Construcciones Genéticas

With the new ANN model trained, it can be implemented into a transit model in the same way as the original ANN method. The difference between the two methods is the way that the stellar radius is defined differently for each. This means that the values determined in the transit fit (as parameterised in this work) for the transit depth (R_p/R_⋆) and the stellar density (ρ_⋆) will require adjustment to reflect the definition of the stellar radius desired. The transit model using this ANN model will have included the starlight originating from outside the conventional definition ofR_⋆, which a real star has and will affect the shape of a real transit, but is usually not included in the model.

7.4. Implementing into transit model Sc al ed in te ns ity , I (μ )/ I(1 )

Log (μ), log cos limb angle

Sc al ed in te ns ity , I (μ )/ I(1 )

Log (μ), log cos limb angle

Figure 7.5:Figure showing two example limb profiles for different stellar parameters for the new ANN model. The upper plot is the predicted limb profile forTeff=5700 K, logg=4.5, and[Fe/H] = +0.5.

from that defined in the atmosphere model to that expected for the definition described in Section 6.2.2. The factor predicted by the ANN model then allows the determined values of

R_p/R_⋆andρ_⋆to reflect the conventional definitions of the stellar radius for that bandpass.

7.5

Discussion

The new ANN approach is very effective at modelling the full shape of the limb profile across the stellar parameter space. The architecture and training of the model is not optimised in its current state, but despite this, the feasibility of the concept behind the method can be clearly seen.

To optimise the model, to ensure that the limb profiles across the stellar parameter space are well represented by the trained model, adjustments to the architecture of the model and potentially the form of the input parameterisation should be tested to find a good enough model for the required purpose. This process is time consuming, as each instance of training a model takes a significant amount of computation time (∼1 hour for 100 training epochs and batch size 100).

Once an optimised model has been trained, the efficacy of the method should be validated through fitting example transit lightcurves. The optimal use for this method is in studies where transit lightcurves for multiple bandpasses for the same system are considered together. The current structure would requite training separate ANN models for each bandpass, or to use the bandpass as a categorical variable with the full training set used to inform the ANN model.

The approach described here is to use the radius defined in the atmosphere models as the comparison stellar radius, but this radius does not relate to any physical definition of the value ofR_⋆– it is selected to be a position at which the star is known to be optically thin across the modelled wavelengths. A more practical comparison radius may be one for a selected wavelength where the position of the radius is not effected by elemental absorption lines.

8

Conclusions and next steps

8.1

Conclusions

The field of exoplanet research is awash with exciting discoveries, and the work in this thesis provides some part in colouring in some part of that landscape. I present the discovery of some new planets, and I present work to improve the ability of future researchers to learn more about planets that are already detected.

In Chapter 2, I present the discovery and system parameter determination for three new hot Jupiter planets – WASP-92b, WASP-93b and WASP-118b. I modelled the transit lightcurves and RV measurements of the systems to determine the system parameters. For WASP-93b and WASP-118b there were time series spectral measurements during the transit, which were analysed for each to determine the potential spin-orbit alignment (or misalignment) of the system. I also investigated the tidal interactions of each of the planets with their host star, and was able to show the tidal migration that each planet will undergo depending on the spin-orbit alignment of the systems.

The remainder of the thesis contains studies of the modelling of stellar limb darkening. In Chapter4, I describe a novel method for interpolating between tabulated coefficients for limb darkening, which utilises a Gaussian Process to train the interpolation surface in stellar atmo- sphere parameter space. The Gaussian Process is conditioned on an existing grid of tabulated coefficients, and with optimised hyperparameters can then be used to predict limb darkening coefficients for given stellar atmospheric parameters. The technique is demonstrated for fits of simulated transit lightcurves, and for real transit lightcurves in Chapter6. The method is effective at constraining the values of the limb darkening coefficients based on the existing knowledge of the stellar atmosphere parameters, and prevents the introduction of biases from linearly interpolating between tabulated coefficients where the variation between them is not linear and is multi-dimensional.

Chapter6provides the description of another novel method for modelling limb darkening. The approach presented in this Chapter is prefaced on the knowledge that parametric models for limb darkening do not fully represent the CLIV for the stellar surface. The technique pro- posed the use of an Artificial Neural Network (ANN), which is trained directly from the outputs of stellar atmosphere models. The method removes the need for a parametric approximation of the form of the limb darkening, and is able to predict the limb darkening for any position on the stellar surface for the given stellar atmosphere parameters, even for stellar parameters not corresponding to an existing atmosphere model. The technique is validated through fitting a lightcurve of the transit of Venus, and for a transit of TRES-2b.

The final results Chapter,7, explores the potential for the ANN method described in Chapter

6to be extended to include the consideration of the wavelength-dependent nature of the stellar radius. I have developed a model architecture and training methodology that demonstrates the feasibility of using an ANN to model the full output shape from stellar atmosphere models with spherical geometry. The trained model matches well to the training data, and the potential to use this method to model limb darkening where very high precision is required has been demonstrated.