Collisional Evolution in the Vulcanoid Region: Implications for Present-Day Population Constraints

We explore the effects of collisional evolution on putative Vulcanoid ensembles in the region between 0.06 and 0.21 AU from the Sun in order to constrain the probable population density and population structure of this region today. Dynamical studies have shown that the Vulcanoid Zone (VZ) could be populated. However, we find that the frequency and energetics of collisional evolution this close to the Sun, coupled with the efficient radiation transport of small debris out of this region, together conspire to create an active and highly intensive collisional environment that depletes any very significant population of rocky bodies placed in it, unless the bodies exhibit orbits that are circular to ∼10 ^-3 or less or highly lossy mechanical properties that correspond to a fraction of impact energy significantly less than 10% being imparted to ejecta. The most favorable locale for residual bodies to survive in this region is in highly circular orbits near the outer edge of the dynamically stable Vulcanoid Zone (i.e., near 0.2 AU), where collisional evolution and radiation transport of small bodies and debris proceed most slowly. If the mean random orbital eccentricity in this region exceeds ∼10 ^-3, then our work suggests it is unlikely that more than a few hundred objects with radii larger than 1 km will be found in the entire VZ; assuming the largest objects have a radius of 30 km, then the total mass of bodies in the VZ down to 0.1 km radii is likely to be no more than ∼10 ^-6 M _⊕, <10 ^-3 the mass of the asteroid belt. A 0.01-AU-wide ring near the outer stability boundary of the VZ at 0.2 AU would likely not contain over a few tens of objects with radii larger than 1 km. Despite the dynamical stability of large objects in this region (Evans, N. W., and S. Tabachnik, 1999, Nature 399, 41-43), it is plausible that the entire region is virtually empty of kilometer-scale and larger objects.