Spectroscopic model characterisation of hot exoplanet atmospheres

Abstract

Hot Jupiters are gas giants under intense stellar radiation with short orbital periods of only a few days. Due to their large radii, hot temperatures, and large scale heights, hot Jupiters can be observationally characterised in detail through spectroscopy over an entire orbital phase. Transmission spectroscopy is one of the tools that aid us in understanding the complex chemistry of exoplanet atmospheres.

Observations are not the only method of estimating atmospheric compositions. For example, we can use advanced codes to model an exoplanet’s chemical compositions and radiative transfer. However, advanced models are computationally expensive. When performing abundance retrievals where you have to create hundreds of thousands of model templates, we need approximations that are fast enough for retrieval algorithms.

In this project, we have used the semi-analytical code FastChem to model atmospheric chemical composition and petitRADTRANS to model the radiative transfer. From petitRADTRANS, we can model transmission spectra for different planetary parameters and choose whether we want a constant abundance throughout the atmosphere and whether we want to include variable gravity or not. We then wish to compare these solutions for different species with a fast analytical approximation. Heng & Kitzmann (2017) derived an analytical solution for the transit radius, which assumes an isothermal and isobaric atmosphere. They tested it for the WFC3 water band between 1.15-1.65 μm for a planet with a temperature of 1500 K. We wish to see whether it still holds for higher temperatures and other species.

The analysis has been performed for temperatures of 1500 K, 2500 K, and 3500 K, for the hot Jupiter HD 209458b. We have investigated H2O, CO, Fe, Fe II, Ti, V, Mg, and Cr. These are interesting when studying ultra-hot Jupiters as they become detectable when the temperature is high. We found that the analytical approximation by Heng & Kitzmann (2017) works remarkably well for the species when the temperature is 1500 K. However, once we increase the temperature, we find that the approximation usually underestimates the spectral line strengths. For H2O, it instead overestimates the spectral line strengths.

The analytical approximation by Heng & Kitzmann (2017) would benefit from including mass fractions, gravity, and mean molecular weight, which all vary with pressure and temperature for each atmospheric layer. However, the more we expand the approximation to improve its accuracy, the more computationally expensive it becomes. We need these fast models for retrieval algorithms, and there must be a balance between the approximation’s accuracy and its computational speed.

We conclude that we must be careful when using the Heng & Kitzmann (2017) approximation and ensure that our application of the approximation is logical and within the scope of its capabilities. We must proceed with caution when analysing ultra-hot Jupiters, as the approximation’s accuracy quickly deteriorates as we approach high temperatures. This is especially true for species such as Fe II that have a mass fraction that increases with altitude. Furthermore, we find that the approximation does poorly to varying degrees for different species. Therefore, it should not be used to perform relative abundance retrievals, especially for ultra-hot Jupiters.

Popular Abstract

The light emitted from a star can reveal details of its chemistry, formation, and evolution. It can also aid us in uncovering the exciting secrets of exoplanets, which we cannot directly observe. Since exoplanets are so small and dim compared to their host stars, we need sensitive instruments to distinguish between them. We find exoplanets through various detection methods. The transit method is most successful, followed by the radial velocity, gravitational microlensing, and direct imaging methods. We have discovered nearly 4000 exoplanets through the transit method, which is four times more than we have discovered through the radial velocity method.

A transit happens when an exoplanet passes before its host star, and a small fraction of the light gets blocked. An exoplanet is detected when these happen periodically and get confirmed by observations with other methods. However, the information from the transits also allows us to characterise exoplanets and uncover information regarding their atmospheric chemical composition. We can uncover these because starlight gets absorbed or scattered in the atmosphere. The imprint left on the stellar spectrum reveals details of the transiting exoplanet's chemical composition. The imprint is better known as transmission spectroscopy, where photons of different energies, or wavelengths, will have varying strengths depending on the atmosphere's chemical composition. Hot Jupiters are excellent targets for transmission spectroscopy due to their short orbital periods and giant puffy atmospheres with rich chemistry. They are also larger and hotter than other planets, making them easier to observe and characterise.

The information we receive from transmission spectroscopy must be analysed through models so we can characterise the exoplanet. Analysing the data is not a simple task since many parameters shape the appearance of the spectrum. Fast models and approximations are vital to interpreting these results. We must investigate different values of many parameters until we find the combination that best describes our transmission spectrum. The advantage of advanced models is that they include a comprehensive list of parameters that we can alter to represent the physical processes of the atmosphere accurately. However, the time it takes to fit a model to the data successfully can be too long due to the model's complexity. At this point, we need appropriate approximations to speed up the computations without a considerable loss of accuracy.

Approximations make analyses incredibly fast, though we sacrifice the wide range of physical parameters and lose reliability. However, there are instances where approximations do an incredible job at computing near-identical results to the complicated models. In these instances, using approximations is advisable as they are time-efficient. Unfortunately, a similar outcome between models and approximations is not always the case, and sometimes the solutions are vastly different. Therefore, we must quantify where we can reliably use the fast approximations without doubting their accuracy. Where and when we can confidently use these turns out to be a complicated matter, as will be investigated and explained further in this project.

• author: Sandvik, Elin
• supervisor: Jens Hoeijmakers
• organization: Lund Observatory - Undergoing reorganization; Department of Physics
• course: ASTM32 20221
• year: 2022
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: Transit method, Transmission spectroscopy, Exoplanets, Hot Jupiter, Modelling
• publication/series: Lund Observatory Examensarbeten
• report number: 2022-EXA-198
• language: English
• id: 9096624
• date added to LUP: 2022-08-08 10:11:24
• date last changed: 2023-08-30 15:16:22