Exoplanet Cartography Using Light Curves With Multiple Reflection Models

Exoplanet Cartography Using Light Curves With Multiple Reflection Models

Gort, Timo (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Applied Sciences)

Visser, P.M. (mentor)
Adam, A.J.L. (graduation committee)
Hart, K.P. (graduation committee)
Endo, A. (graduation committee)

Delft University of Technology

Applied Mathematics | Applied Physics

2022-10-13

Context. In the near-future, exoplanets can be observed directly through telescopes. Although the resolution of the planet's image will only be one pixel at first, the intensity of this pixel will change over time because of the orbit around its host star and its diurnal rotation. This intensity as a function of time is called the light curve of an exoplanet. The changes in the light curve as a result of annual and diurnal rotation can in turn be used to obtain information about the surface of the planet, this is called spin-orbit tomography.

Aims. The aim of this study is to determine if an exoplanet's surface can be retrieved from its light curve for planet surfaces that can be described by Lambertian, Lommel-Seeliger or Fresnel reflection, or a combination of these. The variation in the light curve due to differences in the planet's surface will be used to find a map of its continents and oceans and to determine what surface types the planet is made of.

Methods. This thesis starts by composing a near-equal area segmentation of a sphere to maximize the retrieval of information per pixel of the exoplanet's surface. Additionally, a method for generating artificial planets is described, such that the following method can be tested on light curves, since the current telescopes are not powerful enough to measure an exoplanet's light curve. A linear transformation from the surface to the light curve is constructed to obtain the light curve from the surface. Consequently, this transformation is inverted in order to obtain information about the surface from the light curve. This method is applied to exoplanets with a stationary surface, i.e. no clouds or changing ice caps and is consistent of the following surfaces: water, vegetation, sand and snow, each described by a different reflection model. Lastly, surface retrieval is tested from a light curve with a realistic amount of photon shot noise (SNR ≈ 14).

Results. The composed near-equal area segmentation of a sphere is the Voronoi diagram of the Fibonacci lattice. It is a very appropriate near-equal area segmentation, because the maximum difference in facet area is 12% for 1001 points. Furthermore, the retrieval of an exoplanet's surface from its reflected light curve is close to perfect for exoplanets that are described by a combination of the three reflection models if the light curve does not contain noise and there are a sufficient number of data points. If the light curve does contain shot noise, parts of the surface that are described by the Lommel-Seeliger law, are not retrieved correctly. However, the general shape of the surface that is described by Lambertian or Fresnel reflection is still retrieved correctly. If the surface can be described by one single reflection model, the planet's features are retrieved correctly from a light curve with shot noise regardless of the reflection model.

Conclusions. Spin-orbit tomography in the form of a linear transformation between the light curve and albedo map of an exoplanet is a very accurate method to retrieve the albedo map from a single observed pixel, even with a realistic amount of shot noise.

Exopcartography
Exoplanets
Light curve
Surface mapping
Astronomy
Spin-Orbit tomography

http://resolver.tudelft.nl/uuid:5d605729-da84-4955-ae0d-8e55b2eaca3a

2022-07-21

https://github.com/SwederB/BEP-Exocartography/tree/main/Code_Timo Code used for the project

Student theses

bachelor thesis

© 2022 Timo Gort