Modelling of compaction in planetesimals

Abstract

Aims. Compaction of initially porous material prior to melting is an important process that has influenced the interior structure and the thermal evolution of planetesimals in their early history. On the one hand, compaction decreases the porosity resulting in a reduction of the radius and on the other hand, the loss of porosity results in an increase of the thermal conductivity of the material and thus in a more efficient cooling. Porosity loss by hot pressing is the most efficient process of compaction in planetesimals and can be described by creep flow, which depends on temperature and stress. Hot pressing has been repeatedly modelled using a simplified approach, for which the porosity is gradually reduced in some fixed temperature interval between ≈650 K and 700 K. This approach neglects the dependence of compaction on stress and other factors such as matrix grain size and creep activation energy. In the present study, we compare this parametrised method with a self-consistent calculation of porosity loss via a creep related approach. Methods. We use our thermal evolution model from previous studies to model compaction of an initially porous body and consider four basic packings of spherical dust grains (simple cubic, orthorhombic, rhombohedral, and body-centred cubic). Depending on the grain packing, we calculate the effective stress and the associated porosity change via the thermally activated creep flow. For comparison, compaction is also modelled by simply reducing the initial porosity linearly to zero between 650 K and 700 K. As we are interested in thermal metamorphism and not melting, we only consider bodies that experience a maximum temperature below the solidus temperature of the metal phase. Results. For the creep related approach, the temperature interval in which compaction takes place depends strongly on the size of the planetesimal and is not fixed as assumed in the parametrised approach. Depending on the radius, the initial grain size, the activation energy, and the initial porosity and specific packing of the dust grains, the temperature interval lies within 500−1000 K. This finding implies that the parametrised approach strongly overestimates compaction and underestimates the maximum temperature. For the cases considered, the post-compaction porous layer retained at the surface is a factor of 1.5 to 4 thicker for the creep related approach. The difference in the temperature evolution between the two approaches increases with decreasing radius and the maximum temperature can deviate by over 30% for small bodies.

Modelling the internal structure of Ceres: Coupling of accretion with compaction by creep and implications for the water-rock differentiation

“…These factors have been discussed in detail in Neumann et al (2014b). Here, we emphasise the intensity of heating, the duration of heating, and the intensity of pressing.…”

“…The remaining parameters in Eq. (4) were not varied with the mineralogy and correspond to the values used in Neumann et al (2014b). Implications of a variation of these parameters are discussed in Sect.…”

“…For the details of the model we refer to some of our previous publications, Neumann et al (2012Neumann et al ( , 2014b. In the following, we describe the details of the model that are particularly crucial and specific here.…”

“…where φ(t) is the average porosity of the asteroid at time t. The initial porosity of φ 0 ≈ 50% and the intrinsic geometry of the dust assemblage described by the simple cubic packing of uniform spherical grains is reasonably assumed here (see Neumann et al 2014b). The model computes the loss of porosity by hot pressing using a creep law,…”

“…Alternatively, water vapour available for reactions in the primitive solar nebula could have led to direct condensation of hydrous minerals. In Neumann et al (2012Neumann et al ( , 2014b we used an activation energy of 356 kJ mol −1 (85 kcal mol −1 ) calculated by Schwenn & Goetze (1978) for olivine. Compaction took place in this model at a temperature of about 700 K. On the other hand, a creep activation energy of 356 kJ mol −1 is rather high for a carbonaceous chondritic composition, which is dominated by phyllosilicates / serpentine.…”