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]SiO), olivine ([Fe,Mg]
SiO
), 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)
,
``normal'' silicates (NRM) with Fe/(Fe+Mg)
, and
``iron-poor'' (IPS) silicates with Fe/(Fe+Mg)
. 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
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 therein). We suppose that destruction of
dust materials occurs in a narrow range of temperatures (
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,
K. Thus, we account for six principal temperature regions:
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
gcm
).
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
,
, and
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 (m -
m) 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.