An idealized short-period comet model: Surface insolation, H2O flux, dust flux, and mantle evolution

Abstract

A model of cometary activity is developed which integrates the feedback processes involving heat, gas, and dust transport, and dust mantle development. The model includes the effects of latitude, rotation, and spin axis orientation. Results are obtained for various grain size distributions, dust-to-ice ratios, and spin axis orientations. Attention is focused on the development, change of structure and distribution of dust mantles and their mutual interaction with ice surface temperature and gas and dust production. In this model the dust mantle controls the mechanism of gas transport not onlu by its effect on the temperature but, more importantly, by its own dynamic stability. Results suggest that an initially homogeneous short-period comet with a “cosmic” dust-to-water ice ratio, typical orbit, rotation rate, and grain size distribution would develop at most only a thin (<1 mm) cyclic mantle at all points on the nucleus. Such a fully developed temporary mantle would exist throughout the diurnal cycle only beyond ∼4AU. Thus, cyclic behavior would be expected for such an idealized comet, at least for most of its lifetime. Long-term irreversible mantle development on comets with typical rotation rates was not found except regionally on Encke and also on objects with perihelia ≳1.5 AU. Even in these cases, free silicate exists, after a few cycles, only as relatively rare large grains and agglomerates with radii ∼1 cm scattered over exposed ice. Full mantle development would require hundreds to thousands of cycles. In the case of an initially homogeneous comet Encke, this slow incipient mantle development is shown to be the direct result of its peculiar axial orientation. High obliquity appears required for long-term mantle development for typical rotation rates and perihelia ≲1.5 AU. Heat conduction into the nucleus for an incompletely mantled or bald comet has been found to be very important in maintaining relatively higher ice surface temperatures, and hence fluxes, during those portions of the diurnal and orbital cycles which would otherwise be cooler. It is also shown to be at least one cause of post perihelion brightness asymmetries, especially in lower obliquity comets. Maximum heliocentric distances at which 1-μm dust, sand, pebbles, cobbles, and boulders can be permanently ejected from the subsolar point by H2O (CO2) are (in AU): 6.9 (16.8), 5.2 (11.5), 1.8 (3.0), 0.21 (0.34) and 0.07 (0.11), respectively. A detailed anatomy of temperature, gas and dust fluxes vs latitude and longitude for a homogeneous rotating comet with fixed axis is given for comparison with future observations. Most H2O flux histories deduced from brightness data are found to be in reasonable agreement with the model, allowing for uncertainty in radius and albedo. A clear exception is Encke. It is shown that the large discrepancy between Encke's observed and model predicted fluxes, based on radar cross section, can be used to evaluate the extent of exposed ice (<10%). The model is then used to place an active area so as to explain a reported sharp drop in flux on approach to the Sun at 0.78 AU. An active area or areas, <10% of the comet's surface, centered near 65°N latitude appears indicated. Although cyclic mantles are generally indicated for the set of parameters we used, our results show that a global mantle only 1 to 3 cm thick (depending on the orbit) consisting of a full range of grain sizes can cause irresversible evolution to a noncometary body. We investigated the long-term evolution of such a postulated initially thinly mantled cometary object. It was found that after the first few passes and until the end of its dynamic lifetime the object averaged <3 × 10−12 g cm−1 sec−1 H2O flux. Therefore, if cometary objects evolve into Apollo asteroids, ice should always be accessible within 10 m of the surface despite numerous close perihelion passages. The possible impact of factors not included in the model, such as initial inhomogeneities, coma scattering of radiation, and global redistribution of ejected silicate around the nucleus, are discussed.