Estimating stellar limb darkening using exoplanet transits
(2023) ASTK03 20231Astrophysics
Department of Physics
- Abstract
- The brightness of the stars is not uniform over the surface as it varies depending on the wavelength and the atmosphere that the light propagates. Limb darkening is an optical effect caused by a decrease in brightness of the star towards the edge. Depending on which point on the star is observed, the optical depth reaches different atmospheric media, which results in different intensities of light. In the case of limb darkening, the light gets absorbed more as it is observed in the outer atmosphere and hence, appears darker than the center. The transit method is one of the exoplanet observation methods which measures a transit depth, a drop in stellar flux due to the exoplanet transit. Such a measurement can be utilized to derive a ratio... (More)
- The brightness of the stars is not uniform over the surface as it varies depending on the wavelength and the atmosphere that the light propagates. Limb darkening is an optical effect caused by a decrease in brightness of the star towards the edge. Depending on which point on the star is observed, the optical depth reaches different atmospheric media, which results in different intensities of light. In the case of limb darkening, the light gets absorbed more as it is observed in the outer atmosphere and hence, appears darker than the center. The transit method is one of the exoplanet observation methods which measures a transit depth, a drop in stellar flux due to the exoplanet transit. Such a measurement can be utilized to derive a ratio between stellar radius and planetary radius. Hence, the accurate observation of transit depth is essential for the measurement of the planetary radii. The limb darkening can alter the profile of the transit light curve by making the transit depth deeper, which then affects the measurement of the planetary radii. Several models of limb darkening have been established and improved over the past years. The power-2 limb darkening law is one of the examples, and it provides a good estimation of limb darkening.
The primary goal of this Bachelor’s project is to estimate limb darkening by using the light curves observed by one of the ongoing space missions, CHaracterising ExOPlanet Satellite (CHEOPS), and to compare them to the theoretical values calculated with the power-2 limb darkening law. Throughout this project, the light curves of a target, WASP-8b, are analyzed using a Python package, PYCHEOPS. The observational value of limb darkening parameters h1 and h2 are calculated from the analysis of two light curves and compared to the theoretical values listed in Borsato et al. (2021). I also investigated how an increase in the number of analyzed light curves can affect the derived limb darkening parameters.
From the analysis of two light curves, I constrained the h1 parameter to h1 = 0.70 ± 0.03 while for the h2 parameter, I only managed to calculate the 95% percentile of h2 = [0.125, 0.708]. For the h1 parameter, the observational value shows an agreement within 1-σ with the theoretical one. For the h2 parameter, the theoretical value lies in the 95% percentile range. When the number of light curves is doubled, the h1 parameter got more constrained with the value of h1 = 0.71 ± 0.01. The h2 parameter, on the other hand, remained unconstrained such that I could only calculate the 95% percentile of h2 = [0.093, 0.679]. Nevertheless, I found a statistical improvement of the observational values and fitted models where a decrease in reduced chi-square value and two times lower BIC are obtained from doubling the number of analyzed light curves. The results and statistical analysis indicate that the limb darkening can be estimated from the CHEOPS light curves using the power-2 limb darkening law. (Less) - Popular Abstract
- We have once wondered, does a planet like Earth exist in outer space, or are there any possibilities of encountering other life forms? If we consider the scale of our Universe and the number of stars in it, the chances of finding an Earth-like planet is not so low. The planets outside our solar system are called exoplanets, and more than 5000 exoplanets have been discovered in the past century. The study of exoplanets is one of the fast-growing research fields in astrophysics, and the observation methods and instruments have been improved over the years for more accurate and efficient data collection.
A planet-star radius ratio is one of the most important characteristics in determining the size, and more specifically, the radius of... (More) - We have once wondered, does a planet like Earth exist in outer space, or are there any possibilities of encountering other life forms? If we consider the scale of our Universe and the number of stars in it, the chances of finding an Earth-like planet is not so low. The planets outside our solar system are called exoplanets, and more than 5000 exoplanets have been discovered in the past century. The study of exoplanets is one of the fast-growing research fields in astrophysics, and the observation methods and instruments have been improved over the years for more accurate and efficient data collection.
A planet-star radius ratio is one of the most important characteristics in determining the size, and more specifically, the radius of exoplanets. There are a couple of ongoing space missions that are capable of measuring the radius of exoplanets. CHaracterising ExOPlanets Satellite (CHEOPS) is one of the space missions that is dedicated to observing known exoplanets. CHEOPS looks at stars that host exoplanets in their system and collects data on the star’s brightness over a certain period of time. As the planets pass in front of their host stars, the brightness of the stars drops slightly. Such a change in the brightness is known as a transit depth and can be used to derive the radius ratio. Thus, the accurate measurement of a star’s brightness is crucial to exoplanet study.
One of the factors that can affect the accuracy of such a measurement is an optical effect called limb darkening. Limb darkening is a decrease in a star’s brightness towards the edge of the star. One can visualize this effect as the shade that appears on the edge of a ball when it is illuminated with a flashlight. Limb darkening can significantly alter the transit depth and hence, can affect the derivation of planetary radii. The study of limb darkening is relatively new, yet it has been constantly updated in past years. In recent exoplanet research, the estimation of limb darkening is taken into consideration in order to acquire accurate observation and analysis of exoplanets.
The primary goal of this project is to estimate limb darkening by using the data collected by CHEOPS and to compare the results with a theoretical estimation listed in a research paper by Borsato et al. (2021). The comparison of the two estimates can be interpreted as the capability of CHEOPS to detect limb darkening from its observations. The estimation of limb darkening and the accurate measurement of planetary radii can lead to the characterization of exoplanets in a more accurate manner.
The investigation of exoplanets continues to grow as more discoveries of exoplanets are expected from the most recent and upcoming space missions like the James Webb Space Telescope. Our Sun is now halfway through its life span and keeps on growing, indicating that the Earth will no longer be habitable after a couple of billion years. It is never too early to start searching for a new home for our kids, thousands of generations away. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9123972
- author
- Ishida, Sora LU
- supervisor
- organization
- course
- ASTK03 20231
- year
- 2023
- type
- M2 - Bachelor Degree
- subject
- keywords
- Limb-darkening, CHEOPS, Transit, Exoplanet, PYCHEOPS
- report number
- 2023-EXA202
- language
- English
- additional info
- Registration number: 2023-EXA202
- id
- 9123972
- date added to LUP
- 2023-06-16 09:02:38
- date last changed
- 2023-08-30 15:12:44
@misc{9123972,
abstract = {{The brightness of the stars is not uniform over the surface as it varies depending on the wavelength and the atmosphere that the light propagates. Limb darkening is an optical effect caused by a decrease in brightness of the star towards the edge. Depending on which point on the star is observed, the optical depth reaches different atmospheric media, which results in different intensities of light. In the case of limb darkening, the light gets absorbed more as it is observed in the outer atmosphere and hence, appears darker than the center. The transit method is one of the exoplanet observation methods which measures a transit depth, a drop in stellar flux due to the exoplanet transit. Such a measurement can be utilized to derive a ratio between stellar radius and planetary radius. Hence, the accurate observation of transit depth is essential for the measurement of the planetary radii. The limb darkening can alter the profile of the transit light curve by making the transit depth deeper, which then affects the measurement of the planetary radii. Several models of limb darkening have been established and improved over the past years. The power-2 limb darkening law is one of the examples, and it provides a good estimation of limb darkening.
The primary goal of this Bachelor’s project is to estimate limb darkening by using the light curves observed by one of the ongoing space missions, CHaracterising ExOPlanet Satellite (CHEOPS), and to compare them to the theoretical values calculated with the power-2 limb darkening law. Throughout this project, the light curves of a target, WASP-8b, are analyzed using a Python package, PYCHEOPS. The observational value of limb darkening parameters h1 and h2 are calculated from the analysis of two light curves and compared to the theoretical values listed in Borsato et al. (2021). I also investigated how an increase in the number of analyzed light curves can affect the derived limb darkening parameters.
From the analysis of two light curves, I constrained the h1 parameter to h1 = 0.70 ± 0.03 while for the h2 parameter, I only managed to calculate the 95% percentile of h2 = [0.125, 0.708]. For the h1 parameter, the observational value shows an agreement within 1-σ with the theoretical one. For the h2 parameter, the theoretical value lies in the 95% percentile range. When the number of light curves is doubled, the h1 parameter got more constrained with the value of h1 = 0.71 ± 0.01. The h2 parameter, on the other hand, remained unconstrained such that I could only calculate the 95% percentile of h2 = [0.093, 0.679]. Nevertheless, I found a statistical improvement of the observational values and fitted models where a decrease in reduced chi-square value and two times lower BIC are obtained from doubling the number of analyzed light curves. The results and statistical analysis indicate that the limb darkening can be estimated from the CHEOPS light curves using the power-2 limb darkening law.}},
author = {{Ishida, Sora}},
language = {{eng}},
note = {{Student Paper}},
title = {{Estimating stellar limb darkening using exoplanet transits}},
year = {{2023}},
}