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Astron. Astrophys. 358, 299-309 (2000)

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4. Computations of the positions and radial velocities of the test particles. Results

4.1. Standard analytical solution for the low velocities

We adopted the value of [FORMULA] and the position of the observer consistent with Olano's (1982) accretion models. These were derived for [FORMULA] considering the effect of braking forces in the galactic gas layer. In the following we will consider Olano's model 1 ([FORMULA] Myr, [FORMULA] pc, [FORMULA]) and assume [FORMULA] Myr. Tests with [FORMULA] and 120 Myr supplied no adequate fit of the OCCs. All the adopted parameters are listed in Table 1.


Table 1. Adopted parameters for the standard solution

We started by assuming an isotropic ejection of the test particles ([FORMULA], [FORMULA]), and [FORMULA] pc. The values assumed for [FORMULA] covered an interval of only 3 km [FORMULA] in order to be consistent with a shell-like structure. It turned out that the resulting velocity-dispersion of the test particles was smaller than the one of the OCCs by a factor of about 3. Increasing the range of [FORMULA] produced no significant improving since the solutions were not very sensitive to [FORMULA] at intermediate and high latitudes. A variation of [FORMULA] was more effective. An adequate V-dispersion was obtained for the set of values of [FORMULA] given in Table 1. This suggests that our test particles were ejected from a small volume, as is consistent with Blaauw's (1983, 1991) suggestions about the minimum sizes of the initial configurations in OB associations. Furthermore, we adopted [FORMULA] pc (e.g. Cohen 1995, Ng et al. 1997, Minezaki et al. 1998) and fitted [FORMULA] km [FORMULA].

As the mean altitude of the explosion center E is [FORMULA] pc, our model predicts asymmetries between both galactic hemispheres. Since [FORMULA], particles ejected northwards ([FORMULA]) with [FORMULA] [FORMULA] km [FORMULA] will be already in the southern hemisphere shortly after [FORMULA]. As a result, there will be more particles in the south than in the north. This should be reinforced by the effect of [FORMULA]. Moreover, the particles in the south ([FORMULA]) will be at earlier phases on their motions back to the galactic plane, than those in the north. On the other hand, a gap in the distribution of the test points in the GQ II at some northern latitudes could be fitted by a cutoff at [FORMULA].

In the following we describe the results obtained for a standard solution with the set of free parameters given in Table 1. For each [FORMULA] we computed the position and radial velocities of 19008 test particles in order to have an adequate coverage in the polar diagrams for a comparison with the OCCs. We considered the same latitude intervals as in Sect. 2. The solutions included the distances of the fitted test particles.

4.2. Comparison of the results of the standard solution with the observations

A representative sample of the results of the standard solution were plotted in Figs. 1-2. In most cases the test points form a stripe extending along the entire range of l, with a thickness between about 4 and 10 km [FORMULA]. In the following we make a comparison of the computed test points with the OCCs.

i) The low latitudes [FORMULA] (cf. Figs. 1a and 2a).

Here the predominance of positive velocities among the test points is overwhelming, as is expected of an expanding ring, which is observed from the inside. Consequently, the loosely clumped population of OCCs with negative velocities down to -40 km [FORMULA] in the GQs II and IV are not fitted. Analogously, the loosely clumped OCCs with [FORMULA] km [FORMULA] in GQs I and III are not fitted as well. This is consistent with the interpretation that most of these OCCs correspond to more distant objects, which are mainly in differential rotation about the galactic center.

The standard solution fits a large fraction of the dense stripe of OCCs with low positive velocities in the GQs II and III. In particular, the fit includes many prominent OCCs with peculiar velocities, like those near to [FORMULA]. However, in the GQs I and IV the dense stripe of OCCs has either small positive velocities, which are lower than the predicted ones, or slightly negative velocities. This suggests that the braking forces cannot be neglected. Our standard solution fits only a small fraction of these OCCs. Olano's model 1 predicts lower velocities and makes a more successful fitting attempt in GQs I and IV. Actually, it fits the smooth dense stripe with peculiar velocities along [FORMULA]-[FORMULA] at [FORMULA]. The latter should belong to the Sco-Cen shells.

ii) The low latitudes [FORMULA] (cf. Figs. 1b and 2b).

Here the standard solution predicts mostly [FORMULA] as well as some moderately [FORMULA]. It fits dense stripes of OCCs in the GQs I (at [FORMULA]), II and III, including some with peculiar velocities, like those at [FORMULA]-[FORMULA]. Nevertheless, the effect of the braking forces appears to be still present in some regions, like in the GQ I at [FORMULA], where the velocities of the broad dense stripes of OCCs are systematically lower than the predicted ones. We quote the peculiar negative velocities at [FORMULA]-[FORMULA], [FORMULA] (belonging to the Sco-Cen shells), and at the spikes at [FORMULA], and [FORMULA], [FORMULA]. On the other hand, at [FORMULA] most of the OCCs with [FORMULA] km [FORMULA] in GQ II, and [FORMULA] km [FORMULA], in the range [FORMULA]-[FORMULA] at [FORMULA] could correspond to more distant objects moving on circular orbits about the galactic center. Finally, in the GQ IV many of the OCCs of the Sco-Cen shells have [FORMULA], whereas a smaller group has [FORMULA]. They are fitted only marginally by the standard solution.

iii) The intermediate latitudes: [FORMULA] and [FORMULA] (cf. Figs. 1c-1e and 2c-2e).

Here we expect that the OCCs should be mainly nearby objects. The predicted values of V are low, either positive or negative. Only in the GQs I and IV at [FORMULA] the predicted velocities are still mainly positive. At the negative latitudes the standard solution fits the bulk of the OCCs in the GQs I (somewhat marginally at [FORMULA]), II and IV, as well as many OCCs in the GQ III. Among the non-fitted OCCs with [FORMULA] we quote: a) the dense clumps with [FORMULA]-5 km [FORMULA] in the region [FORMULA]-[FORMULA], which should belong to the Ori-Eri bubble; b) some clumps with [FORMULA] km [FORMULA] in the regions [FORMULA]-[FORMULA], [FORMULA], and [FORMULA]-[FORMULA], [FORMULA], which should all belong to the Sco-Cen shells; c) several clumps with [FORMULA] km [FORMULA] in the GQ I. Among the non-fitted OCCs with [FORMULA] the most notorious are some dense clumps having velocities in the range [FORMULA] to -20 km [FORMULA], which are concentrated at: a) [FORMULA]-[FORMULA], [FORMULA] and [FORMULA], as well as [FORMULA]-[FORMULA], [FORMULA] (presumably, all related to the Ori-Eri bubble), and b) the region [FORMULA]-[FORMULA], [FORMULA] and [FORMULA]. Some of these OCCs have peculiar motions . Furthermore, a few OCCs with [FORMULA] km [FORMULA] at [FORMULA] and [FORMULA] are not fitted as well.

At the positive latitudes the predicted velocities are more negative than at [FORMULA]. The test particles form a horseshoelike arc along the GQs III, IV and I, which fits the broad bulk of OCCs. In the GQ II, the large gap at [FORMULA] and [FORMULA], which is related to the HI-hole, is fitted roughly by the cutoff at [FORMULA] (cf. Table 1). The non-fitted OCCs in GQ II have mainly [FORMULA] and should be related to the puzzling NCPL mentioned in Sect. 2. Notorious non-fitted clouds with [FORMULA] are the plumes at [FORMULA], [FORMULA] [FORMULA] (Her shell, e.g. Bates et al. 1995), [FORMULA]-[FORMULA], and [FORMULA]. We point out the densely populated areas of OCCs with [FORMULA], which should be related to the extensive Sco-Cen shells in the GQ IV. They are fitted only marginally at [FORMULA] and [FORMULA], and much better at [FORMULA]. At this latitude we quote also a group of IVCs.

iv) The high latitudes: [FORMULA] and [FORMULA] (cf. Figs. 1f-1h and 2f-2h).

Here the predicted velocities are negative in almost all the cases. The standard solution fits most of the OCCs with [FORMULA] at [FORMULA]. At [FORMULA] the fit is rather less complete, because of the presence of the IVCs, most of which are in the range [FORMULA] [FORMULA]-[FORMULA]. Moreover, some puzzling non fitted OCCs with [FORMULA], appear mainly in the GQs III and IV at positive and negative latitudes. They could be outlayers of the Sco-Cen shells.

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Online publication: June 26, 2000