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Xavier Bonfils

Publications and source records attributed to Xavier Bonfils.

At least 73 records · Page 4Linked to original sources

LHS 1815b: The First Thick-Disk Planet Detected By TESS

We report the first discovery of a thick-disk planet, LHS 1815b (TOI-704b, TIC 260004324), detected in the TESS survey. LHS 1815b transits a bright (V = 12.19 mag, K = 7.99 mag) and quiet M dwarf located $ 29.87\pm0.02 pc$ away with a mass of $0.502\pm0.015 M_{\odot}$ and a radius of $0.501\pm0.030 R_{\odot}$. We validate the planet by combining space and ground-based photometry, spectroscopy, and imaging. The planet has a radius of $1.088\pm 0.064 R_{\oplus}$ with a $3 σ$ mass upper-limit of $8.7 M_{\oplus}$. We analyze the galactic kinematics and orbit of the host star LHS1815 and find that it has a large probability ($P_{thick}/P_{thin} = 6482$) to be in the thick disk with a much higher expected maximal height ($Z_{max} = 1.8 kpc$) above the Galactic plane compared with other TESS planet host stars. Future studies of the interior structure and atmospheric properties of planets in such systems using for example the upcoming James Webb Space Telescope (JWST), can investigate the differences in formation efficiency and evolution for planetary systems between different Galactic components (thick and thin disks, and halo).

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GJ 1252 b: A 1.2 $R_{\oplus}$ planet transiting an M3-dwarf at 20.4 pc

We report the discovery of GJ 1252 b, a planet with a radius of 1.193 $\pm$ 0.074 $R_{\oplus}$ and an orbital period of 0.52 days around an M3-type star (0.381 $\pm$ 0.019 $M_{\odot}$, 0.391 $\pm$ 0.020 $R_{\odot}$) located 20.385 $\pm$ 0.019 pc away. We use TESS data, ground-based photometry and spectroscopy, Gaia astrometry, and high angular resolution imaging to show that the transit signal seen in the TESS data must originate from a transiting planet. We do so by ruling out all false positive scenarios that attempt to explain the transit signal as originating from an eclipsing stellar binary. Precise Doppler monitoring also leads to a tentative mass measurement of 2.09 $\pm$ 0.56 $M_{\oplus}$. The host star proximity, brightness ($V$ = 12.19 mag, $K$ = 7.92 mag), low stellar activity, and the system's short orbital period make this planet an attractive target for detailed characterization, including precise mass measurement, looking for other objects in the system, and planet atmosphere characterization.

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The high-energy environment and atmospheric escape of the mini-Neptune K2-18 b

K2-18 b is a transiting mini-Neptune that orbits a nearby (38 pc) cool M3 dwarf and is located inside its region of temperate irradiation. We report on the search for hydrogen escape from the atmosphere K2-18 b using Lyman-$α$ transit spectroscopy with the Space Telescope Imaging Spectrograph (STIS) instrument installed on the Hubble Space Telescope (HST). We analyzed the time-series of the fluxes of the stellar Lyman-$α$ emission of K2-18 in both its blue- and redshifted wings. We found that the average blueshifted emission of K2-18 decreases by $67\% \pm 18\%$ during the transit of the planet compared to the pre-transit emission, tentatively indicating the presence of H atoms escaping vigorously and being blown away by radiation pressure. This interpretation is not definitive because it relies on one partial transit. Based on the reconstructed Lyman-$α$ emission of K2-18, we estimate an EUV irradiation between $10^1-10^2$ erg s$^{-1}$ cm$^{-2}$ and a total escape rate in the order of $10^8$ g s$^{-1}$. The inferred escape rate suggests that the planet will lose only a small fraction (< 1%) of its mass and retain its volatile-rich atmosphere during its lifetime. More observations are needed to rule out stellar variability effects, confirm the in-transit absorption and better assess the atmospheric escape and high-energy environment of K2-18 b.

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Three Red Suns in the Sky: A Transiting, Terrestrial Planet in a Triple M Dwarf System at 6.9 Parsecs

We present the discovery from TESS data of LTT 1445Ab. At a distance of 6.9 parsecs, it is the second nearest transiting exoplanet system found to date, and the closest one known for which the primary is an M dwarf. The host stellar system consists of three mid-to-late M dwarfs in a hierarchical configuration, which are blended in one TESS pixel. We use data from MEarth and results from the SPOC DV report to determine that the planet transits the primary star in the system. The planet has a radius 1.38 R_Earth, an orbital period of 5.35882 days, and an equilibrium temperature of 433 K. With radial velocities from HARPS, we place a three-sigma upper mass limit of 8.4 M_Earth on the candidate. The planet provides one of the best opportunities to date for the spectroscopic study of the atmosphere of a terrestrial world. The presence of stellar companions of similar spectral type may facilitate such ground-based studies by providing a calibration source to remove telluric variations. In addition, we present a detailed characterization of the host stellar system. We use high-resolution spectroscopy and imaging to rule out the presence of any other close stellar or brown dwarf companions. Nineteen years of photometric monitoring of A and BC indicates a moderate amount of variability, in agreement with the observed low-level, short-term variability in the TESS light curve data. We derive a preliminary astrometric orbit for the BC pair that reveals an edge-on and eccentric configuration. The presence of a transiting planet in this system raises the possibility that the entire system is co-planar, which implies that the system may have formed from the early fragmentation of an individual protostellar core.

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Experimental test of a 40 cm-long R=100 000 spectrometer for exoplanet characterisation

High-resolution spectroscopy is a key element for present and future astronomical instrumentation. In particular, coupled to high contrast imagers and coronagraphs, high spectral resolution enables higher contrast and has been identified as a very powerful combination to characterise exoplanets, starting from giant planets now, up to Earth-like planet eventually for the future instruments. In this context, we propose the implementation of an innovative echelle spectrometer based on the use of VIPA (Virtually Imaged Phased Array, Shirasaki 1996). The VIPA itself is a particular kind of Fabry-Perot interferometer, used as an angular disperser with much greater dispersive power than common diffraction grating. The VIPA is an efficient, small component (3 cm x 2.4 cm), that takes the very advantage of single mode injection in a versatile design. The overall instrument presented here is a proof-of-concept of a compact, high-resolution (R > 80 000) spectrometer, dedicated to the H and K bands, in the context of the project High-Dispersion Coronagrahy developed at IPAG. The optical bench has a foot-print of 40 cm x 26 cm ; it is fed by two Single-Mode Fibers (SMF), one dedicated to the companion, and one to the star and/or to a calibration channel, and is cooled down to 80 K. This communication first presents the scientific and instrumental context of the project, and the principal merit of single-mode operations in high-resolution spectrometry. After recalling the physical structure of the VIPA and its implementation in an echelle-spectrometer design, it then details the optical design of the spectrometer. In conclusion, further steps (integration, calibration, coupling with adaptive optics) and possible optimization are briefly presented. Keywords: Echelle Spectrometer, High Spectral Resolution, Exoplanets, High-Dispersion Coronography, Infrared, Adaptive Optics, SPHERE

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A second terrestrial planet orbiting the nearby M dwarf LHS 1140

LHS 1140 is a nearby mid-M dwarf known to host a temperate rocky super-Earth (LHS 1140 b) on a 24.737-day orbit. Based on photometric observations by MEarth and Spitzer as well as Doppler spectroscopy from HARPS, we report the discovery of an additional transiting rocky companion (LHS 1140 c) with a mass of $1.81\pm0.39~{\rm M_{Earth}}$ and a radius of $1.282\pm0.024~{\rm R_{Earth}}$ on a tighter, 3.77795-day orbit. We also obtain more precise estimates of the mass and radius of LHS 1140 b to be $6.98\pm0.89~{\rm M_{Earth}}$ and $1.727\pm0.032~{\rm R_{Earth}}$. The mean densities of planets b and c are $7.5\pm1.0~\rm{g/cm^3}$ and $4.7\pm1.1~\rm{g/cm^3}$, respectively, both consistent with the Earth's ratio of iron to magnesium silicate. The orbital eccentricities of LHS 1140 b and c are consistent with circular orbits and constrained to be below 0.06 and 0.31, respectively, with 90% confidence. Because the orbits of the two planets are co-planar and because we know from previous analyses of Kepler data that compact systems of small planets orbiting M dwarfs are commonplace, a search for more transiting planets in the LHS 1140 system could be fruitful. LHS 1140 c is one of the few known nearby terrestrial planets whose atmosphere could be studied with the upcoming James Webb Space Telescope.

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Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star

The angle between the spin of a star and its planets' orbital planes traces the history of the planetary system. Exoplanets orbiting close to cool stars are expected to be on circular, aligned orbits because of strong tidal interactions with the stellar convective envelope. Spin-orbit alignment can be measured when the planet transits its star, but such ground-based spectroscopic measurements are challenging for cool, slowly-rotating stars. Here we report the characterization of a planet three-dimensional trajectory around an M dwarf star, derived by mapping the spectrum of the stellar photosphere along the chord transited by the planet. We find that the eccentric orbit of the Neptune-mass exoplanet GJ 436b is nearly perpendicular to the stellar equator. Both eccentricity and misalignment, surprising around a cool star, can result from dynamical interactions (via Kozai migration) with a yet-undetected outer companion. This inward migration of GJ 436b could have triggered the atmospheric escape that now sustains its giant exosphere. Eccentric, misaligned exoplanets orbiting close to cool stars might thus hint at the presence of unseen perturbers and illustrate the diversity of orbital architectures seen in exoplanetary systems.

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A temperate exo-Earth around a quiet M dwarf at 3.4 parsecs

The combination of high-contrast imaging and high-dispersion spectroscopy, which has successfully been used to detect the atmosphere of a giant planet, is one of the most promising potential probes of the atmosphere of Earth-size worlds. The forthcoming generation of extremely large telescopes (ELTs) may obtain sufficient contrast with this technique to detect O$_2$ in the atmosphere of those worlds that orbit low-mass M dwarfs. This is strong motivation to carry out a census of planets around cool stars for which habitable zones can be resolved by ELTs, i.e. for M dwarfs within $\sim$5 parsecs. Our HARPS survey has been a major contributor to that sample of nearby planets. Here we report on our radial velocity observations of Ross 128 (Proxima Virginis, GJ447, HIP 57548), an M4 dwarf just 3.4 parsec away from our Sun. This source hosts an exo-Earth with a projected mass $m \sin i = 1.35 M_\oplus$ and an orbital period of 9.9 days. Ross 128 b receives $\sim$1.38 times as much flux as Earth from the Sun and its equilibrium ranges in temperature between 269 K for an Earth-like albedo and 213 K for a Venus-like albedo. Recent studies place it close to the inner edge of the conventional habitable zone. An 80-day long light curve from K2 campaign C01 demonstrates that Ross~128~b does not transit. Together with the All Sky Automated Survey (ASAS) photometry and spectroscopic activity indices, the K2 photometry shows that Ross 128 rotates slowly and has weak magnetic activity. In a habitability context, this makes survival of its atmosphere against erosion more likely. Ross 128 b is the second closest known exo-Earth, after Proxima Centauri b (1.3 parsec), and the closest temperate planet known around a quiet star. The 15 mas planet-star angular separation at maximum elongation will be resolved by ELTs ($>$ 3$λ/D$) in the optical bands of O$_2$.

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A temperate rocky super-Earth transiting a nearby cool star

M dwarf stars, which have masses less than 60 per cent that of the Sun, make up 75 per cent of the population of the stars in the Galaxy [1]. The atmospheres of orbiting Earth-sized planets are observationally accessible via transmission spectroscopy when the planets pass in front of these stars [2,3]. Statistical results suggest that the nearest transiting Earth-sized planet in the liquid-water, habitable zone of an M dwarf star is probably around 10.5 parsecs away [4]. A temperate planet has been discovered orbiting Proxima Centauri, the closest M dwarf [5], but it probably does not transit and its true mass is unknown. Seven Earth-sized planets transit the very low-mass star TRAPPIST-1, which is 12 parsecs away [6,7], but their masses and, particularly, their densities are poorly constrained. Here we report observations of LHS 1140b, a planet with a radius of 1.4 Earth radii transiting a small, cool star (LHS 1140) 12 parsecs away. We measure the mass of the planet to be 6.6 times that of Earth, consistent with a rocky bulk composition. LHS 1140b receives an insolation of 0.46 times that of Earth, placing it within the liquid-water, habitable zone [8]. With 90 per cent confidence, we place an upper limit on the orbital eccentricity of 0.29. The circular orbit is unlikely to be the result of tides and therefore was probably present at formation. Given its large surface gravity and cool insolation, the planet may have retained its atmosphere despite the greater luminosity (compared to the present-day) of its host star in its youth [9,10]. Because LHS 1140 is nearby, telescopes currently under construction might be able to search for specific atmospheric gases in the future [2,3].

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The SOPHIE search for northern extrasolar planets - XII. Three giant planets suitable for astrometric mass determination with Gaia

We present new radial velocity measurements for three low-metallicity solar-like stars observed with the SOPHIE spectrograph and its predecessor ELODIE, both installed at the 193 cm telescope of the Haute-Provence Observatory, allowing the detection and characterization of three new giant extrasolar planets in intermediate periods of 1.7 to 3.7 years. All three stars, HD17674, HD42012 and HD29021 present single giant planetary companions with minimum masses between 0.9 and 2.5 MJup. The range of periods and masses of these companions, along with the distance of their host stars, make them good targets to look for astrometric signals over the lifetime of the new astrometry satellite Gaia. We discuss the preliminary astrometric solutions obtained from the first Gaia data release.

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Magnetic activity in the HARPS M-dwarf sample. The rotation-activity relationship for very low-mass stars through R'HK

Atmospheric magnetic fields in stars with convective envelopes heat stellar chromospheres. Starting with the historical Mount Wilson monitoring program, CaH&K lines have been widely used to trace stellar magnetic activity, and as a proxy for rotation period and consequently for stellar age. Monitoring stellar activity has also become essential in filtering out false-positives due to magnetic activity in extra-solar planet surveys. The Ca H&Kemission is traditionally quantified through the R'HK-index, which compares the chromospheric flux in the doublet to the overall bolometric flux of the star. Much work has been done to characterize this index for FGK-dwarfs, but M-dwarfs were left out of these analyses and no calibration of their Ca ii H&K emission to an R'HK exists to date. We set out to characterize the magnetic activity of the low and very low-mass stars by providing a calibration of the R'HK-index that extends to the realm of M-dwarfs, and by evaluating the relation between R'HK and the rotation period. We calibrated the bolometric and photospheric factors for M-dwarfs to properly transform the S-index into the R'HK. We monitored magnetic activity through the Ca ii H&K emission lines in the HARPS M-dwarf sample. The R'HK index, like the fractional X-ray luminosity L_X/Lbol, shows a saturated correlation with rotation, with saturation setting in around a ten days rotation period. Above that period, slower rotators show weaker Ca ii activity, as expected. Under that period, the R'HK index saturates to ~10^-4. Stellar mass modulates the Ca ii activity, with R'HK showing a constant basal activity above 0.6Msun and then decreasing with mass between 0.6Msun and the fully-convective limit of 0.35Msun. Short-term variability of the activity correlates with its mean level, stars with higher R'HK index show larger R'HK variability, as previously observed for earlier spectral types.

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A rocky planet transiting a nearby low-mass star

M-dwarf stars -- hydrogen-burning stars that are smaller than 60 per cent of the size of the Sun -- are the most common class of star in our Galaxy and outnumber Sun-like stars by a ratio of 12:1. Recent results have shown that M dwarfs host Earth-sized planets in great numbers: the average number of M-dwarf planets that are between 0.5 to 1.5 times the size of Earth is at least 1.4 per star. The nearest such planets known to transit their star are 39 parsecs away, too distant for detailed follow-up observations to measure the planetary masses or to study their atmospheres. Here we report observations of GJ 1132b, a planet with a size of 1.2 Earth radii that is transiting a small star 12 parsecs away. Our Doppler mass measurement of GJ 1132b yields a density consistent with an Earth-like bulk composition, similar to the compositions of the six known exoplanets with masses less than six times that of the Earth and precisely measured densities. Receiving 19 times more stellar radiation than the Earth, the planet is too hot to be habitable but is cool enough to support a substantial atmosphere, one that has probably been considerably depleted of hydrogen. Because the host star is nearby and only 21 per cent the radius of the Sun, existing and upcoming telescopes will be able to observe the composition and dynamics of the planetary atmosphere.

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A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b

Exoplanets orbiting close to their parent stars could lose some fraction of their atmospheres because of the extreme irradiation. Atmospheric mass loss primarily affects low-mass exoplanets, leading to suggest that hot rocky planets might have begun as Neptune-like, but subsequently lost all of their atmospheres; however, no confident measurements have hitherto been available. The signature of this loss could be observed in the ultraviolet spectrum, when the planet and its escaping atmosphere transit the star, giving rise to deeper and longer transit signatures than in the optical spectrum. Here we report that in the ultraviolet the Neptune-mass exoplanet GJ 436b (also known as Gliese 436b) has transit depths of 56.3 +/- 3.5% (1 sigma), far beyond the 0.69% optical transit depth. The ultraviolet transits repeatedly start ~2 h before, and end >3 h after the ~1 h optical transit, which is substantially different from one previous claim (based on an inaccurate ephemeris). We infer from this that the planet is surrounded and trailed by a large exospheric cloud composed mainly of hydrogen atoms. We estimate a mass-loss rate in the range of ~10^8-10^9 g/s, which today is far too small to deplete the atmosphere of a Neptune-like planet in the lifetime of the parent star, but would have been much greater in the past.

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Near-infrared transmission spectrum of the warm-uranus GJ 3470b with the Wide Field Camera-3 on the Hubble Space Telescope

The atmospheric composition of low-mass exoplanets is the object of intense observational and theoretical investigations. GJ3470b is a warm uranus recently detected in transit across a bright late-type star. The transit of this planet has already been observed in several band passes from the ground and space, allowing observers to draw an intriguing yet incomplete transmission spectrum of the planet atmospheric limb. In particular, published data in the visible suggest the existence of a Rayleigh scattering slope, making GJ3470b a unique case among the known neptunes, while data obtained beyond 2 um are consistent with a flat infrared spectrum. The unexplored near-infrared spectral region between 1 and 2 um, is thus key to undertanding the atmospheric nature of GJ3470b. Here, we report on the first space-borne spectrum of GJ3470, obtained during one transit of the planet with WFC3 on board HST, operated in stare mode. The spectrum covers the 1.1--1.7-um region with a resolution of about 300. We retrieve the transmission spectrum of GJ3470b with a chromatic planet-to-star radius ratio precision of 0.15% (about one scale height) per 40-nm bins. At this precision, the spectrum appears featureless, in good agreement with ground-based and Spitzer infrared data at longer wavelengths, pointing to a flat transmission spectrum from 1 to 5 um. We present new simulations of transmission spectra for GJ3470b, which allow us to show that the HST/WFC3 observations rule out cloudless hydrogen-rich atmospheres (>10 sigma) as well as hydrogen-rich atmospheres with tholin haze (>5 sigma). Adding our near-infrared measurements to the full set of previously published data from 0.3 to 5 um, we find that a cloudy, hydrogen-rich atmosphere can explain the full transmission spectrum if, at the terminator, the clouds are located at low pressures (<1 mbar) or the water mixing ratio is extremely low (<1 ppm).

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Telluric-line subtraction in high-accuracy velocimetry: a PCA-based approach

Optical velocimetry has led to the detection of more than 500 planets to date and there is a strong effort to push m/s velocimetry to the near-infrared to access cooler and lighter stars. The presence of numerous telluric absorption lines in the nIR brings an important challenge. As the star's barycentric velocity varies through the year, the telluric absorption lines effectively varies in velocity relative to the star's spectrum by the same amount leading to important systematic RV offsets. We present a novel principal component analysis-based approach for telluric line subtraction and demonstrated its effectiveness with archival HARPS data for GJ436 and τ Ceti, over parts of the R-band that contain strong telluric absorption lines. The main results are: 1) a better RV accuracy with excluding only a few percentage of the domain, 2) better use of the entire spectrum to measure RV and 3) a higher telescope time efficency by using A0V telluric standard from telescope archive.

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Spitzer Observations of GJ3470b: a Very Low-density Neptune-size Planet Orbiting a Metal-rich M dwarf

We present Spitzer/IRAC 4.5-micron transit photometry of GJ3470b, a Neptune-size planet orbiting a M1.5 dwarf star with a 3.3-day period recently discovered in the course of the HARPS M-dwarf survey. We refine the stellar parameters by employing purely empirical mass-luminosity and surface brightness relations constrained by our updated value for the mean stellar density, and additional information from new near-infrared spectroscopic observations. We derive a stellar mass of M_star = 0.539+0.047-0.043 M_sun and a radius of R_star = 0.568+0.037-0.031 R_sun. We determine the host star of GJ3470b to be metal-rich, with a metallicity of [Fe/H] = +0.20 +/- 0.10 and an effective temperature of Teff = 3600 +/- 100 K. The revised stellar parameters yield a planetary radius R_pl = 4.83+0.22-0.21 R_Earth that is 13 percent larger than the value previously reported in the literature. We find a planetary mass M_pl = 13.9+1.5-1.4 M_Earth that translates to a very low planetary density, rho_pl = 0.72+0.13-0.12 gcm-3, which is 33% smaller than the original value. With a mean density half of that of GJ436b, GJ3470b is an example of a very low-density low-mass planet, similar to Kepler-11d, Kepler-11e, and Kepler-18c but orbiting a much brighter nearby star that is more conducive to follow-up studies.

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Hint of a transiting extended atmosphere on 55 Cancri b

The naked-eye star 55 Cancri hosts a planetary system with five known planets, including a hot super-Earth (55 Cnc e) extremely close to its star and a farther out giant planet (55 Cnc b), found in milder irradiation conditions with respect to other known hot Jupiters. This system raises important questions on the evolution of atmospheres for close-in exoplanets, and the dependence with planetary mass and irradiation. These questions can be addressed by Lyman-alpha transit observations of the extended hydrogen planetary atmospheres, complemented by contemporaneous measurements of the stellar X-ray flux. In fact, planet `e' has been detected in transit, suggesting the system is seen nearly edge-on. Yet, planet `b' has not been observed in transit so far. Here, we report on Hubble Space Telescope STIS Lyman-alpha and Chandra ACIS-S X-ray observations of 55 Cnc. These simultaneous observations cover two transits of 55 Cnc e and two inferior conjunctions of 55 Cnc b. They reveal the star as a bright Lyman-alpha target and a variable X-ray source. While no significant signal is detected during the transits of 55 Cnc e, we detect a surprising Lyman-alpha absorption of 7.5 +/- 1.8% (4.2 sigma) at inferior conjunctions of 55 Cnc b. The absorption is only detected over the range of Doppler velocities where the stellar radiation repels hydrogen atoms towards the observer. We calculate a false-alarm probability of 4.4%, which takes into account the a-priori unknown transit parameters. This result suggests the possibility that 55 Cnc b has an extended upper H I atmosphere, which undergoes partial transits when the planet grazes the stellar disc. If confirmed, it would show that planets cooler than hot Jupiters can also have extended atmospheres.

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Dynamical evolution of the Gliese 436 planetary system - Kozai migration as a potential source for Gliese 436b's eccentricity

The close-in planet orbiting GJ 436 presents a puzzling orbital eccentricity considering its very short orbital period. Given the age of the system, this planet should have been tidally circularized a long time ago. Many attempts to explain this were proposed in recent years, either involving abnormally weak tides, or the perturbing action of a distant companion. We address here the latter issue based on Kozai migration. We propose that GJ 436b was formerly located further away from the star and that it underwent a migration induced by a massive, inclined perturber via Kozai mechanism. In this context, the perturbations by the companion trigger high amplitude variations to GJ 436b that cause tides to act at periastron. Then the orbit tidally shrinks to reach its present day location. We numerically integrate the 3-body system including tides and General Relativity correction. We first show that starting from the present-day location of GJ 436b inevitably leads to damping the Kozai oscillations and to rapidly circularizing the planet. Conversely, starting from 5-10 times further away allows the onset of Kozai cycles. The tides act in peak eccentricity phases and reduce the semi-major axis of the planet. The net result is an evolution characterized by two phases: a first one with Kozai cycles and a slowly shrinking semi-major axis, and a second one once the planet gets out of the Kozai resonance characterized by a more rapid decrease. The timescale of this process appears in most cases much longer than the standard circularization time of the planet by a factor larger than 50. This model can provide a solution to the eccentricity paradox of GJ 436b. Depending on the various orbital configurations, it can take several Gyrs to GJ 436b to achieve a full orbital decrease and circularization. According to this scenario, we could be witnessing today the second phase of the scenario where the semi-major axis is already reduced while the eccentricity is still significant. We then explore the parameter space and derive in which conditions this model can be realistic given the age of the system. This yields constraints on the characteristics of the putative companion.

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