Jacek Leliwa-Kopystynski

Metamorphism of Solar System Ices

This chapter reviews the metamorphic processes of grain growth and densification as they apply to solar system ices. These processes are driven by the thermodynamic constraint of minimum surface energy and their kinetic equations have been studied extensively by material scientists. The application of these equations to solar system ices requires the knowledge of the relevant material parameters. This chapter presents the equations and describes techniques used in compaction experiments. Ice metamorphism explains several observations about various solar system objects and is likely to have played an important role in their internal evolution.

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

Abstract 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.

Kinetics of pressure-induced effects in water ice/rock granular mixtures and application to the physics of the icy satellites

Abstract This paper concerns the rheological experiments on compaction of water ice and water ice/rock samples prepared from granular material. The rock to total mass ratio was C = 0, 0.25, 0.465, 0.5, 1 for five different samples. The temperature was kept constant, T = 213 K, for all experimental runs. The pressure regime, p = 80–820 MPa, is that which is interesting from the point of view of the physics and evolution of the interiors of the icy satellites of the giant planets. The densification rate, (dp/dt)/p, encountered in the experiments decreased from some 10−4s−1 at the beginning of a run to (10−7–10−8)s−1 at the end, some hours later. The densification rate itself mainly represents: (I) the rate of decrease of porosity (dq/dt)/q, when the pressure is relatively low (lower than the phase transition pressure ice I ⇒ ice II, approximately 200 Mpa), and (ii) the kinetics of the phase transitions ice I ⇒ ice II ⇒ ice VI when the pressure exceeds 200 and 600 MPa, respectively. The appropriate formulae were fitted to the experimental data: (i) the formula for the rate of decrease of porosity; it is of the same type as it was established previously for pressure up to 17.7 Mpa (Leliwa-Kopystynski and Maeno. J. Glaciology39, 645–655, 1993); (ii) the formula for the phase transition rate. The experimental results, when extrapolated to lower temperatures, provide date appropriate for the icy/rocky regolith of satellites; it is very plausible that the porous regolith layer extended in the past or it extends even now, to the deep interiors of medium size satellites (Kossacki and Leliwa-Kopystynski, Planet. Space Sci. 41, 729–741, 1993). The kinetics of the phase transitions within the icy component of satellites must influence the convection and differentiation processes and therefore it is related to the tectonics of satellites.

Impact cratering of granular mixture targets made of H2O Ice–CO2 Ice–pyrophylite

Abstract Experiments related to impacts onto three-component targets which could simulate cometary nucleus or planetary regolith cemented by ices are presented here. The impact velocities are from 133 to 632 m s −1 . The components are powdered mineral (pyrophylite), H 2 O ice, and CO 2 ice mixed 1:1:0.74 by mass. The porosity of fresh samples is about 0.48. Two types of the samples were studied: nonheated samples and samples heated by thermal radiation. Within the samples a layered structure was formed. The cratering pattern strongly depended on the history of the samples. The craters formed in nonheated targets had regular shapes. The volume was easy to be determined and it was proportional to impact energy E . The crater depth scales as E 0.5 . Impacts on the thermally stratified target led to ejection of a large amount of material from the loose sub-crustal layer. For some particular interval of impact velocity a cratering pattern can demonstrate unusual properties: small hole through the rigid crust and considerable mass transfer (radially, outward of the impact point) within sub-crustal layer.

Kinetics of compaction of granular ices H2O, CO2 and (NH3)x(H2O)1 −x at pressures of 2–20 MPa and in temperatures of 100–270 K. Application to the physics of the icy satellites

Abstract Experimental studies of compaction of ices are dealt with. They are in the form of granular, then initially porous samples. The ices are: H2O, CO2, and (NH3)x(H2O)1−x. A piston-cylinder device is used. The initial volume of the samples is around 50 cm3. Their initial porosity (prior to compaction) is between 0.2 and 0.4. The duration of one run is 10–15 h. The pressures applied in the experiments are 3.7, 6.55, and 13.1 MPa. Temperature ranges from that of a liquid nitrogen cooling medium (78 K) up to about 270 K for H2O ice, about 195 K for CO2 ice, and about 150 K for water/ammonia ices. A formula for the rate of decrease of porosity q ˙ = − q f ( q , p , T ) exp (−Q/RT) is fitted to the experimental data. It is found that Q = 25 kJ mol−1 for CO2 ice and Q = (39−105x) kJ mol−1 for water/ammonia ices with 0 ⩽ x ⩽ 0.28. The consequences of the kinetics of densification of different ices on the growth of the icy satellite Mimas are discussed.

Compression effects in rock-ice mixtures: an application to the study of satellites

Abstract The behaviour of a porous material consisting of mixed rock and ice grains is studied theoretically. Two aspects are considered: (1) self-compression of a rock and ice mixture forming a celestial body, and (2) the heat conduction coefficient of the mixture. The work is aimed at an application to the study of the internal structure of medium-sized icy satellites. A compaction time-scale for the porous structure of the latter is calculated. It is suggested that Mimas could be porous down to its center even today, provided it accreted in a cold environment. Mimas thus appears to be the most suitable object to which our model could be applied. For a realistic porosity-pressure relation the equation governing pressure distribution within a non-rotating spherical body is solved numerically for Mimas. It is shown that the presence of voids may significantly lower the moment of inertia. Our results also suggest that porosity is sufficient to explain the actual shape of Mimas. The heat conduction coefficient of a porous rock-ice mixture is calculated by means of a Monte Carlo method based on the random resistor concept. It is suggested that the results so obtained could be useful in a study of thermal evolution. Throughout the paper the need for an experimental determination of the various material parameters used in this work is emphasized.

Solid state convection in the icy satellites: numerical results

Abstract Solid state convection in the mantle of icy satellites of giant planets is investigated using numerical models. We consider differentiated and non-differentiated satellites with both free (that is no horizontal stresses) and rigid (that is zero velocity) boundary conditions at the body surface. Internal heating originates from long lived radioactive elements uniformly distributed within rocky component of satellites (with initial chondritic concentration). Two modes of internal heating by radioactive sources are considered: uniform distribution of radioactive elements within undifferentiated bodies and heating of the icy mantle by heat flux from the rocky core. The calculations were performed for the range of Rayleigh number from 10 000 to 300 000. It corresponds to the medium size icy satellites in radii from the range 200 – 800 km. We found that convection velocity of the order of 1 mm yr −1 is typical for considered bodies. This is at least one order of magnitude less than the velocity in the Earths mantle but even such slow convection could be an important factor changing global tectonic activity, asymmetry of hemispheres, gravitational field and shape of the satellites.

Solid state convection in the icy satellites: discussion of its possibility

Abstract Surface features of Enceladus, Tethys, Dione, Iapetus, Miranda, Ariel, and Titania indicate that these satellites, with radii from the range 252–879 km, are highly or at least moderately modified due to internal tectonic activity. Detailed studies of known surfaces show that Enceladus is probably still geologically active at present while Tethys, Dione, Miranda, Ariel, and Titania were active in the recent past. Convection is one of the processes responsible for the evolution of the bodies of Solar System, including the evolution of icy satellites. We focus on studying the possibility of convection within the medium sized icy satellites. Thermally driven convection of solid satellite material as potential cause of surface evolution is considered for two cases: non-differentiated icy-mineral satellites and differentiated satellites with icy mantle and rocky core. Discussion of the parameters of icy/rocky mixture indicates that the Rayleigh number is higher than critical value for onset of convection.

Cratering of a comet nucleus by meteoroids

Abstract The two-dimensional axisymmetric hydrocode model of free particles is applied to the calculation of response of a comet nucleus to a meteorite impact. The nucleus is assumed to be spherical with a radius of 1 km. It is composed of a porous granular mixture of water ice and of mineral. Initial temperature is 50 K. Porosity is ψ = 0.6 and the mean density is ϱ = 400 kg m −3 . Impactor radius is equal to 1 m and its mean density is equal to that of the nucleus. Impact velocity is 10 km s −1 . A normal impact is considered. Particular forms for the equations of state (EOS) for the real medium (water ice and rock) as well as for an artificial medium of very low-density (40 kg m −3 ) filling up the voids are used. The cohesion is included in the constitutive model of the constituents. Numerical modelling provides the time dependent fields of pressure, density, temperature, and particle velocity in the vicinity of an impact point. The evolution of the field of temperature correlated with the function for kinetics of amorphous to crystalline phase transition permits discussion of the impact-induced crystallization of presumably initially amorphous ice.

Remarks on the Iapetus’ bulge and ridge

Iapetus is a medium sized icy satellite of Saturn. It has two spectacular features: the equatorial ridge (ER) and the abnormally large flattening. The flattening is usually explained in terms of large non-hydrostatic fossil equatorial bulge (EB) supported by a thick lithosphere. Here we show, building on the principle of isostasy, that EB and ER could be a result of low density roots underlying the lithosphere below the equator. The low density matter formed the layer over the core of the satellite. Such situation was unstable. The instability led to origin of axially symmetric plumes that formed equatorial bulge and equatorial ridge. So, we explain both: EB and ER in the frame of one hypothesis.