We present visible and thermal infrared observations of the Martian surface acquired during three Phobos transits. Observations show a decrease of up to ∼20% of the reflected solar energy, consistent with the fraction of the Sun disk eclipsed by Phobos, and no measurable surface cooling. Thermal modeling indicates that the top millimeter of the regolith has a thermal inertia larger than 100 J m−2 K−1 s−1/2 regardless of the surface morphology, and is consistent with TES regional thermal inertia values derived from diurnal cycles (e.g. ∼200 J m−2 K−1 s−1/2). The thermophysical properties of the top millimeter of the regolith exclude the presence of widespread thermally-thick dust layers, are consistent with those of the diurnal skin depths at TES and THEMIS spatial resolutions, are in accordance with high-resolution images of the surface showing no surface mantling, with General Circulation Model results, thermally derived rock abundance values, albedo, and spectroscopic data.
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 On November 19, 22, and 24 2010, the Thermal Emission Imaging System (THEMIS) onboard the 2001 Mars Odyssey spacecraft acquired a set of visible (VIS) and infrared (IR) images of the Martian surface during three transits of Phobos (Table 1) owing to a series of spacecraft maneuvers and accurate predictions of the orbits of Mars and Phobos. During these events lasting a few seconds, ∼20% of the disk of the Sun was eclipsed, reducing the incoming solar flux, and resulting in the momentary cooling of the Martian surface.
ΔEVIS (W m−2) is the difference of solar energy reflected off the surface within and outside the shadow as measured with THEMIS VIS. Tau is the atmospheric dust opacity. “Reference VIS” and “Reference IR” list THEMIS observations of the same region but before or after the transits. Other abbreviations are given in the text.
Local Solar Time
% Sun Disk Eclipsed
31 ± 1
31 ± 1
31 ± 1
I (J m−2 K−1 s−1/2)
V14955013 V18025019 V26873030
 The amplitude of the temperature change in response to solar flux variations is a function of the thermal inertia I of the surface layer (J m−2 K−1 s−1/2), which is primarily controlled by the thermal conductivity k of the bulk material (J m−1 K−1 s−1) [Wechsler and Glaser, 1965; Neugebauer et al., 1971; Kieffer et al., 1973]. The conductivity k is a function of the physical characteristics of the solid phase, mainly the typical grain size and the presence of cement [Kieffer et al., 1973; Jakosky and Christensen, 1986]. The skin depth δ (m) defines the thickness of surficial material impacted by a thermal wave:
with ρ the material density (kg m−3), CP the specific heat (J kg−1 K−1), and P the period of the illumination cycle (s). The majority of the thermal inertia studies and maps take advantage of diurnal illumination cycles (P ∼ 88776 s) [Kieffer et al., 1977; Mellon et al., 2000; Putzig et al., 2005], and are associated with skin depths ranging from ∼3 mm (dust) to ∼25 cm (bedrock). Seasonal skin depths are significantly thicker, i.e., ranging from ∼15 cm (dust) to ∼7 m (bedrock and water ice) because they are associated with longer annual variations of the solar flux (P ∼ 5.9 107 s). Seasonal variations of the apparent thermal inertia have been used to map the depth of the water ice table at high latitudes [Bandfield, 2007; Bandfield and Feldman, 2008] and identify subsurface layering [Putzig and Mellon, 2007]. With their very short periods (e.g., P ∼ 30 s), Phobos transits offer the unique possibility to probe a much thinner surface layer (δ ∼60 μm for dust, ∼500 μm for sand, and ∼5 mm for bedrock) without much influence of the material properties at greater depth, but they are rarely observed due to spatial and timing constraints [Bills and Comstock, 2005].
 Orbital and surface-based observations of Phobos and its transits have been performed and have helped refine the orbital parameters of the Martian moon [Duxbury, 1978; Viking Lander Imaging Team, 1978; Bell et al., 2005; Bills et al., 2005], but surface temperature observations have only been measured by Betts et al.  in four locations using the Thermoskan radiometer onboard the Phobos 2 spacecraft. The surface cooling associated with these transits was found to range from 0 to 5 K depending on the location, time since the beginning of transit, and surface layer thermal inertia. Data analysis confirmed the thermal inertia values derived from the InfraRed Thermal Mapper (IRTM) onboard Viking orbiter, and detected a possible physical layering in the top 100's of microns in the Tharsis region. Near Hershel Crater, no cooling was observed in accordance with high rock abundance values and IRTM thermal inertias.
 In this Letter, we present new THEMIS observations of the Martian surface during three Phobos transits, at visible and thermal infrared wavelengths, and we discuss the results in terms of surface material properties and geological context.
 At the regional scale, the Phobos shadow observations are located in three thermophysically similar regions near the equator characterized by moderate thermal inertia (∼180–220 J m−2 K−1 s−1/2) and albedo (0.23–0.24) values (Figure 1). However, at the 10s to 100s of meter scale, all three regions show distinct morphological and thermophysical characteristics.
 The first site (Table 1 and Figure 1a) lies in Amenthes Planum, in the same region as Hershel Crater [Betts et al., 1995]. The terrains where Phobos shadow is observed consists mainly of undulating resurfaced units (∼200 J m−2 K−1 s−1/2, Figure 1) characterized at MOC resolution by the eroded remnants of 100's meter size impact craters whose central depressions are only limited to a few 10's of meters (Figure 2, panel 1). The walls and rims remain associated with steep slopes, but the floors are flat indicating post-formation filling. Aeolian material accumulates in the largest and deepest features. On the western side of the ellipse, the fraction of a ∼10 km impact crater is observed during the transit and associated with steep walls and high thermal inertia values (i.e., ∼600 J m−2 K−1 s−1/2). A similar feature is presented in Figure 2, panel 2, where high thermal inertia values are clearly associated with bouldery slopes. Nearby depressions show parallel wind-related features associated with lower nighttime temperatures. Other features are regionally present (large flat floored impact craters, channels, small craters), but they are not located within the Phobos shadow ellipse.
 The second location (Table 1 and Figure 1b) belongs to Lunae Planum, and is adjacent to the low thermal inertia region of Tharsis. Overall, this region is much smoother than the previous one with flat plains (Figure 2, panel 3, ∼250 J m−2 K−1 s−1/2), numerous meter size craters and some larger (e.g. hundreds of meters) less preserved depressions. The lowest thermal inertia values of the region (∼150 J m−2 K−1 s−1/2) are consistent with sand size material, and associated with oriented aeolian features (Figure 2, panel 4) located in depressions or protected by local topographic highs. The high thermal inertia channels (walls and floors at ∼400 J m−2 K−1 s−1/2) are prominent features of this region. Figure 2 (panel 5) shows that these high thermal inertia values are associated with the layered walls of the channels.
 The third site (Figure 1c and Table 1) is located 600 km East of the first site, but at much lower elevation (∼−1700 m vs. ∼300 m for the other sites), just North of the Southern Highlands-Northern Lowlands boundary. The area is relatively rough at the km scale, with numerous hills and mesas, modified and fresh craters of all sizes (I∼500 J m−2 K−1 s−1/2) where rocky material is identified (Figure 2, panel 6), and small units of nearly flat and monotonous terrains displaying moderate (∼250 J m−2 K−1 s−1/2, Figure 2, panel 7) to high (∼600 J m−2 K−1 s−1/2, Figure 2, panel 8) thermal inertia values. In the later case, the surface material seems indurated, based on the sharp transitions and arêtes near depressions, whereas the substrate of the former may be covered by a layer of particulates based on the rounded and smooth transitions.
 All the transit observations have been acquired near 16.5 H local time, when the Sun is ∼20° above the horizon. In this configuration (i.e., near-horizon transit), the angular radius of Phobos is close to minimal (i.e., ∼0.17°) [Bills and Comstock, 2005] and only ∼20% of the Sun disk is eclipsed (versus ∼38% for a zenith transit). Because the three observations presented are nearly identical (i.e., local time, season, event duration, amplitude of the transit, surface albedo, latitude, regional thermal inertia, absence of surface temperature drop) the modeling results and interpretations are nearly identical as well. Therefore, only one event is discussed as a type case, and the results and interpretations presented are representative of all three observations reported in Table 1.
 THEMIS VIS images (band 3, centered at 0.654 μm) show a clear decrease of the energy reflected off the surface (Table 1 and Figures 3a and 3b). A comparison with other images acquired at other times by THEMIS VIS, Viking Camera, Context Camera (CTX) and High Resolution Stereo Camera (HRSC) confirms that the surface darkenings are transient, and do not correspond to albedo or topographic features (Table 1). The radiances measured within the shadows and on the surrounding terrains indicate a ∼20% decrease of reflected energy in all three cases, consistent with the predicted ratio of the angular disks of Phobos and the Sun (Table 1).
 Simultaneously, radiometric surface temperatures have been measured with THEMIS IR. At 16.5 H, Martian surface temperatures are mainly controlled by the local topography, and weakly by the surface material thermal inertia [Zimbelman and Kieffer, 1979]. As a result, the temperature fields displayed on the three THEMIS IR stamps acquired during the transits (Table 1) are homogeneous, with high values on Sun facing slopes (i.e., ∼15 K above scene average) and low values in the areas that have been shaded for most of the afternoon (i.e., ∼15 K below scene average). In all three events, no obvious surface cooling is measurable (Figure 3c), despite 1) the timing of the observations targeting the trailing side of the shadows, where the theoretical temperature drops are the largest, and 2) THEMIS' ability to detect relative temperature differences as low as 0.5 K at 245 K [Christensen et al., 2004], especially considering the large number of pixels coadded (i.e., >7 × 105). Relative temperature variations smaller than 0.5 K are not considered reliable in the context of this study.
 To ensure that the observed transit surface temperatures are not, indeed, cooler than usual and unnoticed due to subtle variations of the local topography or surface material thermophysical properties, we have compared them with other THEMIS surface temperature measurements acquired at similar local times but on other days (Table 1 and Figure 3d). To remove the temperature differences due to variations of the heliocentric range and latitude, each image has been untilted and normalized with respect to the average scene temperature. The resulting images display the temperature variations within each scene with respect to the average temperature (Figure 3d), which we refer as ΔT. Again, the comparison between those normalized surface temperatures during and before (or after) the shadow transits does not show any anomalous cooling (Figures 3c and 3d).
Figure 3e shows two latitudinal ΔT profiles, resulting from the longitudinal average of the surface temperatures during and before the transit. No surface cooling is detected in the latitude range of the transit (e.g., 5.18–6.15°N), and high frequency ΔT variations can be individually associated with localized steep topographic features. To avoid summing pixels where the times since the beginning of the eclipses are different, the transit and reference stamps (Figures 3c and 3d) have been discretized in the longitudinal direction, in elements ranging from ∼32 km (1 element of 320 pixels, no discretization) to ∼1 km (32 elements of 10 pixels), and averaged longitudinally to generate several sets of latitudinal ΔT profiles at different longitudes. These profiles do not reveal any longitudinal or latitudinal surface cooling, and are similar to the profiles shown in Figure 3e. For this reason, they are not shown on Figure 3.
3. Heat Transfer Modeling and Discussion
 The surface temperature observations are compared with the results of a finite element algorithm predicting Martian regolith temperatures. Our model is defined by a 1 μm surface element (1.15 growth factor at depth), and an output time step of one second. The atmospheric effect and the initial temperatures are computed using H.H. Kieffer's KRC model [Fergason et al., 2006a]. Our model runs for ten Martian days before the transit occurs, to minimize residuals stemming from the initial conditions. The timing of the events (durations, local times), and the angular sizes of the Sun and Phobos are given in Table 1. This information was used to adapt the heat flux contributed to the surface by direct solar illumination S (W m−2) as a function of the Phobos-Sun angular size ratio (i.e., ∼20%,Table 1), the absolute time (∼16.5 H, Table 1) and duration of the events. Overall, the model solves for:
with ε the surface emissivity, σthe Stefan-Boltzmann constant, TS the surface temperature (K), i the incidence angle, FIR the downwelling atmospheric flux (W m−2), and Z the depth (m).
 Modeled regolith thermal inertias are variable and range from 10 J m−2 K−1 s−1/2 (common low thermal inertia value mapped on Mars by TES at the global scale [Putzig and Mellon, 2007]) corresponding to ∼1 μm atmospherically sedimented dust, [Conrath, 1975; Pang and Ajello, 1977] to 100 J m−2 K−1 s−1/2 (i.e., >50 μm grains or cemented material). Higher thermal inertia values are associated with a transit surface cooling that would potentially not be detectable with THEMIS (i.e., <0.5 K).
 To simplify the discussion, the modeling results are discussed in terms of relative surface cooling, and not absolute temperatures. Modeling results (Figure 4) show that low surface thermal inertia material (i.e., 10–100 J m−2 K−1 s−1/2) should be associated with a measurable temperature drop at the end of a transit (i.e., 0.5–3.0 K), whereas moderate thermal inertia material (i.e., >100 J m−2 K−1 s−1/2) does not yield any significant surface cooling (0.5 K or less). In the absence of observable temperature change at the end of the transits, THEMIS temperatures are consistent with moderate (or higher) surface material thermal inertia within the top 1 mm (derived from equation (1)), excluding the presence a continuous thermally thick layer of dust.
 The presence of near-surface layering cannot be assessed in the absence of observable cooling, but is unlikely because 1) the low surface albedo (i.e., ∼0.24) in the three regions excludes a continuous layer of surface dust (dust albedo is ∼0.28 [Mellon et al., 2000]), and 2) TES diurnally derived thermal inertia values (i.e., ∼200 J m−2 K−1 s−1/2) are not consistent with a dusty substrate (which would dominate the temperature cycle, as observed in nearby regions).
 The absence of detectable cooling on the trailing side of the shadows indicates that the thermal inertia of the top ∼1 mm of regolith is larger than 100 J m−2 K−1 s−1/2, which is consistent with TES and THEMIS diurnal thermal inertia values integrating thicker surface layers (i.e., ∼200 J m−2 K−1 s−1/2 and 150–600 J m−2 K−1 s−1/2 respectively) and suggests the absence of thermally thick widespread surface dust. In addition, the surface morphologies correlate with the THEMIS nighttime thermal inertias: high thermal inertia observations correlate with steep slopes, rocky units, and hardened surfaces (Figure 2, panels 2, 5, 6, and 8) without indication of thermally-thick and morphologically-thin dust accumulation. The thermal inertia of aeolian material is consistent with sand size particles (Figure 2, panel 4) without any indication of a thermally-thick dust cover. This observation is not sufficient to identify active aeolian features, but indicates that the depressions in which they are observed are not currently trapping dust. The overall correlation between surface materials and morphologies is consistent with other visible and thermal observations obtained from the surface [Fergason et al., 2006b].
 Other moderate thermal inertia terrains (Figure 2, panels 1, 3, and 7) show less conclusive characteristic morphological features. However, they do not present the mantled aspect of the low thermal inertia regions (e.g., Tharsis) covering large surfaces on Mars.
 Minimal surface dust is also consistent with a) spectral signatures associated with medium/high dust index values (i.e., ∼0.95 [Ruff and Christensen, 2002]) indicating of regions moderate to modest dust presence; b) medium-high rock abundances (e.g., ∼10%) suggestive of regions of low dust and sand sedimentation [Christensen, 1986; Nowicki and Christensen, 2007]; c) GCM results identifying the three observed regions as areas of dust removal or modest accumulation, under current and/or past atmospheric conditions [Newman et al., 2005]; e) a previous shadow observation by Thermoskan showing no cooling in a similar thermophysical region [Betts et al., 1995].
 Thermal observations of Phobos shadows on the Martian surface provide unique physical constraints on the upper hundreds of micrometers to millimeter of the regolith, in contrast with diurnal or seasonal observations probing millimeters to meters depths. The analysis of the thermal data excludes the presence of a continuous thermally thick (i.e., ∼1 mm) dust layer, and is consistent with other independent remote sensing observations and surface morphologies showing no sign of mantling (Figure 2). Phobos shadow observations can contribute to bridge the gap between high-coverage low-resolution orbital data and punctual-coverage high-resolution surface-based data obtained by rovers and landers.
 This work was funded with a NASA MFRP grant. S.P. would like to thank the THEMIS mission planners and JMARS programmers (K. Murray, S. Anwar, S. Dickenshied, E. Engle, D. Noss, and J. Hill,) for their invaluable help with the data acquisition, as well as J. Bandfield for sharing his DaVinci atmospheric model inspired from H.H. Kieffer's KRC. Scripts shared by C Edwards were critical for the accurate projection of the different datasets. We would like to thank Robin Fergason and Scott Nowicki for their valuable and careful reviews.
 The Editor thanks Scott Nowicki and Robin Fergason for their assistance in evaluating this paper.