Astron. Astrophys. 347, 711-719 (1999)

4. Implications and open problems

What are the implications of the results reported above for the origin of Ganymed and the other NEAs with similar orbits? The main constraint is provided by the short dynamical lifetime of this kind of orbits,  Myr as we have seen. In order to understand this constraint, we have to analyse the "demography" of these bodies.

There are about 15 objects with diameters  km among the Mars-crossing asteroids, 3 of them (1036 Ganymed, 2204 Lyyli and 132 Aethra) with Ganymed-type orbits (that is, semimajor axes between the 3:1 and 5:2 resonances and proper inclinations , well above the secular resonance) and 3 more (475 Occlo, 344 Desiderata and 796 Sarita) with somewhat lower inclinations (). We have not checked whether the latter 3 bodies are also located above , but it is interesting to note that one of them, 344 Desiderata, is a fairly big asteroid (about 132 km in diameter). We do not know whether these other Mars-crossers have dynamical lifetimes as short as Ganymed [recall that the MB2 objects of Migliorini et al. (1998) had an average lifetime of about 40 Myr] - but if so, where do they come from?

The simplest solution would be that, like the other types of Mars-crossers, these bodies would be supplied by chaotic diffusion from the main-belt population having similar values of a and i, but lower eccentricities (Migliorini et al. 1998; Morbidelli & Nesvorný 1999; Michel et al. 1999). However, according to the catalogue of asteroid orbits maintained by E. Bowell (http://www.lowell.edu/pub/elgb/astorb.html ), which is almost complete for bodies of diameter  km (V. Zappalà, private communication), there are only 16 such objects in the putative source population, with main-belt orbits above and with semimajor axes between 2.5 and 2.8 AU. This is certainly not enough to sustain a loss of Ganymed-like objects per Myr over the age of the Solar System. Here we have assumed that 3 of the Mars-crossers with Ganymed-like orbits have lifetimes of about 10 Myr: but the basic conclusion would not change much if we had counted only Ganymed, or we had included all the 6 MB2s larger than 20 km and assumed the Migliorini et al. average lifetime of 40 Myr.

Of course there are other conceivable sources for the Ganymed-like (MB2) Mars-crossers, e.g. (i) main-belt asteroids with lower inclinations, and "jumping" through ; (ii) Phocaea-group bodies, which are located above but would have to jump outward through the 3:1 resonance; and (iii) Jupiter-family comets, which may become dynamically decoupled from Jupiter (such as P/Encke, see Valsecchi et al. 1995). However, none of these sources is very attractive, because neither chaotic dynamics nor velocity increments associated to collisions appear likely to provide efficient transfer routes to the MB2 region.

Consider for instance the Maria family, whose largest members have sizes close to that of Ganymed and bear a spectral resemblance to it (Zappalà et al. 1997). This family is located near the outer edge of the 3:1 resonance at relatively high proper inclinations (), which however are much lower than that of Ganymed and such that the entire family lies below . Plausible ejection velocities following the family formation event (a few hundreds m/s) are not enough to raise the inclination beyond , into the MB2 zone. On the other hand, in none of our integrations we have observed the inclination of Ganymed to change by such an amount, unless the body had fell into a strong resonance; but in that case, typically it would survive for only a few Myr, and would not be likely to come back to the initial state. Even if the resonant locking were temporary, as for clones and discussed in Sect. 2, it would be necessary to assume that the 3:1 resonance had pumped up not only the eccentricty but the inclination too (by some ) during the locking interval, and then the body had been extracted out of the resonance (plausibly, by an Earth encounter) and eventually had its eccentricity decreased again to put it into the MB2 region. Clearly, such a scenario cannot be excluded a priori , but does not look likely.

An alternative possibility may be that Ganymed is a former member of a long-lived tail of a primordial main-belt population above , now almost depleted. Were Ganymed a single, peculiar object, this would be plausible; but if 2204 Lyyli and 132 Aethra have also lifetimes as short as 10 (or even 40) Myr, this explanation becomes very unlikely. In summary, we conclude that the origin of Ganymed and its siblings is still an open problem, with no straightforward solution at hand.

Our results have also some implications on the possible connection of Ganymed with the meteorites. Zappalà et al. (1997) have stressed the similarity of Ganymed's visible reflectance spectrum with those of the main-belt asteroids classified by Gaffey et al. (1993) in the S(IV) spectral subclass, the only one within the S taxonomic class which is probably related to the ordinary chondrites (Chapman 1996). If this is the case and Ganymed's composition is chondritic, its current orbit probably implies that ordinary chondritic material exists also out of the so-called inner asteroid belt (inside the 3:1 resonance). On the other hand, the meteorite Earth-delivery efficiency of bodies with this type of orbits is certainly low, because in most cases they are short-lived when they become Earth-crossing. As shown by Morbidelli & Gladman (1998), only about of the particles inserted into the 3:1 resonance eventually collide with the Earth; for the MB2 asteroids, the overall percentage is probably smaller, as many of them eventually fall into the even more inefficient 8:3 and 5:2 resonances. Also, the population in this region and the neighbouring lower-inclination part of the main belt is quite sparse, and cannot supply a large flux of small fragments. Therefore we conclude that this region of the asteroid belt is not likely to provide many meteorites.

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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