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Register a new userAtmospheric characterization of hot Jupiters using hierarchical models of Spitzer observations
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The field of exoplanet atmospheric characterization is trending towards comparative studies involving many planets, and using hierarchical modelling is a natural next step. Here we demonstrate two use cases. We first use hierarchical modelling to quantify variability in repeated observations, by reanalyzing a suite of ten Spitzer secondary eclipse observations of the hot Jupiter XO-3b. We compare three models: one where we fit ten separate eclipse depths, one where we use a single eclipse depth for all ten observations, and a hierarchical model. By comparing the Widely Applicable Information Criterion (WAIC) of each model, we show that the hierarchical model is preferred over the others. The hierarchical model yields less scatter across the suite of eclipse depths, and higher precision on the individual eclipse depths, than does fitting the observations separately. We do not detect appreciable variability in the secondary eclipses of XO-3b, in line with other analyses. Finally, we fit the suite of published dayside brightness measurements from Garhart (2020) using a hierarchical model. The hierarchical model gives tighter constraints on the individual brightness temperatures and is a better predictive model, according to the WAIC. Notably, we do not detect the increasing trend in brightness temperature ratios versus stellar irradiation reported by Garhart (2020) and Baxter (2020). Although we tested hierarchical modelling on Spitzer eclipse data of hot Jupiters, it is applicable to observations of smaller planets like hot neptunes and super earths, as well as for photometric and spectroscopic transit or phase curve observations.
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We probe the structure and composition of the atmospheres of 5 hot Jupiter exoplanets using the Hubble Space Telescope Wide Field Camera 3 (WFC3) instrument. We use the G141 grism (1.1-1.7 $mu$m) to study TrES-2b, TrES-4b, and CoRoT-1b in transit, TrES-3b in secondary eclipse, and WASP-4b in both. This wavelength region includes a predicted absorption feature from water at 1.4 $mu$m, which we expect to be nondegenerate with the other molecules that are likely to be abundant for hydrocarbon-poor (e.g. solar composition) hot Jupiter atmospheres. We divide our wavelength regions into 10 bins. For each bin we produce a spectrophotometric light curve spanning the time of transit and/or eclipse. We correct these light curves for instrumental systematics without reference to an instrument model. For our transmission spectra, our mean $1-sigma$ precision per bin corresponds to variations of 2.1, 2.8, and 3.0 atmospheric scale heights for TrES-2b, TrES-4b, and CoRoT-1b, respectively. We find featureless spectra for these three planets. We are unable to extract a robust transmission spectrum for WASP-4b. For our dayside emission spectra, our mean $1-sigma$ precision per bin corresponds to a planet-to-star flux ratio of $1.5times10^{-4}$ and $2.1times10^{-4}$ for WASP-4b and TrES-3b, respectively. We combine these estimates with previous broadband measurements and conclude that for both planets isothermal atmospheres are disfavored. We find no signs of features due to water. We confirm that WFC3 is suitable for studies of transiting exoplanets, but in staring mode multi-visit campaigns are necessary to place strong constraints on water abundance.
Kepler-13Ab (= KOI-13.01) is a unique transiting hot Jupiter. It is one of very few known short-period planets orbiting a hot A-type star, making it one of the hottest planets currently known. The availability of Kepler data allows us to measure the planets occultation (secondary eclipse) and phase curve in the optical, which we combine with occultations observed by warm Spitzer at 4.5 mic and 3.6 mic and a ground-based occultation observation in the Ks band (2.1 mic). We derive a day-side hemisphere temperature of 2,750 +- 160 K as the effective temperature of a black body showing the same occultation depths. Comparing the occultation depths with one-dimensional planetary atmosphere models suggests the presence of an atmospheric temperature inversion. Our analysis shows evidence for a relatively high geometric albedo, Ag= 0.33 +0.04 -0.06. While measured with a simplistic method, a high Ag is supported also by the fact that the one-dimensional atmosphere models underestimate the occultation depth in the optical. We use stellar spectra to determine the dilution, in the four wide bands where occultation was measured, due to the visual stellar binary companion 1.15 +- 0.05 away. The revised stellar parameters measured using these spectra are combined with other measurements leading to revised planetary mass and radius estimates of Mp = 4.94 - 8.09 Mjup and Rp = 1.406 +- 0.038 Rjup. Finally, we measure a Kepler mid-occultation time that is 34.0 +- 6.9 s earlier than expected based on the mid-transit time and the delay due to light travel time, and discuss possible scenarios.
We study the feasibility of observationally constraining the rotation rate of hot Jupiters, planets that are typically assumed to have been tidally locked into synchronous rotation. We use a three-dimensional General Circulation Model to solve for the atmospheric structure of two hot Jupiters (HD 189733b and HD 209458b), assuming rotation periods that are 0.5, 1, or 2 times their orbital periods (2.2 and 3.3 days, respectively), including the effect of variable stellar heating. We compare two observable properties: 1) the spatial variation of flux emitted by the planet, measurable in orbital phase curves, and 2) the net Doppler shift in transmission spectra of the atmosphere, which is tantalizingly close to being measurable in high-resolution transit spectra. Although we find little difference between the observable properties of the synchronous and non-synchronous models of HD 189733b, we see significant differences when we compare the models of HD 209458b. In particular, the slowly rotating model of HD 209458b has an atmospheric circulation pattern characterized by westward flow and an orbital phase curve that peaks after secondary eclipse (in contrast to all of our other models), while the quickly rotating model has a net Doppler shift that is more strongly blue-shifted than the other models. Our results demonstrate that the combined use of these two techniques may be a fruitful way to constrain the rotation rate of some planets, and motivate future work on this topic.
With a scheduled launch in October 2018, the James Webb Space Telescope (JWST) is expected to revolutionise the field of atmospheric characterization of exoplanets. The broad wavelength coverage and high sensitivity of its instruments will allow us to extract far more information from exoplanet spectra than what has been possible with current observations. In this paper, we investigate whether current retrieval methods will still be valid in the era of JWST, exploring common approximations used when retrieving transmission spectra of hot Jupiters. To assess biases, we use 1D photochemical models to simulate typical hot Jupiter cloud-free atmospheres and generate synthetic observations for a range of carbon-to-oxygen ratios. Then, we retrieve these spectra using TauREx, a Bayesian retrieval tool, using two methodologies: one assuming an isothermal atmosphere, and one assuming a parametrized temperature profile. Both methods assume constant-with-altitude abundances. We found that the isothermal approximation biases the retrieved parameters considerably, overestimating the abundances by about one order of magnitude. The retrieved abundances using the parametrized profile are usually within one sigma of the true state, and we found the retrieved uncertainties to be generally larger compared to the isothermal approximation. Interestingly, we found that using the parametrized temperature profile we could place tight constraints on the temperature structure. This opens the possibility to characterize the temperature profile of the terminator region of hot Jupiters. Lastly, we found that assuming a constant-with-altitude mixing ratio profile is a good approximation for most of the atmospheres under study.
WASP-12 b, WASP-33 b, WASP-36 b, and WASP-46 b are four transiting planetary systems which we have studied. These systems light curves were derived from observations made by the Transiting Light Exoplanet Survey Satellite (TESS) and some ground-based telescopes. We used Exofast-v1 to model these light curves and calculate mid-transit times. Also, we plotted TTV diagrams for them using derived mid-transit times and those available within the literature. O-C analysis of these timings enables us to refine the linear ephemeris of four systems. We measured WASP-12s tidal quality factor based on adding TESS data as Q*=(2.13+-0.29)*10^5. According to the analysis, the orbital period of the WASP-46 b system is increasing. The WASP-36 b and WASP-33 b systems have not shown any obvious quadratic trend in their TTV diagrams. The increase in their period is most likely due to inaccurate liner ephemeris that has increased over time. So, more observations are needed to evaluate whether or not there is an orbital decay in the WASP-36 b and WASP-33 b systems.
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