  We use an updated self-consistent kinetic/gasdynamic model of the solar
wind/interstellar flow interaction to compute the Lyman-alpha absorption by
hydrogen atoms of both interstellar and solar origin generated in the
heliospheric interface. We apply this model to the direction of the star
Sirius. We show that the neutralized, compressed solar wind from the
heliosheath explains the extra absorption at positive redshifts observed in the
Lyman-alpha line with the HST/GHRS. This removes the need for the interstellar
hot gas previously proposed to explain this extra absorption. We also show that
extra absorption in the blue wing can possibly be explained by H atoms formed
in an astrosphere around Sirius, providing the stellar wind is at least as
massive and fast as the solar wind.
