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

RELEVANCE TO PROBLEMS IN PLANETARY SCIENCE

The use of specific heat capacity as a parameter in thermal modeling is not limited to asteroids. A wide spectrum of planetary science scenarios, such as crystallization of the lunar magma ocean, cooling of materials in thick ejecta blankets, and the thermal histories of larger planetary bodies (see Table 1) employ specific heat capacity as a parameter. In assessing the temperature increase resulting from the Earth's collision with a Mars-size impactor, Melosh ( 1990) assumed a constant heat capacity but acknowledged that this parameter had a significant temperature dependence. Although the present study concerns itself with the effects of variable specific heat capacity on asteroidal thermal history, the same basic laws of heat transfer would apply to all thermal models. Because heat conduction and radiation are very slow, it follows that specific heat capacity is second in importance only to the term for heat generation in the heat transfer equation. Although the heat source determines the amount of heat supplied, the specific heat capacity determines the change in temperature. Thus, it is ironic that although there has been considerable work to constrain the amount and distribution of live 26Al in the early solar system ( e.g., Russell et al., 1996; MacPherson et al., 1995, and references therein), which in effect constrains the heat generation term, there has been surprisingly little work on measurement of specific heat

capac1t1es of minerals found in meteorites. Robie et al. ( 1978) produced a detailed compilation of specific heat capacities of selected minerals and their variation with temperature. Yomogida and Matsui (1983) measured thermal conductivity, density and thermal diffussivity in selected meteorites from which cp can be calculated. Otherwise, there has been no recent work that addresses the temperature dependence of specific heat capacity of common minerals phases found in meteorites or the variation of specific heat with degree of crystallinity or change of the proportion of cations in solid solution minerals. In thermal models, the effect of specific heat capacity has been understated. Table 1 notes that most workers have used constant values of specific heat capacity, whereas others have not mentioned the value of specific heat capacity in their publications (which speaks to the perception of specific heat capacity as a parameter with negligible effect in modeling). This work shows that specific heat capacity is a crucial parameter in asteroidal modeling and points out why it is important to use temperature- and composition-dependent specific heat capacity for accurate results. The paucity of experimental data calls for greater work in this area, which could help constrain thermal models.