Modeling the Ly$\alpha$ transit absorption of the hot Jupiter HD 189733b

Hydrogen-dominated atmospheres of hot exoplanets expand and escape hydrodynamically due to the intense heating by the X-ray and extreme ultraviolet (XUV) irradiation of their host stars. Excess absorption of neutral hydrogen has been observed in the Ly$\alpha$ line during transits of several close-in gaseous exoplanets, indicating such extended atmospheres. For the hot Jupiter HD~189733b, this absorption shows temporal variability. Variations in stellar XUV emission and/or variable stellar wind conditions have been invoked to explain this effect. We apply a 1D hydrodynamic planetary upper atmosphere model and a 3D MHD stellar wind flow model to study the effect of variations of the stellar XUV irradiation and wind conditions at the planet's orbit on the neutral hydrogen distribution, including the production of energetic neutral atoms (ENAs), and the related Ly$\alpha$ transit signature. We are able to reproduce the Ly$\alpha$ absorption observed in 2011 with a stellar XUV flux of $1.8\times10^4$ erg cm$^{-2}$ s$^{-1}$, rather typical activity conditions for this star. Flares with parameters similar to the one observed 8 h before the transit are unlikely to have caused a significant modulation of the transit signature. We find that the resulting Ly$\alpha$ absorption is dominated by atmospheric broadening, whereas the contribution of ENAs is negligible. Thus, the absorption does not depend on the stellar wind parameters. Since the transit absorption can be modeled with typical stellar XUV and wind conditions, it is possible that the non-detection of the absorption in 2010 was affected by less-typical stellar activity conditions, such as a very different magnitude and/or shape of the star's spectral XUV emission, or temporal/spatial variations in Ly$\alpha$ affecting the determination of the transit absorption.