Estimating the porosity structure of granular bodies using the Lane-Emden equation applied to laboratory measurements of the pressure-density relation of fluffy granular samples

The porosity structure of a granular body is an important characteristic that affects evolutionary changes in the body. We conducted compression experiments using fluffy granular samples with various particle sizes, shapes, and compositions. We approximated the pressure-filling factor relationship of each sample with a power law (a modified polytropic relationship). We also fit our previous data and literature data for fluffy granular samples using a power-law equation. The fitting with a power-law form was as good as that achieved with the equations used for powders in previous studies. The polytropic indices obtained in the current study ranged from ~0.01 to ~0.3 and tended to decrease with increasing particle size for samples of similar porosities. We calculated the radial porosity structure and bulk porosity of granular bodies with various radii using the Lane-Emden equation. The results provide the initial, most porous structures of accreted primordial bodies, or re-accumulated rubble-pile bodies consisting of particles that have compression properties similar to those of the assumed granular materials. A range of porosity structures is allowed for a body of given size and macroporosity, depending on the compression properties of the constituent granular material.
Comment: 2 Tables, 5 Figures Accepted for publication in ApJ. Table 2 and some typos corrected