Fractal signatures in analogs of interplanetary dust particles

https://doi.org/10.1016/j.jqsrt.2014.01.017Get rights and content

Highlights

  • We analyze the morphology of cosmic dust aggregates using a structure factor technique.

  • These aggregates are mass fractals with a fractal dimension of −1.75.

  • The same fractal dimension (−1.75) is found for diffusion limited aggregation aggregates.

  • Laboratory analogs of cosmic dust are thus formed by an aggregation of small particles.

Abstract

Interplanetary dust particles (IDPs) are an important constituent of the earth׳s stratosphere, interstellar and interplanetary medium, cometary comae and tails, etc. Their physical and optical characteristics are significantly influenced by the morphology of silicate aggregates which form the core in IDPs. In this paper we reinterpret scattering data from laboratory analogs of cosmic silicate aggregates created by Volten et al. (2007) [1] to extract their morphological features. By evaluating the structure factor, we find that the aggregates are mass fractals with a mass fractal dimension dm1.75. The same fractal dimension also characterizes clusters obtained from diffusion limited aggregation (DLA). This suggests that the analogs are formed by an irreversible aggregation of stochastically transported silicate particles.

Introduction

Fractal geometries provide a description for many forms in nature such as coastlines, trees, blood vessels, fluid flow in porous media, burning wavefronts, dielectric breakdown, diffusion-limited-aggregation (DLA) clusters, bacterial colonies, and colloidal aggregates. [2], [3], [4]. They exhibit self-similar and scale-invariant properties at all levels of magnification and are characterized by a non-integer fractal dimension. These features arise because the underlying processes have an element of stochasticity in them. Such processes play an important role in shaping the final morphology, and their origin is distinctive in each physical setting.

Irregular and rough aggregates have also been observed in the astronomical context. Naturally found cosmic dust aggregates, known as interplanetary dust particles (IDPs), are collected in earth׳s lower stratosphere. They are formed when dust grains collide in a turbulent circumstellar dust cloud, such as the solar nebula, and are an important constituent of the interstellar medium, interplanetary medium, cometary comae and tails, etc. Mass spectroscopy analysis of IDPs has revealed that their primary constituents are (i) silicates of Fe, Mg, Al and Ca, (ii) complex organic molecules of C, H, O and N, (iii) small carbonaceous particles of graphite, coal and amorphous carbon and (iv) ices of CO2, H2O and NH3 [5], [6], [7], [8], [9]. Among these, there is an exclusive abundance of silicates which aggregate to form particle cores. They have been described as fluffy, loosely structured particles with high porosity. The other constituents contribute to the outer covering or the mantle and are usually contiguous due to flash heating from solar flares and atmospheric entry [10]. The core, being deep inside retains its morphology. The latter is believed to have a fractal organization characterized by a fractal dimension, but this belief is not on firm grounds as yet [11], [12]. As the core morphology affects the physical and optical characteristics of IDPs, its understanding has been the focus of several recent works [13], [14], [15], [16], [17], [18].

Two classes of stochastic fractals are found in nature. The first class is that of surface fractals whose mass M scales with the radius of gyration R in a Euclidean fashion, i.e., M~Rd, where d is the dimensionality. However, the surface area S increases with the radius as S~Rds, where ds is the surface fractal dimension and d1ds<d [19]. Interfaces generated in fluid flows, burning wavefronts, dielectric breakdown and deposition processes are examples of surface fractals. The second class is that of mass fractals which obey the scaling relationship, M~Rdm, where dm is the mass fractal dimension and 1dm<d. Examples of mass fractals are DLA clusters, bacterial colonies and colloidal aggregates. Further, in many situations, mass fractals are bounded by surface fractals [2], [3], [4]. As a matter of fact, the above mass fractals belong to this class.

There are many unanswered questions in the context of fluffy cores or silicate aggregates of IDPs. For example, are they mass fractals, bounded by surface fractals? What is their mass and surface fractal dimension? What kind of aggregation mechanisms are responsible for this morphology? What are the consequences of fractal organization on the evolution of clusters? In this paper, we provide answers to some of these questions using the real-space correlation function C(r) and the momentum-space structure factor S(k). Smooth morphologies are characterized by the Porod law [20], [21]. The signature of fractal domains and interfaces is a power-law decay with non-integer exponents in C(r) and S(k). As typical experimental morphologies are smooth on some length scales and fractal on others, the behaviors of C(r) vs. r and S(k) vs. k are characterized by cross-overs from one form to another. We identify these features in laboratory analogs of cores of IDPs created by Volten et al. using magnesio-silica grains, by reinterpreting their light-scattering data [1]. We find that these aggregates are mass fractals with a fractal dimension dm1.75. The same fractal dimension characterizes diffusion limited aggregation (DLA). We therefore infer that aggregation mechanisms of silicate cores in IDPs are stochastic and irreversible as in DLA.

This paper is organized as follows. In Section 2, we describe the tools for morphology characterization and their usage to obtain mass and surface fractal dimensions. In Section 3, we describe the experimental analogs of silicate cores in IDPs and obtain the structure factor from their light scattering data to extract fractal properties. In Section 4, we present a simulation of the DLA cluster, and the evaluation of its structure factor and the corresponding mass fractal dimension. Finally, we conclude with a summary and discussion of our results in Section 5.

Section snippets

Tools for morphology characterization

A standard tool to obtain information about sizes and textures of domains and interfaces is the two-point spatial correlation function [21]C(r)=ψ(ri)ψ(rj)ψ(ri)ψ(rj),where ψ(ri) is an appropriate order parameter and r=|rirj|. (We assume the system to be translationally invariant and isotropic.) The angular brackets denote an ensemble average.

The scattering of a plane wave by a rough morphology can yield useful information about the texture of the domains and interfaces in it.

Analysis of silicate cores

We now investigate the morphological characteristics of silicate cores using the correlation function and the structure factor. As real samples are scarce, it has been customary to create them in the laboratory using a condensation flow apparatus followed by flash heating to mimic the environment required for the formation of cosmic silicates and circumstellar dust. A significant contribution in this context is the work of Volten et al. [1]. They created a variety of magnesio-silica samples

Diffusion limited aggregation

A relevant question now is: What kind of mass-transport mechanisms leads to fluffy aggregates with dm1.75? To answer this question, we create aggregates of particles using the DLA model. We performed this simulation on a cubic lattice adopting the algorithm introduced by Meakin [27]: (i) A particle is placed at the origin or the center of the cube. (ii) A new particle is released at a distance R from the center and performs a random walk. (iii) On encountering an occupied neighboring site, it

Conclusion

Interstellar dust particles (IDPs) found in the earth׳s stratosphere are an important constituent of cosmic matter. These comprise loosely structured silicate cores or aggregates ensconced in a mantle of organic and carbonaceous compounds [5], [6], [7], [8], [9]. The organization and optical characteristics of the IDPs are greatly influenced by the morphology of the core. In this paper, we have re-interpreted scattering data from laboratory analogs of silicate cores in IDPs created by Volten et

Acknowledgement

The authors would like to thank the anonymous reviewers for their constructive comments that helped to improve the quality of the paper. VB would like to acknowledge the support of DST Grant No. SR/S2/CMP-002/2010.

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