Modeling the Dielectric Properties of Minerals From Crystals to Bulk Powders for Improved Interpretation of Asteroid Radar Observations

Abstract

Planetary radar has provided a growing number of data sets on the inner planets and near‐Earth and main belt asteroid populations in the solar system. Physical interpretation of radar data for inference of surface properties requires constraints on the constitutive parameters of the material making up a given surface. In this study, the complex permittivity of seven minerals as a function of frequency and porosity is measured using the coaxial transmission line method to determine the mixing equation that best describes the relationship between the real part of the complex permittivity of single mineral crystals and granular mineral powders. We find the Looyenga‐Landau‐Lifshitz and Bruggeman symmetric mixing equations to describe our experimental results with the highest accuracy. The variation in the real part of the permittivity of solid mineral crystals between different minerals is shown to depend on the grain density and the chemical composition of the minerals. These mixing relationships are incorporated into an asteroid radar model and used to calculate the porosity in the near‐surface of seven asteroids visited by robotic spacecraft using Earth‐based radar observations. The results of the asteroid radar model support the presence of significant porosity in the boulders on the surface of asteroid 101955 Bennu. This research highlights the ability of radar to measure the porosity on asteroid surfaces and provides theoretical and experimental justification for the inversion of permittivity to bulk density assumed by the asteroid radar model.

The Surface of (16) Psyche from Thermal Emission and Polarization Mapping

“…The dielectric constant of a material is in general a function of the frequency of radiation, and laboratory measurements of rocks and meteorites at millimeter wavelengths (∼100-300 GHz) are very limited. However, numerous measurements exist at lower frequencies, and Campbell & Ulrichs (1969) and Hickson et al (2020) find minimal variation in solid-rock permittivities across 20 MHz to 35 GHz. Brouet et al (2014) find that the real dielectric constant of particulate materials increases with increasing frequency from 50 MHz up to 190 GHz but stays within the 2-4 range.…”

“…For low-density particulate material, the real part of the dielectric constant is roughly set by the bulk density alone; the bulk density is in turn a function of the porosity and the solid grain density. Past studies have used this fact to convert radar reflectivity to bulk density and hence composition (Ostro et al 1985;Magri et al 2001;Shepard et al 2010;Hickson et al 2020). Ostro et al (1985) used the empirical formula R(ρ bulk )=0.12ρ bulk -0.13 where R is the average Fresnel reflection coefficient, adopting densities of 3.2 and 7.8 g/cm 3 for rock and metal respectively, to jointly constrain the porosity and metal fraction of an asteroid regolith from the radar albedo.…”

“…Garvin et al (1985) use the relation (ρ bulk ) = 1.87 ρ bulk , which is an improvement on a formula derived from lunar measurements (Olhoeft & Strangway 1975). Hickson et al (2020) evaluated a number of such formulas relating dielectric properties to composition and density, and instead find that the relationship solid = 1.85ρ grain + 1 for the solids, combined with the Looyenda-Landau-Lifshitz (LLL) model…”

“…While models that derive dielectric constant from bulk density alone may provide a good fit to porous, low-metal-content regoliths, most are not able to produce the high dielectric constants of metal-rich materials. The linear relationship solid = 1.85ρ grain + 1 recommended by Hickson et al (2020) is unable to produce solid dielectric constants above 15, even for a grain density of 8 g/cm 3 (at the extreme upper end for meteorites), while the measured values for essentially all classes of chondrites are at this value or higher (Campbell & Ulrichs 1969). Ulaby et al (1988) proposed a similar linear relationship between solid and ρ grain , but added a correction term based on the content of various metal oxides.…”

“…Kirchoff's law for thermal radiation states that, for a body in thermal equilibrium, the amounts of energy absorbed and emitted are equal. This law is stated in terms of emissivity, E, and reflectivity, R in Equation 9and is abbreviated as simply E = 1 − R. Assuming the regolith dielectric constant does not vary significantly between mm and cm wavelengths (Campbell & Ulrichs 1969;Hickson et al 2020), we may use this relationship to check for consistency between the radar albedo at S-band (12.6 cm) and emissivity at 1.3 mm. Magri et al (1999Magri et al ( , 2001 describe an approximate relationship between an asteroid's radar albedo, σoc , and surface Fresnel reflectivity, R, for asteroids with radar echoes dominated by first surface reflections: σoc = gR (17)…”