Simulation of Ultra hot Jupiter atmospheres with JWST

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Simulation of Ultra hot Jupiter atmospheres with JWST

Ilse de Langen (11255129) July 10, 2020

Report Bachelor Project Physics and Astronomy (15 EC) University of Amsterdam, Faculty of Science

Anton Pannekoek Institute Supervisor: Prof. dr. Jean-Michel Désert

Daily supervisor: dr. Lorenzo Pino Second examiner: Prof. dr. Carsten Dominik Conducted between: 26-03-2020 and 10-07-2020

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Abstract

Ultra hot Jupiters are an emerging class of exoplanets, favourable for transit spectroscopy because of their short orbital periods, high temperatures and extended atmospheres. Their atmospheric composition, particularly the C/O, N/O and Fe/O ratio, reveal information over the formation history. In this research I explored if the James Webb Space Telescope can constrain these abundances. I developed an algorithm using a Monte Carlo Markov Chain to retrieve the C/O, N/O and Fe/O ratio from simulated transmission spectra. It was found that at higher temperatures, H– opacity complicates the retrieval as it blocks absorption features. For UHJs of 1700 and 2275 K, the C/O and Fe/O ratios could be retrieved with 1 sigma confidence level. The N/O ratio is retrieved within 1 sigma at 1700 K. Despite masked H2O features, the

C/O ratio could be retrieved with 2 sigma confidence for 2850, 3425 and 4000 K planets. This means JWST can put constraints on the formation history and atmospheric characterization. Furthermore, an linear interpolation method is explored, which could be advantageous when temperature and reference pressure are included as free parameters in the MCMC as well. The obtained results are compromising, but further research has to elaborate this improved analysis.

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Populaire samenvatting

Exoplaneten zijn planeten die om een andere ster dan de zon draaien. Je kunt deze niet di-rect zien, maar je weet dat ze er zijn doordat hun ster een beetje minder fel wordt als ze ervoor langs bewegen. Het sterlicht beweegt dan ook door de atmosfeer van de planeet heen en reageert daar met deeltjes, die bepaalde golflengtes absorberen uit het licht. Hierdoor kan je uit het spectrum, waarin de geabsorbeerde golflengtes minder aanwezig zijn, achterhalen welke deeltjes in de atmosfeer zitten. Uit de samenstelling van de atmosfeer kan je interes-sante gegevens halen, zoals hoe ver van de ster de planeet is gevormd. Dit kan je namelijk afleiden uit de verhouding tussen koolstof en zuurstof. Daarnaast zegt de verhouding tussen NH3en zuurstof iets over of er stoffen uit de onderste naar de bovenste lagen worden

getrans-porteerd. Tot slot kunnen we uit de verhouding tussen ijzer en zuurstof afleiden hoeveel vaste stoffen en gassen er in de atmosfeer zitten. In dit onderzoek heb ik gekeken naar Ultra hete Jupiters, dit zijn planeten die erg dicht bij hun ster staan en daardoor heel warm zijn. Volgend jaar wordt de James Web Space Telescoop gelanceerd, die onder andere deze exoplaneten gaat observeren. Daarom wil ik graag weten of met deze telescoop, enkele verhoudingen tussen elementen (C/O, N/O, Fe/O) in de atmosfeer van Ultra hete Jupiters kunnen worden bepaald. Het blijkt dat dit mogelijk is, maar het is lastiger voor hetere planeten. Dit komt onder an-dere door het waterstofion veel aanwezig is bij hogere temperaturen. Het waterstofion zorgt ervoor dat het spectrum er platter uitziet, waardoor je moeilijker kunt zien welke moleculen er in de atmosfeer zitten. De James Webb Space Telescope kan veel betekenen voor deze Ultra hete Jupiters, omdat het interessante informatie kan geven over de atmosfeer en over hoe de planeet is gevormd.

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1 Introduction

1.1 Observation of exoplanets

Since the first discovery of an exoplanet (1), extensive research is conducted about these plan-ets. They generally get detected using transit spectroscopy, which is based on the decrease in light coming from the star, caused by the planet moving in front of it. A large group of the detected exoplanets are Hot Jupiters. This class of planets orbit their host star closely, result-ing in equilibrium temperatures of 1000-2000 K. Their high temperatures and short orbital periods makes them interesting candidates to observe using transmission spectroscopy. (2)

1.1.1 Transmission spectroscopy

Transmission spectroscopy is performed during a planet’s transit. Light from the host star goes through the outer layers of the planet on its way to the observer, where it interacts with atoms, molecules and particles in the atmosphere (fig. 1). Some species have the property to absorb light at certain wavelengths, causing the atmosphere to be opaque. As a result, the planet will appear larger when it is observed at these characteristic wavelengths. The planet’s transit radius plotted against wavelength shows the spectrum, in which the absorption features of present species can be detected. From this transmission spectrum, the abundant molecules in the exoplanet’s atmosphere can be determined. (3)

Figure 1: Starlight interacts with the exoplanet atmosphere, to produce the characteristic spectrum.

1.2 Chemistry of exoplanet atmospheres

Hot Jupiters have atmospheres that are dominated by H and He, because these were cap-tured from the protoplanetary nebula. Next to these, trace elements are C, O and N. The main carriers of these elements at the high temperatures are considered to be CO, H2O and NH3.

These molecules feature absorption bands particularly strong in the near and mid infrared (fig. 2). The amount of the molecules can be described in terms of mixing ratio, which generally varies with height. In common exoplanet models, the atmosphere is believed to be in thermo-chemical equilibrium. Under this condition, the mixing ratios are entirely determined by the

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temperature, pressure and elemental abundances. For some planets it was found they are not in thermochemical equilibrium, because processes occur that alter the chemistry. One of the main processes is vertical mixing, which is caused by convection in the atmospheric layers.(13)

Figure 2: This plot shows wavelength against transit depth. Each species has a vertical offset, to reveal how the spectrum would look like if it would be the only molecule in the atmosphere. Every molecule has its characteristic absorption features. (4)

1.3 C/O ratio and planet formation

Of particular interest in determining the chemistry of exoplanet atmospheres is the C/O ratio, which is considered to be the ratio between CO and H2O. As pointed out in (5), the C/O plays

an important part in the regulation of the general chemistry in the atmosphere. Furthermore, the C/O ratio can put constraints on where in the protoplanetary disk the planet was formed. If this was close to the host star, planets will have a solar composition atmosphere (C/O = 0.55). This ratio increases behind the ’snowline’ where H2O condensates, as this reduces O in the gas

phase (fig. 3). A higher C/O ratio implies the planet was formed at larger separation which makes this an important parameter regarding the history of the planet. As Hot Jupiters are now situated close to their host star, a C/O ratio larger than solar suggests the planet should have migrated inward. (6)

1.3.1 Other ratios of elemental abundances

Next to the C/O ratio, the N/O ratio is interesting in exoplanet atmospheres. N bearing species are sensitive to chemical disequilibrium. During vertical mixing, NH3 (and HCN) are being

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Figure 3: The C/O ratio in gas increases at higher orbital separation, due to the different condensation boundaries.(6)

expected in chemical equilibrium. Therefore, the N/O ratio is an indicator for non equilibrium chemistry. Second, the Fe/O ratio gives implications about the ratio between refractory and volatile elements.

1.4 Ultra hot Jupiters

Next to the hot Jupiters, a new class of exoplanets is emerging: the ultra hot Jupiters (UHJ). These planets orbit their host star even closer, which results in equilibrium temperatures up to 4000 K. At these conditions, atmospheric phenomena occur that are not observed in our own Solar system. The high stellar irradiation causes ionization of abundant molecules, which in-creases the amount of free electrons. Dissociation of various molecules can be induced by the high temperatures. As a result, the absorption features from these molecules will be removed from the spectrum. However, the atmosphere will be enriched in newly formed H– and metal hydrides like FeH, which are not or in lesser extent observed at other planets. Spectra of UHJ are characterized by the corresponding absorption features. H– is known to be a photospheric absorber in stellar atmospheres. It was found that the H– opacity also strongly dominates UHJ spectra, which appear to mask spectral features from line absorbers.(7)

1.5 James Webb Space Telescope

The launch of the James Webb Space Telescope (JWST) next year will create new opportunities for the observation of exoplanet atmospheres. It will observe in the near- and mid infrared, where many absorption features reside that are important for exoplanets (fig.2). JWST has improved features compared to current observing instruments. It will orbit the Sun instead of the Earth, in the second Lagrangian point. At this position, the telescope will not feel forces from both the Sun or the Earth, which results in a very stable orbit. Moreover, it uses shields to block the sunlight, which will reduce noise on observations. It is equipped with four in-struments that differ in wavelength coverage and resolution (fig.4), in which it surpasses the present operating telescopes. Depending on what kind of object needs to be observed, there will be an applicable instrument. (8)

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Figure 4: The instruments of JWST, indicated with their wavelength range and resolution R. (9)

1.6 My research project in a nutshell

During this project, I will focus on UHJs. Regarding the upcoming launch of the JWST, an exploration of what it can do for these exoplanets is valuable. Therefore, I look at what can be retrieved in terms of the C/O, N/O and Fe/O ratios. In order to do this, I developed a framework that simulates an observation of an UHJ and use a Markov Chain Monte Carlo method to retrieve these ratios of elemental abundances. These are of scientific interest, as they put meaningful constraints on planet formation and atmospheric characterization.

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2 Methods

In order to constrain the elemental abundances, I used several different public codes. I did sev-eral testing with these codes and adjusted them in order to link them to each other. Eventually I developed an algorithm that combines these codes to simulate spectra and analyse them. A set of planetary parameters are required as input. The radiative transfer code PetitRAD-TRANS calculates a transmission spectra based on these paremeters of a planet with known input values. It uses the equilibrium chemistry calculator FastChem to compute mixing ratios in the atmosphere. This forward model is passed to Pandexo, a package which generates JWST observation data of the planet. A retrieval code using a Monte Carlo Markov Chain (emcee), computes synthetic spectra using PetitRADTRANS. It tries to find the best fit spectrum, which reveals the input values.

Figure 5: Flowchart that shows what each code produces and how they use each other.

2.1 Generate model spectra with Petitradtrans

Model spectra need to be computed with known values, that can be compared with the a sim-ulated spectrum from a JWST observation. This is done using the Python package PetitRAD-TRANS (10), which calculates transmission or emission spectra for user defined planets. It creates a model atmosphere for the planet, based on the temperature-pressure profile and which molecules are present. The package uses opacity data of common species to calculate how the spectrum will appear. PetitRADTRANS requires some input parameters about the planet: radius, mass and reference pressure. Furthermore, the mixing ratios of the abundant molecules need to be specified. To compute these, another package called FastChem is used.

2.2 Calculating mixing ratios with FastChem

FastChem (11) calculates volume mixing ratios in the atmosphere, which is divided in 108 layers, given a temperature-pressure profile and the elemental abundances. It hereby assumes thermochemical equilibrium. In this research, the elemental abundances of C, O, N or Fe are being retrieved. A 401x401 grid is defined with abundances of these species varying from -10 times solar to 10 times solar, in different combinations. Solar abundance is assumed for the elements that do not need to be retrieved. For each combination of elemental abundances at the grid points, FastChem computes the mixing ratios. In order to examine the effect of different

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temperatures, each grid is computed for five different temperatures. PetitRADTRANS can use these mixing ratios as input to compute the corresponding transmission spectrum. The forward models, which we use as input to simulate the observations, have solar abundances.

2.3 Simulating observation data from JWST

In order to investigate what can be observed from JWST data, a package called Pandexo is launched (12). This package simulates observations, to give the community a sense about what information can be extracted from these spectra. It requires an input model spectrum, which in this research is computed using petitRADTRANS. Moreover, it needs information about the host star and observation parameters. It computes the amount of noise that will be present during an observation and adds this to the input model. The noise added by Pandexo consists of different components: Gaussian noise and noise floor. Noise floor needs to be added by the user itself, and this noise will be present under all conditions. Gaussian floor is different as this will be averaged out when the amount of transits is increased. This amount needs to be specified by the user. Finally, Pandexo simulates an observation and generates the spectrum of the observed object. This can be done using one of the available instrument modes (fig. 4).

2.4 Retrieval methods

2.4.1 Reduced chi-squared

As a first attempt do to the retrieval, the chi-squared calculation is performed, using a sim-plified model. Chemical equilibrium is not taken into account, hence constant abundances are assumed. H₂O abundance and temperature are retrieved instead of elemental abundances. For each combination of H2O and temperature, a model spectrum is made with petitRADTRANS.

These spectra are compared with the simulated spectrum created by Pandexo using the chi-squared calculation: χ2 =X i (xi− mi)2 σi (1) where xiare the Pandexo data points,σithe correponding errors, and mithe data points from

the syntetic petitRADTRANS spectra. Dividing this by the amount of data points gives the reduced chi-squared. This gives an indication about how well it resembles the input spectrum: a value close to one means the retrieved spectrum is close to the input spectrum.

2.4.2 MCMC

The retrieval is also done using an Monte Carlo Markov Chain (MCMC), implemented in the Python package emcee (18). This is a statistical method that explores parameter space effi-ciently. It is based on Bayesian statistics and makes use of probability distribution functions, that indicate how likely each value is to occur. At first is specified if there are some beliefs about what the retrieved value will be, before the measurement. This is called the prior distribution. The parameters that are being retrieved are the elemental abundances of the picked species, which accordingly define the parameter space. All other input parameters are fixed. The chain starts with several ‘walkers’, that are situated at different points in parameter space. They start walking and at every step they make a function call. During this, the combination of elemental abundances the walkers have at that point (a sample), is used to compute a model spectrum with petitRADTRANS. If this synthetic spectrum resembles the simulated spectrum,

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it is likely that this combination of elemental abundances is equal to the input model. Us-ing the differences between the model and observation data, the likelihood P of this sample is calculated as follows:

P ∝ e−χ2/2 (2)

where_χ2is specified in equation 1. P is multiplied with the prior distribution to determine the posterior distibution. The posterior reveals which samples are most likely to match the true values. While the walkers are exploring parameter space, they get a sense of which combina-tions of elemental abundances have the highest likelihood. They will try to move towards the best solution, in stead of iterating over all grid points which is done in the chi-squared method. The most function calls should be made near the correct combination of elemental abundances, because this area contains the samples that are most likely to match the input values.

2.5 Set up of the models

The codes described above need several input parameters like planet radius, mass and stellar type to define what kind of planet is being examined. This research focuses on retrieving the atmospheric constraints of a real case example, WASP 121b. This is an Ultra hot Jupiter, and it believed to have H2O in its atmosphere (14), which makes it an interesting target for retrieving

oxygen-related ratios. In addition, it is part of the JWST ERS. This set of planets will be ob-served as a first test for JWST’s capabilities, which motivates the choice for this planet. Planet and host star properties that are required as input are adopted from the TEPCat database (15). Isothermal atmospheres were examined with temperatures from 1700 to 4000 K.

In the model atmospheres, different sets of molecules are included that contribute to the opac-ity. He, H₂and H– are included as continuum opacity species in all cases. Line absorbers are added depending on which ratio is being retrieved. In order to retrieve the C/O ratio, CO and H2O are included, as these are the main carriers of C and O. Next to these, HCN and NH3were

added as absorbers for the N/O ratio retrieval and FeH for Fe/O.

JWST has many instruments to simulate the observation with. For the C/O and N/O ra-tio, NIRSpec Prism is used. Since the FeH features are situated near shorter wavelengths, NIRISS SOSS is picked for the Fe/O retrieval. All observation data is obtained with 5 transits. The noise floor is adapted from Greene et al.(2016) (17). Figure 6 shows the model spectra and their simulated observations for an atmosphere containing CO and H₂O, for different temper-atures. The syntetic spectra are rebinned to the same resolution as the observation.

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Figure 6: This figure shows the wavelength against flux, which reveals spectra at different tempera-tures. The forward models for atmospheres containing C and O (coloured) and the corresponding ob-servation data (grey) obtained using PetitRADTRANS and Pandexo. The instrument used is NIRSpec Prism, combining 5 transits.

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3 Results

3.1 Chi-squared retrieval

Figure 7 shows the results from the chi-squared analysis. The red dot in the middle represents the forward model that is computed with the input values. The reduced chi-squared calculation is performed for the shown grid, divided over 5 steps. Contour lines are plotted to indicate areas with equal reduced chi-squared.

Figure 7: Contour plot obtained with the chi-squared retrieval method, with at each contour the reduced chi-squared value shown. The red dot is the input model.

3.2 Mixing ratios

The mixing ratios calculated by FastChem for two isothermal atmospheres are presented in figure 8. For some molecules, like water and NH₃, the abundance decreases in the upper part of the atmosphere. This effect is stronger towards higher temperatures and is caused by thermal dissociation of those molecules. H– is more abundant in the hotter atmospheres (7). One reason for this is the larger amount of free electrons (e–) because of ionization. In addition, H2 gets dissociated, leaving more H available to produce H–.

3.3 C and O retrieval with MCMC

The MCMC was set up with 25 walkers and 1000 iterations. A constant prior distribution was assumed for the elemental abundance grids. The results for the C and O abundances are shown in a corner plot for each temperature (fig. 9). At the margins, the posteriors are shown for both log C and log O. The axes do not represent the absolute log values, but the factor by which the solar abundance is multiplied. If a certain value has more counts, it implies a larger probability. The central plots show a projection of the two posteriors to see how they are related to each other, which results in a contour plot. Darker colors represent areas with higher likelihood and thick blue lines indicate the true values. If the retrieval is successful,

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Figure 8: The mixing ratios of relevant molecules of the input models for two different temperatures.

most samples should be situated near the true values. For the coldest temperatures (1700 K and 2275 K) the retrieval resulted in samples mostly concentrated around the input data, from which the true abundances could be retrieved within 1 sigma confidence. However, there are also some samples in the upper right and bottom left directions. Something else is observed in the 2850 K and 3425 K cases, where the samples are divided in two areas with high probability. In the case of the hottest model, the samples are continuously spread over a boomerang-shaped region. However, the C and O abundances could be retrieved, but with lower precision (2 sigma).

3.3.1 C/O ratio

The posterior distributions for 2275 K are converted to a single histogram for the C/O ratio, by calculating this ratio for every sample. This is presented in figure 10. The mean and standard deviations of this histogram are indicated, together with the true value. The true value is in between 1 sigma from the mean, which means that they are not statistically different. An overview of the retrieved ratios for other temperatures is listed in table 1.

3.4 N and O abundances

It turned out that the NH3 and HCN features are not distinguishable in the spectrum next

to the CO and H2O features, which will complicate the retrieval. Inspection of the mixing

ratios of the planet (fig 8) reveal that NH3 and HCN are thermally dissociated, which results

in low abundances at the probed pressures. In this situation chemical equilibrium is assumed, which might not always be the case. In order to perform a proper retrieval, another scenario is assumed, where strong vertical mixing occurs. In this case, the mixing ratio is constant with height and has the same value as at P = 103, which is approximately 10−4. The corner plots of 1700 and 2275 K are shown in figure 11. For the O abundance, a narrow posterior distribution is derived than for the N abundance. The derived N/O ratios from are shown in table 1.

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Figure 9: Corner plots obtained in the C and O abundance retrieval, for different isothermal atmo-spheres. Blue lines are true vales, red lines indicate the mean and standard deviation of the posterior distributions.

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Figure 10: Histogram that represents the amount of function calls for specified C/O value, including the mean and 1 sigma values (red). This is obtained using NIRSpec Prism during 5 transits, at 2275 K.

Figure 11: Posterior distribution for N and O abundance for different temperatures. This is derived from a spectrum obtained with NIRSpec Prism during 5 transits. Blue indicate true values, red indicate mean and sigma levels.

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3.5 Fe and O abundances

The corner plots for two different temperatures obtained during the Fe and O retrieval is shown in figure 12. Similar to the N retrieval, the O posteriors are very narrow. The Fe distributions are more spread, but the true value is between the 1 sigma level.

Figure 12: Posteriors for the Fe and O abundance for two temperatures, from observation data obtained with NIRSpec Prism (5 transits). Blue lines indicate true values, red lines show the mean and sigma level.

3.6 Including reference pressure and temperature

With previous results, all parameters other than the retrieved elemental abundances are un-changed during the MCMC. However, there might be a degeneracy between reference pressure and elemental abundances. Reference pressure is at which pressure the planet radius is as-sumed to be. An increase or decrease in this value shifts the complete spectrum upward or downward, which means it can have the same effect as a change in abundances. Therefore, an-other calculation was done, where temperature and reference level P0 were retrieved as well.

The corner plots for C and O at 2275 and 2850 K are shown in figure 13.

3.7 Interpolation

In previous results, a grid of temperature and C and O abundances defines parameter space in the retrieval. For every function call, the mixing ratios corresponding to the nearest grid point are used. However, this can cause certain ’islands’ in the corner plots in figure 13, which is particularly observed in the the temperature result. In order to prevent this, a higher res-olution of the grid is needed. As this will require a lot of memory and computation time, it is more efficient to implement a linear multivariate interpolation method in the MCMC. For this analysis, a smaller grid of 21x21 (instead of 401x401) is defined. Instead of only using the pre–computed mixing ratios at the nearest grid points, samples are interpolated. As a result, more precise results are obtained (fig. 14). However, at 2850 K, many samples are remarkably situated around log O=-0.2, inconsistent with the true value.

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Figure 13: Posteriors for a 2275 and 2850 K planet, using NIRSpec Prism (5 transits). Next to C and O abundances, reference pressure P0and temperature T are retrieved as well.

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Figure 14: Posteriors for a 2850 K planet, using NIRSpec Prism (5 transits). A linear multivariate interpolation between a 21x21 grid is used to obtain these results. Blue lines indicate true values, red lines show mean value and 1 sigma levels of the distribution.

True value (solar) 1700 K 2275 K 2850 K 3425 K 4000 K

C/O 0.55 _{0.59 ±0.07} _{0.55 ±0.05} _{1.28 ±0.64} _{1.89 ±1.22} _{2.08 ±2.25}

N/O 0.14 _{0.11 ±0.03} - - -

-Fe/O 0.0065 _{0.060 ±0.006} _{0.063 ±0.005} - -

-Table 1: Retrieved atmospheric abundances for different temperatures for a WASP-121b-like planet using simulated observation data from JWST.

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4 Discussion

4.1 Chi-squared

The areas with lowest reduced chi-squared are situated around the input value, which means that the best fits indeed resemble the forward model. However, there is a degeneracy with the reference pressure level, which affects the transit radius at the same way the H2O abundance

does. To take this into account, this parameter should be explored as well. This requires much computational time with chi-squared as the calculation needs to be done with a third dimension added to the grid. MCMC will be able to perform a more efficient analysis, which is why I switched to this statistical method to do the calculations from here on.

4.2 C/O ratio and the effect of temperature

The 1700 K and 2275 K corner plots (fig.9) show that the C and O abundances could be retrieved within the 1 sigma confidence level. The samples towards the top right and bottom left part of the plots show that C and O are degenerate, which is because CO contains O as well. The forward models (fig. 6) corresponding to 2850, 3425 and 4000 K reveal that the H2O absorption

features are absent in these hotter planets, complicating the retrieval of O. Why the spectrum lacks these absorption bands, becomes clear when looking at the mixing ratios (fig. 8). Here it can be observed that a higher temperature increase the H– abundance and lower the H2O

abundance, because of ionization and thermal dissociation. A lower H2O abundance decreases

the amplitude of the absorption features, whereas more H– results in a higher continuum. These effects complicate the detection of H2O in the spectrum. Because H2O is the main carrier

of O, it is harder to retrieve this elemental abundance than for the colder temperatures. CO is less sensitive to thermal dissociation. This can be observed in the figure as well, as the CO abundance remains unchanged at all pressures and temperatures. This explains why there are still some CO features detectable. Nevertheless, the increasing H– opacity complicates the CO detection as well at 4000 K. At this high temperature, the H– dominates the spectra even more, leaving only some subtle CO features to be observed. Despite the lack of H2O features, the C/O

ratio could be retrieved with a lower precision level of 2 sigma. Because of the degeneracy between C and O, as CO is containing O as well, indications can be given about the C/O ratio from only the CO features.

Previous research (20) retrieve the CO abundance for a 4000 K Ultra hot Jupiter, using a parameterization for the CO mixing ratio. They additionally retrieve the H– opacity, which results in constraints on the CO ratio, even when the transmission spectrum is nearly flat. The modelling of H– could be integrated in the developed algorithm, in order to possibly produce more precise posteriors.

4.3 N/O ratio

While the O abundance could get retrieved within 1 sigma, the precision decreases to 2 sigma for N (fig.11). The corner plots show a wider posterior distribution for the N values, which in-dicates there are many samples with similar likelihood. This can be explained when looking at the forward model, shows in figure 15. The majority of the spectral features belong to H₂O, the main carrier of O. HCN and NH3, the N-bearing molecules, only make a small contribution to

the overall spectrum. Consequently, it will be more complicated to retrieve the N abundance. At 2275 K, the N features are not detectable in the spectrum. Therefore the N/O ratio can not

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Figure 15: Forward models with and without N-bearing species (NH3, HCN) at 1700 K, including

obser-vation spectrum obtained with NIRSpec Prism (5 transits).

be accurately determined at this planet.

4.3.1 Chemical disequilibrium

N-bearing species are generally dissociated in UHJs, which would make them undetectable in the spectrum. In this retrieval of the N/O ratio, vertical mixing is assumed in order to retrieve the abundances. This assumption could possibly occur, as NH₃and HCN are sensitive to vertical mixing. The retrieved N abundance can put constraints on the occurence of vertical mixing and on the other hand, if chemical equilibrium is a valid assumption.

4.4 Fe/O ratio

The results of the Fe and O retrieval (fig. 12) show similar behavior to the N/O ratio, but more accurate results are obtained. The H2O absorption bands are stronger than FeH, which

explains the higher precision obtained for the O abundance. However, at the examined tem-peratures are both Fe and O features still detectable. At temtem-peratures where these absorption bands disappear, the retrieval will probably get more complicated. However, this means that JWST can be used to retrieve this elemental ratio in Ultra hot Jupiters, unless they have tem-peratures below 2850 K. This Fe/O ratio can give indications about the amount of volatile and refractory elements, which can help characterizing exoplanet atmospheres.

4.5 Degeneracy with reference pressure

The abundances might be degenerate with reference pressure, which possibly occurred at the chi-squared analysis as well. This pressure, together with temperature, are parameters that are not known a priori, which is why these should in fact be included in the retrieval. Figure 13 therefore gives better constraints on the retrieved elemental abundances. This figure shows

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that reference pressure and temperature can both be retrieved for a 2850 K planet observed with JWST within the 1 sigma level. These parameters appear to have no correlation with the C and O abundance. However, this is evaluated for a single case and should be explored for a broader range of temperatures.

4.6 Interpolation

Linear interpolation of the mixing ratios is faster than a pre–computed grid when the resolu-tion needs to be increased. However, at the first result, the extended area of samples at log O=-0.2 (14) seem to bias the posteriors. As a result, the retrieved C and O abundances do not seem to converge to the true value. This discrepancy might be caused by a chemical transition at C/O = 1 as described by Madhusudhan (2012) (5), which is in this case reached at log C = 0.00 and log O = -0.26. From this point, there will be less O than C. When the C abundance increases, it seems no more CO will form, maybe because there is no O available (figure 16). Therefore, it is not possible to distinguish spectra with varying C abundances, hence the sam-ples are situated across this whole region. Furthermore, at the C/O = 1 transition, the mixing ratios of H2O change rapidly with abundance steps. Because the differences between the grid

points are too large, the interpolation fails. This is observed in figure 17, as there are large differences between the interpolated H2O mixing ratio and the true mixing ratio in the region

where C/O = 1. The discontinuity should be taken into account by increasing the number of steps in this area. A linear interpolation with adaptive step size is required in order to perform a proper retrieval for this grid.

Figure 16: The mixing ratios of CO and H2O in the atmosphere, for different C abundances. In both

abundances, a transition occurs between C=0.0 and C=0.1. This is where the C/O ratio becomes larger than unity. Despite increasing C abundance from C=0.1, the CO mixing ratio remains mainly un-changed.

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Figure 17: This figure shows a grid of C and O abundances. The colors represent the difference between the interpolated H2O mixing ratio and the true mixing ratio with abundances in between grid points.

Along the line where C/O = 1, the interpolation did not approximate the true profile well, as there is a large difference between them.

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5 Conclusion

I developed an algorithm to assess the capability of JWST (using the NIRSpec Prism and NIRISS SOSS instruments) to measure the C/O, N/O and Fe/O ratio, observing a WASP 121b-like planet for 5 transits. To achieve this result, I combined public codes to model equilibrium chemistry (FastChem) and radiative transfer (PetitRadtrans) to create simulated transmission spectra (Pandexo). Eventually I retrieved planetary parameters from these observation data with a code combining PetitRadtrans and emcee.

• For 1700 K and 2275 K atmospheres, the C/O ratio could be retrieved with 1 sigma con-fidence level. For temperatures of 2850, 3425 and 4000 K, H– opacity causes a lack of H2O features in the spectrum. With the simulation I developed, the C/O ratio could still

be retrieved. However, the precision decreased to 2 sigma for these cases. This means JWST can give information about formation history of UHJs.

• Under the assumption of equilibrium chemistry, NH3can not be retrieved as its features

are not present in the spectrum. With a simple vertical mixing parameterization, assum-ing that the NH3abundance in the upper atmosphere is determined by its abundance at

a pressure of 103bar, I found it can be detected in the 1700 K with 1 sigma confidence. • Fe/O can be retrieved with 1 sigma confidence at 1700 and 2275 K, which means JWST

can give implications about the ratio of refractory to volatile elements that can charac-terize UHJ atmospheres.

• Linear multivariate interpolation of the mixing ratios in equilibrium chemistry is advan-tageous when performing a retrieval with sufficient resolution (>100x100), as a pre–computed grid requires more disk space and computation time.

5.1 Future work

In order to get a better understanding of JWST capabilities, the retrievals should be performed for the complete temperature range and additionally for different stellar magnitudes. The pre-cision of these results can be computed in order to see which kind of UHJs are best suitable to observe with JWST in terms of C/O, N/O and Fe/O ratio.

A retrieval including reference pressure and temperature as free parameters for a broad tem-perature range, in addition to 2850 K (fig. 14), will reveal if these parameters are degenerate with the C and O abudances. In order to do this efficiently, the interpolation method should be further elaborated. One way to do this would be to implement an adaptive step size.

Instead of using the simplified assumption where the dragging up of NH3 causes an constant

abundance, the chemistry of this species in the atmosphere could be modeled (21). The develop-ment of the NH₃abundance will give more detailed insights about how strong vertical mixing is present in an atmosphere.

The retrieval of FeH at UHJs can be interesting for other purposes. It is dependent on the amount of H2 in the atmosphere, which is usually dissociated into H– at the dayside but is

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this recombination and elucidate in what extent this happens. An exploration of TP profiles that are valid for the night-side could possibly reveal if the night-side chemistry is observable in the spectrum.

6 Acknowledgements

I want to thank Jean-Michel Désert and Lorenzo Pino for their assistance during this project. Everything was a little bit different due to the Covid-19 crisis, but they still offered me all the help that was needed and motivated me to get the best out of my research. Because of their extensive and useful feedback, I learned a lot and became a better scientist.

Jean-Michel Désert acknowledges support from the Amsterdam Academic Alliance (AAA) Pro-gram, the European Research Council (ERC) European Union’s Horizon 2020 research and innovation program (grant agreement no. 679633; Exo-Atmos).

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