Transient redshifted events monitored in the spectrum of beta Pic-toris have been interpreted for many years as resulting from the evaporation of numerous comet-like bodies in the vicinity of this stars. This motivated the investigation of dynamical mechanisms responsible for the origin of these star-grazing comets. Among various ideas, a model involving mean-motion resonances with a jovian-like planet was proposed a few years ago and applied to the beta Pictoris case (H. Beust and A. Morbidelli 1996 Icarus 120, 358-370). According to this model, the 4:1 and possibly the 3:1 mean-motion resonances are able to generate numerous star-grazers from an initially dynamically cold disk of planetesimals. In this paper, detailed numerical simulations of this dynamical process over a large number of particles are presented, showing in particular that the model is robust toward the presence of additional planets around the star. The question of the evaporation rate of the comet-like bodies is also investigated, showing that, in order to explain the observed spectral events, the comet-like bodies should be larger than 10-20 km, rather than 1 km as previously conjectured. This in turn makes it possible to estimate the typical density of the planetesimal disk required to explain the observed spectral phenomena, i.e., similar to 10(8) bodies per astronomic unit in the resonance at 4 AU from the star. Apart from the main redshifted spectral events, a few blueshifted events were observed over the past few years. These spectral events are clearly distinct from the main redshifted ones and cannot be considered as outliers, although they are far less numerous. Tn the simple framework of the mean-motion resonance model, these events, which should correspond to bodies moving on differently oriented orbits, should not be expected. We show that assuming the presence of a terrestrial-like planet, well inside the orbit of the jovian planet, may generate these additional events. Close encounters with a terrestrial planet may extract some particles from the resonance, and bring some of them to star-grazing orbits, but with a different orbital orientation so that they generate blueshifted events. The question of the refilling of the resonance is investigated. Two basic models may be invoked: First, collisions among planetesimals may replenish the resonance. This appears to be possible, but the mass density of the planetesimal disk in the vicinity of the resonance needs to be similar to 10 M+ per astronomic unit or more, which is hardly realistic. Planetary migration may be a second possible mechanism. A migrating resonance can capture new bodies as it sweeps the disk. We show that this model is realistic only if the migration velocity is high enough, i.e., compatible with models invoking a tidal interaction with the disk, but the reality of this mechanism in the beta Pictoris disk must be questioned. (C) 2000 Academic Press.
