Quasi‐Stationary States of Dust Flows under Poynting‐Robertson Drag: New Analytical and Numerical Solutions

Abstract

The effect of solar or stellar radiation on dust particles' trajectories (the Poynting-Robertson drag) has been studied by a number of authors and applied to interplanetary dust dynamics in numerical computations. Meanwhile some important features of dust flows can be studied analytically by implementing our novel hydrodynamical approach to use the continuity equation written in the particle's orbital elements as coordinates (Gor'kavyi, Ozernoy, & Mather 1997). By employing this approach and integrating the continuity equation, we are able to find two integrals of motion when the Poynting-Robertson drag dominates the dissipative forces in the dust flow. These integrals of motion enable us to explore basic characteristics of dust flows from any sources in the Solar system (such as asteroids, comets, Kuiper belt, etc.) or in another planetary system. In particular, we have reproduced the classical solution n(r) ∝ r −1 that approximately represents the overall distribution of dust in the Solar system. We have also investigated various factors that could be responsible for the deviations of the power law index in n(r) ∝ r δ from δ = −1, including the influences of the orbital characteristics of dust sources, the evaporation of dust particles, as well as mixtures of dust particles of both asteroidal and cometary origin. We have calculated the masses and number densities of asteroidal and cometary components of the zodiacal cloud at different distances from the Sun.Subject headings: interplanetary medium -infrared: solar system

Microwave thermal emission from the zodiacal dust cloud predicted with contemporary meteoroid models

“…The flux of meteoroids with m > 10 −5 g is lower in IMEM than in the Grün model since the impact velocities of big meteoroids are higher at 1 AU from the Sun in IMEM and they produce larger craters on the lunar rocks than in the Grün model, which assumed a single impact velocity for all meteoroid sizes. evolutionary paths (Gor'kavyi et al 1997). Their distributions are also established theoretically in IMEM, with the normalization factors being inferred from the fit to observations.…”

“…One would expect a similarly shaped "edge-brightened" radial density with the peaks at the perihelion and aphelion distances of the parent body orbit (e.g., Sect. 3 in Gor'kavyi et al 1997). However, the dust in asteroid bands is proven to be migrating toward the Sun under the PoyntingRobertson drag; Reach (1992) has demonstrated that the temperatures of particles and parallaxes of the bands measured from the moving Earth are both higher than those expected in the respective asteroid families of their origin, implying that the bands extend farther toward the Sun than their ancestor bodies.…”

“…The orbital distributions of meteoroids more than 10 −5 g in mass are constructed by counting the numbers of catalogued asteroids per orbital space bins. The orbital distributions of meteoroids less than 10 −5 g in mass are described as the flow of particles along the Poynting-Robertson evolutionary paths (Gor'kavyi et al 1997) starting from the source distributions defined earlier. The mass distributions are adopted from the interplanetary meteoroid flux model by Grün et al (1985) for each mass range as shown in Fig.…”

Indicator of Exo-Solar Planet(s) in the Circumstellar Disk Around β Pictoris

“…In the absence of a planet, the surface density of dust between the star and the pericenter of dust sources is constant, while the number density of dust varies as r-1 , r being heliocentric distance (Gorkavyi et al 1997). The presence of a planet induces dramatic changes in the cometary and dust distribution.…”

Wavelike Patterns in Precessing Elliptical Rings for Swarming Systems

“…Moreover, Gor'Kavyi et al [9,10] used a continuum approach in orbital element space serving as a tool to analyse the transport of interplanetary dust grains as well as their long-term dynamical evolution.…”