Updated estimates of Mercury's global K/Th ratio: An unmixing approach to surface composition analysis

Introduction

Observations by the Mercury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft detected abundant volatiles on Mercury’s surface [1]. The K/Th ratios observed by Gamma-Ray Spectrometer (GRS), 6600 ± 2800, were higher than those on the other terrestrial planets [2, 3]. These observations led to several hypotheses regarding Mercury’s unique formation and evolutionary history [4-6]. However, these estimates were derived by integrating a whole GRS dataset, possibly biasing the global estimate. Indeed, due to MESSENGER’s elliptical orbit, GRS data were most effectively collected over Mercury’s northern high latitudes. To estimate a representative K/Th ratio over Mercury’s global surface, this study aims to determine the spatial variability of K and Th abundances. As a first step, we assumed geologically consistent spatial patterns of K and Th abundances and estimated the corresponding values.

Method

In this study, we assumed four geological end-member units on Mercury, each of which has a representative elemental composition. Based on this assumption, we applied a linear mixing model, where each GRS observation reflects a linear mixing of end-member compositions within observational footprint [7].

First, we produced an end-member map (Fig.1) by defining four end-member units that reflect diversity in surface geological context: Northern Plains (NP), Caloris Plains (CP), High-Mg Region (HMR), and Intercrater Plains (IcP). NP and CP are smooth plains with low crater densities, likely formed by young volcanism [7-9]. The HMR unit was identified in areas with elevated Mg/Si ratios (>0.55) [10], likely ancient terrain formed by early volcanic or impact-related processes [11,12]. All remaining regions were designated as the IcP unit.

Fig.1. End-member unit map showing the spatial distribution of the four end-member units, NP (yellow), CP (light green), HMR (red), and IcP (light blue). The sub-nadir points of the GRS measurements used in this study (black points) were limited to the northern hemisphere.

The footprint areas for each GRS observation were calculated using spacecraft’s orbital and attitude data. For each footprint, we determined the fractional coverage of the four end-member units by comparing it with the end-member unit map. To parametarize the GRS’s detection efficiency of gamma-rays emitted from the surface, a weighting scheme was applied based on the distance and emission angle between the spacecraft and a given point on the surface.

We then selected GRS observations with similar mixing ratio of the four units and integrated them to generate 20 composite gamma-ray spectra. From each spectrum, we estimated K and Th abundances from the 1461 keV and 2615 keV gamma-ray peaks, respectively. Finally, we solved an inverse problem using the fitted K and Th values and their associated mixing ratios to estimate the elemental abundances for each end-member unit (Fig. 2).

Fig.2. K abundances (vertical axis) and mixing ratios of the four end-member units (horizontal) for 20 gamma-ray spectra (colored circles) and the estimated end-member compositions (colored pentagrams).

Results and Discussion

Our analysis successfully estimated the K and Th abundances of the four end-member (Table 1). The K abundance was highest in the NP, exceeding that of the CP by over a factor of four. Relatively uniform Th abundance was estimated except in the HMR, which showed more than twice compared to the other units. As a result, the K/Th ratio showed a wide spatial variation, with the highest K/Th ratio of ~14,000 observed in NP.

Table 1. The end-member K and Th abundances [ppm], and K/Th ratios, and absolute and relative surface areas occupying the northern hemisphere, A_u [km2] and A_N,rel[%].

Using the estimated end-member compositions and their spatial coverage, we derived average values for Mercury’s northern hemisphere: K and Th abundances of 620 ± 20 and 0.13 ± 0.01 ppm, respectively, and K/Th ratio of 4900 ± 600. The estimated K/Th ratio is lower than, but consistent with previous global estimates, within the error bar range [2,3], suggesting that our model reduces the observational bias caused by uneven spatial coverage of the GRS observations.

To investigate the influence of exogenous contaminations by cratering impacts, we compared K/Th ratios with crater density, a proxy for impact frequency experienced by present surface. No clear trend was observed: NP and CP, both with low crater densities, exhibited the highest and lowest K/Th ratios, respectively, while HMR and IP with higher crater densities had intermediate values. In contrast, a negative correlation was found between K abundance and average surface temperature across units. This is consistent with the “thermal redistribution” hypothesis, where volatile elements concentrate in colder regions through surface-exosphere interactions [3,14]. These results imply that thermal redistribution dominates current surface K and Th compositions rather than the surface contamination of impact-delivered materials.

Conclusions

The reported high surface K/Th ratio was considered a clue to Mercury’s evolutionary history. This study re-analyzed MESSENGER GRS data using a compositional mixing model. Significant variation among four geologically defined end-member units was observed, with the Northern Plains showing the highest potassium concentrations. The estimated global average K/Th ratio was slightly lower than previous estimates, indicating succesful removal of observational bias. While no clear correlation was found with crater density, K abundances showed a negative correlation with surface temperature, supporting the thermal redistribution hypothesis. Applying this approach to thermal models or future observations may further improve our understanding of volatile behavior on Mercury.

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