Interaction of the solar wind with interstellar matter involves, among other, charge exchange between interstellar neutral atoms and plasma, which results in the creation of secondary population of interstellar neutral (ISN) atoms. The secondary population of interstellar He was detected by Interstellar Boundary Explorer (IBEX), but interpretation of these measurements was mostly based on an approximation that the primary interstellar neutral population and the secondary population were non-interacting homogeneous Maxwell-Boltzmann functions in the outer heliosheath. We simulate the distribution function in the outer heliosheath and inside the heliopause using method of characteristics with statistical weights obtained from solutions of the production and loss equations for the secondary atoms due to charge-exchange collisions in the outer heliosheath. We show that the two-Maxwellian approximation for the distribution function of neutral He is not a good approximation within the outer heliosheath but a reasonable one inside the termination shock. This is due to a strong selection effect: the He atoms able to penetrate inside the termination shock are a small, peculiar subset of the entire secondary He population. Nevertheless, the two-Maxwellian approximation reproduces the density distribution of ISN He inside the termination shock well and enables a realistic reproduction of the orientation of the plane defined by the Suns velocity vector through the local interstellar matter and the vector of unperturbed interstellar magnetic field.
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