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Notes to Table 3.10.1: n is the pickup ions injection efficiency, rsh is the heliocentric distance to the heliospheric shock, 5 is the sub-shock compression ratio, L - the extent of precursor, Au/u, - the total solar wind deceleration (u = 400 km/s).

According to Le Roux and Fichtner (1997a,b), case 1 in Table 3.10.1 corresponds to a solar wind expansion unaffected by the presence of pickup ions and CR. Consequently the heliospheric shock is strong, with a compression ratio 5 = 4.0, and there is no deceleration upstream. The mere presence of neutral particles and, subsequently, pickup ions, i.e., case 2 (dashed lines in Fig. 3.10.2a and Fig. 3.10.26), decelerates the solar wind on 12.8% according to Table 3.10.1. A higher temperature of the gas mixture in the outer Heliosphere causes its Mach number to decrease from 141 to 4.3; thus the compression ratio decreases to 5 = 3.5. Because of the lower solar wind ram pressure the heliospheric shock moves in from 80.8 to 73.7 AU. Reference case 3 also includes galactic CR. The effect is twofold: besides further reducing the heliocentric distance of the heliospheric shock to 71.8 AU as a consequence of the increased external pressure (pth,LisM + RgCR), galactic CR enhance the solar wind deceleration. Compared with case 2 the deceleration is increased in a region of ~ 37 AU upstream by 14.5%, resulting in a total increase in deceleration of 17.3%. In the following, Le Roux and Fichtner (1997a,b) refer to this region of deceleration in excess of that owed to pickup ions

(case 2) as the 'precursor'. If such a precursor exists, the shock transition is referred to as a sub-shock. The extended precursor of case 3 can be attributed to the high effective diffusion length (k/u) of galactic CR. The results obtained for these reference cases correspond to those reported by Ko et al. (1988), Lee and Axford (1988), Lee (1997).

Let us now turn to the situation where all three energetic particle populations are present simultaneously, i.e. cases (a) and (b) in Table 3.10.1. Fig. 3.10.2 shows the heliospheric shock structure resulting from (a) low and (b) high injection. According to Grzedzielski and Ziemkiewicz (1990) and Lee (1997), the anomalous CR should push the heliospheric shock away from the Sun. Results of Le Roux and Fichtner (1997a,b) confirm this finding (see Table 3.10.1). While the effects of galactic CR and anomalous CR on the sub-shock location nearly compensate each other, so that the location is close to that of the pure pickup ions (case 2 in Table 3.10.1), the other parameters defining the heliospheric shock structure are distinctly different. For the low injection (case (a) in Table 3.10.1) the compression ratio is slightly lower than for case 3, the extent of the precursor is somewhat shorter (~ 34 AU), and the deceleration of the solar wind is more pronounced (19.8%). Even so, the precursor is determined mainly by galactic CR and the sub-shock by pickup ions. For case (b) the solar wind deceleration is 45.0% and both the compression ratio (s = 1.5) and the precursor extent (~ 12 AU) are significantly reduced, indicating that anomalous CR with a relatively small effective diffusion length dominate the overall structure of the heliospheric shock.

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