Calculated density distributions and energy spectra of heliosheath energetic He ions for the hydrodynamic, Parker, and ad hoc models. Upper/middle/lower rows correspond to hydrodynamic/ad hoc/Parker models. Left column of the panels corresponds to the peak velocity of the initial kappa-distributions of α-particles injected at TS equal to 170 km s^-1; right column, correspondingly, to 320 km s^-1. He⁺ injection as described in the text. In a given row, the upper (lower) half of each heliosphere map represents density distribution of α-particles (He⁺ ions). Distance scale is in AU. Density scales (equal for α-particles and He⁺ ions only in the two upper rows) are indicated on vertical strips on the right side of each half-heliosphere map. Small panels placed above (below) maps illustrate the evolution of energy spectra of α-particles (He⁺ ions) as the background plasma parcel is carried over points I, II, III, IV along the flow line. The line starting at the TS point 90° away from the apex is shown. Horizontal (vertical) axis in small panels describes ion energy in keV (ion density in cm^-3 keV^-1).