Medium-sized icy satellites: thermal and structural evolution during accretion

The evolution of internal parameters (pressure, temperature, density, porosity) characterizing a satellite during accretion is calculated. Growth of the satellite occurs by capture of icy and rocky grains and thus a satellite in its young stage represents an icy/rocky regolith ball with nonzero porosity. The accretion period covers a time interval from the embryo stage of a satellite until it is almost completely formed (when it reaches nearly its present mass). The accretion period is assumed to be a free parameter in the range from 10 3 to 10 6 years; within this range there are the most of the results provided by the different theories. Thus the model discussed at present covers at most a fraction 10 6/4.5 × 10 9 = 0.02% of the time of existennce of a satellite. The mass increase rate of the satellite is assumed to be a known function of time. Apart from accretion time, the second free parameter of our model is the steepness of the accretion curve. A satellite is assumed to be a heat conducting and nonconvecting spherical body. The equations of internal structure are those of mass conservation, of energy transfer, of porosity decrease rate (the rheological equation), and material equations (for specific heat and for thermal conductivity). The rheological equation is based on our experiments concerning time-dependent compressibility of icy/rocky granular mixtures at 2.3–17.7 MPa and 140–262K. The aim of our calculations is to find the porosity distribution within the satellites during their formation until the moment when accretion is completed. It is possible to combine the presented model with one concerning the post-accretional evolution of a satellite. From this point of view our final results can be considered as the initial conditions for studying the post-accretional evolution of the satellites. The definitive results concern Mimas, Miranda and Enceladus with radii 199,236 and 252 km, respectively. Comparison of the porosity distributions, in the interior of these satellites just immediately after their formation shows that the porosity is very important for the smallest satellites, especially if their formation temperature was low.