Random sampling technique for ultra-fast computations of molecular opacities for exoplanet atmospheres

Opacities of molecules in exoplanet atmospheres rely on increasingly detailed line-lists for these molecules. The line lists available today contain for many species up to several billions of lines. Computation of the spectral line profile created by pressure and temperature broadening, the Voigt profile, of all of these lines is becoming a computational challenge. We aim to create a method to compute the Voigt profile in a way that automatically focusses the computation time into the strongest lines, while still maintaining the continuum contribution of the high number of weaker lines. Here, we outline a statistical line sampling technique that samples the Voigt profile quickly and with high accuracy. The number of samples is adjusted to the strength of the line and the local spectral line density. This automatically provides high accuracy line shapes for strong lines or lines that are spectrally isolated. The line sampling technique automatically preserves the integrated line opacity for all lines, thereby also providing the continuum opacity created by the large number of weak lines at very low computational cost. The line sampling technique is tested for accuracy when computing line spectra and correlated-k tables. Extremely fast computations (~3.5e5 lines per second per core on a standard current day desktop computer) with high accuracy (< 1 % almost everywhere) are obtained. A detailed recipe on how to perform the computations is given.Comment: Accepted for publication in A&

The ARCiS framework for Exoplanet Atmospheres: The Cloud Transport Model

Understanding of clouds is instrumental in interpreting current and future spectroscopic observations of exoplanets. Modelling clouds consistently is complex, since it involves many facets of chemistry, nucleation theory, condensation physics, coagulation, and particle transport. We develop a simple physical model for cloud formation and transport, efficient and versatile enough that it can be used in modular fashion for parameter optimization searches of exoplanet atmosphere spectra. The transport equations are formulated in 1D, accounting for sedimentation and diffusion. The grain size is obtained through a moment method. For simplicity, only one cloud species is considered and the nucleation rate is parametrized. From the resulting physical profiles we simulate transmission spectra covering the visual to mid-IR wavelength range. We apply our models towards KCl clouds in the atmosphere of GJ1214 b and towards MgSiO3 clouds of a canonical hot-Jupiter. We find that larger cloud diffusivity $K_{zz}$ increases the thickness of the cloud, pushing the $\tau=1$ surface to a lower pressure layer higher in the atmosphere. A larger nucleation rate also increases the cloud thickness while it suppresses the grain size. Coagulation is most important at high nuclei injection rates ($\dot\Sigma_n$) and low $K_{zz}$. We find that the investigated combinations of $K_{zz}$ and $\dot\Sigma_n$ greatly affect the transmission spectra in terms of the slope at near-IR wavelength (a proxy for grain size), the molecular features seen at ~1\micr (which disappear for thick clouds, high in the atmosphere), and the 10\micr silicate feature, which becomes prominent for small grains high in the atmosphere. The result of our hybrid approach -- aimed to provide a good balance between physical consistency and computational efficiency -- is ideal towards interpreting (future) spectroscopic observations of exoplanets.Comment: language and other tiny correction

Diagnostic value of far-IR water ice features in T Tauri disks

This paper investigates how the far-IR water ice features can be used to infer properties of disks around T Tauri stars and the water ice thermal history. We explore the power of future observations with SOFIA/HIRMES and SPICA's proposed far-IR instrument SAFARI. A series of detailed radiative transfer disk models around a representative T Tauri star are used to investigate how the far-IR water ice features at 45 and 63 micron change with key disk properties: disk size, grain sizes, disk dust mass, dust settling, and ice thickness. In addition, a series of models is devised to calculate the water ice emission features from warmup, direct deposit and cooldown scenarios of the water ice in disks. Photodesorption from icy grains in disk surfaces weakens the mid-IR water ice features by factors 4-5. The far-IR water ice emission features originate from small grains at the surface snow line in disks at distance of 10-100 au. Unless this reservoir is missing in disks (e.g. transitional disks with large cavities), the feature strength is not changing. Grains larger than 10 micron do not contribute to the features. Grain settling (using turbulent description) is affecting the strength of the ice features by at most 15%. The strength of the ice feature scales with the disk dust mass and water ice fraction on the grains, but saturates for dust masses larger than 1.e-4 Msun and for ice mantles that increase the dust mass by more than 50%. The various thermal histories of water ice leave an imprint on the shape of the features (crystalline/amorphous) as well as on the peak strength and position of the 45 micron feature. SOFIA/HIRMES can only detect crystalline ice features much stronger than simulated in our standard T Tauri disk model in deep exposures (1 hr). SPICA/SAFARI can detect the typical ice features in our standard T Tauri disk model in short exposures (10 min). (abbreviated)Comment: accepted for publication in A&

Observing transiting planets with JWST -- Prime targets and their synthetic spectral observations

The James Webb Space Telescope will enable astronomers to obtain exoplanet spectra of unprecedented precision. Especially the MIRI instrument may shed light on the nature of the cloud particles obscuring planetary transmission spectra in the optical and near-infrared. We provide self-consistent atmospheric models and synthetic JWST observations for prime exoplanet targets in order to identify spectral regions of interest and estimate the number of transits needed to distinguish between model setups. We select targets which span a wide range in planetary temperature and surface gravity, ranging from super-Earths to giant planets, and have a high expected SNR. For all targets we vary the enrichment, C/O ratio, presence of optical absorbers (TiO/VO) and cloud treatment. We calculate atmospheric structures and emission and transmission spectra for all targets and use a radiometric model to obtain simulated observations. We analyze JWST's ability to distinguish between various scenarios. We find that in very cloudy planets such as GJ 1214b less than 10 transits with NIRSpec may be enough to reveal molecular features. Further, the presence of small silicate grains in atmospheres of hot Jupiters may be detectable with a single JWST MIRI transit. For a more detailed characterization of such particles less than 10 transits are necessary. Finally, we find that some of the hottest hot Jupiters are well fitted by models which neglect the redistribution of the insolation and harbor inversions, and that 1-4 eclipse measurements with NIRSpec are needed to distinguish between the inversion models. Wet thus demonstrate the capabilities of JWST for solving some of the most intriguing puzzles in current exoplanet atmospheric research. Further, by publishing all models calculated for this study we enable the community to carry out similar or retrieval analyses for all planets included in our target list.Comment: 24 pages, 7 figures, accepted for publication in A&

Machine learning as an ultra-fast alternative to Bayesian retrievals

1Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands 2SRON Netherlands Institute for Space Research, Utrecht, The Netherlands 3Centre for Exoplanet Science, University of Edinburgh, Edinburgh, UK Introduction: Inferring physical and chemical properties of an exoplanet's atmosphere from its transmission spectrum is computationally expensive. A multitude of forward models, sampled from a high dimensional parameter space, need to be compared to the observation. The preferred sampling method is currently Nested Sampling [7], in particular, the MultiNest implementation [2, 3]. It typically requires tens to hundreds of thousands of forward models to converge. Therefore, simpler forward models are usually favoured over longer computation times. A possible workaround is to use machine learning. A machine learning algorithm trained on a grid of forward models and parameter pairs can perform retrievals in seconds. This would make it possible to use complex models that take full advantage of future facilities e.g., JWST. Not only would retrievals of individual exoplanets become much faster, but it would also enable statistical studies of populations of exoplanets. It would also be a valuable tool for retrievability analyses, for example to assess the sensitivity of using different chemical networks. The main obstacle to overcome is being able to predict accurate posterior distributions and error estimates on the retrieved parameters. These need to be as close as possible to their Bayesian counterparts. Methods: Expanding on the 5-parameter grid in [5], we used ARCiS (ARtful modelling Code for exoplanet Science) [6] to generate a grid of 200,000 forward models described by the following parameters: isothermal temperature (T), planetary radius (RP), planetary mass (MP), abundances of water (H2O), ammonia (NH3) and hydrogen cyanide (HCN), and cloud top pressure (Pcloud). The models contain 13 wavelength bins, matching those of WASP-12b's observation with HST/WFC3 [4]. We added normally distributed random noise with σ=50 ppm. We trained a random forest following the details in [5] and a convolutional neural network (CNN). We divided the data into a training set of 190,000 spectra and a test set of 10,000. For the CNN we reserved 19,000 spectra (10%) from the training set for validation. These are needed to update the network weights at each training iteration. The CNN was trained with the loss function introduced in [1] to output a probability distribution. To account for the observational noise, we combined the distributions predicted for multiple noisy copies of the spectrum. To evaluate the performance of the machine learning algorithms, we retrieved all the spectra in the test set and plotted our predictions against the true values for the parameters. We repeated the experiment with only 1,000 spectra for Nested Sampling, reflecting the increased computational overhead of each of these retrievals. We then used a transmission spectrum of WASP-12b observed with HST/WFC3 [4] as a real-world test case. Results: Although the random forest trains faster, the CNN provided better results. Figures 1 and 2 show the predicted versus the true parameters for the CNN and Nested Sampling bulk retrievals. Remarkably, we observe the same structures in both plots. This shows that the CNN is able to learn the relationship between spectral features and parameters. We also found that both the CNN and Nested Sampling provide correct error estimates, with ~60% of predictions within 1σ of the true value, ~98% within 2σ, and virtually all within 3σ. This is in almost perfect agreement with expectation from statistical errors. Figures 3 and 4 show the CNN and Nested Sampling retrieval of WASP-12b. Again, we see very similar results, although the CNN provides broader posterior distributions. Work is ongoing to try to fix this issue. We found that a training set of 180,000 spectra is unnecessarily large, and the same performance can be reached with only 20,000 spectra. This implies that the number of forward model computations needed to train a CNN is smaller than the number needed for a single Bayesian retrieval. If this holds for more complex forward models and higher quality spectra, it would make machine learning an extremely attractive alternative to Nested Sampling. Conclusion: The existing literature on machine learning retrievals of exoplanet atmospheres only has comparisons between machine learning and Nested Sampling for a handful of test cases [1, 5, 8]. In this work we present a comparison of bulk retrievals done with both methods, showing that machine learning can indeed be a viable and fast alternative to Nested Sampling. We are currently working on extending these results to models with equilibrium chemistry and to JWST/NIRSpec simulated spectra. Acknowledgements: This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 860470. References: [1] Cobb, A. D., Himes, M. D., Soboczenski, F., Zorzan, S., O'Beirne, M. D., Baydin, A. G., Gal, Y., Domagal-Goldman, S. D., Arney, G. N., Angerhausen, D. (2019, 5). An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval. [2] Feroz, F., Hobson, M. P. (2008). Monthly Notices of the Royal Astronomical Society 384 (2). [3] Feroz, F., Hobson, M. P., Bridges, M. (2009). Monthly Notices of the Royal Astronomical Society 398(4). [4] Kreidberg, L., Line, M. R., Bean, J. L., Stevenson, K. B., Desert, J.-M., Madhusudhan, N., Fortney, J. J., Barstow, J. K., Henry, G. W., Williamson, M. H., Showman, A. P. (2015). A DETECTION OF WATER IN THE TRANSMISSION SPECTRUM OF THE HOT JUPITER WASP-12b AND IMPLICATIONS FOR ITS ATMOSPHERIC COMPOSITION. Technical report. [5] Marquez-Neila, P., Fisher, C., Sznitman, R., Heng, K. (2018). Supervised machine learning for analysing spectra of exoplanetary atmospheres. [6] Min, M., Ormel, C. W., Chubb, K., Helling, C., Kawashima, Y. (2020). The ARCiS framework for exoplanet atmospheres. Astronomy &amp; Astrophysics 642. [7] Skilling, J. (2006). Nested sampling for general Bayesian computation. Bayesian Analysis 1 (4). [8] Zingales, T., Waldmann, I. P. (2018). The Astronomical Journal 156 (6)