https://orcid.org/0000-0002-2077-4877
ABSTRACT
The first in situ measurements of thermal properties of lunar regolith at a high latitude location (69.36°S, 32.34°E) in the South Polar region were made by the Chandra’s Surface Thermophysical Experiment (ChaSTE) probe aboard India’s Chandrayaan-3 lander during 2023 August 24 to September 1. The probe with 10 closely spaced temperature sensors was inserted vertically into the regolith up to a depth of 10 cm to measure the lunar daytime temperature profiles. The vertical temperature gradient was independently measured by inserting the probe by 1 cm and the average value is 3.8|$\pm$|0.24 K cm−1 for depths ranging from 2 to 10 cm at |$\sim$|09:00 Lunar Local Time (lt). Sub-zero temperature (in |$^{\circ }$|C) exists within the 10 cm layer prior to |$\sim$|10 LT. The daytime temperature variations show a systematic phase delay with depth: the warmest temperature is attained at 12 LT near the surface while that is attained at 14:40 LT at 10 cm depth. The daytime temperature variations, the significant lapse rate changes with depth, and. the phase progression of the diurnal variation observed up to 10 cm depth, provide important insight into the influence of surface heat flux further deeper into the regolith layer as well as the thermal properties of the high latitude region. The daytime variations of the in situ measured temperature are affected by local topography, solar radiation reflected from the lander body, the infrared emission from the lander and lunar surface heat flux reflected by the lander, which are estimated in this study to be |$\sim$|40 per cent. This information is critical for planning future lander missions.
1 INTRODUCTION
Lunar regolith is the surface layer extending to a depth of about 3–10 m covering the Moon’s surface, primarily composed of fine-grained material (Carrier 1973; Langevin & Arnold 1977; McKay et al. 1991; Shkuratov 2001) and is formed through continuous meteoroid impacts, space weather, and thermal erosion (Delbo et al. 2015; Pieters & Noble 2016; Kallio et al. 2019). It has low bulk density and thermal conductivity in the near surface layers (Cremers 1972, 1975; McKay et al. 1991; Xiao et al. 2022; Zheng et al. 2023; Bürger et al. 2024), thereby thermally insulating the sub-surface layer beneath a few tens of centimetres, which remain at low temperature with little local time variation. In contrast, the surface temperature varies over a wide range from about 400 K around local noon to less than 100 K in the night over the equatorial region (Hayne et al. 2017; Bürger et al. 2024). Knowledge of the thermal characteristics of lunar regolith, including temperature variations and the regolith physical properties regulating them, is essential for thermal modelling and understanding the natural preservation of stable volatiles like water-ice under the upper regolith layer in the near polar region (Vasavada 1999; Paige et al. 2010), simulations of lunar geological evolution (Fagents et al. 2010) and future lunar habitat development (McKay et al. 1991; Vasavada et al. 2012; Sakatani et al. 2018; Woods-Robinson, Siegler & Paige 2019).
Thermophysical properties of the lunar regolith at the landing sites of Apollo, Luna, and Chang’E missions were explored using in situ measurements (Cremers 1972, 1975; Langseth, Keihm & Peters 1976; McKay et al. 1991; Xiao et al. 2022; Zheng et al. 2023), analyses of returned samples (McKay et al. 1991), syntheses, and experiments with lunar simulants (Sakatani et al. 2018) and integrating measurements from the lunar orbiting missions with model simulations (Vasavada et al. 2012; Hayne et al. 2017; Bürger et al. 2024). Models of the physical and thermal properties of the lunar regolith were developed based on these measurements and most of them are found to be accurate in modelling heat transfer in lunar regolith in the near-equatorial region (Hayne et al. 2017). The temperature measurements using in situ thermal probes (Langseth et al. 1976) and thermal infrared and microwave instruments onboard lunar orbiters (Paige et al. 2010; Yu & Fa 2016; Williams et al. 2017) revealed variability in regolith properties with depth such as increase in density and significant stratification in both composition and thermophysical properties (Carrier, Olhoeft & Mendell 1991). The layering or stratification within the regolith is spatially random on the scale of thermal diffusion. Thermal skin depth would vary from 4 to 10 cm for typical upper lunar regolith (Hayne et al. 2017). Hence, most of the remote sensing measurements of diurnal temperature cycles are limited by thermophysical properties of the uppermost lunar regolith layer of tens of centimeters. The physical properties such as grain size and bulk density have great influence on thermal properties of the lunar regolith medium (Heiken, Vaniman & French 1991; Hayne et al. 2017). Hence information of temperature and its diurnal variability within these layers is pre-requisite for estimating the thermal state of the Moon.
The very low temperature of the Moon’s Polar regions supports for the existence of cold-trapped water-ice (Li et al. 2018; Gläser et al. 2021; Martinez & Siegler 2021). Thermal sublimation induced by the solar insolation causes volatile loss from the lunar surface (Vasavada 1999). Mass spectrometer measurements onboard Chandrayaan-1 orbiter indicated the presence of water vapour molecules in the lunar surface-bound exosphere (Sridharan et al. 2010), while high-resolution spectroscopic measurements mapped the water molecule content at the surface with abundance in the polar region. Radar observations and Neutron detector measurements aboard the Lunar Reconnaissance Orbiter (LRO) have indicated the possibility of buried water-ice on the sunlit surface layer as well (Li et al. 2018; Gläser et al. 2021).
The buried water-ice in the sun-lit area can be protected by a regolith layer having poor thermal conductivity from evaporation caused by the daytime surface temperatures. These advancements have further enhanced interest to explore the Moon’s South Polar region. As the thermal energy is the only cause for the sublimation of trapped/buried water-ice in the highly vacuum condition on the Moon, the thermophysical properties of the regolith are critical factors in the stability of the volatile deposits in the lunar sub-surface.
Physical models have been reported for constraining the thermophysical properties of the lunar regolith in the higher latitudes (Martinez & Siegler 2021). However, validation of these models has been inadequate due to the lack of in situ measurements. Very low thermal conductivity (|$<$|0.03 W m|$^{-1}$| K|$^{-1}$|), wide range of diurnal variation of temperature, variability of regolith density with depth, and the tenuous exosphere make the in situ probing of the lunar surface a challenging task.
Chandrayaan-3 (CH-3), India’s third lunar exploration successfully landed at the high latitude location at 69.36°S 32.34°E on 2023 August 23. The lander is comprised of three scientific payloads of which Chandra’s Surface Thermophysical Experiment (ChaSTE) is designed to probe thermophysical properties of the top 10 cm of the lunar regolith. This paper presents the first in situ measurements of the temperature profiles and their temperature variations in the top 10 cm of the lunar regolith at a high-latitude location on the Moon’s Southern near-Polar region made by the ChaSTE payload during 2023 August 24 to September 1.
2 TEMPERATURE PROBING EXPERIMENT AND DATA
The primary data used in this study is the lunar daytime temperature measured by the ChaSTE probe. Besides the above, the infrared (IR) data of the Diviner onboard LRO mission is also used for comparing the diurnal variation of surface temperature with in situ measurements.
2.1 ChaSTE probe
The scientific objective of the ChaSTE experiment is to measure the vertical temperature profiles, temperature gradient, and the thermal conductivity of the surface regolith up to a depth of 10 cm. The ChaSTE payload consists of three modules: (i) thermal probe; (ii) deployment and penetration mechanisms; and (iii) electronic modules. The probe module (shown in Fig. 1), a 35 cm long hollow cylindrical structure with varying inner diameter from 1 cm at its base to 0.4 cm at the nose end in step increments of 0.2 cm, is fabricated using Cynate-ester composite material which offers very low thermal conductivity (|$\sim$|0.013 W m|$^{-1}$| K|$^{-1}$| in vacuum condition), less mass (0.75–0.8 g cc−1) and high mechanical strength, to withstand the required penetration force. The probe tip is fitted with a sharp cone tip made with Titanium alloy (Ti-6Al-4V ELI Grade) while the other end is fitted with a vespel cylinder to interface with the deployment and penetration mechanisms which are driven by brushless DC (BLDC) motors.
ChaSTE probe (schematic drawing) embedded with 10 PT-1000 RTD sensors (S1-S10) at the levels of 0, 6, 12, 18, 24, 32, 42, 59, 77, and 94 mm distances relative to S1 sensor. The sensors S1, S3, and S5 are fitted on the probe side of 90|$^{\circ }$| with respect to other sensors to preserve the structural strength of the probe. The sharp cone tip made with Titanium alloy (Ti-6Al-4V ELI Grade) while the other end is fitted with a vespel cylinder to interface with the deployment and penetration mechanisms.
The thermal probe houses 10 resistance temperature devices (RTD) made of Platinum (PT-1000) [S1(top) to S10 (bottom)] located at different seperations (0.6 cm to 1.8 cm) along the axial direction of the probe. Kapton foil heater (0.1 W) strip of 0.4 cm wide is wrapped around the probe at the location of the sensor S9. The sensors are placed along the contour of the body of the probe (Fig. 1) such that they will be in contact with the soil while the probe is deployed into the lunar surface. The sensors are isolated from the body of the probe through very low thermal conductivity (0.04–0.05 W m−1 K−1) potting compound (Urethane modified epoxy filled with glass microballoons). The leads of the platinum resistance thermometer (PRT) sensors and heater are rooted to the electronic module housed inside the lander. The instrumented part of the probe is designed for inserting into the lunar regolith down to a depth of |$\sim$|10 cm for the temperature measurements.
After the soft-landing of the lander on the Moon and completing the pre-sched uled operations, the probe which was stowed to the +Y panel of the lander body was deployed downwards (90|$^{\circ }$| with respect to the bottom horizontal plane of the lander). Once deployed, the probe was mechanically locked in that position to avoid any lateral movement during the probe insertion and then slowly pushed (2.5 mm per telecommand) into the lunar regolith using the penetration motor and ball screw mechanism, so that the disturbance on the regolith is the least. This ensures that the regolith is not much disturbed, unlike in the case of drilling or agile movements. The complete insertion took place over a period of |$\sim$|1 h Lunar Local Time (LT) period (corresponding to |$\sim$|29 h on Earth). The probe penetration mechanism was designed to provide a stroke of up to |$\sim$|300 mm (including length of the probe and clearance from the ground) to achieve the required depth of penetration on different possible landing conditions at the local terrain. The entire deployment, penetration, RTD excitations, data collection, telemetry, and the probe retraction operations were carried out by giving telecommands from the mission control centre.
ChaSTE operations started on 2023 August 24 at 12:19 UTC (|$\sim$|08:18 LT) 1 day after landing, waited for the settlement of any plumes until and operated till 2023 September 2 at 09:19 UTC (|$\sim$|16:05 LT) |$\sim$|8 Earth days covering most part of lunar daytime. In this mode of experiment, continuous in situ measurements of temperature at different depths were carried out from 09:12 to 15:20 LT.
2.2 Chandrayaan-3 landing site
CH-3 landing site is at a Southern hemisphere high latitude location (69.373°S, 32.319°E) characterized with slopes |$< 7^{\circ }$|, boulders |$<$|0.32 m of diameter, sunlit for at least 11–12 Earth days, less craters and boulders so that topography of local terrain do not cast shadows for long durations (Amitabh et al. 2023) (Fig. 2). The position of the ChaSTE probe insertion was selected such that it should be in the maximum sunlit side and the lander does not cast any shadow on the penetrated location on the surface, since the maximum solar zenith angle is |$\sim 80^{\circ }$|. The primary landing site is finalized based on better safe grid distribution in the entire area of 4 km |$\times$| 2.4 km and satisfied the criteria with a slope |$<$|7|$^{\circ }$|. Near the landing site, 78 per cent of the area has a slope of less than 4|$^{\circ }$| and relatively higher slopes were found only in crater walls and ejecta layers (Amitabh et al. 2023). The inclination of the lander was |$\sim$|6|$^{\circ }$| in the Northward and ChaSTE probe was deployed and penetrated near a crater wall in the Sunward local slope angle.
The image of CH-3 landing site at 69.373|${^\circ}$|S, 32.319|${^\circ}$|E taken by OHRC camera onboard Chandrayaan-2 (www.issdc.gov.in). Inset in Fig. 2 shows the average diurnal temperature with standard deviation obtained from Diviner Lunar Radiometer Experiment over the site.
The surface around the landing location was disturbed by the plumes of the thruster nozzles. The detection and characterization of ejecta halo around the vicinity of the Vikram lander using pre- and post-landing images from the Orbiter High-Resolution Camera (OHRC) from the orbiter of Chandrayaan-2 were reported (Singh et al. 2023). Displacement of ejecta was observed by the lander’s Landing Image Camera (LIC) and the mass of ejecta material which is empirically related to the mass of the and was estimated to be |$\sim$|2.06 tonnes over a wide area (Singh et al. 2023) which might have disturbed or partially removed the top-most fluffy layer. The post-landing Dual Frequency SAR (DFSAR) onboard Chandrayaan-2 orbiter image reveals a 177 m|$^2$| area, surrounding the CH-3 landing location is characterized by high CPR and elevated even bounce and volume scattering which is due to presence of module and disturbance in the regolith structure in the landing area (Chakraborty et al. 2024).
An estimation of erosion depth caused by the plume impact on the lunar surface is derived from the reported values obtained from the post landing studies. For an assumed average density of 1300 kg m−3 for the near-surface layers, erosion depth of |$\sim$|8.9 mm is estimated. Accounting for an assuming error margin of about 25 per cent in the estimate of displaced mass, a depth of |$\sim$|6.7 mm is estimated. However, as the approaches closer to surface, the landing area may have experience greater erosion. CH-3 was equipped with four engines, but only two engines were fired during the soft-landing operation and were not from the side of the panel where ChaSTE was bonded. Thus, the specific area on the surface where ChaSTE penetrated may not have been severely affected, as it is more than |$\sim$|1 m away from the nozzle centre lines. An analysis of plume impact and lunar soil erosion during the Chang’E-4 landing, reported |$\sim$|6 mm depth crater appeared at |$\sim$|1 m distance from the nozzle centerline and decreases to 2–3 mm at 2 m distance (You et al. 2021). Based on these estimations, the thickness of the ejecta emplaced at the location of the ChaSTE measurements could be 2–6 mm.
2.3 Background thermal condition of the landing site
During the daytime, the thermal radiation emitted from the lunar surface is balanced by the solar radiation absorbed by the lunar surface and heat conducted to the lunar regolith through the surface, i.e.
where K is thermal conductivity (1.5e|$^{-3}$|–3e|$^{-3}$| W m−1 K−1), |${\it K}(\frac{\partial T}{\partial z})$| is the conducted heat flux (the estimated value of the conducted part of heat flux is 0.75–1.5 W m−2 which depends on the thermal conductivity of the lunar regolith), |$\epsilon$| is the emissivity of the lunar surface [|$\sim$|0.98 following the Diviner observations (Hayne et al. 2015)], |$\sigma$| is the Stefan–Boltzmann constant, T|$_s$| is the surface temperature, F|$_{\mathrm{ rad}}$| is the external radiation flux absorbed by the lunar surface. If the lunar surface is exposed directly towards the sunshine, the external radiation flux is given by
where I|$_0$| is the solar constant (|$\sim$|1361W m−2), R is the Sun–Moon distance in au, A is the albedo of the lunar surface (highland |$\sim$|0.12; Hayne et al. 2017) and i is the solar incidence angle which varies with local time at a given location.
The solar flux over a flat surface condition at the landing site is estimated using equation (2) varies from 180 to 400 W m−2 during 08:00 LT to 12:00 LT. This corresponds to solar zenith angle of 81.4|$^{\circ }$|–70.5|$^{\circ }$| at location. The temperature during the lunar day, simulated by the thermal equilibrium model with the assumption of direct solar illumination correspond to maximum surface temperature of |$\sim$|291 K (18|$^{\circ }$|C) at local noon. The local topography (slope) is also a critical component in determining the incident angle of solar radiation (Yu & Fa 2016), in the form,
where i is the solar incident angle, |$\theta _p$| is the slope angle, |$\phi _p$| is the slope aspect (0|$^{\circ }$|is considered), Z|$_s$| is the solar zenith angle, and A|$_s$| is the solar azimuth angle. The ChaSTE probe/CH-3 was penetrated in the rim of a crater which has a local slope of |$\sim 6.27^{\circ }$|. This can contribute maximum |$\sim$|520 W m−2 over the ChaSTE probe location.
In the context of ChaSTE, the external radiation falling on the lunar regolith can also be affected by the thermal infrared radiation emitted by the and reflected sunlight from the to the lunar surface. Hence, the measured temperature has contributions from solar radiation, IR radiation emitted by the , reflected sunlight from the to the lunar surface, and IR radiation emitted by the lunar surface. Therefore, the effective emitted radiation of the regolith |$F_{\mathrm{ eff}}$|, under thermal equilibrium, can be calculated from measured surface temperature using equation (4),
where T|$_m$| is the measured surface temperature.
2.4 Diviner Lunar Radiometer experiment
Lunar Reconnaissance Orbiter (LRO)/7Diviner Lunar Radiometer measures the IR emission in seven channels spanning from 7.55 to 400 |$\mathrm{\mu }$|m with a resolution of |$\sim$|160 m by 320 m on the lunar surface (Paige et al. 2010). For the present study, Global Cumulative Products (GCP) accessible through the Planetary Data System (PDS) to acquire a gridded data set with a 2-pixel-per-degree spatial resolution (|$\sim$|15 km) and 0.25 h local time resolution is used (Paige 2020). This data set includes radiance measurements from all Diviner infrared channels and calculated bolometric brightness temperatures. The bolometric temperature (Tbol) mean data for 68.75°S to 69.75°S; 30.25°–33.25°E is used to represent the average surface temperature of the regolith over the CH-3 Vikram landing site region (Fig. 2).
3 IN SITU MEASUREMENT OF REGOLITH TEMPERATURE AT THE LANDING SITE USING ChaSTE
The controlled movement of the ChaSTE probe based on telecommand and observing the sudden change in the temperature measured by each thermal sensor in a sequence were followed to identify the surface touch down of the sensors and estimate the depth to which the probe was inserted into the regolith medium. During this entire probe penetration operation period, the payload was kept in switch ON mode to continuously monitor the sensor temperatures.
3.1 Probe penetration and depth confirmation
Fig. 3 shows the temperature measured by the 10 sensors embedded on the ChaSTE probe, after switching on the payload till the completion of penetration operation and subsequent stabilization. After driving out the probe by 201.6 mm from the case of deployment mechanism, the touchdown of the bottom-most sensor (S10) was detected by the sudden decrease in temperature measured by the S10 sensor at |$\sim$|08:30 LT (shown in the bottom panel of Fig. 3). This trend was sequentially followed by the other nine sensors (S9-S1) when they subsequently touched the lunar regolith (Fig. 3). The probe was further penetrated to a depth of 6.6 cm where temperature measured by S10 varied from 303 to 269.4 K within |$\sim$|3 min time interval. This is because the probe was exposed to the Sun for hours before insertion to the regolith and the heat carried by the probe body was dissipated through conduction to the soil. The probe was further penetrated to 9.1 cm depth where it measured temperature of 267.6 K, with sub-zero temperature (in |$^{\circ }$|C) observed at |$\sim$|6.6 cm depth at |$\sim$|08:33 LT. The onboard data collection was halted at 08:34 LT as part of spacecraft operation and was resumed at |$\sim$|09:00 LT. At 09:11 LT the probe was further penetrated by 1 cm. At this fully penetrated condition the position of the 10th sensor (S10) was at |$\sim$|101 mm beneath the top surface. The location of other sensors at this fully deployed condition was, S1:|$\sim$|7 mm, S2:|$\sim$|13 mm, S3:|$\sim$|19 mm, S4:|$\sim$|25 mm, S5:|$\sim$|31 mm, S6:|$\sim$|39 mm, S7:|$\sim$|49 mm, S8:|$\sim$|66 mm, and S9:|$\sim$|84 mm.
(Top panel) The temperature measured by all the 10 RTD sensors (S1–S10) of ChaSTE thermal probe of CH-3 during penetration operation. (Bottom panel) Touch down of S10 sensor is shown.
The rate of change of temperature estimated from the temperatures measured by different sensors (S1–S10) during the 1 cm downward movement of the probe in the last phase of the insertion can be used to determine the actual thermal gradient rate of temperature with depth in the lunar regolith. The time required for the last operation of 1 cm penetration was less than 10 s. This provides an opportunity to independently assess the vertical temperature gradient, when the movement caused only a change in temperature due to vertical displacement and hence provide a better handle on lapse rate estimation. The estimated temperature gradient with depth based on the above method is depicted in Fig. 4(a), which shows a higher gradient of 5.6 to 6 K cm−1 at |$\sim$|2 cm depth and decreases downwards with average vertical thermal gradient of 3.8|$\pm$|0.24 K cm−1 below 2 cm at 09:12 LT.
(a) Estimated temperature gradient with depth using the temperature measurement before and after the final 10 mm of the ChaSTE probe penetration into lunar regolith. (b) Temperature profile measured by ChaSTE sensors at 09:12 LT (black curve) and estimated temperature profile (red curve) based on thermal gradient estimated from ChaSTE measurement.
As discussed earlier, the temperature measurements by the probe might be affected by the factors, including any conduction through probe, even after sufficiently longer time after insertion. In order to set the lower bound of the actual temperature profile, the above derived temperature gradient was used to estimate the temperature profile by keeping S10 temperature constant (equal to measured) as shown in the Fig. 4(b). The thermal gradient was computed at each depth using temperature measurement by ChaSTE sensors carried out before and after final 1 cm penetration into the regolith by computing the gradient in the temperature during that duration. The estimated profile (red line) and the observed profile (black line) are shown in Fig. 4(b) which shows a maximum difference of |$\sim$|28 K above 2 cm depth. The vertical temperature profile thus reconstructed is the lower bound of the temperature profile if there was no external heating by any source like direct heating by the probe and body. The near-surface regolith layer is directly influenced (maximum) by the lander heating and solar radiation and affected by the partial displacement or deposit of regolith during the landing processes. The influence of heating from the lander is highly localized and will be affecting that layer resulting in higher thermal gradient. In contrast, as we go deeper, the layers are more influenced by heating through conduction. This led to the substantial difference between the observed profile at 09:12 LT and simulated profile using lapse rate estimation for the sudden insertion by 1 cm.
3.2 Sub-surface lunar regolith temperature
Fig. 5 shows the temporal variations of daytime temperature profile measured by the 10 sensors (S1–S10) embedded on ChaSTE probe from surface to 10 cm depth. The first two sensors which are close to surface at |$\sim$|1 cm depth show temperature variations from 328 to 340 K. The top two sensors could be directly affected by the solar radiation or IR radiation emitted by the lander, since they need not be fully inside the soil due to cavity effects (Zheng et al. 2023). This is also evident in the very close temperatures observed by the S1 and S2 sensors and the distinctly higher temperature compared to that measured by S3. At 09:12 LT the gradient of temperature between surface and 100 mm depth is |$\sim$|62 K and decreases with time and at 15:20 LT it becomes |$\sim$|36.5 K. The smaller temperature gradients in comparison with theoretical surface models could be due to the removal (disturbed) of fluffy layer during the soft landing processes, localized compaction of the regolith over the landing site (after landing of the lander and insertion of the probe), and the thermal conductivity of lunar regolith (Malla & Brown 2015).
Daytime variations of lunar regolith temperature at different depths as measured by the temperature sensors on ChaSTE thermal probe from surface (S1 is top most sensor) to 10 cm depth with depth spacing of 6, 6, 6, 6, 8, 10, 17, 18, and 17 mm (S10 is bottom most sensor).
The lunar daytime temperature profile derived from the observations is depicted in the Fig. 6. The temperature gradient in the uppermost 6 cm appears to be slightly more gradual than from 6 to 10 cm. Due to cavity effect first two sensors are affected by the solar radiation. When the lunar surface is covered with a thin layer of loosely packed dust layer with very low thermal conductivity causes large variation in temperature with depth in the near surface regolith layer and lesser temperature variation in the subsurface layers as depth increases. Any disturbance in the surface dust layer can lead to significant deviations in sub-surface regolith temperatures from those modelled based on infrared remote sensing measurements. The impact of the plume on the lunar surface during the soft landing of the CH-3 lander has been confirmed by several studies conducted after its landing. Sub-surface analyses conducted throughout the lunar cycle on a densely compacted lunar regolith without a layer of fluff showed a notable increase in temperature within the sub-surface layers compared to conditions with a dusty surface layer (Malla & Brown 2015). However, a trend of a higher temperature gradient in the 6–10 cm layer has also been noted, which differs from previously reported and simulated sub-surface temperature values, warranting further investigation.
Temporal variations of vertical temperature profiles upto 10 cm depth for every hour (LT) during the ChaSTE experiment.
Phases of daytime variations of temperature varied at different depths. This phase delay progression or diffusivity with depth is expected when heating source (solar radiation) is from the top. The magnitude of the delay is a characteristic property of the thermal conductivity of the soil. The delays in the occurrence of peak temperature at different depths (sensor positions) are obtained by taking the time rate of change of temperature at each level and are shown in Fig. 7(a). The time derivative of temperature shows the time delay in attaining the peak temperature at different depths. The time at which the rate of change of temperature is turns to negative corresponds to peak temperature with transition from warming to cooling. Note that S1 temperature peaks at 12:00 LT, S3 sensor peaks at |$\sim$|12:30 LT and finally the S10 peaks at |$\sim$|14:40 LT which indicates the thermal and physical properties of the regolith with depth. The delay estimated for different sensor is plotted against the depth (shown in Fig. 7b).
(a) Phase delay in the peaking of temperature at five depths measured by the sensors S1 (|$\sim$|0.7 cm), S3 (|$\sim$|1.9 cm), S6 (|$\sim$|3.9 cm), S8 (|$\sim$|6.6 cm), and S10 (|$\sim$|10 cm). (b) The variability of peaking time of all the 10 sensors with depth.
3.3 Regolith thermal properties over the landing site
The phase delay in reaching the maximum temperature at different depths of regolith is related to the thermal diffusivity of the medium, which in turn is linked to the bulk density (|$\rho$|), thermal conductivity (K), and heat capacity (|${\it c}_p$|) of the medium. Thus, phase delay information obtained from ChaSTE measurements can be used to infer the physical and thermal properties of the regolith in the landing site, under the assumption that the time elapsed for the phase delay is inversely proportional to the diffusivity (|$\kappa$|) of the medium (|$\kappa \sim \frac{depth^{2}}{time}$|). The estimated values of |$\kappa$| range from 0.53e|$^{-8}$| to 0.903e|$^{-8}$| m|$^{2}$| s−1, revealing two distinct layers with different diffusivities above and below |$\sim$|4 cm. The lower value of |$\kappa$| is associated with finer regolith particles and is less conductive than the layer beneath it (Hayne et al. 2017). For comparison, Langseth et al. (1976) reported diffusivity values in the range of 0.4e|$^{-8}$|–1e|$^{-8}$| m|$^{2}$| s−1.
Table. 1 presents the thermal conductivity and thermal inertia of the regolith of the landing site for different bulk density values. These values were computed using the relations K = |$\kappa \rho {\it c}_p$| and I = |$\sqrt{{\it K}\rho {\it c}_p}$|, where I is thermal inertia. For the top layer (0.7–4 cm), the thermal conductivity and thermal inertia vary from 0.004 to 0.009 W m−1 K−1 and 60 to 101 J m−1 K−1 |$\sqrt{s}$|−1, respectively, while assuming a less dense regolith of bulk density between 1100 and 1300 kg m|$^{-3}$|. Below |$\sim$|4 cm, with an assumed denser regolith layer of bulk density between 1600 and 1800 kg m|$^{-3}$|, the thermal conductivity ranges from 0.02 to 0.03 W m−1 K−1, and the thermal inertia exceeds 100 J m−1 K−1 |$\sqrt{s}$|−1. In situ measurements by Langseth et al. (1976) and laboratory experiments by Cremers (1972, 1975) show thermal conductivities of the lunar regolith on the order of 10|$^{-3}$| to 10|$^{-2}$| W m−1 K−1. Hayne et al. (2017) reported a globally averaged thermal inertia of |${\it I}_{273K}$| |$\sim$| 55|$\pm$|2 J m−1 K−1 |$\sqrt{s}$|−1 based on the the Diviner Lunar Radiometer Experiment.
Thermal parameters over the landing site.
| Bulk | Heat | Diffusivity | Thermal | Thermal |
|---|---|---|---|---|
| density | capacity | conductivity | inertia | |
| (kg m|$^{-3}$|) | (J kg−1 K−1) | (m|$^{2}$|s−1) | (W m−1 K−1) | (J m−1 K−1|$\sqrt{s}$|−1) |
| 1100 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0048–0.0081 | 65.66–85.73 |
| 1300 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0056–0.009 | 77.6–101.12 |
| 1600 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.022–0.026 | 158.4-172.04 |
| 1800 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.025–0.029 | 178.3–193.68 |
| Bulk | Heat | Diffusivity | Thermal | Thermal |
|---|---|---|---|---|
| density | capacity | conductivity | inertia | |
| (kg m|$^{-3}$|) | (J kg−1 K−1) | (m|$^{2}$|s−1) | (W m−1 K−1) | (J m−1 K−1|$\sqrt{s}$|−1) |
| 1100 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0048–0.0081 | 65.66–85.73 |
| 1300 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0056–0.009 | 77.6–101.12 |
| 1600 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.022–0.026 | 158.4-172.04 |
| 1800 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.025–0.029 | 178.3–193.68 |
Thermal parameters over the landing site.
| Bulk | Heat | Diffusivity | Thermal | Thermal |
|---|---|---|---|---|
| density | capacity | conductivity | inertia | |
| (kg m|$^{-3}$|) | (J kg−1 K−1) | (m|$^{2}$|s−1) | (W m−1 K−1) | (J m−1 K−1|$\sqrt{s}$|−1) |
| 1100 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0048–0.0081 | 65.66–85.73 |
| 1300 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0056–0.009 | 77.6–101.12 |
| 1600 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.022–0.026 | 158.4-172.04 |
| 1800 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.025–0.029 | 178.3–193.68 |
| Bulk | Heat | Diffusivity | Thermal | Thermal |
|---|---|---|---|---|
| density | capacity | conductivity | inertia | |
| (kg m|$^{-3}$|) | (J kg−1 K−1) | (m|$^{2}$|s−1) | (W m−1 K−1) | (J m−1 K−1|$\sqrt{s}$|−1) |
| 1100 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0048–0.0081 | 65.66–85.73 |
| 1300 | 820 (|$\sim$|320 K) | 0.53e|$^{-8}$|–0.90e|$^{-8}$| | 0.0056–0.009 | 77.6–101.12 |
| 1600 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.022–0.026 | 158.4-172.04 |
| 1800 | 709.5 (|$\sim$|268 K) | 1.95e|$^{-8}$|–2.3e|$^{-8}$| | 0.025–0.029 | 178.3–193.68 |
4 EVALUATION OF ChaSTE MEASUREMENTS
In order to evaluate the daytime temperature from ChaSTE measurements, intercomparison of the temperatures from different sources and conditions are carried out.
Fig. 8 shows the daytime surface temperature simulated using thermal equilibrium model (equation 1) for flat and sloped terrain, the temperature derived from the Diviner measurements and ChaSTE surface temperature observations (S1, S3). The surface temperature by Diviner measurements are the average temperature of the area that includes the landing site and the vertical lines indicates standard deviation (SD) of the temperature (blue curve in Fig. 8). On comparing these temperature values of the landing site, the IR measurements from the orbiter shows the lowest temperature values (270–290 K) while the ChaSTE in situ measurements give temperature values by |$>$|50 K compared to the IR measurements (Fig. 8).
Simulated and observed daytime temperature variation at the landing site of CH-3 lander (a) daytime temperatures measured by ChaSTE S1 sensor (black line with filled black circles); (b) daytime temperatures measured by S3 sensor on the ChaSTE probe (green line with filled green circles); (c) daytime temperature simulated using thermal equilibrium model with the assumption of direct solar illumination (red line with filled red circles); (d) daytime temperature simulated using thermal equilibrium model with the assumption of direct solar illumination and local terrain slope of |$\sim$|6|$^{\circ }$| (green line with filled green triangles); and (e) Diviner bolometric temperatures at the region including CH-3 landing site and the vertical bars represent standard deviation (blue line with filled blue squares).
The temperature computed for plane local terrain (red curve in Fig. 8) of the landing site showed very close agreement with that of IR measurements (blue curve in Fig. 8). The lander after post landing indicated an inclination about 6|$^{\circ }$|. On incorporating the slope of |$\sim$|6|$^{\circ }$| in equation (3) and estimated solar flux using equation (3), the simulated surface temperature values got an enhancement by about 20 K (green curve in Fig. 8) and the discrepancy between the simulation and in situ measurements is |$\sim$|25 K. At higher latitudes, particularly near polar region the local topography is a critical parameter that can influence the local surface temperature significantly (Hayne et al. 2015). In case of orbiter based observations, the influences of the local roughness and slopes get reduced while averaging over the pixel area.
The temperature profile simulated using vertical thermal gradient (Fig. 4) at 09:12 LT shows S1 at |$\sim$|300 K which matches with the temperature derived for sloped terrain. Hence, the lower bound of the temperature measurement over the landing site could be 298 K to 312 K (at noon) and the remaining discrepancy could be due to the influence of thermal radiation by the lander body which also heated up the lunar surface close to its neighbourhood. Since the ChaSTE experiment was carried out from lander body, the location of the probe insertion was close to the lander boundary. The plume during the soft landing and highly hot throttles of the thrusters also could contributed to the heating of the landing sites. However, it would only heat an insignificant layer of lunar regolith due to the short duration of the landing compared to the diurnal cycle. Apart from the above, the multi-layer insulation (MLI) shielding attached to the bottom pannel of lander might also reflect the surface reflected solar radiation and the emitted radiation from the landing site and its surrounding area. The enhanced difference between Diviner–IR measurements and the ChaSTE measurements can be attributed to the local slope effect, partially disturbed fluffy layer and the lander IR emission.
Fig. 9 shows the variation of the temperature measured by S1 sensors of ChaSTE along with temperature measured by thermal sensors attached to the lander legs that are in the +Y, −Y plane panels of the lander body and bottom part of the lander. The daytime temporal variability of surface temperature measured by S1 is depicted in the Fig. 9 (black curve) which shows that observed surface temperature increases from |$\sim$|330 K at |$\sim$|09:12 LT to maximum temperature of |$\sim$|340 K at noon and decreases gradually as S1 is in contact with the regolith. S1 also shows up the cooling down trend of the surface temperature with the decrease in the incident solar flux. The change of temperature is gradual from 330 to 340 K (|$\sim$|7 K) during the warming up of the lunar surface after 09:00 LT and from 340 to 323 K during cooling down period after 16:00 LT and are comparable with that reported from the Chang’E-4 lander in situ measurements (Xiao et al. 2022) which carried out temperature measurements in the far side of the Moon, though there is difference in the magnitude of the measured temperature values at the CH-3 and Chang’E-4 landing sites.
Temperature variations measured by the RTD sensors attached to the legs of the lander during the CH-3 lander experiment and measured by S1 sensor in the ChaSTE probe (black line) during the daytime.
During the daytime, the lander is also heated by both solar radiation and infrared radiation emitted from the lunar surface (Liu & Huang 2023). The temperature of the lander body at different parts including the legs can be used as a proxy for estimating the IR radiation emitted by the lander. The temperature of the lander body (including the lower leg above the ground) varies in the range of 290 to 350 K. The corresponding estimated IR radiation emitted would be 400 to 750 W m−2. The downwelling part of this radiation will be absorbed by the lunar surface and can act as a heat source in addition to the solar radiation. To quantify the extra flux required for heating lander site by 25 K more (as seen in Fig. 8), simulated the flux (Hayne & Aharonson 2015) required to generate the PRT sensors temperature of +Y legs of lander, which have a slope of 6|$^{\circ }$| and close to S1 temperature (Fig. 9). The local slope of 6|$^{\circ }$| varied the flux from 400 W m−2 (for slope of 0|$^{\circ }$|) to 520 W m−2 at 12 LT. An additional increment of |$\sim$|230 W m−2 was making a good comparison with PRT sensor temperature of +Y legs. Except during local morning before 11 LT and in the evening during the cooling down period, (after 15 LT) the temperatures of S1 and RTD on the legs are in agreement. The deviation of S1 temperature from that of lander temperature values are attributed to thermal inertia of the lunar regolith. Due to poor thermal conductivity of the regolith, the temperature of the S1 which is in contact with the regolith lags the temperature variation observed at the lander body measurements.
Hence the net flux over the lunar regolith, |${\it F}_{\mathrm{ eff}}$| would be |$\sim$|1.4F|$_{\mathrm{ rad}}$| as estimated from equation (4) to coincide with the observed surface temperature, S1. This 40 per cent excess radiation required (beyond to the solar flux) is contributed by the combined effect of the (1) solar heat flux reflected by lander, (2) lunar surface IR heat flux reflected by the lander, and (3) thermal emission by the lander.
5 CONCLUSION
The in situ measurements of lunar thermophysical properties are of great interest as potential ground truth for similar temperature measurements acquired through remote sensing from lunar orbit particularly over high southern latitude site. The temperature profiles during the lunar daytime measured by ChaSTE thermal probe onboard the CH-3 Vikram lander, during 2023 August 24 to September 1, is the first if its kind in situ measurements conducted at a high latitude location (69.36°S, 32.34°E) of the Moon. During the ChaSTE experiment, the continuous variations of temperature of lunar regolith at 10 levels, distributed from very near surface to 10 cm depth, were measured for a period of |$\sim$|6 h (|$\sim$|9:12 to 15:20 LT; correspond to |$\sim$|7 Earth days period). Analysis of the thermal structure of the lunar regolith during the warming (pre-noon) and cooling (post-noon) period of lunar daytime based on these measurements is reported here. The maximum temperature difference between surface and 10 cm depth of |$\sim$|62 K was observed at |$\sim$|09:12 LT indicating rather slow downward propagation of the surface temperature during the warming period. The vertical temperature difference during the cooling period, at |$\sim$|15:20 LT, was |$\sim$|36 K over the 10 cm depth and mainly due to the radiative cooling of surface layer and conduction of heat towards sub-surface.
The daytime temperature variations of lunar regolith with depth lead to the following conclusions: (1) a systematic phase delay in temperature variation with depth such as highest temperature attained at 12 LT in the near surface while it was attained after |$\sim$|2 h 45 min of lunar time period, at |$\sim$|10 cm depth; (2) from the phase delay information from each sensor (S1–S10) the thermal parameters such diffusivity, thermal conductivity, and thermal inertia are computed and found to be in agreement with the reported values, and also a distinct variation in the thermal properties is observed in the layers below and above |$\sim$|4 cm; and (3) a significant difference in temperature gradient was seen in the regolith layer above and below of |$\sim$|6 cm depth irrespective of the lunar warming and cooling period. The vertical temperature gradient was estimated independently from the temperature variation observed by each sensor when the probe was inserted by 1 cm, showed average vertical thermal gradient of |$\sim 3.8\pm$|0.24 K cm−1 below |$\sim$|2 cm depth at |$\sim$|09:00 LT. The estimated temperature profiles based on the gradient observations show that the surface temperature could be warmer than the actual value by |$\sim$|20 K, presumably due to the IR heating by the lander body. Sub-zero temperature presented within the 10 cm layer till |$\sim$|10 LT while the temperature increased upto 291 K at 10 cm depth by about 14:40 LT.
These observations provide insight on the influence of surface heat flux further deeper into the regolith layer as well as the changes in the thermophysical characteristics of the lunar surface regolith at the landing site in the high latitude region. The daytime surface temperature measured by ChaSTE at the landing site was |$\sim$|50 K higher than that observed by Diviner in the landing area. The observed high temperatures are attributed to (1) the local slope of the landing site by |$\sim$|6|$^{\circ }$| was causing an increase solar flux at landing site and (2) local heating by the lander body through its thermal IR emission and reflected solar radiation by the lander body to the surface and lunar surface heat flux reflected by the lander, which are estimated to be |$\sim$|40 per cent. This study also provide observational support for the potential impact of the lander in modifying the site and altering the temperature especially through IR emission.
ACKNOWLEDGEMENTS
This work is supported by Indian Space Research Organization, Department of Space, Govt. of India. The authors would like to acknowledge ChaSTE development team of Space Physics Laboratory; Solid Propulsion and Research Entity; Mechanisms and Vehicle Integration Testing Entity; Propellants, Polymers, Chemicals and Materials Entity; Aeronautics Entity; Structural Engineering Entity; Systems Reliability Entity; Electronics Systems and Actuators Entity; Materials and Mechanical Entity of VSSC and Physical Research Laboratory, Ahmedabad. We sincerely thank the Chandrayaan-3 project, ISSDC, and ISTRAC teams for payload operations.
Discussion with Dr. K. Rajeev, Director, Space Physics Laboratory, VSSC, helped in refining the inferences. We acknowledge the reviewer for the suggestions which helped to improve the manuscript significantly.
DATA AVAILABILITY
ChaSTE data used in this article are available in the Planetary Data System at the PRADAN portal: https://pradan.issdc.gov.in/ch3/ of the Indian Space Science Data Centre (ISSDC).
REFERENCES
Author notes
Formerly with Space Physics Laboratory, VSSC, ISRO.
