Modeling Extinction and Infrared Emission from Fractal Dust Grains: Fractal Dimension as a Shape Parameter

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Abstract
In astrophysical environments, dust grains are most likely formed by stochastic growth processes, e.g., particle aggregation or cluster aggregation, and should have irregular shapes. Yet spherical grains are often assumed in astrophysical models. We have constructed detailed radiation transport models to study the effects of nonspherical dust grains on the spectra of circumstellar envelopes and interstellar dust clouds. In general, nonspherical grains have larger absorption cross sections at long wavelengths. Being less compact and having lower ratios of volume to surface area, they are generally cooler than their spherical counterparts, typically by 10%-20%. Hence radiation transport models of infrared sources with nonspherical grains would show a shift in the peak flux toward longer wavelengths. Furthermore, the flux ratio of 10 μm to 20 μm silicate emission features decreases for the less compact nonspherical grains. We have also examined the effects of grain shape on a standard model of the interstellar extinction curve. In addition, we find that the error introduced by using bulk optical constants for submicron particles is significantly smaller than that introduced by assuming spherical grains. We have identified, for the first time, fractal dimension D as a shape parameter characterizing the optical, thermal, and radiative properties of dust grains. The fractal dimension D depends on the ratio of volume to surface area and is defined by the relation N(r) ~ rD, where N(r) is the number of monomers within a sphere of radius r. In general 1 < D < 3, and a smaller D implies a more filamentary and less compact grain morphology. For a given mass, grains with the same D, independent of detailed shape, show no significant difference in their absorption cross sections, temperatures, and energy spectra. Hence in modeling phenomena involving irregularly shaped grains, we need to introduce just one parameter, the fractal dimension D, to characterize the shape. There are several important astrophysical implications of removing the unrealistic assumption of spherical grains: (1) determination of dust column density based on models assuming spherical grains would lead to an overestimate; (2) models of the interstellar extinction curve using fractal grains instead of spherical grains would require less elemental depletion, typically by one-third; and (3) in the study of radiation-driven mass loss in evolved stars, both the mass-loss rates and details of outflow dynamics may need to be revised since radiation pressure on dust depends sensitively on the extinction cross sections of newly formed grains.