High-precision stellar limb-darkening in exoplanetary transits

Characterization of the atmospheres of transiting exoplanets relies on accurate measurements of the extent of the optically thick area of the planet at multiple wavelengths with a precision $\lesssim$100 parts per million (ppm). Next-generation instruments onboard the James Webb Space Telescope (JWST) are expected to achieve $\sim$10 ppm precision for several tens of targets. A similar precision can be obtained in modelling only if other astrophysical effects, including the stellar limb-darkening, are accounted for properly. In this paper, we explore the limits on precision due to the mathematical formulas currently adopted to approximate the stellar limb-darkening, and to the use of limb-darkening coefficients obtained either from stellar-atmosphere models or empirically. We propose a new limb-darkening law with two coefficients, `power-2', which outperforms other two-coefficient laws adopted in the literature in most cases, and particularly for cool stars. Empirical limb-darkening based on two-coefficient formulas can be significantly biased, even if the light-curve residuals are nearly photon-noise limited. We demonstrate an optimal strategy to fitting for the four-coefficients limb-darkening in the visible, using prior information on the exoplanet orbital parameters to break some of the degeneracies that otherwise would prevent the convergence of the fit. Infrared observations taken with the James Webb Space Telescope (JWST) will provide accurate measurements of the exoplanet orbital parameters with unprecedented precision, which can be used as priors to improve the stellar limb-darkening characterization, and therefore the inferred exoplanet parameters, from observations in the visible, such as those taken with Kepler/K2, JWST, other past and future instruments

PyLightcurve-torch: a transit modelling package for deep learning applications in PyTorch

We present a new open source python package, based on PyLightcurve and PyTorch, tailored for efficient computation and automatic differentiation of exoplanetary transits. The classes and functions implemented are fully vectorised, natively GPU-compatible and differentiable with respect to the stellar and planetary parameters. This makes PyLightcurve-torch suitable for traditional forward computation of transits, but also extends the range of possible applications with inference and optimisation algorithms requiring access to the gradients of the physical model. This endeavour is aimed at fostering the use of deep learning in exoplanets research, motivated by an ever increasing amount of stellar light curves data and various incentives for the improvement of detection and characterisation techniques.Comment: 7 pages, 3 figures; submission status updated, fig 2 caption adde

Detrending Exoplanetary Transit Light Curves with Long Short-Term Memory Networks

The precise derivation of transit depths from transit light curves is a key component for measuring exoplanet transit spectra, and henceforth for the study of exoplanet atmospheres. However, it is still deeply affected by various kinds of systematic errors and noise. In this paper we propose a new detrending method by reconstructing the stellar flux baseline during transit time. We train a probabilistic Long Short-Term Memory (LSTM) network to predict the next data point of the light curve during the out-of-transit, and use this model to reconstruct a transit-free light curve - i.e. including only the systematics - during the in-transit. By making no assumption about the instrument, and using only the transit ephemeris, this provides a general way to correct the systematics and perform a subsequent transit fit. The name of the proposed model is TLCD-LSTM, standing for Transit Light Curve Detrending LSTM. Here we present the first results on data from six transit observations of HD 189733b with the IRAC camera on board the Spitzer Space Telescope, and discuss some of its possible further applications.Comment: 12 pages, 10 figures, 4 tables, accepted for publication in The Astronomical Journa

Water vapour in the atmosphere of the habitable-zone eight Earth-mass planet K2-18 b

In the past decade, observations from space and ground have found H$_2$O to be the most abundant molecular species, after hydrogen, in the atmospheres of hot, gaseous, extrasolar planets. Being the main molecular carrier of oxygen, H$_2$O is a tracer of the origin and the evolution mechanisms of planets. For temperate, terrestrial planets, the presence of H$_2$O is of great significance as an indicator of habitable conditions. Being small and relatively cold, these planets and their atmospheres are the most challenging to observe, and therefore no atmospheric spectral signatures have so far been detected. Super-Earths -- planets lighter than ten M$_\oplus$ -- around later-type stars may provide our first opportunity to study spectroscopically the characteristics of such planets, as they are best suited for transit observations. Here we report the detection of an H$_2$O spectroscopic signature in the atmosphere of \planet\ -- an eight M$_\oplus$ planet in the habitable-zone of an M-dwarf -- with high statistical confidence (ADI = 5.0, $\sim$3.6$\sigma$). In addition, the derived mean molecular weight suggests an atmosphere still containing some hydrogen. The observations were recorded with the Hubble Space Telescope/WFC3 camera, and analysed with our dedicated, publicly available, algorithms. While the suitability of M-dwarfs to host habitable worlds is still under discussion, \planet\ offers an unprecedented opportunity to get insight into the composition and climate of habitable-zone planets.Comment: Published in Nature Astronom

Disentangling Atmospheric Compositions of K2-18 b with Next Generation Facilities

Recent analysis of the planet K2-18b has shown the presence of water vapour in its atmosphere. While the H2O detection is significant, the Hubble Space Telescope (HST) WFC3 spectrum suggests three possible solutions of very different nature which can equally match the data. These solutions include a primary cloudy atmosphere with traces of water vapour and a secondary atmosphere with a substantial amount of H2O and/or an undetectable gas such as N2. Additionally, the atmospheric pressure and the possible presence of a liquid/solid surface cannot be investigated with currently available observations. In this paper we used the best fit parameters from Tsiaras et al. (2019) to build JWST and Ariel simulations of the three scenarios. We have investigated 18 retrieval cases, which encompass the three scenarios and different observational strategies with the two observatories. Retrieval results show that twenty combined transits should be enough for the Ariel mission to disentangle the three scenarios, while JWST would require only two transits if combining NIRISS and NIRSpec data. This makes K2-18b an ideal target for atmospheric follow-ups by both facilities and highlights the capabilities of the next generation of space-based infrared observatories to provide a complete picture of low gravity planets.Comment: 12 pages, 12 figure

KELT-11 b: Abundances of water and constraints on carbon-bearing molecules from the Hubble transmission spectrum

In the past decade, the analysis of exoplanet atmospheric spectra has revealed the presence of water vapour in almost all the planets observed, with the exception of a fraction of overcast planets. Indeed, water vapour presents a large absorption signature in the wavelength coverage of the Hubble Space Telescope's (HST) Wide Field Camera 3 (WFC3), which is the main space-based observatory for atmospheric studies of exoplanets, making its detection very robust. However, while carbon-bearing species such as methane, carbon monoxide and carbon dioxide are also predicted from current chemical models, their direct detection and abundance characterisation has remained a challenge. Here we analyse the transmission spectrum of the puffy, clear hot-Jupiter KELT-11 b from the HST WFC3 camera. We find that the spectrum is consistent with the presence of water vapor and an additional absorption at longer wavelengths than 1.5um, which could well be explained by a mix of carbon bearing molecules. CO2, when included is systematically detected. One of the main difficulties to constrain the abundance of those molecules is their weak signatures across the HST WFC3 wavelength coverage, particularly when compared to those of water. Through a comprehensive retrieval analysis, we attempt to explain the main degeneracies present in this dataset and explore some of the recurrent challenges that are occurring in retrieval studies (e.g: the impact of model selection, the use of free vs self-consistent chemistry and the combination of instrument observations). Our results make this planet an exceptional example of chemical laboratory where to test current physical and chemical models of hot-Jupiters' atmospheres.Comment: 24 pages, 14 figures, Accepted in A

The Transmission Spectrum of WASP-17 b From the Optical to the Near-infrared Wavelengths: Combining STIS, WFC3, and IRAC Data Sets

We present the transmission spectrum of the inflated hot Jupiter WASP-17 b, observed with the STIS and WFC3 instruments aboard the Hubble Space Telescope, allowing for a continuous wavelength coverage from ∼0.4 to ∼1.7 μm. Observations taken with IRAC channels 1 and 2 on the Spitzer Space Telescope are also included, adding photometric measurements at 3.6 and 4.5 μm. HST spectral data were analyzed with Iraclis, a pipeline specialized in the reduction of STIS and WFC3 transit and eclipse observations. Spitzer photometric observations were reduced with the TLCD-LSTM method, utilizing recurrent neural networks. The outcome of our reduction produces incompatible results between STIS visit 1 and visit 2, which leads us to consider two scenarios for G430L. Additionally, by modeling the WFC3 data alone, we can extract atmospheric information without having to deal with the contrasting STIS data sets. We run separate retrievals on the three spectral scenarios with the aid of TauREx 3, a fully Bayesian retrieval framework. We find that, independently of the data considered, the exoplanet atmosphere displays strong water signatures and, potentially, the presence of aluminum oxide and titanium hydride. A retrieval that includes an extreme photospheric activity of the host star is the preferred model, but we recognize that such a scenario is unlikely for an F6-type star. Due to the incompleteness of all STIS spectral light curves, only further observations with this instrument would allow us to properly constrain the atmospheric limb of WASP-17 b, before the James Webb Space Telescope or Ariel will come online

Hubble WFC3 Spectroscopy of the Habitable-zone Super-Earth LHS 1140 b

Atmospheric characterisation of temperate, rocky planets is the holy grail of exoplanet studies. These worlds are at the limits of our capabilities with current instrumentation in transmission spectroscopy and challenge our state-of-the-art statistical techniques. Here we present the transmission spectrum of the temperate Super-Earth LHS 1140b using the Hubble Space Telescope (HST). The Wide Field Camera 3 (WFC3) G141 grism data of this habitable zone (T$_{\rm{eq}}$ = 235 K) Super-Earth (R = 1.7 $R_\oplus$), shows tentative evidence of water. However, the signal-to-noise ratio, and thus the significance of the detection, is low and stellar contamination models can cause modulation over the spectral band probed. We attempt to correct for contamination using these models and find that, while many still lead to evidence for water, some could provide reasonable fits to the data without the need for molecular absorption although most of these cause also features in the visible ground-based data which are nonphysical. Future observations with the James Webb Space Telescope (JWST) would be capable of confirming, or refuting, this atmospheric detection.Comment: Accepted for publication in AJ on 30th October 202

Evidence for Atmospheric Cold-trap Processes in the Noninverted Emission Spectrum of Kepler-13Ab Using HST/WFC3

We observed two eclipses of the Kepler-13A planetary system, on UT 2014 April 28 and UT 2014 October 13, in the near-infrared using Wide Field Camera 3 on the Hubble Space Telescope. By using the nearby binary stars Kepler-13BC as a reference, we were able to create a differential light curve for Kepler-13A that had little of the systematics typically present in HST/WFC3 spectrophotometry. We measure a broadband (1.1–1.65 μm) eclipse depth of 734 ± 28 ppm and are able to measure the emission spectrum of the planet at R ≈ 50 with an average precision of 70 ppm. We find that Kepler-13Ab possesses a noninverted, monotonically decreasing vertical temperature profile. We exclude an isothermal profile and an inverted profile at more than 3σ. We also find that the dayside emission of Kepler-13Ab appears generally similar to an isolated M7 brown dwarf at a similar effective temperature. Due to the relatively high mass and surface gravity of Kepler-13Ab, we suggest that the apparent lack of an inversion is due to cold-trap processes in the planet's atmosphere. Using a toy model for where cold traps should inhibit inversions, as well as observations of other planets in this temperature range with measured emission spectra, we argue that with more detailed modeling and more observations we may be able to place useful constraints on the size of condensates on the daysides of hot Jupiters