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Scientific paper
Apr 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998exdu.work..272h&link_type=abstract
Exozodiacal Dust Workshop, p. 272
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1
Mathematical Models, Zodiacal Dust, Asymmetry, Eccentric Orbits, Cosmic Background Explorer Satellite, Orbital Elements, Orbit Perturbation, Eccentricity, Aphelions, Perihelions, Sine Waves, Ecliptic, Spatial Distribution
Scientific paper
There is a possible connection between structure in circumstellar dust clouds and the presence of planets, our own zodiacal cloud being the prime example. Asymmetries in such clouds could be diagnostic of planets which would be otherwise undetectable. One such feature is an offset of the center of symmetry of the disk with respect to the central star. The offset is caused by the forced eccentricities (ef) of particles in the cloud. The orbit of a particle can be described by a set of five orbital elements: the semi-major axis (a), eccentricity (e), inclination (I), longitude of ascending node (Omega) and the argument of pericenter (omega). In low order secular perturbation theory, osculating elements of small bodies are decomposed into proper and forced elements. The proper elements are dependent on initial conditions while the forced elements are imposed on the particle's orbit by the gravitational perturbations of the planets. This decomposition is still applicable in the presence of drag forces. We compare COBE observations of the variation in average polar brightness of the background cloud, (N + S)/2, with ecliptic longitude of Earth with those of a model cloud made of asteroidal particles which populate the inner solar system according to a 1/rgamma where (gamma) = 1 (Poynting Robertson light drag) distribution. The variation with ecliptic longitude of Earth in mean polar brightness is shown in for the 25 micron waveband. Sine curves are fit to both the COBE observations and the model. The variation in (N+S)/2 with ecliptic longitude of Earth can be represented as a superposition of two sine curves: one for the variation in (N + S)/2 due to the Earth's eccentric orbit and the other for the variation in (N + S)/2 due to the forced eccentricities of particles in the cloud. If the cloud were symmetric about the Sun (i.e., if there were no offset), the maximum and minimum brightnesses of the cloud would occur at perihelion and aphelion, respectively. Looking at the model, one can see that the minimum does occur at Earth's aphelion (282.9 deg). However, the minimum of the COBE curve is clearly displaced from aphelion, showing that the center of symmetry of the cloud is displaced from the Sun. If we could turn off the effect of the Earth's eccentricity, we could isolate the sine curve due to ef. When we do this for the model cloud however, we do not see a variation in (N + S)/2 for two reasons: 1) Although the particle orbits are circularized due to Poynting Robertson drag (PR drag), the wedge shape of the cloud cancels out any number density variation as a function of radial distance; and 2) Even though we would expect the orbits of the particles to be more densely spaced at perihelion than at aphelion (provided all the particles had the same ef and omegaf, due to Kepler's Second Law the particles spend less time at perihelion than at aphelion thus canceling out any noticeable effect on the number density. However, when we build a new model cloud governed by a constant distribution of particles (1/rgamma where gamma = 0) instead of a 1/r distribution, we do see a sinusoidal variation in (N + S)/2 with ecliptic longitude of Earth. These results imply that the particles contributing to the observed offset do not have a PR drag distribution (i.e., they are not simply asteroidal particles). Future work will determine whether cometary particles (having a theoretical gamma = 1.5), collisionally evolved asteroidal particles, or a combination of both types of particles are responsible for the offset of the center of symmetry of the zodiacal cloud.
Dermott Stanley F.
Holmes Elizabeth Katherine
Jayaraman Sumita
Wyatt Mark
Xu Yu-Liang
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