A comparison of the ultraviolet to near-infrared spectral properties of Mercury and the Moon as observed by MESSENGER

Icarus 209 (2010) 179–194

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A comparison of the ultraviolet to near-infrared spectral properties of Mercury and the Moon as observed by MESSENGER Gregory M. Holsclaw a,*, William E. McClintock a, Deborah L. Domingue b, Noam R. Izenberg c, David T. Blewett c, Ann L. Sprague d a

Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA Planetary Science Institute, 1700 E. Fort Lowell, Suite 106, Tucson, AZ 85719-2395, USA Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA d Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA b c

a r t i c l e

i n f o

Article history: Available online 13 May 2010 Keywords: Mercury, Surface Moon, Surface Spectroscopy Spectrophotometry

a b s t r a c t Measurements of the disk-integrated reflectance spectrum of Mercury and the Moon have been obtained by the MESSENGER spacecraft. A comparison of spectra from the two bodies, spanning the wavelength range 220–1450 nm, shows that the absolute reflectance of Mercury is lower than that of the nearside waxing Moon at the same phase angle with a spectral slope that is less steep at visible and near-infrared wavelengths. We interpret these results and the lack of an absorption feature at a wavelength near 1000 nm as evidence for a Mercury surface composition that is low in ferrous iron within silicates but is higher in the globally averaged abundance of spectrally neutral opaque minerals than the Moon. Similar conclusions have been reached by recent investigations based on observations from both MESSENGER and Mariner 10. There is weak evidence for a phase-reddening effect in Mercury that is slightly larger in magnitude than for the lunar nearside. An apparent absorption in the middle-ultraviolet wavelength range of the Mercury spectrum detected from the first MESSENGER flyby of Mercury is found to persist in subsequent observations from the second flyby. The current model of space weathering on the Moon, which also presumably applies to Mercury, does not provide an explanation for the presence of this ultraviolet absorption. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction The similarity between the surfaces of Mercury and the Moon has been well-established through a variety of remote sensing techniques. Ground-based observations of Mercury employing reflectance spectroscopy, emission spectroscopy, photometry, polarimetry, and radar span most of the last century. A resemblance between these two bodies was noted early, through the close similarity of polarization characteristics (Lyot, 1929). Irvine et al. (1968) showed that the shape of the visible-light reflectance spectrum of Mercury is similar to previous measurements of the Moon, and noted evidence of phase reddening – the steepening of spectral slope with increasing phase angle – at wavelengths longer than 600 nm with a magnitude also similar to that of the Moon. McCord and Adams (1972) suggested that the similarity in reflectance and spectral shape between the Moon and Mercury is evidence for a similar mineralogy and composition. Images of Mercury obtained by Mariner 10, which flew by the planet three times * Corresponding author. Fax: +1 303 492 6444. E-mail address: [email protected] (G.M. Holsclaw). 0019-1035/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2010.05.001

in 1974–1975, showed that the morphology and optical properties of Mercury’s surface were similar to those of the Moon (Murray et al., 1974). Photometric properties down to the 20-km scale were found to be consistent with those of the Moon (Hapke et al., 1975b). A recent review of the results from Mariner 10 regarding surface properties was given by Cremonese et al. (2007). Lunar remote sensing campaigns have exploited absorption features centered near the wavelengths of 1 lm and 2 lm, indicative of ferrous-iron-bearing silicates, to characterize the mineralogical composition of the nearside surface (Adams, 1968, 1974; Adams and Jones, 1970; McCord et al., 1981). Thermal emission from the hot surface of Mercury can dominate the observed disk-integrated flux near 2 lm (McCord and Clark, 1979). Therefore, many of the ground-based telescopic observations of Mercury have involved searches for the presence of the absorption feature near 1 lm. Given the planet’s close proximity to the Sun, Mercury is a difficult object to observe from Earth. Nighttime observations are challenging due to the high airmass, while daytime observations suffer from high atmospheric turbulence and high background (Cremonese et al., 2010). In spite of many careful observations unambiguous identification of a silicate ferrous iron feature in Mercury

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reflectance spectra has been elusive. McCord and Adams (1972) reported the presence of a weak feature centered at 0.95 lm, but Vilas and McCord (1976) found the feature to be absent in their spectra. McCord and Clark (1979) found the feature to be weak and centered at a wavelength of 0.89 lm. Vilas (1985), in a review of Mercury observations, concluded that the apparent absorption near 1 lm was due to telluric contamination. More recently, Warell et al. (2006) detected a feature centered at 1.1 lm in a subset of disk-resolved spectra. This feature was seen in two of the three spectra obtained, suggesting that the surface of Mercury is heterogeneous. Reviews of the various ground-based remote sensing campaigns of Mercury have been given by Vilas (1988), Sprague et al. (2007), and Domingue et al. (2010). In the apparent absence of an iron-silicate absorption feature, the spectral slope of Mercury has been compared to those of spatially resolved, compositionally distinct areas of the Moon. Comparison of Clementine ultraviolet–visible UV–VIS camera (415– 1000 nm) multispectral reflectance images of the Moon with ground-based spectra of Mercury led (Blewett et al., 2002) to the conclusion that Mercury’s disk-integrated spectra were similar to that of specific regions on the lunar farside. These lunar areas are thought to be composed of mature anorthosite, a rock low in iron dominated by the Ca-rich end-member (anorthite) of the silicate mineral plagioclase feldspar. This inference is qualitatively consistent with identifications of plagioclase feldspar from ground-based thermal emission spectra of Mercury (Sprague et al., 2002, 2009). Although Na-bearing plagioclase feldspar was identified from the thermal emission spectra, discrimination among the range of plagioclase compositions is uncertain because of the absence of laboratory spectra obtained in a vacuum environment for comparison to those from Mercury. The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft flew by Mercury twice in 2008 and obtained both spatially resolved and disk-integrated spectra of Mercury. Initial results suggested that the surface is low in ferrous-iron-bearing silicates because of the absence of the 1-lm absorption feature in both mature and immature materials (McClintock et al., 2008; Robinson et al., 2008). Neutron spectroscopy measurements indicate a relatively large abundance of neutron absorbing elements, suggesting substantial amounts of Fe and Ti (Lawrence et al., 2010). Although neutron measurements alone cannot discriminate among the possible absorbing elements, the data were found to be consistent with lunar soils containing 13 wt.% Fe and 0.6–2 wt.% Ti. An upper limit on the average iron abundance of 7.0 ± 3.4 wt.% Fe was obtained from MESSENGER gamma-ray spectroscopy made during MESSENGER’s first two Mercury flybys (Rhodes et al., 2009). These results from MESSENGER have led several investigators to interpret the average composition of the Mercury to be low in iron-bearing silicate minerals, consistent with studies from ground-based reflectance spectroscopy, but relatively high in opaque oxides containing Fe and Ti as compared to the lunar highlands (Robinson et al., 2008; Denevi et al., 2009a,b). Variations in the abundance of spectrally neutral opaque minerals have also been shown to explain the primary color trends between distinct Mercury surface units (Robinson and Lucey, 1997; Blewett et al., 2007, 2009). This paper explores the compositional information that can be inferred from a comparison of disk-integrated reflectance measurements of Mercury and the Moon by spectroscopic and multispectral datasets acquired by MESSENGER instruments. Measurements of both the Moon and Mercury were acquired with the same instrumentation, so the ratio of the data from these objects should be independent of radiometric calibration. (The radiometric calibration divides out in the ratio only if the instruments are well understood and complicating effects such as scattered light, dark current, and detector nonlinearity are included in the

data reduction process.) However, photometric considerations are still required since the two bodies were observed at different solar phase angles. Measurements of the disk-integrated spectral reflectance of Mercury from MESSENGER are also compared with ground-based multispectral observations of the Moon (Kieffer and Stone, 2005) and broadband photometric observations of Mercury (Mallama et al., 2002). Because Mercury has been found to possess optical characteristics similar to those of the Moon, the extensive experience from the Apollo program and various remote-sensing studies is often leveraged by researchers in order to understand the differences found in the Mercury data. However, the Moon and Mercury are likely to have differing bulk compositions, geological evolution, and space weathering environments, so the applicability of this analogy is limited. 2. Instrumentation The MESSENGER spacecraft is equipped with seven science instruments (Solomon et al., 2007). One of these, the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) consists of a Cassegrain telescope that simultaneously feeds the Visible and Infrared Spectrograph (VIRS) and the Ultraviolet and Visible Spectrometer (UVVS) (McClintock and Lankton, 2007). VIRS is a point spectrometer with a 0.023° field-of-view (FOV), covering the wavelength range 320–1450 nm at 5-nm resolution in two spectral channels: visible or VIS (320–950 nm), and near-infrared or NIR (900–1450 nm). The UVVS is a scanning–grating monochromator with three spectral channels: far-ultraviolet or FUV (115– 190 nm), middle-ultraviolet or MUV (160–320 nm), and visible or VIS (250–600 nm). The UVVS has a long-slit entrance aperture that subtends 1°  0.04° for atmospheric observations and includes a mechanism to reduce the aperture to 0.05°  0.04° for surface observations. UVVS surface scans are limited to the FUV and MUV channels, as the sunlit surface is too bright for the VIS channel. The Mercury Dual Imaging System (MDIS) consists of a multispectral wide angle camera (WAC) and a monochrome narrow angle camera (NAC) (Hawkins et al., 2007). The WAC and NAC are frame imagers that spatially subtend 10.5°  10.5° and 1.5°  1.5°, respectively. Both cameras are co-aligned on a common pivot platform and use identical 1024  1024 pixel charge-coupled device detectors. The WAC features a 12-position filter wheel including 11 narrow-band spectral filters across the visible and near-infrared (430–1010 nm) plus one wideband navigation filter. 3. Observations Disk-integrated measurements of the Moon and Mercury were obtained with the MASCS and MDIS instruments. For both targets the angular diameter of the body was larger than a single spatial pixel of VIRS or UVVS by a factor of 10 and 5, respectively. The MASCS spectra were therefore collected in a raster fashion during which the projections of the spectrometer entrance apertures were slewed back and forth across the body in such a way that a disk-integrated spectrum could be obtained through a summation, with adjustments for oversampling (described in Appendix A). The observations of the Moon were obtained close in time by MASCS and MDIS, and so the solar phase angle was nearly the same. Due to the greater flexibility in pointing afforded by the MDIS pivot platform, observations of Mercury were obtained both during approach and departure at a variety of phase angles. MASCS, a body-fixed instrument with no independent pointing capability, was required to wait several days after each encounter before being able to observe Mercury in order to comply with the spacecraft operational constraints. The observations of Mercury

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by MASCS and MDIS were therefore obtained at different phase angles. 3.1. VIRS On 31 July 2005, an Earth gravity assist flyby provided an opportunity to view the Moon with MESSENGER’s remote-sensing instruments. During approach, spectra from MASCS were obtained of the 65°-phase Moon, covering the southern hemisphere of the farside (the sub-spacecraft coordinates were 59.1°S, 86.6°E). The observations were obtained at a distance of 980,000 km (the Moon was 0.2° in diameter) and the spatial resolution is 380 km for VIRS and 650 km for UVVS at the nadir point. For these observations, the spacecraft was first slewed in the X–Z plane (rotation about the Y-axis) at a rate of 0.00773°/s. The Xaxis of the spacecraft coordinate system is aligned with the solar

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panel arms; the Y-axis points anti-sunward through the Magnetometer boom; and the Z-axis passes through the principal instrument deck on which MASCS and MDIS are mounted (Leary et al., 2007). At an integration time of 3 s, the VIRS FOV traveled a distance equivalent to about one instantaneous FOV (0.023°). After a displacement of 0.5°, the spacecraft was stepped in the Y–Z plane (rotation about the X-axis) by 0.00781°. The spacecraft was then slewed back across the body in the X–Z plane, and the process repeated until an area of sky measuring 0.5°  0.5° was covered. The slew rate and line spacing given here are empirically derived average values and are in good agreement with the commanded values. During MESSENGER’s first Mercury flyby on 14 January 2008, VIRS obtained an extensive dataset consisting of 677 high-spatial-resolution (1  4 km on the surface) spectra (McClintock et al., 2008). Nine days later, on 23 January 2008, the spacecraft turned back to view the distant, 0.068°-diameter planet at a phase angle of 87°. For this observation, an 8-s integration time, an X–Z plane slew rate of 0.00045°/s, a Y–Z plane line step size of 0.01°, and a raster grid size of 0.1°  0.1° were used. It was found that the planet was not centered within the raster grid, and so the area sampled was expanded to 0.2°  0.2° for similar observations immediately following the second Mercury flyby. Two of these full-disk observations were acquired by MASCS at phase angles of 76° and 91°. An example of a typical MASCS raster scan is illustrated in Fig. 1. Additional specifications of the VIRS observations are given in Table 1.

3.2. UVVS

Fig. 1. Diagram of the 15 October 2008 VIRS raster scan across Mercury. Each symbol represents the location of the boresight midway through an integration, and is color-coded by the total signal measured. The coordinate axes refer to the local instrument frame, but since the VIRS boresight is approximately aligned with the spacecraft z-axis, the x, y, and z directions are synonymous with the spacecraft frame. The underlying image of Mercury is a simulated view using an MDIS-NAC mosaic in orthographic projection. The effective field-of-view of a single MASCS– VIRS spatial pixel during the slew in the X–Z plane is shown in the lower left, and includes the spatial smearing due to spacecraft motion coupled with the finite integration time. For this observation, the boresight motion during an integration is 15% of an instantaneous field-of-view.

Observations of both the Moon and Mercury were obtained by the UVVS channel almost concurrently with VIRS. However, there are significant differences in the operation of the two channels. As a spectrograph, the VIRS acquires a complete spectrum of all light that passes through the entrance aperture during a single integration. The UVVS operates as a scanning–grating monochromator so that during each integration the detector measures the reflected light within a single narrow spectral bandpass. A complete spectrum is obtained by scanning the grating in discrete steps across a specified wavelength range. For the lunar observation, a complete UVVS-MUV spectrum was obtained in 4.8 s using the surface slit. For the spacecraft slew rate of 0.0078°/s the FOV drifted by 0.037°, or about the width of the FOV, over the time required to scan the spectrum. As a result of the slewing, the area sampled at the first wavelength is different from the area sampled by the last wavelength. Therefore, in order to interpret a complete spectrum an assumption must be made regarding the relative spectral homogeneity of the surface at the two-slit-width scale.

Table 1 Instrument parameters, spacecraft geometry, and target body orientation during observations of the Moon and Mercury by VIRS.

Start date (UTC) Stop date (UTC) Integration time, Ti (s) Integration period, Tp (s) Distance to body (km) Angular diameter of body (°) Raster grid size (X-by-Y) (°) Slew rate (°/s) Line spacing (°) Phase angle (°) Sub-solar coordinates (lat., lon. E) Sub-observer coordinates (lat., lon. E)

Moon

Mercury flyby 1

Mercury flyby 2

2005 July 31 (DOY 212) 00:46:51 2005 July 31 02:01:42 3.0 3.25 980,889 0.203 0.5  0.5 0.00773 (X–Z) 0.00781 (Y–Z) 65.4 1.4, 117.9 59.1, 86.6

2008 January 23 (DOY 023) 09:00:11 2008 January 23 09:43:54 8.0 8.25 4,089,169 0.068 0.1  0.1 0.00045 (X–Z) 0.01004 (Y–Z) 87.2 0.0, 179.6 1.1, 92.4

2008 October 15 (DOY 289) 23:26:11 2008 October 16 02:06:24 4.0 4.25 4,361,886 0.064 0.2  0.2 0.00046 (X–Z) 0.01004 (Y–Z) 76.0 0.0, 0.1 0.0, 76.1

2008 October 19 (DOY 293) 06:37:11 2008 October 19 09:17:24 4.0 4.25 5,417,088 0.052 0.2  0.2 0.00046 (X–Z) 0.01005 (Y–Z) 91.0 0.0, 0.5 0.0, 90.5

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Table 2 Instrument setup parameters, spacecraft geometry, and target body orientation during the Moon and Mercury observations by UVVS-MUV.

Start date (UTC) Stop date (UTC) Integration time, Ti (s) Scan time (s) Slit position Distance to body (km) Angular diameter of body (°) Raster grid size (X-by-Y) (°) Slew rate (°/s) Line spacing (°) Phase angle (°) Sub-solar coordinates (lat., lon. E) Sub-observer coordinates (lat., lon. E)

Moon

Mercury flyby 1

Mercury flyby 2

2005 July 31 (DOY 212) 02:03:45 2005 July 31 02:41:53 0.012 4.752 Surface (0.04°  0.05°) 965,786 0.204 0.5  0.5 0.00780 (X–Z) 0.01544 (Y–Z) 65.7 1.4, 118.4 59.3, 86.5

2008 January 23 (DOY 023) 00:30:33 2008 January 23 04:10:24 0.055 14.396 Atmospheric (0.04°  1°) 3,974,052 0.070 0.1  1.1 0.00092 (Y–Z) 0.01010 (X–Z) 85.7 0.0, 179.6 1.1, 94.0

2008 October 15 17:02:35 2008 October 15 20:41:47 0.011 36.19 Atmospheric (0.04°  1°) 4,266,206 0.066 0.1  1.0 0.00092 (Y–Z) 0.01000 (X–Z) 74.9 0.0, 0.2 0.0, 75.1

2008 October 19 00:12:35 2008 October 19 03:51:47 0.011 36.19 Atmospheric (0.04°  1°) 5,356,163 0.052 0.1  1.0 0.00092 (Y–Z) 0.01000 (X–Z) 89.8 0.0, 0.5 0.0, 89.3

Table 3 Spacecraft geometry and target body orientation during the full-disk Mercury observations by WAC.

Sequence name Start date (UTC) Distance to body (km) Angular diameter of body (°) Phase angle (°) Sub-solar coordinates (lat., lon. E) Sub-observer coordinates (lat., lon. E)

Moon

Mercury flyby 1

Mercury flyby 2

05212_RADIOMETRIC_CAL

08014_APP_WAC_FRAME_1

08014_DEP_WAC_FRAME_1

08280_APP_WAC_FRAME_1

08280_DEP_WAC_FRAME_1

2005 July 31 00:09:01 1,002,177

2008 January 14 17:43:46 29,597

2008 January 14 20:24:58 29,386

2008 October 06 07:10:57 29,638

2008 October 06 10:09:45 29,618

0.199

9.43

9.49

9.41

9.42

65.0

117.9

52.2

129.0

37.2

1.4, 117.3

0.0, 174.9

0.0, 175.1

0.0, 3.1

0.0, 3.0

58.9, 86.6

2.5, 57.0

1.7, 132.7

1.3, 132.2

0.4, 34.2

The slewing also limits the spectra to regions where the FOV is entirely filled by the lunar disk. The observation sequence during the Mercury scans was different from that for the Moon. In an effort to maintain the same region of the planet within the spectrometer entrance slit during the acquisition of a spectrum, the atmospheric slit was used and the spacecraft was slewed in the perpendicular (Y–Z) direction, parallel to the long axis of the slit. The time to acquire a complete spectrum was 14.4 s. For a slew rate of 0.00092°/s the FOV drifts an angular distance of 0.013°. Thus, the same area of Mercury was contained within the entrance aperture over the entire duration of a single spectral scan. The observational details for the UVVS are listed in Table 2. 3.3. WAC The 0.2°-diameter disk of the Moon subtended about 20 WAC pixels during the observations by MDIS, and thus the spatial resolution is 178 km per pixel at the nadir point. Three 11-color sets of images were obtained at an average phase angle of 65°. At least one 11-color set of images of Mercury was obtained during approach and departure for both flybys. For all observations used in this study the full disk of Mercury subtended about 9.4°, nearly filling the 10.5°-square field-of-view. Therefore, the spatial resolution is 5.3 km per pixel in all Mercury images considered here. The approach and departure images from the first flyby were obtained at phase angles of 118° and 52°, respectively. For the second flyby, the

approach and departure images were obtained at phase angles of 129° and 37°, respectively. Because of the trajectory of the spacecraft, the nadir locations on the planet for all images were nearly equatorial. Additional observational details for the WAC observations are listed in Table 3. 3.4. Other comparable datasets The most accurate measurements to date of the multispectral photometric properties of the disk-integrated reflectance of the Moon come from the Robotic Lunar Observatory (ROLO). The ROLO dataset consists of ground-based telescopic measurements of the Moon spanning phase angles from 90° to +90° phase (negative phase angles refer to times before full Moon, i.e., waxing) and wavelengths from 350 nm to 2450 nm in 32 spectral filters (Stone and Kieffer, 2002). An empirical model, consisting of 18 coefficients for any one wavelength, was fit to the disk-integrated phase curve in each filter. This model was found to provide a relative accuracy of 1%, although the absolute accuracy in any filter is about 5–10% (Kieffer and Stone, 2005; Stone and Kieffer, 2006). The absolute calibration is based on the observed flux of the star Vega (a Lyr) and a modeled stellar spectrum scaled to match measurements from previous investigators. An empirical correction was derived by Kieffer and Stone (2005) to reduce the filter-to-filter variation by fitting the combined spectrum of an Apollo 16 lunar soil (62231) and breccia (67455) to the disk-integrated spectrum at 7° phase. The deviations from this smooth curve, supplied by T. Stone

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(private communication, 2010), provide a correction for each wavelength that is then applied to the model spectrum at any phase angle. Using this model a discrete spectrum of the lunar nearside can be produced at an arbitrary phase angle for comparison with other disk-integrated measurements. Observations of Mercury by Mallama et al. (2002) in the visible (V) photometric filter of the Johnson and Morgan system (546.5 nm center wavelength, 87 nm width at half maximum) (Johnson and Morgan, 1951; Moro and Munari, 2000) have provided the most accurate measurements of the Mercury phase curve to date, covering a range from 2° to 170°. Observations at small and large phase angles were obtained by the Large Angle and Spectrometric Coronagraph (LASCO) instrument on the Solar and Heliospheric Observatory (SOHO) spacecraft, while mid-range phaseangle photometry was obtained from a ground-based telescope (Mallama et al., 2002). The measured V-magnitudes were normalized to a distance of 1 AU, and a seventh-order polynomial was fit to the data. The polynomial coefficients were provided by Mallama et al. (2002) and can be used to estimate the absolute reflectance of Mercury at an arbitrary phase angle.

4. MASCS data reduction and calibration The calibration procedure for MDIS has been described by Hawkins et al. (2007) and briefly reviewed by Domingue et al. (2010). An overview of the MASCS data reduction will be presented here. In addition, in-flight measurements of the spectral irradiance from a star provide a validation of the radiometric sensitivity.

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4.2. Validation of radiometric sensitivity In-flight observations of well-characterized sources (typically stars) provide an opportunity to validate the pre-launch, laboratory-measured radiometric sensitivity of an instrument as well as to track variations over time. For the visible region, ground-based measurements of the spectral irradiance of stars are sufficient for this purpose, while observations in the ultraviolet region require measurements from other flight instruments due to the opacity of Earth’s atmosphere. The primary candidate in the visible region is a Canis Majoris (Sirius), the brightest star in the sky (aside from the Sun, which is far too bright to view directly by MASCS and MDIS). Sirius is actually a binary star system, with the much brighter component (Sirius A) of spectral class A1V and apparent visual magnitude 1.46 (Cowley et al., 1969). The companion (Sirius B) is a white dwarf of visual magnitude 8.44 (Rakos and Havlen, 1977) and thus contributes little to the total irradiance observed by MASCS. During the long cruise phase of MESSENGER, several stars (including Sirius) have been observed by the VIRS and UVVS channels of the MASCS instrument. A search of the VizieR astronomical database (Ochsenbein et al., 2000) for a reference spectrum revealed the existence of the Pulkovo (Alekseeva et al., 1996) and Kharitonov (Kharitonov et al., 1997) catalogs, collections of absolute stellar spectra from the near-ultraviolet to the near-infrared acquired from ground-based observatories. Fig. 2a shows the abso-

4.1. Data reduction The raw instrument output from VIRS, represented as 16-bit data numbers (DNs), are converted to the physical quantity of radiance (power per unit area per unit solid angle) by the following process: first, a background signal, consisting of both dark current and an electrical offset, is subtracted from the raw DN. Dark current arises from the thermal elevation of electrons into the conduction band of a solid-state detector, and so it is a temperaturedependent process. Because the VIRS detectors are not thermally controlled, as the detector temperature varies through an observation so, too, does the average dark current. For the full-disk raster scans analyzed here the dark current is determined by fitting a polynomial as a function of time to those measurements where the field-of-view is off the disk of the planet (except for the Moon, where an internal instrument shutter was used). Next, a small offset due to light scattered by the grating within the spectrograph is subtracted. It is assumed that this offset is proportional to the total signal across the detector, and it has empirically been found to be about 3.8  105 from the residual signal present in the VIS channel at wavelengths less than the transmission cutoff of the detector window. This fraction of the total signal constitutes the estimate for the grating-scattered-light offset and is removed from both the VIS and NIR channels. The integration time is then divided into the result to arrive at a signal rate (DN s1). Finally, the radiometric sensitivity, measured prior to launch in the laboratory using a known radiance target, is divided into the result. This procedure can be summarized by the equation,

L¼

ðC  D  GÞ 1  t S

ð1Þ

where C is the raw DN value, D is the dark current, G is the gratingscattered-light offset, t is the integration time, and S is the sensitivity in units of DN s1 (W m2 sr1 lm1)1. Calibrated spectra, represented by L, thus have spectral radiance units of W m2 sr1 lm1.

Fig. 2. (a) A plot of the absolute spectral irradiance of the star a Canis Majoris (Sirius) as measured in-flight by MASCS–VIRS. Also shown are two spectra obtained from ground-based observatories. (b) Ratio of the MASCS–VIRS spectrum to each ground-based measurement.

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lute spectral irradiance of Sirius as measured by the VIS channel of VIRS in comparison with ground-based measurements, while Fig. 2b shows the ratio of the VIRS spectrum to each ground-based spectrum. The agreement, seen to be within 10% over most of the spectral range, inspires confidence in the absolute and relative calibration of the instrument. There are no obvious systematic spectral trends, though in order to minimize the average deviations in the ratio of Fig. 2b it could be argued that the VIRS spectrum should be raised by 3–5%. The structure in the ratio curves of Fig. 2b is likely the result of low signal to noise in the MASCS data coupled with differences in spectral resolution of the instruments, although an attempt was made to match the resolution of the datasets. Unfortunately, there are no stars of sufficient brightness in the near-infrared to provide a similar comparison for the NIR channel of VIRS. Stellar calibrations with the WAC are difficult. The Atmel TH7888A detector arrays used for MDIS have pixels 14  14 lm in size, but the active area is only 10  14 lm (71% fill factor). Imaging performance is dominated by diffraction, and a spot radius of 8.5 lm is specified at a wavelength of 700 nm (Hawkins et al., 2007). Because a stellar image is therefore of a size similar to that of a pixel, a significant and unknown fraction of the light will be lost to the opaque pixel regions. This is effectively a transmission loss and varies with wavelength and small changes in pointing. 4.3. Derivation of disk-integrated reflectance In the context used here, the term reflectance refers to the ratio of the measured radiance (power per unit area per unit solid angle) scattered from a surface at some photometric geometry specified by the incidence angle, emission angle, and phase angle to the radiance expected from a perfect Lambertian surface normally illuminated by the Sun. This definition of reflectance, also known as the radiance factor (Minnaert, 1961; Hapke, 1993) or sometimes as I/F, can be expressed as

r k ðki Þ ¼

Lk ESun =p

ð2Þ

where L is the measured radiance, ESun is the solar spectral irradiance scaled to the radial distance of the target and convolved to the spectral bandpass of the measurement, the index k can refer to any single spatial element (an MDIS pixel or MASCS entrance aperture), and ki is the center wavelength of MDIS filter i, VIRS pixel i, or UVVS grating step i. The disk-integrated reflectance is the average reflectance (radiance factor) across the entire disk of a planet at some phase angle a. This quantity may be equivalently (and more simply) expressed as the ratio of the radiance from the hemisphere of a planet viewed by an observer to the radiance expected from a perfect Lambertian surface normally illuminated by the Sun. Alternatively, the disk-integrated reflectance can be viewed as the ratio of the total irradiance (power per unit area) from the body to the irradiance from a perfect Lambertian disk of the same apparent size normally illuminated by the Sun,

r¼

Ebody =Xbody ESun =p

ð3Þ

where Ebody is the total irradiance scattered from the body to the observer, and Xbody is the solid angle of the body as seen by the observer (the area of the entire disk divided by the square of the distance to the body). The disk-integrated reflectance has also been termed the disk-equivalent albedo (Kieffer and Stone, 2005). In general, this quantity is a function of both wavelength and phase angle and defines the spectrophotometric phase curve of an object. The disk-integrated reflectance at a phase angle of zero is known as the geometric albedo.

When a camera acquires an image of the full disk of a planet, it is relatively straightforward to calculate the object’s disk-integrated reflectance. Here it is assumed that the image is calibrated such that each pixel k measures radiance Lk. The corresponding irradiance (power per unit area) can be found by multiplying by the solid angle of a pixel, Xpixel. The integrated irradiance from the body is then found by summing the irradiance values for all pixels in the image receiving light:

Ebody ¼ Xpixel 

X

Lk

ð4Þ

k

The quantity Ebody can then be used in Eq. (3) to calculate the disk-integrated reflectance at the wavelength and phase angle of the observation. MDIS images archived in the NASA Planetary Data System are available as derived reflectance. In this case, the diskintegrated reflectance can be calculated by combining Eqs. (2) and (4) and substituting into Eq. (3) to arrive at:

r¼

Xpixel X r Xbody k k

ð5Þ

where rk refers to the reflectance value of pixel k in an MDIS image. This process is repeated for each image in a set of observations that uses the full range of spectral filters so that a discrete spectrum of the body under study can be derived. The approach described here is nearly equivalent to that taken by Domingue et al. (2010) since Xbody/Xpixel is equal to the number of pixels contained within the disk of the planet, and so the summation above can be seen as a simple average. However, the disk-integrated reflectance of Mercury calculated by the approach above is not identical to that reported by Domingue et al. (2010). While the spectral shapes are consistent to within 2% for all phase angles, the average values of the 118° and 129° phase angle curves derived by Domingue et al. (2010) are 4% and 6% below the values derived here, respectively. This discrepancy may be due to the removal of a ‘residual background’, presumably due to the incomplete removal of dark current, in the images used by Domingue et al. (2010). For an instrument (such as MASCS) that acquires a single spatial pixel element for each integration period, the calculation of the disk-integrated reflectance is somewhat more complicated. Because of the necessity of spatially oversampling the scene and other effects considered in depth in Appendix A, the total corrected irradiance from a body as measured by VIRS is given by:

Ebody ¼

X k

Lk  Xen 

  Dx Dy As T p    dx dy Ac T i

ð6Þ

where Lk is the measured radiance at each spatial position k, Xen is the instantaneous solid angle of the entrance aperture (equivalent in concept to the image pixel solid angle Xpixel in Eq. (4)), Dx0 is the slew rate, Dx is the angular distance the boresight travels during an integration (Dx0  Ti), Dy is the angular step size between rows, dx is the width of the field-of-view in one plane, dy is the width of the FOV in the perpendicular plane, As/Ac is the ratio of the area of a square to an inscribed circle (4/p), Tp/Ti is the ratio of the scan period (time between the start of each integration) to the integration time. For VIRS, Tp is typically 0.25 s longer than Ti, dx and dy are equal to 0.023°, and Xen is 1.257  107 sr. The disk-integrated reflectance can be found by substituting Eq. (6) into Eq. (3). For VIRS, a complete spectrum (320–1450 nm) is obtained from a single integration period. The spectral irradiance of the Sun used in this study for visible and near-infrared wavelengths (>300 nm) was measured above the Earth’s atmosphere during a series of Space Shuttle missions (Thuilllier et al., 2000). Although Thuillier et al. (2003) derived a solar spectrum at a uniform spectral resolution of 1 nm using several merged datasets, the version used here has non-uniform sampling

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(and thus spectral resolution): 0.3 nm (200–340 nm), 1 nm (340–870 nm), and 4 nm (870–1500 nm). In order to prepare this spectrum for use with the VIRS data it was first interpolated to 0.2 nm steps, then convolved with the average passband of the visible (3.2 nm) and near-infrared (4.2 nm) channels of VIRS, and finally interpolated to the respective wavelength scales. The variability in the solar flux is known to increase toward shorter ultraviolet wavelengths. In the middle-ultraviolet (200–300 nm), the variability in the solar irradiance during a 27-day solar rotation has been found to be up to 2% while for an 11-year solar cycle the variability is up to 5% (Rottman, 2002). The Mg II emission lines at 280 nm originate in the tenuous chromosphere and so exhibit a larger variation. In order to mitigate these possible effects, the reference solar spectrum used for wavelengths less than 300 nm is provided by nearly concurrent measurements from the SOLar Stellar Irradiance Comparison Experiment (SOLSTICE) instrument (McClintock et al., 2005). Daily averages of the solar spectral irradiance, binned to 1-nm intervals, as measured by SOLSTICE are available from an online database (Pankratz et al., 2007). The photometric model of Mercury from Mallama et al. (2002) is presented as coefficients of a seventh-order polynomial that was fit to the measured visual magnitude as a function of phase angle. This representation must be related to the disk-integrated reflectance defined in Eq. (3). The difference in magnitude between a Solar System body and the Sun is proportional to the logarithm of the irradiance ratio,

mbody  mSun ¼ 2:5log10

  Ebody ESun

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of iron and titanium are associated with the spectrally neutral opaque mineral ilmenite; the inclusion of such a material has the effect of lowering the absolute reflectance and decreasing the spectral slope. We therefore expect the spectral reflectance of the portion of the Moon as seen by MESSENGER to be higher and possibly of a different spectral slope than that of the integrated lunar nearside. An attempt must be made to quantitatively relate the ROLO measurements of the nearside to the geometry of the Moon observed by MESSENGER. The Clementine global multispectral mosaic of the Moon (McEwen and Robinson, 1997) provides a common, intermediate dataset that can be used in this manner. Using the Clementine data, Fig. 3a shows a simulated view of the waxing Moon from the Earth and Fig. 3b a simulated view of the

ð7Þ

where Ebody and ESun are the spectral irradiances of the body and Sun convolved with the V-filter transmission. Solving for the irradiance ratio and substituting into Eq. (3) results in the disk-integrated reflectance,

r¼

p Xbody

1

 10ðmSun mbody Þ2:5

ð8Þ

where Xbody is the solid angle of the full disk of Mercury as seen from 1 AU, mbody is the visual magnitude of Mercury from the photometric model of Mallama et al. (2002), and the magnitude of the Sun in the V-filter at 1 AU, mSun, is taken to be 26.75. 5. Results As a first step in the analysis, we consider how well the lunar spectra from MASCS and MDIS agree with each other as well as with independent measurements from ROLO. While the comparison between MASCS and MDIS is straightforward, the inclusion of ROLO is not. Because of the position of the MESSENGER spacecraft during the Earth–Moon flyby, the hemisphere of the Moon that was observed consisted of mostly farside terrain, including a portion of Oceanus Procellarum, the Orientale impact basin, and the South Pole-Aitken (SPA) basin. The ground-based ROLO measurements necessarily observed the lunar nearside. Therefore, the potential for differences in the spectral properties of these different regions must be considered if we are to use the ROLO photometric model as a reference. Approximately 30% of the lunar nearside is covered by volcanic mare basalts, whereas the farside is covered by only 2% (Wilhelms, 1987). The remaining area is considered highlands. These two basic terrains differ in composition; relative to the highlands, the maria contain a greater abundance of FeO and TiO2. Rava and Hapke (1987) reviewed the qualitative ultraviolet–visible–near-infrared spectral trends associated with varying abundances of FeO and TiO2. An increasing amount of FeO leads to a decrease in absolute reflectance and an increase in spectral slope. Substantial amounts

Fig. 3. Simulated views of the Moon as seen (a) from the Earth and (b) from the MESSENGER spacecraft at 65° phase angle using the Clementine 750-nm reflectance map (McEwen and Robinson, 1997) in orthographic projection. The polar regions and small areas of missing data are filled with the map average value. Each pixel in the map is photometrically adjusted to a geometry of i = 30°, e = 0°.

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Fig. 4. Ratio of the disk-integrated reflectance of the Moon as was seen by MESSENGER (Fig. 3b) to the disk-integrated reflectance of the waxing Moon as seen from the Earth (Fig. 3a). The line is fit to the five data points from Clementine and interpolated to the ROLO filter wavelengths.

Moon as seen from the MESSENGER spacecraft. We consider the waxing Moon (eastern hemisphere illuminated by the Sun) to be more similar to the terrain observed by MESSENGER due to the lower abundance of maria with respect to the waning Moon. The ratio of the disk-averaged reflectance in Fig. 3b to that in Fig. 3a for each spectral filter of the Clementine UVVIS instrument is shown in Fig. 4. Also shown in this figure is a linear interpolation of the Clementine reflectance ratio to the ROLO filter wavelengths. Because the Clementine data are being used only as a ratio, difficulties in the absolute calibration of the UVVIS camera (Hillier et al., 1999; Shkuratov et al., 2001) are avoided. The reflectance of the lunar hemisphere observed by MESSENGER is seen to be 16% higher than the waxing nearside at visible wavelengths and exhibits a slightly steeper spectral slope. This difference in absolute reflectance is consistent with the smaller proportion of low-reflectance mare material on the farside of the Moon. The change in spectral slope is small; the interpolated curve in Fig. 4 is less than 3% larger at 1500 nm than at 350 nm. It should be noted that each pixel in the Clementine mosaic used in Fig. 3a and b is photometrically adjusted to a geometry of i = 30°, e = 0° (McEwen, 1996) so that every illuminated region contributes equally in the average. A more complete comparison – though perhaps no more accurate – would require a lunar photometric function to be applied to the simulated views in Fig. 3 so that the incidence, emission, and phase angles would be realistic. In this way, the regions that appear brighter due to illumination would be weighted appropriately. However, difficulties in the photometric models to accurately represent extreme incidence or emission angles, such as near the terminator and the limb, would remain. A discrete spectrum of the waxing Moon at 65° phase was generated using the empirical ROLO photometric model of the lunar nearside, described in Section 3.4. Next, the interpolated curve from Fig. 4 was applied to this ROLO spectrum, resulting in a reflectance representative of the Moon as observed by MESSENGER. This adjusted ROLO spectrum is shown along with the disk-integrated reflectance of the Moon derived from MASCS and MDIS for a phase angle of 65° in Fig. 5a. In order to provide a more quantitative comparison, the continuous MASCS spectrum was convolved with the spectral transmission of the MDIS and ROLO filters. While the measured spectral transmission curves were used in the case of MDIS, a Gaussian approximation based on the reported spectral filter width was used for ROLO. Fig. 5b shows the ratio of the convolved MASCS

Fig. 5. (a) Spectral reflectance of the Moon at 65° phase as seen by MASCS, MDIS, and ROLO. The ROLO curve was extrapolated from the waxing lunar nearside to the geometry of MESSENGER. (b) Ratio of the MASCS spectrum of the Moon to the measurements from MDIS and ROLO. The continuous MASCS spectrum was first convolved with the transmission of the other instrument’s spectral filters.

spectrum to the discrete reflectance values from MDIS and ROLO. The spectral reflectance of the Moon is expected to be smooth over a wavelength interval of 20 nm, increase monotonically with wavelength, and exhibit a slight depression around 900 nm due to absorption by Fe2+. The channel-to-channel structure seen in the MASCS spectrum above 800 nm in Fig. 5a is likely due to calibration artifacts. These artifacts in the MASCS spectrum, along with the uncertainties in the discrete MDIS and ROLO values, combine and contribute to the structure seen in the ratio plots of Fig. 5b. The mean value of the ratio in Fig. 5b is 1.07 for both MDIS and ROLO. These differences suggest that the VIRS measurement is too high by 5–7%. However, in Section 4.2 a comparison of MASCS measurements of the spectral irradiance from the star a Canis Majoris with independent results from ground-based spectra suggested that values reported by MASCS could be too low by 3–5%. Given the relatively large uncertainty (5–10%) in the absolute value of the reflectance in any ROLO filter (Kieffer and Stone, 2005) coupled with the uncertainty in extrapolating the ROLO measurement of the lunar nearside to the geometry of MESSENGER, it would be difficult to argue that the datasets are inconsistent by a significant amount. Therefore, we consider the agreement of these datasets to the 10% level to validate the radiometric sensitivity of MASCS and MDIS. A detailed discussion of the in-flight performance of MDIS was provided by Hawkins et al. (2009).

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Fig. 6. Absolute reflectance of Mercury from MASCS and MDIS compared with the reflectance of the Moon at equivalent waxing phase angles.

The disk-integrated observations of Mercury by the MASCS and MDIS instruments were acquired at a range of phase angles (37°, 52°, 118°, 129° for MDIS; 76°, 87°, 91° for MASCS). The absolute reflectance and spectral shape of Mercury can be compared to the nearside of the Moon using the ROLO photometric model for phase angles less than about 90°. Fig. 6 shows four measures of the disk-integrated Mercury reflectance: two discrete spectra at 37° and 52° phase from MDIS, and two continuous spectra at 76° and 91° phase from MASCS. Paired with each of these curves is the reflectance of the waxing lunar nearside at the same phase angle. Because of the small wavelength interval (220–300 nm) of the MASCS measurements in the middle-ultraviolet and the special observational challenges, these results are considered separately later in this section. Also shown at each phase angle is the reflectance of Mercury in the V-filter (550 nm) using the photometric model of Mallama et al. (2002). It is seen that for all cases, the absolute reflectance of Mercury is similar to or somewhat lower than that of the nearside waxing Moon for wavelengths less than 550 nm. At 52° phase and at a wavelength of 550 nm, Mercury is found to be 13% (MDIS) and 8% lower (Mallama) in reflectance than the Moon (ROLO). For the same wavelength at 76° phase, Mercury is found to be 8% (MASCS) and 16% (Mallama) lower in reflectance than the Moon (ROLO). The spectral slope of Mercury also appears to be less than that of the Moon for all cases. At 52° phase, the ratio of the reflectance at 750–430 nm is 1.82 for the Moon (ROLO) and 1.68 for Mercury (MDIS), about 8% lower. At 76° phase, the same spectral ratio is 1.88 for the Moon (ROLO) and 1.65 for Mercury (MASCS), about 12% lower. The finding that Mercury is lower in reflectance than the Moon at visible wavelengths is consistent with previous results. An analysis by Warell (2004), using the full-disk photometric measurements of Mercury by Mallama et al. (2002) and of the Moon by Lane and Irvine (1973), found that the Moon exhibits a reflectance 7–17% higher than Mercury in the V-filter at the common phase angles ranging from 2° to 144°. However, it should be noted that no distinction was made between the waxing and waning phases of the Moon. The ROLO model shows that at 45° phase the waxing Moon exhibits a reflectance 8% higher, on average, than that of the waning Moon for wavelengths below 1000 nm; this is likely a result of geographical differences in the proportion of mare basalt covering the eastern and western portions of the lunar nearside. Using images of Mercury and the Moon obtained by the NAC, Robinson et al. (2008) found that the average reflectance of Mercury was 14% lower than that of the nearside Moon (no distinction between waxing and waning phase) at a wavelength of 750 nm. Comparing the near-infrared color trends and absolute reflectance

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(at 750 nm) of Mercury from MESSENGER with the same properties of the Moon obtained from images acquired by the Galileo spacecraft, Blewett et al. (2009) found evidence for the lower average reflectance of Mercury as compared to the lunar highlands. Warell (2004) reviewed estimates of geometric albedo (disk-equivalent albedo at zero phase) of the Moon and Mercury as determined by a range of techniques and investigators finding agreement that the albedo of the Moon is systematically higher (11–12%) than that of Mercury. As noted by Warell (2004), due to the rapid increase in reflectance toward zero phase from the opposition effect, the geometric albedo is a difficult quantity to determine accurately. In contrast, Domingue et al. (2010) found that the geometric albedo of Mercury was higher than that of the Moon by 9%. This was explained by a difference in the opposition surge between the two bodies and evidence for a higher rate of maturation on Mercury. The lower disk-averaged reflectance of Mercury at visible wavelengths relative to the nearside waxing Moon should be placed in context with the relative compositional heterogeneity of the two bodies. A study of the distribution of the absolute reflectance on Mercury and the Moon was performed by Denevi and Robinson (2008) with reprocessed Mariner 10 images and the global Clementine UVVIS mosaic (McEwen and Robinson, 1997). Mercury was found to exhibit a distribution similar to that of the lunar highlands, at an average reflectance intermediate to the lunar mare and highlands. The reflectance of the smooth plains on Mercury, morphologically similar to the maria on the Moon, was shown to be equivalent to the reflectance of the surrounding rugged material or even higher in the case of the smooth plains within the Caloris impact basin and Borealis Planitia. Multispectral imaging from the first MESSENGER flyby of Mercury also showed these spectral trends (Robinson et al., 2008). Therefore, Mercury does not exhibit a dichotomy similar to the lunar highlands and maria, suggesting a more homogeneous composition (Denevi and Robinson, 2008). That the average surface of Mercury has been found to be somewhat lower in reflectance than the average lunar nearside in the present work and by others (Warell, 2004; Robinson et al., 2008; Blewett et al., 2009) implies that the average crust of Mercury contains some as-yet-unidentified component that lowers its reflectance relative to that of the Moon. In order to highlight subtle spectral differences between Mercury and the Moon, the ratios of all MASCS spectra of Mercury (phase angles 76°, 87°, 91°) to the MASCS spectrum of the Moon (phase angle 65°) are shown in Fig. 7. Also presented in this figure are the ratios of all MDIS spectra of Mercury (phase angles 37°, 52°, 118°, 129°) to the MDIS spectrum of the Moon (phase angle 65°). Note that the lunar spectra used in these ratios are those as

Fig. 7. Ratio of the reflectance measured by MASCS and MDIS of Mercury at various phase angles to the Moon at a fixed phase angle of 65°, normalized to 1.0 at 700 nm.

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observed from the unique perspective of MESSENGER (shown in Fig. 5a) and therefore represent mostly farside terrain. No photometric adjustments have been applied to any of the curves in Fig. 7, but they have been normalized to 1.0 at 700 nm. This approach highlights any variations in spectral properties due to compositional differences as well as the different phase angle of each observation. At this early stage in our understanding of the photometric behavior of Mercury, attempts to adjust the data to a common phase angle may introduce artifacts that would mislead the interpretation. Presenting the data as a ratio has the benefit of eliminating the dependence on the absolute calibration of either instrument. Although variations in the radiometric sensitivity of either instrument due to time or temperature effects are not cancelled by the ratio, they are unlikely. Time-dependent changes in the sensitivity have not been seen in repeated MASCS observations of stars. Both MDIS and the visible channel of VIRS employ siliconbased detectors. The long-wavelength response of silicon is known to increase with increasing temperature. From variations noted in the color of intermediate terrain on Mercury measured at different detector temperatures, an empirical, nonlinear adjustment to the temperature response of MDIS has been implemented (Hawkins et al., 2009). The effect of temperature on the VIRS detectors was characterized during ground testing and is included in the calibration used here. However, these adjustments for the VIRS temperature sensitivity are not currently (as of April 2010) implemented in the calibrated data archived in the Planetary Data System. In Fig. 7 Mercury is seen to have a shallower spectral slope than the farside Moon at wavelengths below 700 nm. If Mercury and the Moon exhibited the same spectral slope, then the MDIS curve at 52° phase and the MASCS curve at 76° phase would be fairly flat since the MDIS and MASCS spectra of the Moon were obtained at not greatly different phase angles (65°). Between 800 and 1000 nm the relative rise in the reflectance of Mercury may be due to the lack of a 1-lm ferrous-iron absorption band or an absorption band having a shallower depth than that of the Moon. The region of the Moon observed by MASCS and MDIS was dominated by mature highland terrain, and the ferrous-iron absorption feature near 1 lm would therefore be expected to be weak. While the presence of this feature is not obvious in the MASCS lunar spectrum in Fig. 5, the absence of the feature in the Mercury spectra may still be detectable as a ratio. On the other hand, the data presented here does not preclude the existence of an absorption near 1 lm in the disk-integrated Mercury spectrum. The relative reflectance continues to decline in the near-infrared and then rise again above 1350 nm. This latter trend may be due to a small thermalemission contribution from the much hotter Mercury surface. Clark (1979) found that thermal emission begins to dominate at wavelengths longer than 1.5 lm on the basis of a disk-integrated Mercury spectrum obtained from a ground-based observatory. In order to evaluate the presence of a thermally emitted component in the MASCS data, a model of the temperature distribution across the surface will be required. An informative test of this hypothesis would be to search for emission in the resolved spectra of Mercury obtained by MASCS, which sampled a wide range of solar incidence angles (and thus temperature). However, such an effort is beyond the scope of the present work. In the VIRS visible channel, the MASCS spectra at 87° and 91° phase angle appear nearly identical and slightly steeper sloped than the 76° MASCS curve, consistent with the color trends of the MDIS spectra. In addition, the MASCS spectra appear intermediate between the MDIS spectra at 52° and 118° phase, showing that the color properties measured by the two instruments are consistent. The trends noted in the MASCS visible channel are not continued into the MASCS near-infrared channel. This divergence is not understood and is likely the result of an as-yet uncharacterized instrument artifact. The MASCS near-infrared spectrum at 91° phase appears consistent with the long-wave-

length filters of MDIS, but the other two spectra are not. If the MASCS near-infrared curves at 76° and 87° phase were too low by 5%, then the remaining discrepancies between MASCS and MDIS could be due to differences in observed terrain. More data and further analysis are required to understand these apparent inconsistencies in the near-infrared spectra from MASCS. The wide phase angle coverage of the MDIS dataset enables a study of the phase-reddening effect for Mercury. Evidence for this effect was found in early observations of Mercury for wavelengths greater than 600 nm, with the change in slope similar to that for the Moon (Irvine et al., 1968). A similar conclusion was drawn from an analysis of more recent observations (Warell and Bergfors, 2008). Fig. 8a shows the ratio of the Mercury reflectance from MDIS at the phase angles of 52°, 118°, and 129° to the MDIS reflectance of Mercury at 37° phase. To remove the effect of decreasing brightness with phase angle and highlight the spectral variation, each spectrum is normalized to the mean. A clear trend is evident: the reflectance at larger phase angles exhibits a steeper spectral slope. This trend was also seen by Domingue et al. (2010). A direct comparison of the magnitude of Mercury’s phase-reddening effect with that of the Moon can be made using the ROLO photometric model. Because the ROLO photometric model of the nearside Moon is valid only out to a maximum of 90° phase, this comparison is limited to the measured reflectance of Mercury from MDIS at 37°

Fig. 8. (a) Ratio of Mercury reflectance from MDIS at 52°, 118°, and 129° phase to the reflectance at 37° phase. (b) Ratio of Mercury reflectance from MDIS at 52° to 37° phase, along with the same ratio from ROLO for the nearside Moon and from Mallama et al. (2002) for Mercury in the visible photometric filter.

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and 52° phase. For reference, the absolute disk-integrated reflectance of Mercury from MDIS at 37° and 52° phase, along with the reflectance of the nearside waxing Moon from ROLO at the same phase angles, are shown in Fig. 6. Using these curves, the ratio of the reflectance at 52° to the reflectance at 37° for both Mercury and the waxing Moon is as shown in Fig. 8b. Also included in this plot is the reflectance ratio at the same phase angles for the waning Moon from ROLO and for Mercury derived from the Mercury photometric model of Mallama et al. (2002). The single data point from Mallama et al. (2002) does not inform the phase-reddening effect, but provides a measure of consistency (2.5%) for the photometric change in brightness measured by MDIS at 550 nm. The shape of the ratio for the Moon is seen to be similar for the waxing and waning phases, though the waning Moon appears to have a lower average ratio because of the increasing proportion of low-reflectance maria in the western hemisphere as the phase angle increases. The shape of the Mercury spectral ratio is seen to be slightly steeper than that of the Moon. This difference implies that Mercury’s spectral slope increases at larger phase angles slightly faster than for the Moon, at least between 37° and 52° phase. We can use a spectral ratio to quantitatively compare the phase-reddening effect between Mercury and the Moon. For MDIS, the two filters centered near 480 nm and 947 nm were chosen while for ROLO filters centered near these wavelengths were selected (487 nm, 942 nm). The ratio of the reflectance at the longer wavelength to the shorter wavelength was found to be 1.66 (37° phase) and 1.73 (52° phase) for Mercury, 1.71 (37° phase) and 1.76 (52° phase) for the waxing Moon, and 1.69 (37° phase) and 1.72 (52° phase) for the waning Moon. Therefore, the increase in the spectral ratio from 37° to 52° phase is 4% for Mercury, 3% for the waxing Moon, and 2% for the waning Moon. Fig. 9 shows the disk-integrated reflectance of Mercury (75°, 86°, and 90° phase) and the Moon (66° phase) as measured by the UVVS-MUV channel of MASCS. Because there are few studies of the photometric variation of the Moon or Mercury at ultraviolet wavelengths, there has been no attempt to adjust these spectra to a common phase angle. Each spectrum has been normalized to 1.0 at 300 nm to remove variations in brightness due to photometric effects and to highlight differences in spectral shape. The Mercury spectra were acquired after the two MESSENGER flybys of the planet by rastering the small disk image (0.05–0.07° in diameter) up and down along the atmospheric slit (0.04°  1.0°) of the spectrometer. Several individual spectra were averaged together for

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each of the three observations, corresponding to conditions when the planet was located within the central half of the entrance slit. Although the Mercury spectra were acquired at three different phase angles (75°, 86°, and 90°), the curves appear nearly identical in shape. For the observations of the Moon acquired during the Earth flyby, the body was 0.2° in size, overfilling the UVVS surface slit (0.04°  0.05°). Because of the finite time required to obtain a UVVS spectrum, the wavelength associated with each footprint of the scan varies as the spacecraft slews the aperture across the lunar disk. This aspect of data acquisition creates a spatial and spectral coupling that does not easily facilitate a disk-integrated measurement. Therefore, only spectra that were acquired when the entrance aperture was contained within the illuminated region of the Moon are considered for analysis here. It is seen in Fig. 9 that the average spectrum of the Moon at 66° phase exhibits a shallow slope relative to the Mercury spectra. Part of this difference in slope between Mercury and the Moon could be attributed to photometric (phase angle) differences. 6. Discussion 6.1. Space weathering on the Moon The chemical and physical changes that occur when a material is exposed to the space environment are collectively known as space weathering. On the Moon, it has been demonstrated that fresh material exposed by small impact events exhibits higher reflectance, a shallower spectral slope in the visible and near-infrared, and deeper absorption features than mature material of the same composition (Adams and Jones, 1970; Adams and McCord, 1971; Fischer and Pieters, 1994). The spectral effects of space weathering can depend on composition. An analysis of the maturity trends of lunar mare basalts using the Clementine UVVIS dataset concluded that the visible spectral slope of these materials is relatively unaffected by age (Staid and Pieters, 2000). Space weathering experiments on low-iron olivines and pyroxenes show that larger spectral changes occur in the olivine samples compared to the pyroxenes (Sasaki et al., 2002; Marchi et al., 2005). The primary optical effects associated with an iron-bearing silicate material exposed to the space environment are caused by the deposition of amorphous silicate coatings, which contain small inclusions of reduced (metallic) iron, onto regolith grains (Hapke et al., 1975a). The metallic iron in these coatings (referred to as nanophase iron, npFe0, or submicroscopic iron, SMFe) impedes the entry of incident light into the grains. There are two physical mechanisms thought to be responsible for this vapor-phase deposition: (1) sputtering by high-energy particles (mostly protons in the solar wind) and (2) micrometeoroid impacts (Hapke, 2001). A third possible mechanism in the production of metallic iron requires the implantation of solar wind hydrogen ions (protons) as a reducing agent (Housley et al., 1973; Allen et al., 1993). However, several studies have shown that such a chemical catalyst is not required. Hapke (2001) found that a synthetic lunar rock, irradiated with H ions and then rapidly melted to simulate heating from an impact event, did not exhibit any significant changes in spectral transmission. Laser irradiation experiments, simulating micrometeoroid impacts, have shown that the production of nanophase iron and the associated spectral effects do not require prior irradiation by protons (Sasaki et al., 2001). 6.2. Unique conditions at Mercury

Fig. 9. The UVVS disk-integrated spectral reflectance of the Moon (66° phase) and Mercury (75°, 86°, and 90° phase) in the middle-ultraviolet, normalized to unity at 300 nm. Mercury exhibits a spectrum with a greater slope than that of the Moon.

The role of charged-particle sputtering from the solar wind is often regarded as only a minor weathering process at Mercury due to the assumed diversion by the global magnetic field (Hapke,

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2001; Noble and Pieters, 2003). The interaction of the solar wind with Mercury’s global magnetic field has been modeled using a variety of techniques (e.g., Fujimoto et al., 2007). The incident flux of solar wind protons on the surface of Mercury during several configurations of the interplanetary magnetic field was found in one study to range from 106 cm2 s1 at the equator to 109 cm2 s1 in the latitude range 20–60° (Kallio and Janhunen, 2003). These workers found that during periods of high solar wind speed most of the Sun-facing hemisphere of Mercury was exposed to a proton flux of 108–109 cm2 s1. A model based on measurements of the magnetic field during the first MESSENGER flyby and ambient solar wind conditions gave proton flux rates of 108–109 cm2 s1 at the polar cusps (Sarantos et al., 2009). For comparison, the solar wind proton flux at the Moon is estimated to range from 1  108 cm2 s1 to 8  108 cm2 s1 (Vaniman et al., 1991). While these values represent current conditions, the time-integrated flux of solar wind protons on the surface of Mercury depends on the history of the global magnetic field and the evolution of solar activity. From stellar models and measurements of solar-like stars of different ages, it is thought that the early Sun was much more active than it is today (Ribas et al., 2005). In particular, at 3 Ga ago the average solar wind velocity and density are estimated to have been a factor of 1.5 and 5 larger, respectively, than today’s values (Lundin et al., 2007). The frequency and intensity of episodic coronal mass ejections (CMEs) are also estimated to have been much larger (Ribas et al., 2005). Therefore, it is difficult to accurately estimate the role of charged-particle sputtering from the solar wind over geologic time. However, this mechanism must have played a significant role in altering the physical state of Mercury’s surface. The flux of micrometeoroids at Mercury is expected to be greater and more energetic than at the Moon. The incident particle flux of micrometeoroids at Mercury is a factor of 5.5 greater than at the Moon and with an average velocity 60% greater, resulting in more impact melt by a factor of 14 and more vapor by a factor of 20 (Cintala, 1992). This environment would therefore be expected to mature a regolith at a rate greater than that of the Moon (if micrometeoritic bombardment is the dominant contributor to maturation). On the basis of images from Mariner 10, the higher contrast between immature and mature materials on Mercury (2.0) as compared to the Moon (1.7) was noted as evidence for a more mature mercurian regolith (Denevi and Robinson, 2008). If one assumes that Mercury and the Moon were initially of similar average composition, then from the spectral trends described in Section 6.1, a disk-integrated spectrum of Mercury would be expected to be of lower reflectance and exhibit a steeper spectral slope at visible and near-infrared wavelengths. Our finding that Mercury exhibits a reflectance similar to that of the nearside Moon and has a shallower slope in the visible and near-infrared instead suggests differences in the weathering process, composition, or both. One explanation for the lower reflectance and shallower slope in the Mercury spectrum is that the conditions on Mercury allow for metallic iron to form larger grains on average than those formed on the Moon (Noble and Pieters, 2003). Recent experimental work has shown that the grain size of the metallic iron deposits significantly affects the optical properties of weathered material. Smaller grains (<10 nm) contribute to both the darkening and spectral slope effects, whereas larger grains (>40 nm) primarily lower reflectance without producing large changes in spectral slope (Noble et al., 2007). The optical effects associated with the incorporation of larger iron grains (>40 nm) within vapor deposits would therefore be consistent with the spectral trends noted here: a more mature Mercury surface is lower in reflectance and shallower-sloped than the Moon (assuming a similar average composition). Although differences in the space environment at Mercury may play a role in explaining some of the observed spectral characteristics, the low reflectance of immature material on Mercury argues

against an interpretation based exclusively on a different weathering process (Denevi and Robinson, 2008). Relatively fresh materials (exposed through impacts) on Mercury are lower in reflectance than comparably fresh materials on the Moon (Denevi and Robinson, 2008). This result suggests that a significant contributor to the spectral difference between the two bodies is related to the composition of the surface and is not solely an exogenic process. It should be noted that an early analysis of Mercury photometric properties from the same Mariner 10 images found that immature material on Mercury was of higher reflectance than similar material on the Moon (Hapke et al., 1975b). Improvements to the data reduction and calibration of the Mariner 10 dataset used by Denevi and Robinson (2008) are thought to be responsible for the reversed conclusion. Another possible process that could lower the reflectance of silicate minerals involves a change in crystal structure due to heating. Helbert and Maturilli (2009) found that heating a sample of labradorite (an iron-free feldspar) up to a temperature approaching the maximum expected at Mercury resulted in a visual darkening and color change. However, neither of these properties was quantitatively measured in the wavelength range relevant to MASCS and Helbert and Maturilli (2009) caution that since the sample was exposed to air during the process, a chemical reaction may explain the observed effects. 6.3. Opaque minerals One possible explanation for the spectral differences between Mercury and the Moon involves the relative proportion of spectrally neutral opaque minerals. Opaque minerals are characterized by a very low spectral reflectance with minimal absorption features. A larger abundance of opaque minerals in the average crust of Mercury relative to the Moon would have the effect of lowering the overall reflectance and decreasing the spectral slope (Rava and Hapke, 1987), consistent with the observations described here. Many previous studies have identified spectrally neutral opaques as a plausible component of the Mercury regolith. After decoupling the effects of maturity, Robinson and Lucey (1997) and Blewett et al. (2007) interpreted color heterogeneity in recalibrated Mariner 10 images of Mercury to be the result of variations in opaque abundance among geological units. Also using color images from Mariner 10, Denevi and Robinson (2008) concluded that the low reflectance of immature material on Mercury relative to the Moon could be due to the presence of an opaque mineral such as ilmenite. From multispectral images of Mercury from the first MESSENGER flyby, Robinson et al. (2008) concluded that an end-member color unit characterized by a shallow spectral slope and low reflectance may contain a relatively high proportion of opaque minerals with ilmenite as one possibility. The second MESSENGER flyby of Mercury allowed Denevi et al. (2009b) to expand on the hypothesis regarding the presence of spectrally neutral opaque minerals. Blewett et al. (2009) found that the range and total abundance of ferrous-iron-bearing silicates must be small and that color variations observed within mature areas can be explained by differing abundances of opaque minerals. Ilmenite (FeTiO3), followed by spinel, is the most abundant opaque in the returned Apollo samples (Papike et al., 1991). Ilmenite occurs in some mare basalts, which also contain substantial quantities of iron-bearing silicates (notably Ca-bearing clinopyroxene). The spatially resolved spectra from MASCS (McClintock et al., 2008) and multispectral imaging from MDIS (Robinson et al., 2008) acquired during the first MESSENGER flyby of Mercury did not find indications of iron-bearing silicate minerals in fresh crater deposits (though an upper limit based on these data remains to be quantified). MESSENGER neutron spectroscopy measurements of Mercury were found to be consistent with 7 to 19 wt.% ilmenite, assuming all neutron absorption can be assigned to Fe and Ti

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(Lawrence et al., 2010). To explain the coexistence of low-iron silicates with high-iron opaque minerals, a crystallization sequence that favors the early production of Fe and Ti-rich opaques, thereby prohibiting the inclusion of these elements in later derived silicates, has been proposed (Denevi et al., 2009b). Laboratory measurements by Riner et al. (2009) demonstrate that oxides such as armalcolite and ulvospinel exhibit optical properties similar to ilmenite while also containing a lower abundance of FeO. More magnesian Feand Ti-bearing oxides have also been proposed as potential opaque candidate materials (Riner et al., 2009). Some iron is required, as the Mg-bearing endmember of the solid solution (Fe,Mg)TiO3 has been shown to be higher in reflectance and more steeply sloped than that of opaques such as ilmenite (Denevi et al., 2009a). 6.4. Implications of the UV absorption Silicate minerals (e.g. olivine, pyroxene, feldspar) exhibit a decrease in reflectance toward shorter visible wavelengths attributed to oxygen-metal charge transfer (OMCT) absorptions (Loeffler et al., 1974). Only transition metals exhibit this absorption, the most abundant of which on the Earth and Moon is iron, followed by titanium (Burns, 1993). The apparent UV absorption in the disk-integrated measurement from the first MESSENGER flyby of Mercury was interpreted by McClintock et al. (2008) to result from an OMCT absorption. The position of the UV absorption edge due to OMCT absorptions in terrestrial silicates measured in the laboratory is a function of the abundance of ferric or ferrous iron (Cloutis et al., 2008). The location of the absorption edge in the Mercury spectrum was therefore suggested to result from a low abundance of Fe-bearing silicates (McClintock et al., 2008). As discussed in Section 6.1, the process of space weathering can substantially alter the spectral properties of a planetary regolith. Analysis of color images of Mercury from Mariner 10 yielded evidence for space weathering: fresh craters appeared both higher in reflectance and lower in spectral slope than surrounding material (Hapke et al., 1975b). This correlation was also observed in the multispectral images (Robinson et al., 2008) and resolved spectroscopic measurements (McClintock et al., 2008) from the first MESSENGER flyby of Mercury. The spectral trends of space weathering on Mercury are considered to be consistent with the accumulation of nanophase iron, as is thought to occur on the Moon (Blewett et al., 2009). If we can attribute the space weathering effects on Mercury to relatively opaque vapor-deposited coatings, it is expected that volume absorptions characteristic of the underlying material will be obscured (Hapke, 2001). Furthermore, vitrification (the change in physical state of a material from crystalline to amorphous through melting and rapid solidification) associated with space weathering of minerals has been found to broaden absorption bands in the visible and near-infrared (Cassidy and Hapke, 1975). A mature Mercury regolith is therefore expected to exhibit minimal spectral absorption features. How can we reconcile the evidence that Mercury exhibits significant space weathering effects but also appears to exhibit an OMCT absorption feature in both disk-integrated and resolved mature areas? The present work adds two more measurements of the disk-integrated spectral reflectance of Mercury in the middle-ultraviolet (Fig. 9), showing that the results presented by McClintock et al. (2008) are repeatable. A change in the instrument sensitivity over time is considered unlikely on the basis of the intercomparison of stellar spectra obtained during cruise. An instrument artifact cannot be ruled out, but its origin is not obvious. Compositional differences in the response of a material to space weathering have been noted. Laboratory measurements designed to mimic both the micrometeoritic bombardment (Sasaki et al., 2002) and the ion irradiation process (Marchi et al., 2005) have shown that low-iron olivines experience larger spectral changes than comparable low-iron

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pyroxenes. Thus differences in the maturation process between the Moon and Mercury could be attributed to compositional differences between these two bodies. Staid and Pieters (2000) have shown that the visible slopes of lunar mare basalts are relatively unaffected by weathering, unlike the feldspathic highlands. However, the strength of the ferrous-iron absorption feature near 1 lm in both highlands and maria was found to diminish with age. This observation is consistent with the presence of a vapor-deposited coating that should also diminish an absorption feature in the middle-ultraviolet. It is likely that our understanding of the physical mechanism for space weathering on Mercury is incomplete. During the MESSENGER orbital mission, the acquisition of resolved ultraviolet spectra of immature materials will be important to further understand the spectral differences seen here between the average surface of Mercury and the Moon. 6.5. Spectral modeling challenges Accurate, quantitative spectral modeling of MASCS data is frustrated by three problems. The first concerns the lack of spectral reflectance libraries for realistic mineral end-member compositions at appropriate grain sizes and temperatures. Returned lunar samples from the Apollo program were found to be free of ferric iron (Fe3+) (Papike et al., 1991). Terrestrial analogs of planetary minerals are inevitably contaminated with some amount of ferric iron. Due to the intensity of the Fe3+–O charge transfer absorption at 220 nm, only very small amounts of ferric iron (<0.01 wt.%) are required to produce an observable spectral feature (Cloutis et al., 2008). If Mercury were devoid of Fe3+ as some studies suggest (e.g., Haggerty, 1978), then the ultraviolet-to-visible spectrum of candidate terrestrial minerals (such as plagioclase feldspar or low-Ca pyroxenes) would be expected to yield poor fits to Mercury spectra. The second problem deals with the photometric geometry of spectral reflectance libraries. Many of these laboratory measurements were acquired at a fixed geometry (frequently i = 30°, e = 0°) whereas the MASCS measurements will always be restricted to near 90° phase due to spacecraft pointing limitations. Using these libraries to match MASCS spectra could lead to false identifications given that the spectral shape of the disk-integrated Moon (Lane and Irvine, 1973), lunar samples (Pieters et al., 1991), and powdered planetary analogs (Gradie et al., 1980) is known to change with phase angle. The photometric properties of Mercury as measured by the MESSENGER instruments are discussed in detail by Domingue et al. (2010). The third problem concerns the lack of a model to accommodate the effects of space weathering. Recently, a radiative transfer model attempting to describe the modification of a host material’s absorption coefficient by small particles of metallic iron (Hapke, 2001) was applied to simulated laboratory spectra of weathered material (Lucey and Noble, 2008). Although the model approximately reproduced the laboratory data for iron particles 15 and 30 nm in size, deviations at visible wavelengths were marked for particles >40 nm in size. These larger particles tended to lower the reflectance but not change the spectral slope. The model of Hapke (2001) has been modified by Lucey (2010) to include iron particle size effects, leading to an improved agreement between the model and the experimental data of Noble et al. (2007). More experimental and theoretical work is needed in this area. 7. Summary and conclusions We interpret the disk-integrated spectrum of Mercury to exhibit characteristics consistent with a composition that is low in ferrous-iron-bearing silicates and contains a relatively high proportion of spectrally neutral opaque mineral phases. Evidence for

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these conclusions is based on the determination that Mercury exhibits a spectral reflectance that is similar in magnitude and less steeply sloped than that of the waxing nearside of the Moon at the same phase angle. The spectra obtained so far by MDIS and MASCS do not exhibit any conclusively diagnostic absorption features at visible and near-infrared wavelengths. Low-iron forms of the dominant lunar silicate minerals are consistent with the Mercury spectra. Such minerals include plagioclase feldspar, forsteritic olivine (Mg-rich), enstatitic pyroxene (Mg-rich), and high-Ca clinopyroxene. This interpretation of a Mercury surface composed of low-iron silicates with relatively high abundances of spectrally neutral opaques is consistent with many recent studies of both MESSENGER (Robinson et al., 2008; McClintock et al., 2008; Denevi et al., 2009b; Blewett et al., 2009) and Mariner 10 (Robinson and Lucey, 1997; Denevi and Robinson, 2008) multispectral imaging as well as ground-based observations (Vilas, 1988; Sprague and Roush, 1998; Sprague et al., 2002; Warell et al., 2006). The phase-reddening effect of Mercury has been clearly demonstrated from disk-integrated measurements from MDIS over a wide range of phase angles (37–129°). Between phase angles 37° and 52°, the magnitude of this effect is slightly larger than that of the lunar nearside (4% increase in the spectral ratio 947–480 nm for Mercury compared to 2–3% for the Moon). Irvine et al. (1968) and Warell and Bergfors (2008) had previously found the magnitude of this effect to be similar to that of the Moon. The distinctive spectral feature in the middle-ultraviolet of Mercury noted by McClintock et al. (2008) has been found to be persistent in two more disk-integrated measurements. Several studies have shown that Mercury has experienced notable space weathering effects (McClintock et al., 2008; Robinson et al., 2008; Blewett et al., 2009) Although the spectral response of silicate materials to space weathering effects has been found to depend on composition (Staid and Pieters, 2000; Sasaki et al., 2002; Marchi et al., 2005), the assumed accumulation of vapor-deposited coatings containing metallic iron grains would still be expected to erode an absorption feature in the middle-ultraviolet. It is unclear how to resolve the presence of this feature with current models of the space weathering process. Measurements by MASCS and MDIS during MESSENGER orbital observations beginning in March 2011 will provide additional spatial coverage with which to test the conclusions determined from the limited data so far. Further elemental abundance measurements from gamma-ray, neutron, and X-ray spectroscopy from MESSENGER will provide important constraints on the range of compositional possibilities informed by spectroscopy alone. Acknowledgments We thank Matthew Staid and an anonymous reviewer for constructive comments. This work was supported by the National Aeronautics and Space Administration’s Discovery Program through a contract to the University of Colorado from the Carnegie Institution of Washington. Support was also provided by the NASA MESSENGER Participating Scientist program (Grant No. NNX08AN29G to D.T.B.). This work made use of the Integrated Software for Imagers and Spectrometers (ISIS), developed by the US Geological Survey’s Astrogeology Team; NASA’s Astrophysics Data System Bibliographic Services; and the Set of Identifications, Measurements, and Bibliography for Astronomical Data (SIMBAD) database operated at Centre de Données astronomiques de Strasbourg (CDS). Appendix A. Derivation of correction for non-uniform spatial sampling Theoretically, a single spatial pixel could sample a scene in a perfect grid, replicating the operation of a pixelated camera. This

is a costly strategy in terms of time commitment and may even be prohibitive given the limitations in orienting spacecraft platforms. Actual observations involve rastering the spatial pixel back and forth across the target, i.e., smoothly drifting (slewing) the spatial field-of-view (FOV) first in one direction across the target while acquiring multiple integrations. This operation is followed by stepping the FOV in the perpendicular direction and scanning back across. Oversampling the region by designing the line-to-line spacing to be smaller than the FOV of the device ensures that the entire area will be covered without any gaps. In order to arrive at an accurate determination of the total light emerging from the body, a careful consideration of these non-idealities is required. The first correction involves the integration time. Because of the finite integration period of the instrument and the fixed drift rate of the spacecraft, the spatial FOV will be smeared across some angular region of space. Consider the case where a square FOV drifts a distance equal to the width of the FOV during one integration period. After the end of this integration, another scan begins immediately. Each unit area of sky is observed for a length of time equivalent to the integration period, and no correction is required. However, consider the case where the FOV travels a distance equal to two FOV widths. In this situation, each unit area of sky is observed only for half of the specified integration period. Therefore, the commanded integration time must be multiplied by 0.5, or alternatively the measured radiance (inversely proportional to integration time) must be multiplied by 2. Next consider the case where the FOV drifts a distance of only half the FOV during an integration period. Now each unit area of sky has been observed two times longer than the specified integration period. Therefore, the commanded integration time must be multiplied by 2, or the measured radiance must be multiplied by 0.5. In general, the measured radiance must be multiplied by the ratio of the drift distance (the drift rate multiplied by the integration period) to the instantaneous FOV width. The next correction involves the line-to-line overlap, and the concept is similar to that described above. This adjustment is perhaps better understood as a solid angle correction. If the line-toline spacing is equivalent to the FOV, then no adjustment is required. If the spacing is half the FOV, then twice as much angular area will be covered as each row contains 50% of the light from the previous row. Therefore, the solid angle for each scan must be multiplied by two, or alternatively the radiance (inversely proportional to the solid angle subtended by the FOV) must be multiplied by 0.5. As long as the target is large enough and the scene not changing rapidly, some amount of undersampling (line-to-line spacing larger than the FOV height) can be tolerated. In this situation, some area of the target body will not be sampled at all. For example, consider the case where the line spacing is equivalent to two fields of view. Only half the light from the scene has been sampled, so the solid angle must be multiplied by 0.5, or the radiance must be multiplied by two. This is effectively an interpolation and would be inaccurate for a very small object such as a star. In general, the measured radiance must be multiplied by the ratio of the line-to-line spacing to the FOV height. The instantaneous FOV considered thus far has been square. However, for VIRS the FOV is circular. For a region of space that is uniform in radiance over the extent of the instantaneous FOV, the radiance from a circular field or a square field will be equivalent. The derived irradiance will be greater for the square field by an amount determined by the ratio of the area of a square to that of an inscribed circle. Therefore, the irradiance derived for each scan must be multiplied by this ratio, which is 4/p or 1.27. Consider the consequence of a delay between the end of one integration period and the beginning of the next scan. There will be a small segment of sky that has been undersampled in time. Correcting for this requires the integration time to be multiplied

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(or the radiance divided) by the ratio of the integration period to the scan period (the time interval between the start of each scan). The total corrected irradiance from the target can then be expressed as

Ebody ¼

X

Lk  Xen 

k

  Dx Dy As T p    dx dy Ac T i

ð9Þ

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