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Astron. Astrophys. 317, 193-202 (1997)

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5. Numerical results

The simulation was performed for a number density of oxygen in the unperturbed interstellar medium [FORMULA] equal to [FORMULA]. This corresponds to a ratio of oxygen to hydrogen number densities [FORMULA] of [FORMULA]. This is close to the most recent neutral oxygen/neutral hydrogen relative abundance measurements in the Local Interstellar Cloud (or LIC) of Linsky et al (1993) (see Sect. 6). Since the influence of the oxygen distribution on the protons and neutral H atoms is negligible, the densities resulting from the present calculations are simply scaled by the choosen neutral oxygen density (and the corresponding oxygen ions density). In other words, in case of a different O/H abundance ratio, oxygen atoms and ions density distributions can be obtained from the present results by simply multiplying by the appropriate constant. However, this is no longer t ction of H, since ionizations of O and H in the unperturbed LISM are entirely coupled. In this case, new computations are required.

[FIGURE]Fig. 3. Number density of oxygen LISM atoms in units of the unperturbed LISM density, as a function of the heliocentric distance. Curves 1,2,3 are for upwind, sidewind an d downwind respectively. [FORMULA] is the oxygen atom number density in the unperturbed LISM. Positions of TS, HP and BS are shown by stars.

[FIGURE]Fig. 4. Ratio of the neutral oxygen to the neutral hydrogen density as function of heliocentric distance for the upwind direction (1), the sidewind or perpendicular direction (2) and the downwind direction (3). The ratio is in units of the ratio in the unperturbed LISM. Curve 3 corresponds to the right scale. On the downwind side the oxygen to hydrogen ratio reaches values as high as 40 due to the combined effects of oxygen focusing and hydrogen depletion, and remains larger than one even at very large distances from the Sun, because the hydrogen density remains below the interstellar level (see Fig. 3a). The positions of TS, HP and BS are indicated.

Fig. 3 shows the resulting density of oxygen atoms as a function of the heliocentric distance, as it comes out of the iterative process. Dashed curves correspond to the hypothetical case [FORMULA] in the unperturbed LISM (case a), while the solid curves are for [FORMULA] (case b). In case a) only direct charge exchange is taken into account, because there are no H atoms in the unperturbed LISM. In case b) both direct and reverse charge exchange are taken into account. Fig. 3 shows that the region between the bow shock and the terminal shock acts as a kind of filter for the interstellar oxygen, with a larger transmission on the downwind side as compared with the opposite direction. As a matter of fact, oxygen densities are smaller than one inside the termination shock on the upwind and sidewind directions, and close to one on the downwind side. Closer to the Sun, inside about 10 A.U., the solar gravitation and the photoionization become the essential processes acting on O atoms, creating the ionization cavity and the downwind focusing cone. Close to the Sun on the downwind side ionization and gravitation act in opposite ways: the gravitation increases the number density of atoms near the Sun, while the photoionization decreases it. The gravitational focusing is responsible for high downwind densities only if the ionization is not too strong. The curve 3, which corresponds to the downwind direction, shows the density increase due to the gravitation (the focusing effect).

Fig. 3 also clearly shows a density rise in the region between the outer shock and the heliopause, most pronounced in the upwind direction. The comparison of the solid and dashed curves shows that this density increase (or "oxygen wall") is entirely the consequence of the reverse charge exchange between hydrogen atoms and oxygen ions. This effect becomes very small at large angles from the upwind direction. A similar compression was derived for the first time for the neutral hydrogen by Baranov and Malama (1993) (Fig 2d). The "hydrogen wall" is due to secondary H atoms newly born after charge-exchange with the protons of the decelerated, compressed and heated plasma. While the maximum compression ratio reaches 1.6-1.7 for the H wall (Fig 2d), it reaches an almost equivalent level (1.3-1.4) in the oxygen wall, despite the significantly smaller charge-exchange cross-section.

The comparison between solid and dashed curves also shows that the reverse charge-exchange has as a result to fill the whole heliosphere, but the filling is done preferentially on the downwind side, for regions closer to the Sun than about 100 A.U. The gravitational focusing is responsible for these high downwind densities.

In Fig. 4 is represented the ratio of oxygen to hydrogen atom number densities as a function of heliocentric distance. This ratio has a complex behavior around the interface and increases inside the heliosphere, especially on the downwind side. The differences between the O and H filling of the downwind cavity are related to the differences between oxygen and hydrogen masses. While the bulk velocities of oxygen and hydrogen are the same, the thermal velocities depend on the number larger by a factor of four for oxygen as compared with hydrogen, and then in a larger filling of the downwind cavity. Note that the results of the simulation for the cells closer than 30 A.U. from the Sun on the upwind side are not very precise, because the Monte-Carlo algorithm used here provides poorer statistics in this region.

Fig. 5 shows the distribution of the oxygen ion source derived from the charge exchange processes and the photoionization. This distribution may be used as an input in models which describe how new born ions are picked up by solar wind. There is strong increase of the source at decreasing distance from the Sun. The reason for this increase is mainly the photoionization. Between the bow shock and the heliopause and between the heliopause and the terminal shock the

The volumic density of oxygen ions obtained by assuming the simplest ion pick up model, i.e. immediate assimilation of the ions by the ambient plasma, is displayed on Fig. 6, normalized to the value of O [FORMULA] at infinity. It is clear that the resulting distribution is similar to the proton distribution (fig.2a), while by definition the velocity and temperature of the oxygen ions are identical to those of protons(fig. 2b, Fig. 2c). These model results can be used for the of pick-up ions (Geiss et al, 1994).

[FIGURE]Fig. 5. Sources of oxygen LISM's ions as function of heliocentric distance for upwind direction (1), perpendicular direction (2) and downwind direction (3). The sources are in units of [FORMULA]. Positions of TS, HP and BS are shown points

[FIGURE]Fig. 6. Number density of oxygen pick-up ions normalized to the density of oxygen ions in the unperturbed LISM.

[FIGURE]Fig. 7. Number density of oxygen atoms normalized to the density in the unperturbed ISM with (solid lines) and without (dot-dashed lines) interface perturbations for the same interstellar and solar parameters. Densities have been divided by 1.2 for the classical model without interface.

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