A Model of the Hα and Na Transmission Spectrum of HD 189733b

Abstract

This paper presents a detailed hydrostatic model of the upper atmosphere of HD 189733b, with the goal of constraining its temperature, particle densities, and radiation field over the pressure range 10^-4 to 10 μbar, where the observed Hα transmission spectrum is produced. The atomic hydrogen level population is computed including both collisional and radiative transition rates. The Lyα resonant scattering is computed using a Monte Carlo simulation. The model transmission spectra are in broad agreement with the data. Excitation of the H(2ℓ) population is mainly by Lyα radiative excitation due to the large Lyα intensity. The density of H(2ℓ) is nearly flat over two decades in pressure and is optically thick to Hα. Additional models computed for a range of the stellar Lyman continuum (LyC) flux suggest that the variability in Hα transit depth may be due to the variability in the stellar LyC. Since metal lines provide the dominant cooling of this part of the atmosphere, the atmosphere structure is sensitive to the density of species such as Mg and Na, which may themselves be constrained by observations. Since the Hα and Na D lines have comparable absorption depths, we argue that the centers of the Na D lines are also formed in the atomic layer where the Hα line is formed.