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Aims. Previous results of the study of interplanetary Lyman α background data obtained by the SWAN-SOHO between 1996 and 2005 clearly show that the solar cycle variations of the solar parameters deeply affect the interplanetary background emission. In this work, we compare these observational results with a time-dependent modeling of the interplanetary background. The hydrogen distributions in the model are one-year averages. Methods. The solar wind input in the model is derived from the omniweb dataset. The solar Lyman α flux values used to compute the radiation pressure are derived from the dataset of the SOLSTICE instrument. The hydrogen photo-ionization rate is extrapolated from the solar UV flux. These inputs are used to compute the hydrogen distribution in the heliosphere for two solar cycles. The resulting yearly averages of the interplanetary H distribution are then used as input for a radiative transfer model, which allows us to compute interplanetary background intensities, lineshifts, and linewidths for the geometries of the observations. Results. We find that the upwind intensities computed from the model do not follow variations observed by SWAN-SOHO between 1996 and 2005. On the other hand, the lineshift variations during the solar cycle are correctly reproduced. Comparison of observed linewidths with model results show that we can reproduce the general trend of the linewidth data. Time-dependent variations are not fully reproduced. Conclusions. The agreements obtained with the lineshifts and linewidths suggest that the velocity distribution of hydrogen is adequately represented by the model. On the other hand, we find that the temporal variations of the brightness data are not well reproduced by the model. To explain this, we suggest that the interface effects and radiation pressure are correctly represented whereas the ionization rate used as input in the model needs to be corrected. Further studies including anisotropy of the solar wind will be necessary to check this result.

Time dependent model of the interplanetary Lyman $\sf \alpha$ glow: applications to the SWAN data