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This paper presents a detailed hydrostatic model of the upper atmosphere ofHD 189733b, with the goal of constraining its temperature, particle densities,and radiation field over the pressure range $10^{-4}-10\, \mu \rm bar$, wherethe observed H$\alpha$ transmission spectrum is produced. The atomic hydrogenlevel population is computed including both collisional and radiativetransition rates. The Ly$\alpha$ resonant scattering is computed using aMonte-Carlo simulation. The model transmission spectra are in broad agreementwith the data. Excitation of the H(2$\ell$) population is mainly by Ly$\alpha$radiative excitation due to the large Ly$\alpha$ intensity. The density ofH(2$\ell$) is nearly flat over two decades in pressure, and is optically thickto H$\alpha$. Additional models computed for a range of the stellar Lymancontinuum (LyC) flux suggest that the variability in H$\alpha$ transit depthmay be due to the variability in the stellar LyC. Since metal lines provide thedominant cooling of this part of the atmosphere, the atmosphere structure issensitive to the density of species such as Mg and Na which may themselves beconstrained by observations. Since the H$\alpha$ and Na D lines have comparableabsorption depths, we argue that the center of the Na D lines are also formedin the atomic layer where the H$\alpha$ line is formed.

A Model of the H$\alpha$ and Na Transmission Spectrum of HD 189733b