Discrepancy in Grain Size Estimation of H${}_{2}$O Ice in the Outer Solar System and the Interstellar Medium

TL;DR

This study compares radiative transfer models to estimate water ice grain sizes in the outer solar system, highlighting discrepancies and recommending the Mie model for accuracy and the Hapke slab model for practical use.

Contribution

It evaluates the accuracy of Hapke approximation models versus the Mie theory in estimating water ice grain sizes across different temperatures relevant to the outer solar system.

Findings

Hapke slab model closely matches Mie predictions for crystalline ice.

Hapke ISM shows higher uncertainty in grain size estimation.

Mie model is recommended for unknown spectra analysis.

Abstract

Widespread detection of amorphous and crystalline water (H${}_{2}$O) ice in the outer solar system bodies and the interstellar medium has been confirmed over the past decades. Radiative transfer models (RTMs) are used to estimate the grain sizes of H${}_{2}$O ice from near-infrared (NIR) wavelengths. Wide discrepancies in the estimation of H${}_{2}$O ice grain size on the Saturnian moons (Hansen, 2009), as well as nitrogen (N${}_{2}$) and methane (CH${}_{4}$) ices on Kuiper belt objects have been reported owing to different scattering models used (Emran and Chevrier, 2022). We assess the discrepancy in the grain size estimation of H${}_{2}$O ice at a temperature of 15, 40, 60, and 80 K (amorphous) and 20, 40, 60, and 80 K (crystalline) - relevant to the outer solar system and beyond. We compare the single scattering albedos of H${}_{2}$O ice phases using the Mie theory (Mie, 1908) and Hapke approximation models (Hapke, 1993) from the optical constant at NIR wavelengths (1 - 5 $\mu$m). This study reveals that the Hapke approximation models - Hapke slab and internal scattering model (ISM) - predict grain size of the crystalline phase, overall, much better compared to the amorphous phase at temperatures of 15 - 80 K. However, the Hapke slab model estimates much approximate grain sizes, in general, to that of the Mie model's prediction while ISM exhibits a higher uncertainty. We recommend using the Mie model for unknown spectra of outer solar system bodies and beyond in estimating H${}_{2}$O ice grain sizes. While choosing the approximation model for employing RTMs, we recommend using a Hapke slab approximation model over the internal scattering model.