The Voyager 1 (V1), Voyager 2 (V2), and Pioneer 10 (P10) Lyα data sets are three of several diagnostic data sets available for the study of the very local interstellar medium (VLISM). Selected V1 data obtained on 1989 day 279 at heliocentric distance of 39.1 AU in the upstream direction relative to the incoming interstellar neutral hydrogen flow and V2 data obtained on 1990 day 143 at heliocentric distance of 32 AU, also in the upstream direction, have been used to estimate the local interstellar neutral hydrogen and proton densities and compared with P10 data obtained in 1981 at distances between 23.39 and 23.87 AU in the downstream direction, respectively. State-of-the-art plasma-neutral and radiative transfer models have been used in the interpretation of the data. It has been found that a VLISM heliospheric model with neutral hydrogen density of 0.18 cm-3 and proton density of 0.06 cm-3 best fits both the V1 data and the V2 data. The P10 data are best fitted by a VLISM model with neutral hydrogen density of 0.15 cm-3 and proton density of 0.05 cm-3. The failure to find a single best-fit stationary heliosphere plasma-neutral model suggests, among other possibilities, that a quantitative interpretation of the heliospheric Lyα glow would require the incorporation of magnetic field and time dependence in the heliospheric model.
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