Uncertainty in Grain Size Estimations of Volatiles on Trans-Neptunian Objects and Kuiper Belt Objects

Abstract

We analyze the uncertainty in grain size estimation of pure methane (CH4) and nitrogen saturated with methane (N2:CH4) ices, the most abundant volatile materials on trans-Neptunian objects (TNOs) and Kuiper Belt objects (KBOs). We compare the single scattering albedo, which determines the grain size estimation of outer solar system regolith, of these ices using the Mie scattering model and two other Hapke approximations (Hapke 1993) in radiative transfer scattering models (RTMs) at near-infrared (NIR) wavelengths (1–5 μm). The equivalent slab (Hapke slab) approximation model predicts results much closer to Mie scattering over the NIR wavelengths at a wide range of grain sizes. In contrast, even though the internal scattering model predicts an approximate particle diameter close to the Mie model for particles with a 10 μm radii, it exhibits higher discrepancies in the predicted estimation for larger grain sizes (e.g., 100 and 1000 μm radii). Owing to the Rayleigh effect on single-scattering properties, neither Hapke approximate models could predict an accurate grain size estimation for the small particles (radii ≤5 μm). We recommend that future studies should favor the Hapke slab approximation when employing RTMs for estimating grain sizes of the vast number of TNOs and KBOs in the outer solar system.

Discrepancy in Grain Size Estimation of H2O Ice in the Outer Solar System

“…Consequently, the calculated w using the approximation models is deviant from that of the Mie model (Hansen 2009). Accordingly, for the implementation of RTMs, Hansen (2009) and Emran & Chevrier (2022) recommend using the Mie theory for a spectrum of outer solar system bodies. In this research, therefore, the deviation of estimated grain sizes by the approximation models to Mie's prediction is labeled as the discrepancy in grain size estimation by the approximation models throughout the paper.…”

“…The derivations of the approximate equations for the calculation of S e and S i are given in Hapke (1993) where k is set to be zero, and therefore is not considered, for the slab model. These approximate equations (S e and S i ) can also be found elsewhere in the literature that uses the Hapke models including the study of Emran & Chevrier (2022). The calculation of w using the ISM can be approximated as (Hapke 1993)…”

“…Following the approach of Emran & Chevrier (2022), the Mie w was calculated by utilizing the method of Wiscombe (1979) using the miepython routine (an open-source Python module). The δ-Eddington corrected Mie w' was then adjusted from Mie's w following Equation (1).…”

“…Radiative transfer models (RTMs) have been used to characterize the composition of outer solar system bodies such as Kuiper Belt objects (KBOs) and TNOs (e.g., Grundy & Fink 1991;Dumas et al 2007;Merlin et al 2010;Tegler et al 2010). However, wide discrepancies in the estimation of grain size have been reported for H 2 O ice on Saturnian moons such as Enceladus (Hansen 2009), as well as nitrogen (N 2 ) and methane (CH 4 ) ices on TNOs and KBOs using different scattering models (Emran & Chevrier 2022). These uncertainties are believed to arise due to the use of different single scattering albedo (w) calculations rather than a choice of using bidirectional scattering models (Hansen 2009).…”

“…For the same planetary body, Cook et al (2019) utilized the optical constant of both amorphous and crystalline ices while their scattering model was following the formulations of Roush (1994) and Cruikshank et al (1998) with some modifications. Because w is the primary cause of discrepancies in the grain size estimation of ices (Hansen 2009;Emran & Chevrier 2022), the uncertainty of the grain size estimation of amorphous and crystalline H 2 O ice, at temperatures analogous to the outer solar system (i.e., 15-80 K), using different scattering models is warranted.…”