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heat of crystallization Up: Key
Physical Quantities in Previous: Thermal
conductivity of an
Radioactive nuclides contained in silicate cores of grains heat a cometary
nucleus when they decay. We assume that cometary silicate has similar abundance
of radioactive nuclides as that of carbonaceous chondrites, which are believed
to be one of the most pristine materials in the solar system (see Jessburger
in this volume). Then the major species that contribute the heating are
K,
Th,
U, and
U. Table 4 lists their initial abundance
(i.e. abundance at the time of formation of the solar system), decay
rate
(i.e. the probability of decay per unit time), and heat H
released at decay per unit mass together with the heating rate
per unit mass of the silicate.
It should be noted in Table 4 that
K has the largest heating rate
, and contributes most to the radiogenic heating when
Al is not taken into account.
To see the effect of the radiogenic heating, let us estimate the temperature
increase
when heat conduction is ignored. Denoting specific heat of a cometary nucleus
by
, we have
as:
for
, a typical value for slicates. This estimate indicates that, though only
a small amount of heat is released per year, the radioactivity can heat
a cometary nucleus to very high temperature for a long time on the order
of
yr if the heat loss is ignored.
Al is another possible heat source if its initial abundance was comparative
with that in Ca-Al rich inclusion found some carbonaceous chondrites. The
relevant data for
Al are also listed in Table 4. The life time
of
Al is as short as
yr from its nucleosynthesis, so
Al must be incorporated within this time interval in order for
Al-heating to be effective; otherwise
Al would decay in the gas phase or in the grains before incorporation into
a cometary nucleus. In the following discussion, we shall ignore
Al. See Haruyama et al. (1993) for the effect of the
Al-heating under the low thermal conductivity of amorphous ice.