Dynamics of the Solar System Meteoroid Population
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The purpose of this study is to develop an understanding of the observability of small-scale dynamical Solar System features in meteor orbit radar data, particularly with reference to mean motion resonance effects. Particular focus is placed on the presence of `resonant swarms' in meteoroid streams: the resonant swarm at the 7:2 Jovian mean-motion resonance is used as an example, as it best satisfies radar observability criterion. Furthermore, evidence for this structure exists in visual meteor data. The radar dataset used for this study is that of the Canadian Meteor Orbit Radar (CMOR) as this dataset contains the largest number of meteoroid stream particles. The aim here is to determine whether the Taurid resonant swarm is observable in datasets produced by radars such as CMOR, or what improvements in individual orbital uncertainties are necessary for positive detection to be possible.
The observability of the Taurid swarm in radar data depends on the limitations of the radar data (in terms of the individual measurement uncertainties); and on the properties of the resonance itself. Both aspects are investigated in this thesis. A statistical study is first conducted to assess whether evidence for the swarm exists in a dataset containing CMOR Northern and Southern Taurids from the years 2002 to 2007. It is found that the level of variations present is consistent with that expected due to random fluctuations: there is no evidence for a statistically significant resonant feature at the location of the 7:2 Jovian resonance. Additionally, the observability of various sizes of resonant peak for different sizes of dataset and for different levels of measurement uncertainties is investigated by addition of a modelled resonant feature to the data, followed by replacement of individual meteors by Gaussian profiles to simulate the effect of orbital uncertainties. It is clear that the level of broadening resulting from the uncertainties of the CMOR data used will not allow the observation of a resonant peak of the expected size. Detection is expected to be more likely in a `swarm encounter year' (a year in which the geometry between the resonant swarm and Earth is favourable to detection). The velocity uncertainties of a meteor orbit radar (similar to CMOR) need to be improved by a factor of 5 to 10 (relative to the CMOR uncertainties) in order to detect a resonant swarm that is composed of ~30% to ~5% (respectively) of the total number of observed Taurids in a swarm encounter year. An improvement significantly greater than a factor of ~10 is unlikely to result in a significant improvement in the ability to detect the resonant swarm. It is expected that a factor of 10 improvement in radar measurement uncertainties is achievable with the current techniques of radar systems and signal processing.
These statistical tests require knowledge of the resonant width of the 7:2 Jovian resonance in semi-major axis, as this provides the size of the resonant feature of interest. Such resonant or libration widths can be determined analytically for orbits with low eccentricities. As Taurid orbits have high eccentricities (e~0.83), a hierarchical N-body integrator is used to examine the dynamics in the region of the 7:2 resonance, and determine a resonant width of (0.047±0.005) AU. To verify this method the standard analytic equations and a semi-analytic method are compared (at low eccentricities) with the numerical resonant width values: the agreement is within 10% for eccentricities below 0.4.
It is important to know what proportion of radar Taurids are expected to be resonant in a swarm year in order to evaluate the observability of the swarm in radar data. One important factor that may affect this is the mass distribution of particles in the swarm. This is investigated by ejecting particles in multiple directions from three model comets: the first with a mass and orbit in agreement with those of the current 2P/Encke; the second with 2P/Encke mass and an orbit matching that of the proposed proto-Encke object; and a third with the mass and orbit of proto-Encke. The resulting orbits are examined to determine what proportion will land within the 7:2 resonance, for a range of particle masses and densities. The instantaneous effect of radiation pressure on the orbits of ejected particles is also considered. However, it is difficult to determine accurate capture percentage values due to the uncertainty surrounding cometary ejection mechanisms. Nevertheless, it is found that capture of Taurids into the 7:2 resonance by all comets is possible. Using comparisons between the percentages of visual-sized and radar-sized particles captured, it is determined that in weak swarm years (in which only 20% of visual meteoroids detected are resonant) only 4% to 5% of observed visual Taurids are expected to be resonant. Such a swarm would be on the edge of observability. However, in stronger swarm years (such as 2005), the resonant proportion will exceed that required for detection with a reduction in CMOR measurement uncertainties of a factor of ten.