Limits on Clouds and Hazes for the TRAPPIST-1 Planets

The TRAPPIST-1 planetary system is an excellent candidate for study of the evolution and habitability of M-dwarf planets. Transmission spectroscopy observations performed with the Hubble Space Telescope (HST) suggest the innermost five planets do not possess clear hydrogen atmospheres. Here we reassess these conclusions with recently updated mass constraints and expand the analysis to include limits on metallicity, cloud top pressure, and the strength of haze scattering. We connect recent laboratory results of particle size and production rate for exoplanet hazes to a one-dimensional atmospheric model for TRAPPIST-1 transmission spectra. Doing so, we obtain a physically-based estimate of haze scattering cross sections. We find haze scattering cross sections on the order of 1e-26 to 1e-19 cm squared are needed in hydrogen-rich atmospheres for TRAPPIST-1 d, e, and f to match the HST data. For TRAPPIST-1 g, we cannot rule out a clear hydrogen-rich atmosphere. We also modeled the effects an opaque cloud deck and substantial heavy element content have on the transmission spectra. We determine that hydrogen-rich atmospheres with high altitude clouds, at pressures of 12mbar and lower, are consistent with the HST observations for TRAPPIST-1 d and e. For TRAPPIST-1 f and g, we cannot rule out clear hydrogen-rich cases to high confidence. We demonstrate that metallicities of at least 60xsolar with tropospheric (0.1 bar) clouds agree with observations. Additionally, we provide estimates of the precision necessary for future observations to disentangle degeneracies in cloud top pressure and metallicity. Our results suggest secondary, volatile-rich atmospheres for the outer TRAPPIST-1 planets d, e, and f.Comment: 15 pages, 3 figures, 2 tables, accepted in the Astronomical Journa

Spherical Harmonics for the 1D Radiative Transfer Equation I: Reflected Light

A significant challenge in radiative transfer theory for atmospheres of exoplanets and brown dwarfs is the derivation of computationally efficient methods that have adequate fidelity to more precise, numerically demanding solutions. In this work, we extend the capability of the first open-source radiative transfer model for computing the reflected light of exoplanets at any phase geometry, PICASO: Planetary Intensity Code for Atmospheric Spectroscopy Observations. Until now, PICASO has implemented two-stream approaches to the solving the radiative transfer equation for reflected light, in particular following the derivations of Toon et al. (1989) (Toon89). In order to improve the model accuracy, we have considered higher-order approximations of the phase functions, namely, we have increased the order of approximation from 2 to 4, using spherical harmonics. The spherical harmonics approximation decouples spatial and directional dependencies by expanding the intensity and phase function into a series of spherical harmonics, or Legendre polynomials, allowing for analytical solutions for low-order approximations to optimize computational efficiency. We rigorously derive the spherical harmonics method for reflected light and benchmark the 4-term method (SH4) against Toon89 and two independent and higher-fidelity methods (CDISORT & doubling-method). On average, the SH4 method provides an order of magnitude increase in accuracy, compared to Toon89. Lastly, we implement SH4 within PICASO and observe only modest increase in computational time, compared to two-stream methods (20% increase).Comment: Accepted ApJ; 27 pages; 5 figures; Code available at https://github.com/natashabatalha/picaso; Zenodo release at https://zenodo.org/record/7765171#.ZC3G7uzMI8Y; Tutorials/figure reproducibility at https://natashabatalha.github.io/picaso/notebooks/10b_AnalyzingApproximationsReflectedLightSH.htm

Importance of Sample Selection in Exoplanet Atmosphere Population Studies

Understanding planet formation requires robust population studies, which are designed to reveal trends in planet properties. In this work, we aim to determine if different methods for selecting populations of exoplanets for atmospheric characterization with JWST could influence population-level inferences. We generate three hypothetical surveys of super-Earths/sub-Neptunes, each spanning a similar radius-insolation flux space. The survey samples are constructed based on three different selection criteria (evenly-spaced-by-eye, binned, and a quantitative selection function). Using an injection-recovery technique, we test how robustly individual-planet atmospheric parameters and population-level parameters can be retrieved. We find that all three survey designs result in equally suitable targets for individual atmospheric characterization, but not equally suitable targets for constraining population parameters. Only samples constructed with a quantitative method or that are sufficiently evenly-spaced-by-eye result in robust population parameter constraints. Furthermore, we find that the sample with the best targets for individual atmospheric study does not necessarily result in the best constrained population parameters. The method of sample selection must be considered. We also find that there may be large variability in population-level results with a sample that is small enough to fit in a single JWST cycle ($\sim$12 planets), suggesting that the most successful population-level analyses will be multi-cycle. Lastly, we infer that our exploration of sample selection is limited by the small number of transiting planets with measured masses around bright stars. Our results can guide future development of programs that aim to determine underlying trends in exoplanet atmospheric properties and, by extension, formation and evolution processes.Comment: 16 pages, 7 figures, accepted Ap

The impact of spectral line wing cut-off : recommended standard method with application to MAESTRO opacity data base

KLC acknowledges funding from STFC under project number ST/V000861/1.When computing cross-sections from a line list, the result depends not only on the line strength, but also the line shape, pressure-broadening parameters, and line wing cut-off (i.e. the maximum distance calculated from each line centre). Pressure-broadening can be described using the Lorentz line shape, but it is known to not represent the true absorption in the far wings. Both theory and experiment have shown that far from the line centre, non-Lorentzian behaviour controls the shape of the wings and the Lorentz line shape fails to accurately characterize the absorption, leading to an underestimation or overestimation of the opacity continuum depending on the molecular species involved. The line wing cut-off is an often overlooked parameter when calculating absorption cross-sections, but can have a significant effect on the appearance of the spectrum since it dictates the extent of the line wing that contributes to the calculation either side of every line centre. Therefore, when used to analyse exoplanet and brown dwarf spectra, an inaccurate choice for the line wing cut-off can result in errors in the opacity continuum, which propagate into the modelled transit spectra, and ultimately impact/bias the interpretation of observational spectra, and the derived composition and thermal structure. Here, we examine the different methods commonly utilized to calculate the wing cut-off and propose a standard practice procedure (i.e. absolute value of 25 cm−1 for P ≤ 200 bar and 100 cm−1 for P > 200 bar) to generate molecular opacities which will be used by the open-access MAESTRO (Molecules and Atoms in Exoplanet Science: Tools and Resources for Opacities) data base. The pressing need for new measurements and theoretical studies of the far-wings is highlighted.Publisher PDFPeer reviewe