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The rapid pace of extrasolar planet discovery and characterization is legitimizing the study of their atmospheres via three‐dimensional numerical simulations. The complexity of atmospheric modelling and its inherent non‐linearity, together with the limited amount of data available, motivate model intercomparisons and benchmark tests. In the geophysical community, the Held–Suarez test is a standard benchmark for comparing dynamical core simulations of the Earth’s atmosphere with different solvers, based on statistically averaged flow quantities. In the present study, we perform analogues of the Held–Suarez test for tidally locked exoplanets with the Geophysical Fluid Dynamics Laboratory (GFDL) Princeton Flexible Modelling System (fms) by subjecting both the spectral and finite difference dynamical cores to a suite of tests, including the standard benchmark for the Earth, a hypothetical tidally locked Earth, a ‘shallow’ hot Jupiter model and a ‘deep’ model of HD 209458b. We find qualitative and quantitative agreement between the solvers for the Earth, tidally locked Earth and shallow hot Jupiter benchmarks, but the agreement is less than satisfactory for the deep model of HD 209458b. Further investigation reveals that closer agreement may be attained by arbitrarily adjusting the values of the horizontal dissipation parameters in the two solvers, but it remains the case that the magnitude of the horizontal dissipation is not easily specified from first principles. Irrespective of radiative transfer or chemical composition considerations, our study points to limitations in our ability to accurately model hot Jupiter atmospheres with meteorological solvers at the level of 10 per cent for the temperature field and several tens of per cent for the velocity field. Direct wind measurements should thus be particularly constraining for the models. Our suite of benchmark tests also provides a reference point for researchers wishing to adapt their codes to study the atmospheric circulation regimes of tidally locked Earths/Neptunes/Jupiters.
Context. The TRAPPIST-1 system hosts seven Earth-sized, temperate exoplanets orbiting an ultra-cool dwarf star. As such, it represents a remarkable setting to study the formation and evolution of terrestrial planets that formed in the same protoplanetary disk. While the sizes of the TRAPPIST-1 planets are all known to better than 5% precision, their densities have significant uncertainties (between 28% and 95%) because of poor constraints on the planet's masses. Aims. The goal of this paper is to improve our knowledge of the TRAPPIST-1 planetary masses and densities using transit-timing variations (TTV). The complexity of the TTV inversion problem is known to be particularly acute in multi-planetary systems (convergence issues, degeneracies and size of the parameter space), especially for resonant chain systems such as TRAPPIST-1. Methods. To overcome these challenges, we have used a novel method that employs a genetic algorithm coupled to a full N-body integrator that we applied to a set of 284 individual transit timings. This approach enables us to efficiently explore the parameter space and to derive reliable masses and densities from TTVs for all seven planets. Results. Our new masses result in a five-to eight-fold improvement on the planetary density uncertainties, with precisions ranging from 5% to 12%. These updated values provide new insights into the bulk structure of the TRAPPIST-1 planets. We find that TRAPPIST-1 c and e likely have largely rocky interiors, while planets b, d, f, g, and h require envelopes of volatiles in the form of thick atmospheres, oceans, or ice, in most cases with water mass fractions less than 5%.
The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star. At least seven planets similar to Earth in radius and in mass were previously found to transit this host star. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 Earth radii and an equilibrium temperature of 173 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.Comment: 42 pages, 8 figures, 2 table
A key legacy of the recently launched TESS mission will be to provide the astronomical community with many of the best transiting exoplanet targets for atmospheric characterization. However, time is of the essence to take full advantage of this opportunity. JWST, although delayed, will still complete its nominal five year mission on a timeline that motivates rapid identification, confirmation, and mass measurement of the top atmospheric characterization targets from TESS. Beyond JWST, future dedicated missions for atmospheric studies such as ARIEL require the discovery and confirmation of several hundred additional sub-Jovian size planets (R p < 10 R ⊕ ) orbiting bright stars, beyond those known today, to ensure a successful statistical census of exoplanet atmospheres. Ground-based ELTs will also contribute to surveying the atmospheres of the transiting planets discovered by TESS. Here we present a set of two straightforward analytic metrics, quantifying the expected signal-to-noise in transmission and thermal emission spectroscopy for a given planet, that will allow the top atmospheric characterization targets to be readily identified among the TESS planet candidates. Targets that meet our proposed threshold values for these metrics would be encouraged for rapid follow-up and confirmation via radial velocity mass measurements. Based on the catalog of simulated TESS detections by Sullivan et al. (2015), we determine appropriate cutoff values of the metrics, such that the TESS mission will ultimately yield a sample of ∼ 300 high-quality atmospheric characterization targets across a range of planet size bins, extending down to Earth-size, potentially habitable worlds.
Context. KELT-9 b exemplifies a newly emerging class of short-period gaseous exoplanets that tend to orbit hot, early type stars – termed ultra-hot Jupiters. The severe stellar irradiation heats their atmospheres to temperatures of ~4000 K, similar to temperatures of photospheres of dwarf stars. Due to the absence of aerosols and complex molecular chemistry at such temperatures, these planets offer the potential of detailed chemical characterization through transit and day-side spectroscopy. Detailed studies of their chemical inventories may provide crucial constraints on their formation process(es) and evolution history. Aims. We aim to search the optical transmission spectrum of KELT-9 b for absorption lines by metals using the cross-correlation technique. Methods. We analysed two transit observations obtained with the HARPS-N spectrograph. We used an isothermal equilibrium chemistry model to predict the transmission spectrum for each of the neutral and singly ionized atoms with atomic numbers between three and 78. Of these, we identified the elements that are expected to have spectral lines in the visible wavelength range and used those as cross-correlation templates. Results. We detect (>5σ) absorption by Na I, Cr II, Sc II and Y II, and confirm previous detections of Mg I, Fe I, Fe II, and Ti II. In addition, we find evidence of Ca I, Cr I, Co I, and Sr II that will require further observations to verify. The detected absorption lines are significantly deeper than predicted by our model, suggesting that the material is transported to higher altitudes where the density is enhanced compared to a hydrostatic profile, and that the material is part of an extended or outflowing envelope. There appears to be no significant blue-shift of the absorption spectrum due to a net day-to-night side wind. In particular, the strong Fe II feature is shifted by 0.18 ± 0.27 km s−1, consistent with zero. Using the orbital velocity of the planet we derive revised masses and radii of the star and the planet: M* = 1.978 ± 0.023 M⊙, R* = 2.178 ± 0.011 R⊙, mp = 2.44 ± 0.70 MJ and Rp = 1.783 ± 0.009 RJ.
Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen-and water-rich exoplanets.
Over the past decade, observations of giant exoplanets (Jupiter-size) have provided key insights into their atmospheres, but the properties of lower-mass exoplanets (sub-Neptune) remain largely unconstrained because of the challenges of observing small planets. Numerous efforts to observe the spectra of super-Earths--exoplanets with masses of one to ten times that of Earth--have so far revealed only featureless spectra. Here we report a longitudinal thermal brightness map of the nearby transiting super-Earth 55 Cancri e (refs 4, 5) revealing highly asymmetric dayside thermal emission and a strong day-night temperature contrast. Dedicated space-based monitoring of the planet in the infrared revealed a modulation of the thermal flux as 55 Cancri e revolves around its star in a tidally locked configuration. These observations reveal a hot spot that is located 41 ± 12 degrees east of the substellar point (the point at which incident light from the star is perpendicular to the surface of the planet). From the orbital phase curve, we also constrain the nightside brightness temperature of the planet to 1,380 ± 400 kelvin and the temperature of the warmest hemisphere (centred on the hot spot) to be about 1,300 kelvin hotter (2,700 ± 270 kelvin) at a wavelength of 4.5 micrometres, which indicates inefficient heat redistribution from the dayside to the nightside. Our observations are consistent with either an optically thick atmosphere with heat recirculation confined to the planetary dayside, or a planet devoid of atmosphere with low-viscosity magma flows at the surface.
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