We use self-consistent kinetic/hydrodynamic models of the heliosphere to predict H I Lyα absorption profiles for various lines of sight through the heliosphere. These results are compared with Lyα absorption lines of six nearby stars observed by the Hubble Space Telescope. The directions of these lines of sight range from nearly upwind (36 Oph) to nearly downwind ( Eri). Only three of the Lyα spectra (36 Oph, α Cen, and Sirius) actually show evidence for the presence of heliospheric absorption, which is blended with the ubiquitous interstellar absorption, but the other three spectra still provide useful upper limits for the amount of heliospheric absorption for those lines of sight. Most of our models use a Boltzmann particle code for the neutrals, allowing us to estimate neutral velocity distributions throughout the heliosphere, from which we compute model Lyα absorption profiles. In comparing these models with the data, we find they predict too much absorption in sidewind and downwind directions, especially when higher Mach numbers are assumed for the interstellar wind. Models created assuming different values of the interstellar temperature and proton density fail to improve the agreement. Somewhat surprisingly, a model that uses a multifluid treatment of the neutrals rather than the Boltzmann particle code is more consistent with the data, and we speculate as to why this may be the case.
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