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Thermal conductivity of amorphous ice
was measured and analyzed by Kouchi et al. (1992a) (see also Kouchi
et al., 1992b), and was found to be extremely low. Its value have
been found to be
at temperatures T=125 to
K, which may be compared with the thermal conductivity of crystalline ice
(Klinger, 1975) approximated by
The thermal conductivity of amorphous ice,
, is at least on the order of
times the previous estimate by Klinger (1980), which has been used in many
papers on the thermal history of comets. Furthermore this
is as small as
of the fine particle regolith on the Moon surface, which has one of the
smallest thermal conductivities among natural materials.
To see how low the
is, let us estimate heat conduction time scales in amorphous ice. The time
t for heat to reach distance R by conduction is estimated
from
where
and
are density and specific heat per unit mass of amorphous ice, respectively.
The value of
is on the order of
at
K. For
km, size of a small cometary nucleus, we have
yr, comparable with the age of the solar system (
yr). Even for a body as small as
cm, the time required is
yr! This indicates that amorphous ice is an extremely good thermal insulator.
Corresponding to the small conductivity, the sound speed
is also very small. Sound speed
is related to the thermal conductivity as
where
is phonon mean free path in amorphous ice. The smallest estimate of
is a few Å, size of an H
O molecule. Thus
should be