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Astron. Astrophys. 363, 1155-1165 (2000)

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1. Introduction

The characteristics of circumstellar and interstellar dust grains depend generally on three sets of parameters. Each set of parameters is necessary to describe each characteristic of the grains: their size, morphology and composition. These parameters are determined by comparison between observations and theoretical models (Lafon & Berruyer 1991). In general, these parameters cannot be derived directly from observations, and there remain partly adhoc free parameters in theoretical computation of optical properties of grains (extinction, absorption and scattering cross sections, and also, polarization of light radiated by dust). Among these optical properties, the scattering efficiencies and the degree of polarization are very sensitive to the structure and shape of the grains (Bohren & Huffman 1983).

Several approaches have been proposed to model dust grains. One of the most often applied models consists of a power-law size distribution of homogeneous spherical and bare grains of different materials (Mathis et al. 1977, hereafter MRN). Unfortunately, we cannot expect grains formed under complicated processes to be spherical or to have a regular shape. More recent models use inhomogeneous grains in shape and/or composition, for example core/mantle grains (Hagen et al. 1983) or porous grains. The latter are thought to be formed through coagulation rather than by accretion (Mathis & Whiffen 1989), which implies a high level of porosity of the grains. Principal models of these grains are grains with random inclusions (e.g. Wolff et al. 1994; Lumme & Rahola 1994; Perrin & Sivan 1991), although fractal models are sometimes preferred (e.g. Ossenkopf 1993; Stognienko et al. 1995; Kozasa et al. 1993).

To calculate the optical properties of such grains, two approximations are currently available. One is the Discrete Dipole Approximation (DDA) introduced by Purcell & Pennypacker (1973), and improved by Draine (1988). In this model, the grain is replaced by a set of electric dipoles which are macroscopic compared to atoms and microscopic compared to the size of the grain. The other approximation is Effective-Medium Theories (EMT) where the dielectric functions of the porous grain is replaced by an effective function, see for example Bohren & Huffman (1983). As the latter approximation is not suitable to describe the special effect of grain morphology and in particular, surface roughness (Ossenkopf 1991), we use the DDA to study the effect of shape of grains.

On the other hand, porous grains as well as fractal aggregates have a fluffy structure but a rough surface that has to be taken into account in calculations of the scattering properties of the grains (Ossenkopf 1991). Moreover, porous internal structure can modify the measured dielectric functions of the grains compared to the optical bulk constants. In order to fully separate the effects of internal structure from the effects of shape, we keep the size and composition of grain constant to study in detail the effect of surface roughness on the linear polarization of the scattered light of an initially spherical grain.

A review of previous work on roughness and a description of our approach to the problem is given in Sect. 2. In Sect. 3, we review the characteristics of the model (DDA) used for our statistical simulations and emphasize why it is convenient for our study. We also describe the roughness modeled. In Sect. 4, we present in detail the new statistical method applied: a Gaussian kernel method from which we deduce the probability density function of the polarization which characterizes some typical roughness of grains. We display and discuss our results obtained for one wavelength where water ice is non-absorbing. Sect. 5 is devoted to a general conclusion including possible development of this approach.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000