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

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3. Collision velocities

From the obtained data base of close encounters, histograms of the collision velocities for the eight collision populations are shown in Fig. 1, and their mean, median and rms collision velocities are given in Table 2. Some general conclusions can be drawn from these histograms. There is a large spread in the collision velocities, from 1 to 15 [FORMULA]. The high velocity tails and sharp cut-off at low velocities gives a clear non-Gaussian shape of the velocity distributions. There are also very narrow peaks in the velocity distributions probably from specific asteroid pairs making series of encounters at similar geometries (these are smoothed out by the binning in the histograms in Fig. 1). Considering the wide range in semi-major axes of the objects, the mean velocities are quite similar, ranging from 4.1 to 5.3 [FORMULA] in the different collisional populations, with one exception, HH collisions which have [FORMULA] = 3.1 [FORMULA]. The velocity distribution of TT collisions have a less pronounced and broader peak than the other populations. The MM distribution have mean, median and rms velocities of 5.28, 4.97, and 5.78 [FORMULA], which is remarkably similar to the result by Bottke et al. (1994) in their Fig. 7, (5.29, 5.03, and 5.79 [FORMULA]).


Table 2. The obtained mean, median, rms collision velocities, standard deviations, and number of close encounters for the populations and groups shown in Figs. 1 and 2.

[FIGURE] Fig. 1. Histograms of collision velocities for the different populations: MM) main-belt-main-belt, CC) Cybele-Cybele, HH) Hilda-Hilda, TT) Trojan-Trojan, CM) Cybele-main-belt, HC) Hilda-Cybele, HM) Hilda-main-belt, and HT) Hilda-Trojan collisions (see also Table 2). The bin size is 0.5 [FORMULA].

As mentioned above only mutual collisions among the Hilda asteroids have a significantly lower mean velocity. As pointed out by Marzari et al. (1996) there are three main reasons for this: i) lower keplerian velocities at larger semi-major axes. ii) quite low eccentricities and inclinations of Hilda asteroids (Table 1). iii) a non-random distribution of the apsidal lines of the Hilda orbits preventing collisions between two Hilda asteroids if one is close to aphelion and the other is close to perihelion, which is the orbital configuration giving the largest relative velocity. The corresponding [FORMULA] for HH collisions in the study by Marzari et al. (1996) is 2.9 [FORMULA].

The mean collision velocity for HM is about 0.4 [FORMULA] lower than in MM collisions. This difference is quite small because the Hilda asteroids plunge into the outer parts of the main-belt when they approach their perihelia (i.e., at their highest orbital velocity), and will collide with main-belt objects having higher keplerian velocities. The mean velocity of HC collisions is about 1.1 [FORMULA] lower than MM collisions, mainly due to lower keplerian velocities of the objects in the Cybele and Hilda groups.

The mean collision velocity of Trojan asteroids are similar to the main-belt value, despite the lower keplerian velocities at the heliocentric distance of the Trojan clouds. This is fully compensated by a higher mean inclination of the Trojan asteroids compared to main-belt objects (Table 1). The collision velocities of the Trojan asteroids is likely to increase when the Trojan sample is complete, due to the discovery bias against high inclination Trojan asteroids. This bias arises from from the observing strategy applied by most surveys (i.e., they only search for objects relatively close to the ecliptic plane). This is consistent with our result, which is about 0.2 [FORMULA] higher than the result by Marzari et al. (1996) which used a smaller sample (114 Trojans) which had a smaller mean inclination ([FORMULA] = 15.5[FORMULA]) compared to the sample used in this paper [FORMULA] = 16.5[FORMULA]. The collision velocity distributions of the four groups (Fig. 2 and Table 2) are similar to the dominating collision population in each group, (i.e., MM, CM, HM, and TT collisions for main-belt, Cybele, Hilda, and Trojan asteroids, respectively).

[FIGURE] Fig. 2. Histograms of the obtained collision velocities for main-belt, Cybele, Hilda and Trojan asteroids. The bin size is 0.5 [FORMULA].

3.1. Velocity components of the collisions

The Cartesian velocity components ([FORMULA]) of the collisions are given in Table 3, which lists the mean velocities and the standard deviations for the populations. The [FORMULA] components (i.e., perpendicular to the ecliptic plane) are 1.5-5.0 times larger than the corresponding [FORMULA] and [FORMULA] components. The populations involving Hilda asteroids (HH, HM, HC, and HT) have [FORMULA] / [FORMULA] in the lower part of this range, from [FORMULA] / [FORMULA] = 1.5 for HH collisions to [FORMULA] / [FORMULA] = 2.2 for HT collisions. This is due to the low mean inclinations of Hilda asteroids ([FORMULA] = 7[FORMULA]) giving a more isotropic distribution of the velocity components than in the other groups. This leads to the conclusion that the inclinations of the orbits to a large extent determine the relative velocities in the asteroid belt, which is consistent with the result from earlier investigation (Farinella & Davis 1992; Bottke et al. 1994; Marzari et al. 1996).


Table 3. The obtained collision velocity components [FORMULA], and [FORMULA] of the populations. The mean and standard deviations of the relative velocity components are given.

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© European Southern Observatory (ESO) 1998

Online publication: July 27, 1998