Lyman $alpha$ observations of the transiting exoplanet HD 209458b enable the study of exoplanets exospheres exposed to stellar EUV fluxes, as well as the interacting stellar wind properties. In this study we present 3D hydrodynamical models for the stellar-planetary wind interaction including radiation pressure and charge exchange, together with photoionization, recombination and collisional ionization processes. Our models explore the contribution of the radiation pressure and charge exchange on the Ly$alpha$ absorption profile in a hydrodynamical framework, and for a single set of stellar wind parameters appropriate for HD 209458. We find that most of the absorption is produced by the material from the planet, with a secondary contribution of neutralized stellar ions by charge exchange. At the same time, the hydrodynamic shock heats up the planetary material, resulting in a broad thermal profile. Meanwhile, the radiation pressure yielded a small velocity shift of the absorbing material. While neither charge exchange nor radiation pressure provide enough neutrals at the velocity needed to explain the observations at $-100~mathrm{km~s^{-1}}$ individually, we find that the two effects combined with the broad thermal profile are able to explain the observations.
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