Statistics – Computation
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008phdt.........1q&link_type=abstract
PhD thesis
Statistics
Computation
Circumstellar Debris Disk, Mean Motion Resonances
Scientific paper
This work considers theoretical models of circumstellar debris discs. The main focus is the combination of mean motion resonances between a planet and circumstellar small bodies, which create structures, and collisions among the small bodies, which smear the structures out. It is examined to what degree resonances do influence the collisional behaviour. Instead of the often applied, computer-intensive N-body-simulations we make use of statistical methods, especially the kinetic theory. This requires more effort on the mathematical-analytical side, but involves comparably low computational expense.
In the first part collisional velocities and rates for hypothetical circumstellar debris discs are investigated. Hypothetical especially in the sense that several orbital elements are assumed to be distributed uniformly for simplicity, although observations suggest otherwise. The main focus here is not the analysis of certain, observed discs, but instead the investigation and representation of the influence of a mean motion resonance on the collisional behaviour. The results show, that this influence is much smaller than exspected. The changes of the collisional velocity due to resonance, even a very strong one, are negligibly small. The collisional rate is influenced more strongly. It shows a highly nonlinear dependence and especially develops a maximum. But even for a very strong resonance it increases by less than a factor of 4.
In the second part of this work two models aiming to explain the structures observed in debris discs are developed and compared. One which is based upon the transport of small dust grains by Poynting-Robertson and stellar wind drag forces, and one which is based upon cascade-like collisions of planetesimals residing in a resonance. Both models are analytical ones, they take into consideration the most important effects while being kept as simple as possible at the same time. It turns out that the efficiency of the first scenario depends heavily on the stellar wind, which is most difficult to quantify. Scenario II is determined by the details of the collisional process and the whole collisional cascade.
With the experimental and observational data available today it is not possible to determine if the structures in circumstellar discs originate from the first scenario or second one.
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