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Astron. Astrophys. 336, 1056-1064 (1998)

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5. Collisional properties of individual Hilda asteroids

The collision probability of the Hilda asteroids are dominated by HM collisions that only occurs when they are relatively close to their perihelia. Depending on the individual eccentricities of the Hilda asteroids they will reach unequally deep into the main-belt. The deeper into the main-belt the Hilda asteroids can reach they will increase their probability of encountering a main-belt asteroid for two reasons. The Hilda orbit will cross the orbits of a larger fraction of main-belt objects, and the Hilda asteroid will be in the `main-belt space' during a larger fraction of its orbit.

Schubart (1982) showed that the eccentricity of individual Hilda objects oscillates around a fixed mean value for at least [FORMULA] years. An extension of Schubart's study has been made (unpublished) with a numerical integration taking into account perturbations from Venus to Neptune. The results showed that the Hilda orbits are stable for at least [FORMULA] years. Also Franklin et al. (1993) concluded that the orbits of Hilda asteroids seem to be stable during the history of the Solar System.

The stability of the mean eccentricity gives the expectation that there will be a strong correlation between mean eccentricity and collision probability for Hilda objects. This is also indicated by the wide range of [FORMULA] among the Hilda asteroids seen in Fig. 5.

This is verified in Fig. 6, which shows a very strong correlation between the mean eccentricity during time T and the collision probability (correlation coefficient r = 0.90). The scatter in the eccentricity-[FORMULA] correlation is due to objects with higher or lower inclinations than average. Somewhat surprisingly the range in [FORMULA] among the Hilda asteroids is almost a factor of six when including the two low eccentricity objects (334 Chicago and 1256 Normannia), but the range reduces to a factor of three when excluding these two objects. Note that the eccentricity-[FORMULA] correlation is not due to the increased orbital velocity close to perihelia of objects with higher eccentricity.

[FIGURE] Fig. 6. Collision probability [FORMULA] (in units of [FORMULA]) versus mean eccentricity (upper panel), and versus mean collision velocity (lower panel) for 39 Hilda asteroids.

Fig. 6 (lower panel) gives the mean relative velocity versus [FORMULA] for the Hilda asteroids. The mean velocities range from 3.3 to 6.0 [FORMULA], and a tentative correlation between [FORMULA] and [FORMULA] is indicated in the data (r = 0.46), because larger eccentricities result in both higher collision velocities and higher collision probabilities. The [FORMULA] plotted in Fig. 6, together with the obtained mean, median, rms, collision velocities and the standard deviations of the velocity distributions are given in Table 6.


[TABLE]

Table 6. Collision probabilities [FORMULA] for the 39 Hilda asteroids obtained with 909 asteroids with [FORMULA] 50 km, together with mean, median, and rms collision velocities of the Hilda objects. Also the standard deviations of the collision velocities are given. The intrinsic collision probabilities for the Hilda objects can be calculated with [FORMULA].


To illustrate the scatter of collision properties of the Hilda population, the distribution of collision velocities of four Hilda asteroids are given in Fig. 7. The areas under the histograms are proportional to the collision probability [FORMULA] (and [FORMULA]) of the objects. In the velocity distribution of 190 Ismene, 3% of the encounters have a very low velocity, [FORMULA] 0.3 [FORMULA]. All these encounters are with the Hilda asteroid 2246 Bowell. This shows that due to the similar shapes of Hilda orbits the relative velocity between two objects can be very low at an encounter, or at a series of encounters. This gives a low velocity tail in the velocity distributions for some of the Hilda asteroids, which is also seen in the velocity distribution of HH collisions in Fig. 1.

[FIGURE] Fig. 7. Collision velocity distributions for four Hilda asteroids: 190 Ismene, 1256 Normannia, 1877 Marsden and 2483 Guinevere. The areas under the histograms are proportional to the collision probability [FORMULA] (and [FORMULA]) of the objects. The figures are shown to the same scale to facilitate comparison between the objects. The bin size is 0.5 [FORMULA].

The great difference in collisional probability among the Hilda asteroids are illustrated by 1256 Normannia and 2483 Guinevere, which has the lowest and highest [FORMULA], respectively. The spread in collision velocities among the Hilda population are illustrated by 1256 Normannia ([FORMULA] = 3.39 [FORMULA]) and the high inclination object 1877 Marsden (i=17[FORMULA]), which have the highest mean collision velocity ([FORMULA] = 6.0 [FORMULA]), and a high velocity tail reaching velocities of about 14 [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: July 27, 1998
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