Affiliation:
1. Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, NL-1098XH Amsterdam, the Netherlands
2. Astronomical Institute, Graduate School of Science Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai 980-8578, Japan
Abstract
ABSTRACT
In protoplanetary discs and planetary atmospheres, dust grains coagulate to form fractal dust aggregates. The geometric cross-section of these aggregates is a crucial parameter characterizing aerodynamical friction, collision rates, and opacities. However, numerical measurements of the cross-section are often time consuming as aggregates exhibit complex shapes. In this study, we derive a novel analytic expression for geometric cross-sections of fractal aggregates. If an aggregate consists of N monomers of radius R0, its geometric cross-section G is expressed as $G=AN\pi R_0^2/[1+(N-1)\tilde{\sigma }]$, where $\tilde{\sigma }$ is an overlapping efficiency, and A is a numerical factor connecting the analytic expression to the small non-fractal cluster limit. The overlapping efficiency depends on the fractal dimension, fractal prefactor, and N of the aggregate, and its analytic expression is derived as well. The analytic expressions successfully reproduce numerically measured cross-sections of aggregates. We also find that our expressions are compatible with the mean-field light scattering theory of aggregates in the geometrical optics limit. The analytic expressions greatly simplify an otherwise tedious calculation and will be useful in model calculations of fractal grain growth in protoplanetary discs and planetary atmospheres.
Publisher
Oxford University Press (OUP)
Subject
Space and Planetary Science,Astronomy and Astrophysics
Cited by
8 articles.
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