A new method to predict particle sizes of S-type asteroid surfaces based on the laboratory thermal-infrared data.

Introduction: The surface particle size and distribution characteristics of celestial bodies (e.g., the Moon, asteroids) play a crucial role in landing, roving, sampling missions, and in the interpretation of hyperspectral data [1-3]. Existing methods mainly rely on thermal inertia derived from remote sensing data, but often show discrepancies compared with high-resolution imaging results [4]. Thermal Infrared (TIR) spectroscopy is sensitive to particle size, influencing diagnostic spectral features such as the Christiansen Feature (CF), Reststrahlen Bands (RB), and Transparency Features (TF) [5-6]. By analyzing a large number of laboratory TIR spectra of silicate minerals and their mixtures, we identified a strong correlation between particle size and the spectral slope near the long-wavenumber side of the CF. Based on this relationship, a new model is proposed to estimate grain sizes (30–300 µm) of silicate-dominated surfaces, achieving correlation coefficients (R²) greater than 0.9 for most mineral types. This new approach provides an alternative for particle size estimation, with practical implications for spectral interpretation and surface sampling of the S-type asteroids.

Data and methods: Three common silicate minerals (olivine, pyroxene, and feldspar) and the binary mixtures of pyroxene and feldspar were prepared as analogs to lunar and S-type asteroid regolith. Each sample was ground and sieved into seven grain size ranges (Table 1). Thermal infrared spectra were measured using a Bruker 80v FTIR spectrometer with an integrating sphere under ambient conditions. Reflectance data were converted to emissivity using Kirchhoff’s law (E = 1 − R), and all spectra were normalized. The CF position for each sample was determined by polynomial fitting following the method of Donaldson Hanna et al. (2012). This data set provides the basis for building and validating a particle size estimation model.

We focus on the spectral slope near the CF position, which is highly sensitive to grain size variations. To ensure consistency and avoid interference from spectral absorptions, the reference point at 1500 cm^-1 was selected on the long-wavenumber side of the CF. The spectral slope (K) was then calculated using the difference in emissivity values between the CF position and 1500 cm^-1, normalized by their wavenumber interval. This approach captures a consistent trend: as particle size decreases, the spectral slope becomes steeper (Figure 1).

Results and discussion: The relationship between spectral slope and particle size was quantified across a wide range of mineral samples. As particle size decreases, the slope near the CF position becomes steeper, forming a consistent trend across all tested mineral types. Exponential fitting between slope (K-value) and grain size showed strong correlation (R² > 0.9) (Figure 2), especially for olivine and pyroxene-feldspar mixtures (Table 2). This trend is attributed to increased volume scattering in finer grains, which enhances spectral contrast and shifts CF positions toward longer wavelengths.

To evaluate the model's performance, we applied it to spectral data from Apollo soils and terrestrial rock samples(Figure 3). The predicted particle sizes showed a systematic overestimation (Figure 4). This discrepancy is mainly attributed to surface weathering and compositional complexity in natural samples, which reduce spectral contrast and shift the CF positions. A correction function was thus developed to adjust the predicted sizes, improving model accuracy across typical lunar regolith compositions. After calibration, the model demonstrates optimal applicability for silicate-dominated regolith with grain sizes below 300 μm.

This study proposes a new method to estimate particle sizes of silicate-rich regolith using thermal infrared spectral slopes near the Christiansen Feature. The model shows strong correlation in the 30–300 μm range and is validated with both laboratory and returned lunar samples. A correction function improves accuracy by accounting for spectral deviations in natural materials. Future work will focus on integrating additional factors such as porosity, surface roughness, and space weathering to enhance model robustness for more diverse planetary surfaces.

References: [1] Yue et al. 2020, Journal of Deep Space Exploration, 7, 371. [2] Poulet et al. 2007, Journal of Geophysical Research: Planets, 112. [3] Shirley & Glotch, 2019, Journal of Geophysical Research: Planets, 124, 970. [4] DellaGiustina et al. 2019, Nature Astronomy, 3, 341. [5] Logan & Hunt 1970, Journal of Geophysical Research, 75, 6539. [6] Logan et al., 1973, Journal of Geophysical Research, 78, 4983.

Table 1: Description of Samples

Sample Types	Specific Mineral Composition	Particle Size Range
Minerals	Olivine	(1) 30-54μm; (2) 54-76μm; (3) 76-100μm; (4) 100-150μm;(5) 150-200μm; (6) 200-300μm; (7) 300-450μm
Mixed sample 1	10wt% augite + 90wt% labradorite	(1) 30-54μm; (2) 54-76μm; (3) 76-100μm; (4) 100-150μm;(5) 150-200μm; (6) 200-300μm; (7) 300-450μm
Mixed sample 2	30wt% augite + 70wt% labradorite	(1) 30-54μm; (2) 54-76μm; (3) 76-100μm; (4) 100-150μm;(5) 150-200μm; (6) 200-300μm; (7) 300-450μm
Mixed sample 3	50wt% augite + 50wt% labradorite	(1) 30-54μm; (2) 54-76μm; (3) 76-100μm; (4) 100-150μm;(5) 150-200μm; (6) 200-300μm; (7) 300-450μm

Table 2: The coefficients of the exponential function fitting for each sample.

Sample	a	b	c	R2
Olivine	-8.71×10-4	-7.11×10-3	-5.82×10-5	0.99
10wt% augite + 90wt% labradorite	-9.33×10-4	-1.59×10-2	-2.66×10-5	0.97
30wt% augite + 70wt%labradorite	-9.05×10-4	-1.53×10-2	-3.84×10-5	0.94
50wt% augite + 50wt% labradorite	-8.56×10-4	-1.32×10-2	-2.34×10-5	0.95
All mixed samples	-8.95×10-4	-1.48×10-2	-3.02×10-5	0.95

Figure 1: The thermal infrared spectra of minerals and mixtures with different particle sizes,  measured at room temperature and in the Earth’s atmospheric environment. (a) Olivine, (b) the mixture with 10wt% augite and  90wt% labradorite (c) the mixture with 30wt% augite and 70wt% labradorite (d) the mixture with 50wt%  augite and 50wt% labradorite.

Figure. 2: Exponential function fit of the relationship between the particle sizes and the K-values.

Figure. 3: The Thermal Infrared Spectra of Test Samples ((a) Lunar Olivine; (b) Mare Basalt; (c) Gabbro; (d) Anorthositic Gabbro; (e) Apollo 15101319; (f) Apollo 6122041)

Figure. 4: Comparison between predicted and ground-truth particle sizes across test samples. A linear regression method is used to fit the correction formula, see the black dashed line in the figure. The correlation coefficients (R²) is 0.79, and the RMSE of the fitting is 33.62µm.