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conductivity of amorphous
It has been assumed that a grain in a
cometary nucleus is of silicate core - ice mantle structure, and the ice
is initially amorphous. In the course of the thermal evolution of comets
the amorphous ice may partially crystallize in general. Thus thermal conductivity
of a core-mantle individual grain is a function of thermal conductivities
of amorphous ice, crystalline ice, and silicate, respectively denoted by
,
, and
, the crystalline fraction
, and mass fraction of silicate x:
For small degree of crystallization where
,
may be approximated (Haruyama et al., 1993) by
with the use of eq. (7),
where g is a geometrical factor determined by the ratio of the core
radius to the whole radius of a core-mantle grain, and is on the order
of unity. Note that when
,
is independent of
, and is determined by
and
alone.
Thermal conductivity
of a cometary nucleus as a whole is smaller than the thermal conductivity
of an individual grain
because of the porous structure of the nucleus. Introducng a parameter
which we call a reduction factor, we express the thermal conductivity of
the nucleus
by
where the right-hand-side is an approximation which holds when
.
It is difficult to evaluate
quantitatively, since
depends on the porosity of the nucleus as well as spatial configuration
of grains in the nucleus. It is plausible that
because of highly porous structure of a cometary nucleus. Greenberg et
al. (1989) estimate
on the basis of the assumption that each particle interface is about
of its total area and each particle is in contact with an average of five
particles, as deduced from a model of porosity of 0.8 (Greenberg, 1988).
We take
to 0.5 in the model calculations shown later (Haruyama et al., 1993).