CoRoT-27b on a 3.58 day orbit around a 4.2 Gyr-old G2 star. The planet candidate was identified from the CoRoT photometry, and was confirmed as a planet with ground-based spectroscopy. The confirmation of the planet candidate is based on radial velocity observations combined with imaging to rule out blends. The characterisation of the planet and its host star is carried out using a Bayesian approach where all the data (CoRoT photometry, radial velocities, and spectroscopic characterisation of the star) are used jointly. The Bayesian analysis includes a study whether the assumption of white normally distributed noise holds for the CoRoT photometry, and whether the use of a non-normal noise distribution offers advantages in parameter estimation and model selection. CoRoT-27b has a mass of $10.39 \pm 0.55$ $\mathrm{M}_{\rm Jup}$, a radius of $1.01 \pm 0.04$ $\mathrm{R}_{\rm Jup}$, a mean density of $12.6_{-1.67}^{+1.92}$ $\mathrm{g\,cm^{-3}}$, and an effective temperature of $1500 \pm 130$ K. The planet orbits around its host star, a 4.2 Gyr-old G2-star with a mass $M_{\star}=1.06$ $M_{\odot}$, and a radius $R_{\star}=1.05$ $R_{\odot}$, on a $0.048 \pm 0.007$ AU orbit every 3.58 days. The radial velocity observations allow us to exclude highly eccentric orbits, namely, $e<0.065$ with a 99% confidence. Given its high mass and density, theoretical modelling of CoRoT-27b is demanding. We identify two solutions with heavy element mass fractions of $0.11\pm0.08$ $\mathrm{M_{\oplus}}$ and $0.07\pm0.06$ $\mathrm{M_{\oplus}}$, but even solutions void of heavy elements cannot be excluded. We carry out a secondary eclipse search from the CoRoT photometry using a method based on Bayesian model selection, but conclude that the noise level is too high to detect eclipses shallower than 9% of the transit depth.

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Kepler-77b: a very low albedo, Saturn-mass transiting planet around a metal-rich solar-like star

We report the discovery of Kepler-77b (alias KOI-127.01), a Saturn-mass transiting planet in a 3.6-day orbit around a metal-rich solar-like star. We combined the publicly available Kepler photometry (quarters 1-13) with high-resolution spectroscopy from the Sandiford@McDonald and FIES@NOT spectrographs. We derived the system parameters via a simultaneous joint fit to the photometric and radial velocity measurements. Our analysis is based on the Bayesian approach and is carried out by sampling the parameter posterior distributions using a Markov chain Monte Carlo simulation. Kepler-77b is a moderately inflated planet with a mass of Mp=0.430+/-0.032 Mjup, a radius of Rp=0.960+/-0.016 Rjup, and a bulk density of 0.603+/-0.055 g/cm^3. It orbits a slowly rotating (P=36+/-6 days) G5V star with M*=0.95+/-0.04 Msun, R*=0.99+/-0.02 Rsun, Teff=5520+/-60 K, [M/H]=0.20+/-0.05, that has an age of 7.5+/-2.0 Gyr. The lack of detectable planetary occultation with a depth higher than about 10 ppm implies a planet geometric and Bond albedo of Ag<0.087+/-0.008 and Ab<0.058+/-0.006, respectively, placing Kepler-77b among the gas-giant planets with the lowest albedo known so far. We found neither additional planetary transit signals nor transit-timing variations at a level of about 0.5 minutes, in accordance with the trend that close-in gas giant planets seem to belong to single-planet systems. The 106 transits observed in short-cadence mode by Kepler for nearly 1.2 years show no detectable signatures of the planet's passage in front of starspots. We explored the implications of the absence of detectable spot-crossing events for the inclination of the stellar spin-axis, the sky-projected spin-orbit obliquity, and the latitude of magnetically active regions.

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Monitoring young associations and open clusters with Kepler in two-wheel mode

We outline a proposal to use the Kepler spacecraft in two-wheel mode to monitor a handful of young associations and open clusters, for a few weeks each. Judging from the experience of similar projects using ground-based telescopes and the CoRoT spacecraft, this program would transform our understanding of early stellar evolution through the study of pulsations, rotation, activity, the detection and characterisation of eclipsing binaries, and the possible detection of transiting exoplanets. Importantly, Kepler's wide field-of-view would enable key spatially extended, nearby regions to be monitored in their entirety for the first time, and the proposed observations would exploit unique synergies with the GAIA ESO spectroscopic survey and, in the longer term, the GAIA mission itself. We also outline possible strategies for optimising the photometric performance of Kepler in two-wheel mode by modelling pixel sensitivity variations and other systematics.

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From CoRoT 102899501 to the Sun. A time evolution model of chromospheric activity on the main sequence

Using a model based on the rotational modulation of the visibility of active regions, we analyse the high-accuracy CoRoT lightcurve of the active young star CoRoT102899501. Spectroscopic follow-up observations are used to derive its fundamental parameters. We compare its chromospheric activity level with a model of chrosmospheric activity evolution established by combining relationships between the R'HK index and the Rossby number with a recent model of stellar rotation evolution on the main sequence. We measure the spot coverage of the stellar surface as a function of time, and find evidence for a tentative increase from 5-14% at the beginning of the observing run to 13-29% 35 days later. A high level of magnetic activity on CoRoT102899501 is corroborated by a strong emission in the Balmer and Ca II HK lines (logR'HK ~ -4). The starspots used as tracers of the star rotation constrain the rotation period to 1.625+/-0.002 days and do not show evidence for differential rotation. The effective temperature (Teff=5180+/-80 K), surface gravity (logg=4.35+/-0.1), and metallicity ([M/H]=0.05+/-0.07 dex) indicate that the object is located near the evolutionary track of a 1.09+/-0.12 M_Sun pre-main sequence star at an age of 23+/-10 Myrs. This value is consistent with the "gyro-age" of about 8-25 Myrs, inferred using a parameterization of the stellar rotation period as a function of colour index and time established for the I-sequence of stars in stellar clusters. We conclude that the high magnetic activity level and fast rotation of CoRoT102899501 are manifestations of its stellar youth consistent with its estimated evolutionary status and with the detection of a strong Li I 6707.8 A absorption line in its spectrum. We argue that a magnetic activity level comparable to that observed on CoRoT102899501 could have been present on the Sun at the time of planet formation.

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Narrow Band Halpha Photometry of the Super-Earth GJ 1214b with GTC/OSIRIS Tunable Filters

The super-earth planet GJ 1214b has recently been the focus of several studies, using the transit spectroscopy technique, trying to determine the nature of its atmosphere. Here we focus on the Halpha line as a tool to further restrict the nature of GJ1214's atmosphere. We used the Gran Telescopio Canarias (GTC) OSIRIS instrument to acquire narrow band photometry with tunable filters. With our observations, we were able to observe the primary transit of the super-Earth GJ 1214b in three bandpasses: two centered in the continuum around Halpha (653.5 nm and 662.0 nm) and one centered at the line core (656.3 nm). We measure the depth of the planetary transit at each wavelength interval.By fitting analytic models to the measured light curves we were able to compute the depth of the transit at the three bandpasses. Taking the difference in the computed planet to star radius ratio between the line and the comparison continuum filters, we find Delta (Rp/Rstar)_{Halpha-653.5} = (6.60 +/- 3.54) 10^-3 and Delta (Rp/Rstar)_{Halpha-662.0} = (3.30 +/- 3.61) 10^-3. Although the planet radius is found to be larger in the Halpha line than in the surrounding continuum, the quality of our observations and the sigma level of the differences (1.8 and 1.0, respectively) does not allow us to claim an Halpha excess in GJ1214's atmosphere. Further observations will be needed to resolve this issue.

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Transiting exoplanets from the CoRoT space mission XXI. CoRoT-19b: A low density planet orbiting an old inactive F9V-star

Observations of transiting extrasolar planets are of key importance to our understanding of planets because their mass, radius, and mass density can be determined. The CoRoT space mission allows us to achieve a very high photometric accuracy. By combining CoRoT data with high-precision radial velocity measurements, we derive precise planetary radii and masses. We report the discovery of CoRoT-19b, a gas-giant planet transiting an old, inactive F9V-type star with a period of four days. After excluding alternative physical configurations mimicking a planetary transit signal, we determine the radius and mass of the planet by combining CoRoT photometry with high-resolution spectroscopy obtained with the echelle spectrographs SOPHIE, HARPS, FIES, and SANDIFORD. To improve the precision of its ephemeris and the epoch, we observed additional transits with the TRAPPIST and Euler telescopes. Using HARPS spectra obtained during the transit, we then determine the projected angle between the spin of the star and the orbit of the planet. We find that the host star of CoRoT-19b is an inactive F9V-type star close to the end of its main-sequence life. The host star has a mass M*=1.21+/-0.05 Msun and radius R*=1.65+/-0.04 Rsun. The planet has a mass of Mp=1.11+/-0.06 Mjup and radius of Rp=1.29+/-0.03 Rjup. The resulting bulk density is only rho=0.71+/-0.06 gcm-3, which is much lower than that for Jupiter. The exoplanet CoRoT-19b is an example of a giant planet of almost the same mass as Jupiter but a 30% larger radius.

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Transiting exoplanets from the CoRoT space mission - XIX. CoRoT-23b: a dense hot Jupiter on an eccentric orbit

We report the detection of CoRoT-23b, a hot Jupiter transiting in front of its host star with a period of 3.6314 \pm 0.0001 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite, combined with spectroscopic radial velocity (RV) measurements. A photometric search for possible background eclipsing binaries conducted at CFHT and OGS concluded with a very low risk of false positives. The usual techniques of combining RV and transit data simultaneously were used to derive stellar and planetary parameters. The planet has a mass of Mp = 2.8 \pm 0.3 MJup, a radius of Rpl = 1.05 \pm 0.13 RJup, a density of \approx 3 g cm-3. RV data also clearly reveal a non zero eccentricity of e = 0.16 \pm 0.02. The planet orbits a mature G0 main sequence star of V =15.5 mag, with a mass M\star = 1.14 \pm 0.08 M\odot, a radius R\star = 1. 61 \pm 0.18 R\odot and quasi-solar abundances. The age of the system is evaluated to be 7 Gyr, not far from the transition to subgiant, in agreement with the rather large stellar radius. The two features of a significant eccentricity of the orbit and of a fairly high density are fairly uncommon for a hot Jupiter. The high density is, however, consistent with a model of contraction of a planet at this mass, given the age of the system. On the other hand, at such an age, circularization is expected to be completed. In fact, we show that for this planetary mass and orbital distance, any initial eccentricity should not totally vanish after 7 Gyr, as long as the tidal quality factor Qp is more than a few 105, a value that is the lower bound of the usually expected range. Even if Corot-23b features a density and an eccentricity that are atypical of a hot Jupiter, it is thus not an enigmatic object.

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Planetary transit candidates in the CoRoT LRa01 field

Context: CoRoT is a pioneering space mission whose primary goals are stellar seismology and extrasolar planets search. Its surveys of large stellar fields generate numerous planetary candidates whose lightcurves have transit-like features. An extensive analytical and observational follow-up effort is undertaken to classify these candidates. Aims: The list of planetary transit candidates from the CoRoT LRa01 star field in the Monoceros constellation towards the Galactic anti-center is presented. The CoRoT observations of LRa01 lasted from 24 October 2007 to 3 March 2008. Methods: 7470 chromatic and 3938 monochromatic lightcurves were acquired and analysed. Instrumental noise and stellar variability were treated with several filtering tools by different teams from the CoRoT community. Different transit search algorithms were applied to the lightcurves. Results: Fifty-one stars were classified as planetary transit candidates in LRa01. Thirty-seven (i.e., 73 % of all candidates) are "good" planetary candidates based on photometric analysis only. Thirty-two (i.e., 87 % of the "good" candidates) have been followed-up. At the time of this writing twenty-two cases have been solved and five planets have been discovered: three transiting hot-Jupiters (CoRoT-5b, CoRoT-12b, and CoRoT-21b), the first terrestrial transiting planet (CoRoT-7b), and another planet in the same system (CoRoT-7c, detected by radial velocity survey only). Evidences of another non-transiting planet in the CoRoT-7 system, namely CoRoT-7d, have been recently found.

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XX. CoRoT-20b: A very high density, high eccentricity transiting giant planet

We report the discovery by the CoRoT space mission of a new giant planet, CoRoT-20b. The planet has a mass of 4.24 +/- 0.23 MJ and a radius of 0.84 +/- 0.04 RJ. With a mean density of 8.87 +/- 1.10 g/cm^3, it is among the most compact planets known so far. Evolution models for the planet suggest a mass of heavy elements of the order of 800 ME if embedded in a central core, requiring a revision either of the planet formation models or of planet evolution and structure models. We note however that smaller amounts of heavy elements are expected from more realistic models in which they are mixed throughout the envelope. The planet orbits a G-type star with an orbital period of 9.24 days and an eccentricity of 0.56. The star's projected rotational velocity is vsini = 4.5 +/- 1.0 km/s, corresponding to a spin period of 11.5 +/- 3.1 days if its axis of rotation is perpendicular to the orbital plane. In the framework of Darwinian theories and neglecting stellar magnetic breaking, we calculate the tidal evolution of the system and show that CoRoT-20b is presently one of the very few Darwin-stable planets that is evolving towards a triple synchronous state with equality of the orbital, planetary and stellar spin periods.

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