Dynamical Effects from Asteroid Belts for Planetary Systems

The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.Comment: accepted by International Journal of Bifurcation and Chaos in Aug. 2003, AAS Latex, 27 pages with 6 color figure

Testing MSW effect in Supernova Explosion with Neutrino event rates

Flavor transitions in supernova neutrinos are yet to be determined. We present a method to probe whether or not the Mikheyev-Smirnov-Wolfenstein effects occur as SN neutrinos propagate outward from the SN core by investigating time evolutions of neutrino event rates for different flavors in different kinds of detectors. As the MSW effect occurs, the $\nu_e$ flux swaps with the $\nu_x$ flux, which represents any one of $\nu_{\mu}$, $\nu_{\tau}$, $\bar{\nu}_{\mu}$, and $\bar{\nu}_{\tau}$ flux, either fully or partially depending on the neutrino mass hierarchy. During the neutronization burst, the $\nu_e$ emission evolves in a much different shape from the emissions of $\bar{\nu}_e$ and $\nu_x$ while the latter two evolve in a similar pattern. Meanwhile, the luminosity of the the $\nu_e$ emission is much larger than those of the $\bar{\nu}_e$ and $\nu_x$ emissions while the latter two are roughly equal. As a consequence, the time-evolution pattern of the $\nu_e{\rm Ar}$ event rates in the absence of the MSW effect will be much different from that in the occurrence of the MSW effect, in either mass hierarchy. With the simulated SN neutrino emissions, the $\nu_e{\rm Ar}$ and inverse beta decay event rates are evaluated. The ratios of the two cumulative event rates are calculated for different progenitor masses up to $100~{\rm ms}$. We show that the time evolutions of this cumulative ratios can effectively determine whether MSW effects really occur for SN neutrinos or not.Comment: 13 pages, 4 figure

Bifurcation for Dynamical Systems of Planet-Belt Interaction

The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: the one on the inner edge of the belt is asymptotically stable and the one on the outer edge of the belt is unstable. This is consistent with the observational picture of Asteroid Belt between the Mars and Jupiter: the Mars is moving stablely close to the inner edge but the Jupiter is quite far from the outer edge.Comment: AAS Latex file, 31 pages, accepted for publication in International Journal of Bifurcation and Chao