Methods for computing comet core temperatures.

Abstract

General analytic expressions are derived that relate the surface temperature to the temperature deep within the nucleus of a spherically symmetric layered comet in thermal equilibrium. The relation between the average surface temperature and the mean temperature at great depths depends entirely on the temperature dependence of the thermal conductivity. The core temperature is given by the inverse of the anti-derivative of the thermal conductivity, with respect to temperature, operating on the average value of the anti-derivative of the thermal conductivity evaluated at the surface temperature. Using these expressions detailed numerical models of the surface temperature of comets can be used to directly estimate the core temperature. For the special, albeit unphysical, case of an isothermal, low-conductivity comet nucleus, without sublimation, the core temperature can be determined analytically. To illustrate the dependence of core temperature on eccentricity this simple case is solved assuming that the temperatures dependence of the thermal conductivity is given by that of crystalline ice. For an eccentricity of approximately 0.5, the core temperature obtained is 3% colder than the corresponding value obtained assuming constant thermal conductivity an is 11% colder than the result of Klinger's (1981) formula. This method is also applied to a detailed numerical model with a complicated nonintegrable thermal conductivity.