Temperature dependence of specific heat capacity and its effect on asteroid thermal models

Measured (Robie et a/., 1978)
Fayalite (at 320 K)	600 J/kg/K
Forsterite (at 1000 K)	970 J/kg/K
H chondrite (at 1100 K)	800 J/kg/K
H chondrite (at 300 K)	630 J/kg/K

*Thermal models in literature (for asteroids, unless otherwise mentioned)

same as enstatite). Values of cP computed from Robie et al. ( 1978) were then converted to cv using Eq. (1) from Navrotsky (1994). Figure la,b summarizes the temperature dependence of specific heat capacities of the major minerals in chondrites and of the three classes of ordinary chondrites, respectively. Because the purpose of this paper is to evaluate the effect of the temperature dependence of specific heat capacity, we have assumed the same Al abundance per unit mass ( l.13 wt%) for different chondrite compositions. In reality, the absolute abundance of Al varies among various chon­ drites, causing some differences in thermal histories (Ghosh and Mcsween, 1998).

RESULTS

Figure 2 shows the temperature-time profiles at depths of 100 km (i.e., the asteroid center, Fig. 2a,b), and 6 km (Fig. 2c,d). Figure 2a,c shows profiles for different constant values of specific heat capacity, whereas Fig. 2b,d shows results for the various ordinary chondrite classes after taking the temperature and compositional dependence of specific heat capacity into account. Note the diverse thermal histories produced by using different constant values of cv. At the center of a 100 km asteroid (Fig. 2a), the range of values of cv in the literature produce peak temperatures

varying from 1123 K (cv = 600 J/kg/K) to 707 K (cv = 1200 J/kg/K),

a difference of 416 K. At a depth of 6 km from the surface (Fig. 2c), the peak temperatures range from 989 K ( cv = 600 J/kg/K) to 645 K (cv = 1200 J/kg/K), a difference of 344 K. Thus, a mere difference in a single parameter can produce a spectrum of thermal scenarios at the center of the asteroid and in its near-surface layers. In comparison, a temperature- and composition-dependent function of specific heat capacity yields peak temperatures within a narrow

temperature range of <50 K for different ordinary chondrite compositions (Fig. 2b,d). Other than providing a more realistic output to the thermal model, the use of temperature- and composition-dependent specific heat capacity helps us to appreciate subtle differences in thermal histories produced due to a difference in composition. Figure 2b,d shows that H chondrites should attain higher peak temperatures compared to L and LL chondrites. This should result (provided all thermal parameters for the ordinary chondrites are identical) in H chondrites displaying a greater abundance of higher petrologic types compared to lower petrologic types. However, in reality, the slightly lower Al abundance in H chondrites, compared to L and LL chondrites, may offset this effect.

Thermal models typically try to match peak temperatures and chronologic data from meteorites to the output of thermal models (e.g., Wood and Pellas, 1991; Bennett and McSween, 1996), as tests of the models' validity. Table 2 shows peak temperatures and computed isotopic closure ages obtained at depths of I 00 km and 6 km. The closure temperature of Pb-Pb ages is approximated at 727 K (Gopel et al., 1994) and of Rb-Sr and Ar-Ar ages is approximated at 570 and 500 K, respectively (Wood and Pellas, 1991, and references therein). Metallographic cooling rates and fission track retention measure cooling rates in the range 870--670 K (e.g., Lipschutz et al., 1989, and references therein). Because this entire temperature range (870--670 K) was not encountered at all depths in each of our runs, we have computed instantaneous cooling rates from the slopes of the time-temperature curves at specific temperatures (see below).

It is necessary to clarify that we use ordinary chondrite parent bodies in our simulation simply to demonstrate that the temperature dependence of specific heat capacity has an appreciable effect in

Q-1100

Ci

....,¹⁰⁰⁰

c

= 900