Dependence of the Hydration of the Lunar Surface on the Concentrations of TiO₂, Plagioclase, and Spinel

Abstract

We investigate the interrelation between the hydration of the lunar regolith and the mineral composition of the surface of the Moon with respect to the concentrations of plagioclase, TiO${}_2$ (highly correlated with the oxide mineral ilmenite), and Mg-spinel. The spectral properties of lunar regions with a low concentration of plagioclase or a high concentration of TiO${}_2$ or Mg-spinel show a significant reduction in hydration at lunar midday compared to other compositions. This suggests that these oxide minerals contain less of the strongly bound OH component, which is not removed at lunar midday. The time-of-day-dependent variation of the 3 $\mathsf{\mu }$m band depth is greater in TiO${}_2$-rich areas compared to other mare regions. The TiO${}_2$-rich regions therefore appear to have a strong tendency to adsorb solar wind-induced hydrogen into binding states of low energy that can more readily desorb and readsorb OH/${\mathrm{H}}_2\mathrm{O}$ on a daily basis.

1. Introduction

Near-infrared (NIR) hyperspectral data from the Moon Mineralogy Mapper (M${}^3$) instrument reveal an absorption band near 3 $\mathsf{\mu }$m that is found all across the Moon under a variety of thermal conditions. The presence and nature of volatile species on the Moon, especially OH/H${}_2$O, has been studied extensively by many groups (e.g., [1,2,3,4]), but the different processes leading to the hydration of the surface and their relative importance are still under debate. New data provided by the M${}^3$ instrument on Chandrayaan-1 [1] yield NIR spectra that cover the Moon nearly globally for different local times of day. This unique coverage enables the investigation of diurnal changes on the Moon. These M${}^3$ data show an absorption band near 3 $\mathsf{\mu }$m that can be found at all latitudes [3,4,5]. This absorption band is indicative of the presence of hydroxyl/water in the uppermost lunar regolith layer. The strength of the feature, however, varies with the local time of day and latitude (e.g., [6,7]). This observation is also consistent with independent data obtained from telescopic measurements [8,9]. Hendrix et al. [10] investigated far ultraviolet data, which are not affected by thermal emission, and also found that OH/H${}_2$O is variable with local time. Other publicly available data sources cannot match the resolution and coverage of M${}^3$ data in the NIR wavelength range, such that the M${}^3$ data set is still a useful tool to investigate the presence of OH/H${}_2$O until hyperspectral data with similar resolution extending to beyond 3 $\mathsf{\mu }$m are available. The main source of hydroxyl has been commonly attributed to the solar wind, by which protons are implanted into the regolith, where they react with O atoms in the other minerals (e.g., [7,11,12,13]). But there is evidence of endogenous OH as well. For instance, Klima et al. [14] found OH/H${}_2$O signatures at the Bullialdus crater to be of magmatic origin.

The 3 $\mathsf{\mu }$m absorption band has been found to be the strongest in the lunar morning and evening (e.g., [3,5,8]). Its strength decreases towards lunar midday, when sink processes, including diffusive loss and photolysis, become dominant [7]. Because the absorption band persists at lunar midday [3,5,8], Wöhler et al. [5] assert the presence of two components, a weakly and a strongly bound component, with different binding energies in the uppermost regolith layer. The modeling of Grumpe et al. [7] suggested that OH/H${}_2$O with binding energies around 2 eV would be more stable against diffusive loss and photolysis. According to Zhang et al. [15] and Zhuravlev [16], such binding sites exist in silicate minerals. We use this as the definition of strongly bound OH/H${}_2$O. In this setting, weakly bound OH/H${}_2$O is estimated to have binding energies of around $0.8$ eV and evaporates within several hours at lunar daytime temperatures [7]. At lunar midday, it is expected that only the strongly bound component is left in the upper layers of the regolith [5,7]. An extensive review of lunar OH/H${}_2$O is given in Schörghofer et al. [17]. On Earth, mapping the content of OH-bearing minerals is usually performed based on the analysis of the satellite near infrared spectra as well (e.g., see [18]).

The surface of the Moon is mainly covered with silicate minerals such as clinopyroxene, orthopyroxene, olivine, Ca-rich plagioclase, and smaller amounts of oxide minerals such as ilmenite FeTiO${}_3$ and spinel $(\mathrm{Fe},\mathrm{Mg}){(\mathrm{Cr},\mathrm{Al},\mathrm{Fe},\mathrm{Ti})}_2{\mathrm{O}}_4$ [19]. According to spectral modeling studies [20], the broadly occurring featureless spectra (e.g., [21]) of the lunar highlands can be reproduced by assuming a mixture of more than 90% plagioclase and less than 10% pyroxene. The lunar maria consist of up to about 60% plagioclase, 30–40% pyroxene, up to 10% olivine, and up to about 20% ilmenite [19].

Algorithms relying on spectral parameters have been employed successfully to examine the occurrence of specific minerals in the lunar surface material (e.g., [22]). The abundances of FeO and TiO${}_2$ in the lunar surface material were determined based on the parameters of spectral absorption bands such as reflectance ratios and continuum reflectance [23,24], or band depth, position, width, and continuum slope [25,26,27,28]. Such parameter maps have, for example, been used by Wöhler et al. [29] to show a correlation between the 3 $\mathsf{\mu }$m band depth and the abundance of TiO${}_2$ in mare areas. Here, we use the same TiO${}_2$ maps but exclude highland areas that are misleading in the analysis, and we focus in more detail on midday and morning correlations. Early studies on M${}^3$ data have also found that highland materials generally show a stronger 3 $\mathsf{\mu }$m absorption compared to the mare composition (e.g., [6,30]). Those studies, however, relied on an insufficient thermal emission removal of the M${}^3$ level 2 data [3,4,5,31], which tends to underestimate the temperature [3,4,5,31] and consequently underestimates the 3 $\mathsf{\mu }$m band depth. The method of Clark et al. [2] relies on assumptions about the shape of the spectra and is not physically motivated. Newer models, such as Bandfield et al. [4] and Wöhler et al. [5], are based on physical modeling similar to methods that have been applied in the asteroid community for many years and have been proven to be well-suited for estimating the thermal emission of particulate regolith surfaces (e.g., see [32]). Recent works on lunar OH/H${}_2$O, e.g., Honniball et al. [8], also make use of such physically based methods.

Lunar mare areas have high concentrations of different types of pyroxene, exhibiting pronounced absorption bands near 1 $\mathsf{\mu }$m and 2 $\mathsf{\mu }$m (e.g., [22,28]), as well as contributions from the mineral olivine, which displays a broad and deep absorption band near 1–1.2 $\mathsf{\mu }$m but no absorption band at 2 $\mathsf{\mu }$m (e.g., [22]), and the oxide mineral ilmenite (${\mathrm{FeTiO}}_3$), which has a relatively dark, flat, and nearly featureless spectrum in the NIR wavelength range (e.g., [33]). Typical highland surfaces consist of anorthositic rocks showing no or only very weak absorption bands near 1 $\mathsf{\mu }$m and 2 $\mathsf{\mu }$m (e.g., [21]). Minerals of the spinel group are widely distributed on the Moon, but they usually only appear in small fractions [34]. Mg-spinel can be distinguished from other lunar minerals by its deep absorption band at 2 $\mathsf{\mu }$m and the absence of a 1 $\mathsf{\mu }$m band [35,36]. Based on M${}^3$ hyperspectral data, some spatially limited areas were found to contain high Mg-spinel concentrations in several regions of the Moon [36]. Other types of spinel (namely Fe- and/or Cr-spinel) have been detected in Sinus Aestuum [37,38,39]. Ilmenite and some spinels are opaque minerals that strongly influence the measured reflectance spectra in regolith mixtures; therefore, these minerals are easier to distinguish even for low-weight percentages (e.g., [40]).

In this work, we examined time-of-day-dependent and regional variations in the spectral properties due to surficial OH/H${}_2$O in regions containing TiO${}_2$-bearing minerals and Mg-spinel. The purpose of this study was to understand the dependencies between implanted OH/H${}_2$O and the mineral composition of the surface.

2. Data Set and Methods

The studies carried out in this work were based on the level 1B data set acquired by M${}^3$ [41], which was subsequently photometrically calibrated and its thermal emission component removed. We used M${}^3$ images that were resampled to 300 pixels/degree for regional analysis and to 20 pixels/degree to construct a nearly global mosaic. The spectral radiance values were then converted to normalized spectral reflectance values using Hapke’s anisotropic multiple scattering approximation [42] and the topography of the surface, which is represented by a high-resolution Digital Terrain Model (DTM) constructed with the method of Grumpe and Wöhler [43]. All M${}^3$ images were carefully co-registered at the reference WAC mosaic [44] such that all pixels corresponded to the same location on the ground. Absorption features near 3 $\mathsf{\mu }$m for estimating the amount of OH/H${}_2$O were affected by thermal emission, requiring the thermal emission component to be removed from the measured spectral radiance. We used the thermal correction framework described by Wöhler et al. [31], Wöhler et al. [5], and Grumpe et al. [7], which corresponds to an iterative extension of the thermal equilibrium method of Shkuratov et al. [45]. Our method accounts for the influence of surface roughness (see also [4]) and yields an effective surface temperature (see [7] for details). The thermally corrected spectra were then used to determine the OH-integrated band depth (OHIBD) parameter of the 3 $\mathsf{\mu }$m band, which is a measure of the amount of hydroxyl/water in the uppermost layer of the regolith [5,31], according to the following equation:

$$\mathrm{OHIBD}=100\times \frac{{\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}\left(1-\frac{R\left(\lambda \right)}{c\left(\lambda \right)}\right)d\lambda }{{\lambda }_{\max }-{\lambda }_{\min }},$$

(1)

where $R\left(\lambda \right)$ is the thermally corrected reflectance spectrum (e.g., see Figure 1a) and $c\left(\lambda \right)$ the linear continuum fitted to the reflectance values between 2.537 and 2.657 $\mathsf{\mu }$m (see green lines in Figure 1b). The OHIBD parameter can be interpreted as the mean relative absorption across the wavelength interval $\left[{\lambda }_{\min },{\lambda }_{\max }\right]$ with ${\lambda }_{\min }=2.697\mathsf{\mu }$m and ${\lambda }_{\max }=2.936\mathsf{\mu }$m. The part over which the integral was calculated is marked in Figure 1c,d, for the weak and strong absorption, respectively. Differences in gain between M${}^3$ observations did not influence the measured OHIBD.

The other spectral parameters used for this work, characterizing the absorption bands near 1 $\mathsf{\mu }$m and 2 $\mathsf{\mu }$m, were inferred with the framework described by Wöhler et al. [26] and Bhatt et al. [27]. First, the spectra were smoothed by applying an optimization scheme that minimizes the deviation from the reflectance values and the second derivative [46]. The continuum was removed according to the convex hull method [47]. The continuum-removed spectra were then used to calculate the spectral parameters BD1 and BD2, as shown in Figure 1c,d, with BD1 referring to the band depth of the 1 $\mathsf{\mu }$m band and BD2 to the 2 $\mathsf{\mu }$m band, respectively.

In this study, we specifically used the negative logarithmic band depth ratio of the BD1 and BD2 (NLBD) parameters, corresponding to the negative value of the logarithmic band depth ratio (LBD) parameter defined by Bhatt et al. [27]:

$$\mathrm{NLBD}={log}_{10}\frac{\mathrm{BD}2}{\mathrm{BD}1}=-{log}_{10}\frac{\mathrm{BD}1}{\mathrm{BD}2}=-\mathrm{LBD}$$

(2)

Hence, a high NLBD value occurs when the 2 $\mathsf{\mu }$m band is strong and the 1 $\mathsf{\mu }$m band is weak, which is the case when Mg-spinels are present. However, this is only a qualitative description of the mineral abundance—a quantitative analysis is planned to be conducted in future studies, e.g., based on the spectral unmixing framework of Rommel et al. [48]. Areas found to exhibit a high spinel abundance according to the NLBD parameter are very similar to the findings of previous studies relying on other methods (e.g., [35,36,49]).

To study the possible dependence of the NLBD values on the photometric conditions of the observations, we compared the NLBD, BD1, BD2, and OHIBD values from the morning and midday observations (see Figure 2). The measured BD1 parameter changed slightly between morning and midday observations despite the photometric corrections. In the range of the 1 $\mathsf{\mu }$m band, the radiometric corrections are the strongest due to the detector temperatures [50], which might introduce systematic errors in this wavelength range. In contrast, the BD2 parameter is stable between morning and midday (see Figure 2d). The NLBD parameter slightly varies mainly because the BD1 parameter exhibited slight differences between the morning and midday observations. This behavior may well be due to the fact that the correction for the detector temperature applied to the M${}^3$ spectral radiances by the science team is strongest in the 1 $\mathsf{\mu }$m range [51]. However, the correlation between the morning and midday NLBD is high, such that the higher NLBD values in the morning also correspond to the higher NLBD values at midday. Therefore, when determining the NLBD value, we always use spectra that have been optimized by the Hapke model [42] to best fit all available observations from the same location. OHIBD, on the other hand, is systematically lower at midday than it is in the morning. Therefore, we used the spectra of all individual observations to be able to compare different times of day.

Ti, with an abundance highly correlated with the abundance of opaque minerals [23] and whose most important representative is ilmenite [19], is distinguished in the NIR wavelength range by a low albedo and continuum slope towards 2.5 $\mathsf{\mu }$m [52] and a high LBD (low NLBD) value due to partial suppression of the 2 $\mathsf{\mu }$m pyroxene band [27]. In the UV wavelength range, the TiO${}_2$ abundance is linearly correlated with the 321 nm and 415 nm reflectance ratio. This parameter was used by Sato et al. [24] to derive a TiO${}_2$ abundance map from the global WAC mosaic. These abundance maps were used in this work to find relations to the hydration of the regolith. Furthermore, we employed the mineral maps of Lemelin et al. [53] based on Kaguya MI images for the minerals plagioclase, olivine, orthopyroxene, and clinopyroxene.

3. Results

3.1. Abundant Minerals

First, we use the TiO${}_2$ maps of Sato et al. [24] and the mineral maps of Lemelin et al. [53] described in Section 2 to find correspondences between the composition and the OHIBD parameter.

Regional OHIBD maps illustrate the time-of-day-dependent changes in hydration (Figure 3). The ${\mathrm{M}}^3$ images were divided into morning and midday images, and a global mosaic was created by Wöhler et al. [5]. Images taken between 7 AM and 8 AM local time were defined as morning values, and images taken between noon and 2 PM were defined as midday images. The OHIBD maps show artifacts in the form of vertical lines. This variance of OHIBD does not result from an actual change in OHIBD, but most likely from inaccuracies of the detector that may have been caused by temperature effects inside the sensor and inaccuracies of the flat-field corrections [5]. At latitudes beyond 30° the time-of-day-dependent variations of the 3 $\mathsf{\mu }$m band depth are higher than at lower latitudes, leading to systematic latitude-dependent differences. In order to reduce the influence of latitude in our analysis, we omitted the higher latitudes as well as the areas west of 120° W and east of 60° E because there is only very limited M${}^3$ coverage at different times of the day. Figure 3a shows the OHIBD map of the lunar morning, where the OHIBD values are higher compared to the midday values, but the location-dependent variations are small. At midday (Figure 3b), the OHIBD difference between different mare areas is much more pronounced. The ilmenite-rich mare areas in Mare Tranquillitatis and the western part of Oceanus Procellarum show OH/H${}_2$O abundances of approximately 60% less compared to the surrounding mare regions. The data in Figure 3c depicting the difference values are noisier than the OHIBD maps for morning and midday because errors had been enhanced through the subtraction of uncertain quantities. Additionally, some areas lack data for morning or midday values.

Ilmenite shows large abundances in Ti-rich regions, while minor carriers of Ti are rare forms of the pyroxene augite ((Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)${}_2$O${}_6$) or the oxide minerals rutile (TiO${}_2$) and Ti-rich spinels (e.g., ulvöspinel ${\mathrm{Fe}}_2{\mathrm{TiO}}_4$) [19]. Subsequently, we will use the notation of TiO${}_2$ following the nomenclature of Sato et al. [24], referring to minerals where a cation is Ti${}^{+4}$ and the anions are O${}_2^{2-}$ in the crystal structure. Note that we do not refer to rutile, which is very rare on the lunar surface. In the finest fraction of the lunar mare soils (≤45 $\mathsf{\mu }$m in size), 40–60% of the TiO${}_2$ is in the form of ilmenite, 20–40% in agglutinitic glass, 15–20% in volcanic glass, and less than 3% in plagioclase, olivine, and pyroxene [54]. A similar relationship was found by Coman et al. [55] where it was noted that from 1/3 to 2/3 of the TiO${}_2$ content in lunar samples could be attributed to ilmenite, with an average of $52.6$ wt %. Ilmenite is widely assumed to be responsible for the overall remotely sensed TiO${}_2$ abundance based on spectral parameters in the UV and NIR wavelength range (e.g., [24,27,33,55,56]). The ilmenite abundance has also been found to be strongly correlated with the TiO${}_2$ concentration ($r=0.933$) of the lunar mare returned samples [56]. In the mare areas, the TiO${}_2$ abundance is dominantly above 2 wt %. In conclusion, we opted to use a ${\mathrm{TiO}}_2$ map as a proxy to investigate the relationship between ilmenite and OHIBD.

Since the lunar highlands uniformly contain only negligible amounts of TiO${}_2$, we focused on the mare areas to calculate the correlation between ${\mathrm{TiO}}_2$ abundance and OHIBD. To differentiate between mare and highland regions, we used the map by Nelson et al. [57] converted to a binary map and then scaled it to 20 pixels per degree. Figure A1 shows the TiO${}_2$ map for our study site from Sato et al. [24], illustrating that minerals containing TiO${}_2$ can be found in high abundances in some mare areas such as Mare Tranquillitatis and the western part of Oceanus Procellarum. In Figure 1, the selected average M${}^3$ spectra of two $4^{°}\times 4^{°}$ regions of mare areas with high (Mare Tranquillitatis) and low (Mare Serenitatis) TiO${}_2$ concentrations are shown. These spectra illustrate the trend that areas rich in TiO${}_2$, and consequently in ilmenite, have less pronounced absorption bands at 1 $\mathsf{\mu }$m, 2 $\mathsf{\mu }$m, and 3 $\mathsf{\mu }$m (blue curve in Figure 1). Even though the absorption band depths are dependent on the overall composition, the pyroxene absorption bands are dampened by the flat ilmenite spectrum. Overall ilmenite-rich areas are darker compared to the surrounding mare areas.

In this study we always used the correlation coefficient r rather than its square $r^2$ in order to be able to distinguish between positive and negative correlations. The correlation coefficients for all minerals are listed in

Table 1. Correlation coefficients r for the dependence of OHIBD on the abundances of the major minerals on the surface of the Moon.

Mineral	Mare			Highland
	Morning	Midday	Difference	Morning	Midday	Difference
TiO${}_2$ (Ilmenite)	−0.30	−0.71	0.43	$--$	$--$	$--$
Plagioclase	0.20	0.65	−0.54	0.49	0.65	−0.34
Olivine	−0.08	−0.33	0.29	$--$	$--$	$--$
Orthopyroxene	−0.07	−0.36	0.33	−0.55	−0.67	0.30
Clinopyroxene	−0.22	−0.50	0.37	−0.34	−0.46	0.24

. For TiO${}_2$ in the morning, the correlation coefficient is only $r=-0.30$, effectively corresponding to the absence of correlation (see Figure 4a). In the morning hours, the range of OHIBD values is from 5.5% at the lowest to 9% at the maximum. This means that the variance of OHIBD in the morning is relatively small (Figure 4a) compared to that at midday. At midday, the strongly bound component is the dominating factor because the weakly bound component had mostly evaporated by this time. The inverse correlation between midday OHIBD and TiO${}_2$ abundance is clearly visible (Figure 4b). Here, the correlation coefficient r corresponds to $-0.71$. Both correlation coefficients are negative, suggesting that the OHIBD values generally increased with a decrease in TiO${}_2$ abundance. Figure 4c shows that the OHIBD difference between morning and midday, in contrast to the absolute values, increases with increasing TiO${}_2$ abundance. The OHIBD difference values, however, are relatively noisy as a consequence of the propagation of uncertainty due to the subtraction of two uncertain quantities. e.g., both OHIBD morning and OHIBD midday values are subject to uncertainties, which are enhanced in the difference values. This uncertainty is also apparent in the correlation coefficients of the difference values, which show a positive correlation of $r=0.43$ visible in the density plot in Figure 4c.

To make sure that temperature would not affect the observed correlations, we needed to investigate whether the temperature changed significantly between high-Ti and low-Ti maria. Figure 5 depicts the temperature at the borders between the highland and mare of Oceanus Procellarum, and between high-Ti and low-Ti maria. While there is a small difference in temperature between the highland and mare areas (see Figure 5a), there is no significant difference between the temperatures of high-Ti and low-Ti maria (see Figure 5b). The dependence on the latitude is visibly the strongest, such that we had to compare high-Ti and low-Ti maria at similar latitudes. The variance in the mare areas amounts to about 1 K. Therefore, we can rule out the possibility that the trends of TiO${}_2$ and OHIBD could be attributed to temperature alone.

Let us consider correlations of the OHIBD values with the abundances of other minerals on the surface of the Moon. Plagioclase is the most abundant mineral for the majority of the lunar surface. For the lunar nearside in the equatorial region between 30° S–30° N and 120° W–60° E, that relationship is shown in Figure A2. The plagioclase abundance, as determined by Lemelin et al. [58], is shown in Figure A3. In Figure 6, the density plots of the correlation between plagioclase abundance and OHIBD are shown for mare and highland areas separately. According to Figure 6, plagioclase-rich rocks contain more OH/H${}_2$O than other areas. Plagioclase is positively correlated with the OHIBD values at midday in both highland and mare areas, $r=0.65$ for both. In the morning, a moderate correlation ($r=0.49$) can be observed only in the highlands, while the difference values are correlated in the mare areas ($r=-0.54$).

Compositional maps by Lemelin et al. [58] of the orthopyroxene, clinopyroxene, and olivine show only weak correlations with the OHIBD values at different times of the day (see Figure A4, Figure A5 and Figure A6 for orthopyroxene, clinopyroxene, and olivine, respectively). Orthopyroxenes are essentially uncorrelated in the mare areas, but a relatively flat correlation can be observed in the highlands for morning and midday values. In the highlands, the abundance is usually quite low compared to the mare areas, where a correlation is almost absent.

3.2. Spinel

Spinel is the name of a group of cubic oxide minerals with the general formula A${}^{2+}$D${}_2^{3+}$O${}_4^{2-}$, where A is typically a divalent metal cation and D is a trivalent metal cation. Most spinels in returned lunar samples belong to chromite (${\mathrm{FeCr}}_2{\mathrm{O}}_4$), ulvöspinel (${\mathrm{Fe}}_2{\mathrm{TiO}}_4$), and hercynite (${\mathrm{FeAl}}_2{\mathrm{O}}_4$) [19]. Spinel minerals are found in mare basalt (mainly titanium chromites and chromian ulvöspinel) as well as in highland rocks (chromite and pleonaste spinel) [19]. Using M${}^3$ data, minerals of the spinel group have been found in high concentrations at several locations on the Moon [36]. The first region that was identified to have abundant spinel occurrences is the highland immediately west of Mare Moscoviense [35]. Another region showing similar spectral signatures is the Theophilus crater [49]. In the regions of interest, previous studies identified Mg-spinel (${\mathrm{MgAl}}_2{\mathrm{O}}_4$) as the mineral most likely to be present [35,49]. The spectral signature of spinel appears most clearly in the two areas selected for this study, we will use these areas for evaluating the relationship between the parameters NLBD, indicating the presence of spinel, and OHIBD, indicating the integrated 3-$\mathsf{\mu }$m band depth. The spectral properties of spinel can be seen in Figure 7, which shows laboratory spectra from the RELAB database (https://pds-geosciences.wustl.edu/spectrallibrary/default.htm, accessed on 10 June 2021) [59] of nearly pure spinels from terrestrial samples alongside a nearly pure ilmenite spectrum inferred from lunar rocks.

The Mg-spinel spectrum exhibits a strong absorption band at around 2 $\mathsf{\mu }$m and no absorption band at 1 $\mathsf{\mu }$m, which is characteristic of low-Fe spinel [60]. For studies of hercynite, chromite, and ulvöspinel, the reflectance maximum around 1.5 $\mathsf{\mu }$m should be investigated. The spectral difference between the (Fe/Cr)-spinel and the surrounding mare surface, as shown by Weitz et al. [39], is less pronounced than the spectral difference between Mg-spinel and the surrounding highland areas examined by Pieters et al. [35] and Dhingra et al. [49]. Furthermore, it was found that spinels exhibit a broad 2.6–3 $\mathsf{\mu }$m absorption band in an almost anhydrous state [61] or a narrow 2.8 $\mathsf{\mu }$m absorption band [60]. These features can be explained by the presence of Fe${}^{2+}$ [61] and O-H stretching [60]. Hence, even small amounts of hydroxyl (and possibly also Fe${}^{2+}$) might lead to a more pronounced absorption at around 3 $\mathsf{\mu }$m.

In this study, we examined regions in the Theophilus crater and west of Mare Moscoviense because they show the spatially most extended lunar areas with a high content of Mg-spinel [35,36,49]. Regions containing Fe,Cr-spinels are planned to be studied in future papers.

3.2.1. Theophilus Crater

The first region of interest is selected from the Theophilus crater located on the lunar near-side at the northwestern border of Mare Nectaris. The mineralogy of the central peak of the Theophilus crater is quite diverse, with occurrences of plagioclase, pyroxene, spinel, and olivine, but the most common compositions are mafic-free anorthosites [49]. The M${}^3$ image available for this region was taken at 08:45 local time, or about 81 h after sunrise. This crater is located near the equator, so we expected that about half of the weakly bound OH/H${}_2$O component had already been removed at this time of day (see Grumpe et al. [7], compare Figures S1h and S1g for regions 7 and 8 therein). Therefore, we assume that the behavior can be interpreted as being intermediate between morning and midday. There are several areas in the Theophilus crater with high Mg-spinel abundances, and we chose the region with the strongest Mg-spinel signature whose position is shown in Figure 8. The NLBD and OHIBD parameters were then calculated according to the procedure described in Section 2.

Figure 9 shows an overview of the radiance, NLBD, and OHIBD maps along with the estimated surface temperature as a reference. The strongest NLBD values correspond to low OHIBD values. The estimated effective temperature does not correlate with the NLBD values, suggesting that temperature variations in the scene are not associated with mineralogy. The strong temperature variations are due to the uneven terrain and the relatively low elevation of the sun. Therefore, a small moderate positive correlation between temperature and OHIBD is visible in Figure 10.

The analysis of spinel-rich areas differs from the analysis of the other minerals in one significant way. While the other minerals are contained to a certain extent in nearly each mare region, spectrally detectable abundances of spinel are only found in spatially limited areas. This implies that there are two distinct classes, one containing spinel and one (the surrounding terrain) containing no or an undetectable amount of spinel. To distinguish between these two classes, we assume that all pixels having an NLBD parameter higher than $0.3$, which corresponds to a 2 $\mathsf{\mu }$m band depth—twice as deep as compared to the 1 $\mathsf{\mu }$m band depth, contain spinel (in spectra of mature areas without spinel, the 1 $\mathsf{\mu }$m band is deeper than the 2 $\mathsf{\mu }$m band). In Figure 11, areas containing spinel (magenta points) show a correlation, but for the areas that are assumed to contain negligible amounts of spinel (blue points), the values are effectively uncorrelated. For reference, the mean spectra of the two clusters at the Theophilus crater are shown in Figure A7. In general, high NLBD values correspond to lower OH/H${}_2$O abundances. This is apparent in Figure 12 as well, which shows some example spectra and the locations where they have been extracted. In the still darker and cold spinel-rich areas, the correlation between NLBD and OHIBD is less pronounced.

Another important factor that might contribute to the measured OHIBD values is the surface roughness on sub-pixel scales. Shkuratov et al. [62] proposed that phase ratio images could be used to investigate the surface roughness. Because the influence of the albedo is significantly reduced in phase ratio images, they are mostly correlated with the small-scale surface roughness [63]. For the area in Theophilus crater, the phase ratio image is shown in Figure A9a. It can be seen that in the region of interest, there are no anomalies that correlate with the OHIBD values, except for a small part to the northeast where higher phase ratio values (which are presumably due to topography) correspond to lower OHIBD values. The correlation coefficient describing the relationship between the phase ratio values and the OHIBD values at Theophilus is only $r=0.126$ (Figure A10e). All correlation coefficients for the spinel-rich regions are listed in

Table 2. Correlation coefficients r for the spinel-rich regions. Dependence of the OHIBD value on the different factors.

	Theophilus	Mare Moscoviense
	08:45 Local Time	09:20 Local Time	11:15 Local Time
NLBD > 0.3 (spinel)	−0.436	−0.295	−0.563
NLBD < 0.3 (no spinel)	−0.385	0.043	−0.195
Phase ratio	0.126	0.043	0.096
Plagioclase	0.022	0.055	0.019

. The plagioclase abundance in this area (Figure A8a) is also uncorrelated with the OHIBD values (Figure A10f).

Spectra 1–3 and 6 indicate the presence of Mg-spinel, but the spinel-specific signature in spectrum 6 is not nearly as clear as that in the other three examples. Spectra 4 and 5 show a deep absorption at 3 $\mathsf{\mu }$m, while the spinel-rich spectra are comparably flat. The continuum-removed spectrum of location 2 is shown in Figure 12c as a representative of a high spinel abundance region, and the continuum-removed spectrum of location 5 is shown in Figure 12d as an example of a region with low spinel concentration. The OHIBD parameter is high for spectrum 5 and low for spectrum 2 with a spinel signature. This region at the central peak of Theophilus shows that spinel-rich areas correspond to a reduced OH/H${}_2$O integrated band depth when the surface temperatures are so high that large amounts of the weakly bound OH/H${}_2$O component have been removed. Unfortunately, there is no M${}^3$ image of this region available for early morning or late midday.

3.2.2. Mare Moscoviense

High concentrations of spinel were found for the first time in two small areas to the west of Mare Moscoviense [35]. In this section, we examine the larger southern occurrence at the rim of the basin, as shown in Figure 13. The surrounding surface is typical anorthositic highland. For this region, images from two different times of day are available. In the late lunar morning, at 09:20 (image M3G20090125T172601) local time, it can be assumed that the weakly bound OH/H${}_2$O component is still partially present due to the moderately high latitude (see Grumpe et al. [7], compare Figures 22 and 23 for region 17 therein). At the acquisition time of the second image, at lunar midday at around 11:15 (image M3G20081229T101650), Grumpe et al. [7] argued that the weakly bound OH/H${}_2$O component is diminished and only the strongly bound OH/H${}_2$O component remains.

The NLBD values are not dependent on the time of day, allowing this parameter to be calculated based on all available M${}^3$ spectral radiance data simultaneously. The OHIBD parameter maps were constructed separately for both available times of day. At midday, the region with the lowest OHIBD lies in the center of the region characterized by the highest NLBD values, but its immediate surroundings that also show elevated NLBD values are not as strongly deprived in the OHIBD. For this OHIBD-depleted region, temperature variations are only minor (≤3 K). This area also appears to be rather flat in the radiance image, making it unlikely to be influenced by artifacts due to thermal emission removal. In the lunar morning, the high-NLBD areas in part also show lower OHIBD values, but the difference is not as significant. This trend is illustrated in the scatter plots in Figure 14, where the morning values are nearly uncorrelated; at lunar midday, however, high NLBD values correspond to low OHIBD values. The correlation coefficients are listed in Table 2. For the cluster of pixels that are likely to contain spinel (NLBD values $>0.3$), we found a correlation coefficient of $r=-0.295$ in the lunar morning and $r=-0.563$ at lunar midday. Corresponding values for regions with low spinel content (NLBD values below 0.3) are $r=0.043$ and $r=-0.195$, respectively. For reference, the phase ratio image is shown in Figure A9b. In general, the surface is relatively smooth when compared to the Theophilus crater. In Figure A10a,b, the correlation between the phase ratio values and the OHIBD parameter is depicted. There appears to be no correlation in the region of interest between phase ratio and OHIBD, so that we can safely rule out the possibility that the surface roughness influences the observed correlation between the OHIBD and the spinel. The plagioclase abundance is also uncorrelated with the OHIBD values (Figure A8b and Figure A10c,d).

Figure 16 shows some example spectra and their positions in the NLBD map. These spectra indicate that in the lunar morning, the OHIBD values are generally higher than at midday, but at both times of day, the selected spectra 1 and 2 show the typical 2 $\mathsf{\mu }$m absorption band of Mg-spinel and a relatively weak 3 $\mathsf{\mu }$m absorption band. Spectrum 4 is possibly overcompensated in thermal emission due to small-scale localized inaccuracies in the digital elevation model (DEM), leading to an inaccurate estimate of the incidence angle at that specific location.

4. Discussion

Our analysis of M${}^3$ data has demonstrated that the OHIBD values at midday in the mare regions decrease significantly (by a factor of up to about three) with the TiO${}_2$ content of the mare material, increasing from near-zero to its maximum value of about 8 wt % (see [5] for the OHIBD behavior on global scales). At low latitudes, the OHIBD difference between morning and midday, which we interpret as a measure of the amount of weakly bound OH/H${}_2$O in the lunar surface material, is near zero in the highlands and about 20–30 percent of the morning value in the low-Ti maria, but increases with increasing TiO${}_2$ content in the mare areas. This suggests that the TiO${}_2$-bearing minerals contained in the lunar surface material bind small amounts of OH/H${}_2$O strongly and large amounts of OH/H${}_2$O weakly to their crystal structure.

The strength of the OHIBD parameter is influenced by a wide range of factors apart from composition, such as latitude, time of day, and roughness, among others. Additionally, it should be considered that the part of the composition that influences the hydration signatures the most is not always clear. For example, TiO${}_2$-rich regions are depleted in plagioclase because the TiO${}_2$ abundance is highly correlated with plagioclase abundance (see also Figure A2). Therefore, the reduced amount of strongly bound OHIBD in TiO${}_2$-rich regions might be attributed to the absence of plagioclase that has been found to more strongly bind OH/H${}_2$O [64]. Similarly, Poston et al. [65] showed that a feldspathic highland sample retained significantly more OH/H${}_2$O compared to a mare sample. However, the spectral effect of the opaque mineral ilmenite is presumably stronger than to be expected based on its weight fraction. For ilmenite, this behavior was shown in laboratory experiments and was attributed to the excessively high extinction coefficient of ilmenite compared to non-opaque minerals (e.g., [66]). As a consequence, the OHIBD values might also already be strongly influenced by moderate amounts of opaque minerals. Of course, it is not self-evident that this behavior applies in the same way to the ilmenite-bound OH/H${}_2$O; hence, it is necessary to conduct further studies, e.g., focusing on hydrated ilmenite in the laboratory to provide a definite explanation.

In addition to that, another solar wind-implanted volatile, ${}^3$He, is mainly bound by ilmenite, a behavior which has been attributed to the presence of a large number of defect sites in ilmenite (e.g., see [67,68]). Milliken and Mustard [69] further suggested that the measured 3 $\mathsf{\mu }$m band strength is dependent on the albedo. TiO${}_2$-rich regions are generally darker compared to mare areas with low TiO${}_2$ concentration. This effect may have an influence on the overall correlation, but our spectral reflectance data have been carefully photometrically corrected with the model of Hapke [42], and the albedo is not variable during the day in our data. If the albedo had a strong influence on this correlation, we would also expect a stronger correlation in the morning, which is not the case, except for plagioclase in the highlands. High-Ti mare basalt might also be influenced by other phases, such as olivine [70], but we did not observe any correlation between olivine abundance and OHIBD in our study (see Figure A6).

Plagioclase does not release large amounts of OH/H${}_2$O in the course of the lunar day because the lunar highlands show only weak time-of-day-dependent OHIBD variations [5]. Our observations thus suggest that most of the OH/H${}_2$O component in TiO${}_2$-bearing minerals is weakly bound, whereas most of the OH/H${}_2$O component in plagioclase is strongly bound. In this line of thought, the depletion of plagioclase in the TiO${}_2$-rich mare areas explains the low OHIBD values at midday (corresponding to strongly bound OH/H${}_2$O), whereas the presence of large amounts of TiO${}_2$ in the same areas explains the strong time-of-day-dependent OHIBD variations (due to weakly bound OH/H${}_2$O).

However, another factor that is difficult to assess is the influence of agglutinitic glass. As it is difficult to accurately determine the glass content remotely, their effect cannot be estimated directly. It has been found that these glass contain strongly bound OH/H${}_2$O and possibly internal OH/H${}_2$O [71]. The correlation of the agglutinitic glass and TiO${}_2$ abundance from Pieters et al. [56] is $r=-0.408$; therefore, soil with a higher TiO${}_2$ concentration would contain a smaller amount of agglutinates. This could also explain why the plagioclase-deprived and TiO${}_2$-rich regions contain only small amounts of strongly bound OH/H${}_2$O. The moderate correlation found by Pieters et al. [56] in the lunar returned samples is, however, not sufficient to attribute the observed strongly bound component entirely to agglutinates, and the stronger variability during the day compared to other minerals cannot be explained by the strongly bound OH/H${}_2$O component in glass. For the Mg-spinel-rich regions, the difference in agglutinitic glass content with respect to the surrounding areas is expected to be small because there are no measurable maturity differences.

Regarding the midday OHIBD values, we observed a behavior for spinel that is similar to TiO${}_2$. The OHIBD in the spinel-bearing area to the west of Mare Moscoviense is nearly the same as that in the surrounding region in the late morning, whereas it shows a strong contrast (by a factor of about two) at midday. In the surrounding highland-like terrain, almost no difference in OHIBD between morning and midday is apparent. For the spinel-bearing area inside the Theophilus crater, the contrast of OHIBD values between spinel and no-spinel regions at this intermediate time between morning and midday even amounts to a factor of about three. Even though no comparison between morning and midday is possible for the Theophilus crater due to the lack of M${}^3$ data acquired in the early lunar morning or at late midday, studying this region is important as it is the spatially most extended area with the strongest spectral spinel signature in the lunar highlands. The temperature at the Theophilus crater also shows a moderate correlation with OHIBD (see Figure 10). An immediate, unintuitive (and not very pronounced), positive correlation between surface temperature and OHIBD is apparent in Figure 10 for temperature values between 340 and 380 K. A possible explanation for this is: if a surface part that is first shadowed by another surface part still contains a large abundance of OH/H${}_2$O from the previous lunar day, and then heats up as the sun suddenly falls relatively steeply on the same surface part, it will take a while for the OH/H${}_2$O to evaporate and photo-dissociate. In such a configuration, which often occurs in uneven terrain, it may, therefore, well be the case that relatively large amounts of OH/H${}_2$O occur on warm parts of the surface. Such unexpected correlations should be further examined, e.g., by applying the OH model of Grumpe et al. [7] to realistic lunar surface topography, which, however, goes beyond the scope of this paper.

The content of pyroxene and olivine is estimated to be as low as 5 wt % in the regions rich in Mg-spinel in the Theophilus crater and Mare Moscoviense [35,49]. For this reason, the influence of other mafic minerals on the OHIBD values in these regions should be negligible. As shown in Figure A8a,b, the OHIBD values are also not correlated with the plagioclase abundance in these regions of interest. For the spinel-bearing regions, no reliable evaluation of the weakly bound OH/H${}_2$O component can be performed due to the limited amount of data available from different times of day. The strongly bound component, however, is lower in the high-spinel regions when compared to the surrounding low-spinel surface. The general observations at Mare Moscoviense are similar to those at Theophilus in that both show lower OHIBD values for the high-NLBD regions. At Theophilus, this correlation is apparent at an earlier time of day than at Mare Moscoviense. Because Mare Moscoviense is located at a higher latitude than the equatorial crater Theophilus, this observation is consistent with the interpretation that the strongly bound OH/H${}_2$O component is less abundant in Mg-spinel-rich areas [7].

Our observations suggest that lunar minerals containing TiO${}_2$, including ilmenite and spinel-rich materials have similar tendencies to release (in the late morning up to midday) and build up (in the early morning and in the afternoon) large amounts of weakly bound OH/H${}_2$O. In contrast, the amount of strongly bound OH/H${}_2$O that is insensitive to loss processes such as thermal evaporation and photolysis [7] is small for both types of materials, but large for plagioclase. This behavior differs from low-spinel highland areas and low-ilmenite maria, which consist nearly completely of silicate minerals. They show much smaller time-of-day-dependent OHIBD variations than areas rich in TiO${}_2$ or spinel, and thus appear to be dominated by strongly bound OH/H${}_2$O.

5. Summary

In this work, we have investigated the relationship between TiO${}_2$-bearing minerals, plagioclase, and Mg-spinel on the one hand, and the hydration of the surface material on the other. The correlation between TiO${}_2$ abundance and OHIBD values was investigated in the mare areas on the lunar near-side. At lunar midday, the OHIBD values of TiO${}_2$-rich, and consequently probably ilmenite-rich, mare basalt areas were systematically lower than those of other mare terrains, whereas variations of OH/H${}_2$O abundance with time of day were the strongest in Ti-rich areas. Hence, we attribute the variable (weakly bound) OH/H${}_2$O component to the presence of TiO${}_2$-bearing minerals. In contrast, plagioclase is likely to contain most of the strongly bound OH/H₂O component: the plagioclase-rich highland regions showed only weak time-of-day-dependent OHIBD variations so that the OH/H₂O component bound by plagioclase could not be released in large amounts in the course of the lunar day. The abundance of lunar glass could not be reliably determined, but it could also contribute to the observed trends as laboratory samples suggest that the abundance of glass is correlated with plagioclase and TiO${}_2$ abundance.

As Mg-spinel very rarely occurs in high concentrations, the analysis was carried out for two small areas in the Theophilus crater and west of the Mare Moscoviense basin ring. At around midday, when most of the weakly bound OH/H${}_2$O had been released and mainly the strongly bound OH/H${}_2$O remained, both regions exhibited a low OHIBD for areas characterized by high NLBD parameter values. These observations suggest that the ilmenite and Mg-spinel in the lunar surface material are unlikely to bind OH/H${}_2$O strongly, which is in contrast to the behavior of plagioclase.

In future studies, we plan to further examine spinel-rich areas, including Fe and Ti spinels that show less pronounced spectral signatures but have better coverage by M${}^3$ data for different times of day, and to employ spectral unmixing techniques to quantify the abundances of Mg-spinel and ilmenite.