Limb darkening and planetary transits

II. Intensity profile bias factors for a grid of model stellar atmospheres

¹ Department of Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON, M5S 3H4, Canada
e-mail: neilson@astro.utoronto.ca
² Department of Chemical & Physical Sciences, University of Toronto Mississauga, Mississauga, ON L5L 1C6 Canada
³ Center for High Angular Resolution Astronomy, Department of Physics and Astronomy, Georgia State University, PO Box 5060, Atlanta, GA 30302–5060 USA

Received: 13 June 2018
Accepted: 15 November 2021

Abstract

The ability to observe extrasolar planets transiting their stars has profoundly changed our understanding of these planetary systems. However, these measurements depend on how well we understand the properties of the host star, such as radius, luminosity, and limb darkening. Traditionally, limb darkening is treated as a parameterization in the analysis, but these simple parameterizations are not accurate representations of actual center-to-limb intensity variations (CLIV) to the precision needed for interpreting these transit observations. This effect leads to systematic errors for the measured planetary radii and corresponding measured spectral features. We computed synthetic planetary transit light curves using model stellar atmosphere CLIV and their corresponding best-fit limb-darkening laws for a grid of spherically symmetric model stellar atmospheres. From these light curves, we measured the differences in flux as a function of the star’s effective temperature, gravity, mass, and the inclination of the planet’s orbit. We find that the ratio of the planet radius to the radius of the star may have errors up to about 13% depending on stellar type, wavelength, and inclination of the orbit.