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Grain sizes and compositional model

We use the solar elemental abundances for all elements from the compilation of Anders & Grevesse ([1989]) and for carbon from Grevesse et al. ([1991]). Essentially the same dust composition is adopted as described in PHB. This model is defined on the basis of an accurate analysis of a wide range of theoretical, laboratory, and observational dust data. Given that, it has been used in the modelling of the evolution of accretion discs around young stellar objects or estimations on their mass from millimeter observations (e.g., D'Alessio, Calvet, & Hartmann [2001]; Greaves et al. [1998]; Jura & Werner [1999]).

The main dust constituents include amorphous pyroxene ([Fe, Mg]SiO3), olivine ([Fe,Mg]2 SiO4), volatile and refractory organics (CHON material), amorphous water ice, troilite (FeS), and iron1. As in HS, we vary relative iron content in the silicates considering “iron-rich” (IRS) silicates with Fe/(Fe+Mg) = 0.4, “normal” silicates (NRM) with Fe/(Fe+Mg) = 0.3, and “iron-poor” (IPS) silicates with Fe/(Fe+Mg) = 0. However, the absolute amount of metallic iron in all models is kept constant, which leads to the absence of solid iron in first case and enhanced mass fraction of Fe in third case. Such a variety of silicate models allows us to study the influence of iron distribution within the grain constituents on the extinction properties of dust. Another reason is that the exact mineralogical composition of the silicates in the protostellar clouds and protoplanetary discs is poorly constrained and can be different for various environments. Compared to HS, we re-estimated the absolute abundances of the silicates, iron, and troilite by chemical equilibrium calculations. The mass fractions of all dust constituents and their densities are quoted in Table 1 (see also Table 2  in PHB). Note the difference between the iron mass fractions in the different dust models.

The sublimation temperatures of the grain constituents are adopted from PHB (see Table 3  therein). We suppose that destruction of dust materials occurs in a narrow range of temperatures (z 10 –30 K). Given that the evaporation of the silicates and iron happens at approximately the same conditions, we do not distinguish between their evaporation temperatures and assume that they evaporate in one temperature range, DT  z 100 K. Thus, we account for six principal temperature regions:

  1. T  <  155  K - all dust constituents are present;

  2. z 165 K < T  <  270  K - no ice;

  3. z 280 K < T  <  410  K - no ice and volatile organics;

  4. z 440 K < T  <  675  K - silicates, iron, and troilite are present;

  5. z 685 K < T  <  1500 K - silicates and iron are present;

  6. T  <  1500 K - gas-dominated opacities;

We take into account the dependence of the evaporation temperatures of ice, silicates, and iron on gas density (the values shown above are given for a density z 10–10  gcm–3).

We assume that for the fifth temperature region the absolute amount of solid iron raises due to the destruction of troilite. The corresponding mass fractions of metallic iron are 6.15 x 10–4 , 2.42 x 10–4 , and 1.29 x 10–3 for NRM, IRS, and IPS silicate models, respectively.

As for the size distribution, we apply a modified MRN (Mathis et al. [1977]) function suggested by Pollack, McKay, & Christofferson ([1985]). The modification consists of the inclusion of large (0.5µm - 5µm) dust grains. Such particle growth is expected to proceed efficiently at the early phases of the protoplanetary disc evolution due to the coagulation of small dust grains (see, for instance, Mizuno, Markiewicz, & Voelk [1988]). We do not consider other size distributions since the overall effect of the particle sizes on the dust opacity is well studied (e.g., Pollack et al. [1985]; Beckwith, Henning, & Nakagawa [2000]). It further allows us to compare directly our results with other works.


next up previous
Next: Grain structure and topology Up: Dust opacities Previous: Dust opacities
Dimitri Semenov 2003-03-10