Determining which rocky exoplanets have atmospheres, and why, is a key goal for the James Webb Space Telescope. So far, emission observations of individual rocky exoplanets orbiting M stars (M-Earths) have not provided definitive evidence for atmospheres. Here, we synthesize emission data for M-Earths and find a trend in measured brightness temperatures (ratioed to its theoretical maximum value) as a function of instellation. However, the statistical evidence of this trend is dependent on the choice of stellar model, and we consider its identification tentative. We show that this trend can be explained by either the onset of thin/tenuous (<1 bar) CO₂-rich atmospheres on colder worlds, or a population of bare rocks with stronger space weathering and/or coarser regolith on closer-in worlds. Such grain coarsening may be caused by sintering near the melting point of rock or frequent volcanic resurfacing. Furthermore, we highlight considerations when testing rocky planet hypotheses at the population level, including the choice of instrument, stellar modeling, and how brightness temperatures are derived. We also find that fresh (unweathered) fine-grained surfaces can serve as a false positive to the detection of moderate atmospheric heat redistribution through eclipse observations. However, we argue that such surfaces are unlikely given the ubiquity of space weathering in the solar system, the low albedo of solar system airless bodies, and the high stellar wind environments of M-Earths. Emission data from a larger sample of M-Earths will be able to confirm or reject this tentative trend and diagnose its cause through spectral characterization.

We refined our Shape from Shading (SfS) algorithm, which has previously been used to create digital terrain models (DTMs) of the Lunar and Martian surfaces, to generate high-resolution DTMs of Mercury from MESSENGER imagery. To adapt the reconstruction procedure to the specific conditions of Mercury and the available imagery, we introduced two methodic innovations. First, we extended the SfS algorithm to enable the 3D-reconstruction from image mosaics. Because most mosaic tiles were acquired at different times and under various illumination conditions, the brightness of adjacent tiles may vary. Brightness variations that are not fully captured by the reflectance model may yield discontinuities at tile borders. We found that the relaxation of the constraint for a continuous albedo map improves the topographic results of an extensive region removing discontinuities at tile borders. The second innovation enables the generation of accurate DTMs from images with substantial albedo variations, such as hollows. We employed an iterative procedure that initializes the SfS algorithm with the albedo map that was obtained by the previous iteration step. This approach converges and yields a reasonable albedo map and topography. With these approaches, we generated DTMs of several science targets such as the Rachmaninoff basin, Praxiteles crater, fault lines, and several hollows. To evaluate the results, we compared our DTMs with stereo DTMs and laser altimeter data. In contrast to coarse laser altimetry tracks and stereo algorithms, which tend to be affected by interpolation artifacts, SfS can generate DTMs almost at image resolution. The root mean squared errors (RMSE) at our target sites are below the size of the horizontal image resolution. For some targets, we could achieve an effective resolution of less than 10 m/pixel, which is the best resolution of Mercury to date. We critically discuss the limitations of the evaluation methodology.

Digital Elevation Models (DEMs) of planet Mars are crucial for many remote sensing applications and for landing site characterization of rover missions. Shape from Shading (SfS) is known to work well as a complementary method to greatly enhance the quality of photogrammetrically obtained DEMs of planetary surfaces with respect to the effective resolution and the overall accuracy. In this work, we extend our previous lunar shape and albedo from shading framework by embedding the Hapke photometric reflectance model in an atmospheric model such that it is applicable to Mars. Compared to previous approaches, the proposed method is capable of directly estimating the atmospheric parameters from a given scene without the need for external data, and assumes a spatially varying albedo. The DEMs are generated from imagery of the Context Camera (CTX) onboard the Mars Reconnaissance Orbiter (MRO) and are validated for clear and opaque atmospheric conditions. We analyze the necessity of using atmospheric compensation depending on the atmospheric conditions. For low optical depths, the Hapke model without an atmospheric component is still applicable to the Martian surface. For higher optical depths, atmospheric compensation is required to obtain good quality DEMs.

IntroductionRocky airless bodies in the solar system, e.g., Mercury, the Moon, and many asteroids, host a rough silicate regolith layer. The roughness of the surfaces influences the reflectance and emission phase curves of these bodies. At small phase angles, the “opposition effect” increases the reflected radiation and “thermal beaming” leads to higher emitted radiation compared to smooth surfaces (see Figure 1). At higher phase angles, surface roughness leads to “shadowing”, the measured thermal emission is smaller than predicted by the equilibrium model for a smooth surface. The rocky exoplanets LHS 3844 b [1], GJ 1252 b [2], TRAPPIST-1 b [3], and TRAPPIST-1 c [4] are roughly Earth-sized (see Figure 2), likely have no atmospheres, and their surfaces largely remain mysterious. We previously developed and validated a thermal roughness model for airless solar system bodies (the Moon and Mercury) [5]. In this work, we adapt our model to airless exoplanets and analyze how surface roughness and albedo affect the infrared phase curves. The resulting model can then impose constraints on the surface structure of the exoplanets. We will use this approach to analyze upcoming phase curve measurements of LHS 3844 b in the James Webb Space Telescope (JWST) General Observer Program, cycle 2, ID 4008 [6]. Figure 1. The Moon's emission phase curve demonstrates the thermal beaming effect. Adopted from [6]. Figure 2. Radii, temperatures, and stellar distances of the exoplanets studied in this work compared to Mercury, Earth, and the Moon. The radii are not to scale to the distances. The color denotes the dayside surface temperature. Figure 3. Comparison of the different host star radii and surface temperatures. MethodsWe model the reflectance component of the radiation with the Hapke model [7] and fix all parameters except for the spectral single-scattering albedo. We derive two sets of albedo values from lunar satellite and returned sample data. The “mare” set models a darker surface and represents a more basaltic composition. The “highland” set resembles a comparatively brighter surface and more feldspathic composition. We use the thermal roughness model from [5] for the emission component, which is mainly controlled by the albedo and the roughness parameter (average roughness angle). We simulate disk-resolved radiances of the planets for different phase angles and integrate them over the disk to retrieve the phase curves. We focus on the wavelength region of the JWST NIRSpec G395H/F290LP disperser/filter combination (2.7 μm-5.2 μm). ResultsFigure 4 shows the reflectance and emission phase curves for LHS 3844 b for different roughness angles and albedos. The reflected component is smaller than the emitted component in the infrared wavelength region but not negligible. The thermal beaming and shadowing effects are clearly visible. The opposition effect is most likely not detectable due to the occultation of the planet during the secondary eclipse. The simulations of all four exoplanets show that the albedo influences the amplitude of the phase curve, and the surface roughness alters the shape of the phase curve. Figure 5 shows that the two parameters appear interchangeable at small phase angles (close to the secondary eclipse). However, considering the entire phase curve allows albedo and surface roughness to be separated. Figure 6 shows the combined phase curves for the other three exoplanets. The phase curve of GJ 1252 b is like that of LHS 3844 b and the parameter influences can likely be separated. TRAPPIST-1 b and TRAPPIST-1 c have much lower relative flux densities, which makes parameter retrieval difficult. Figure 4. Reflectance and emission phase curves for LHS 3844 b. The upper row corresponds to the shorter wavelength region of NIRSpec, and the lower row corresponds to the longer wavelength region. The columns represent the two albedo sets. Figure 5. Combined reflectance and emission phase curves for LHS 3844 b for different surface roughness angles and albedos. Figure 6. Combined phase curves for GJ 1252, TRAPPIST-1 b and TRAPPIST-1 c. ConclusionThe surface roughness and albedo effects are detectable and most likely separable for LHS 3844 b and GJ 1252 b with NIRSpec on JWST. This would allow the retrieval of one or both parameters from phase curve measurements, which can provide information about the nature of extrasolar planetary surfaces. Additional albedo constraints can further improve the retrieval scheme. Due to extensive space weathering, the closely orbiting exoplanets likely have a low albedo, similar to Mercury or the maria of the Moon. The two planets of the TRAPPIST-1 system are less suited for characterization with NIRSpec. Still, MIRI measurements might enable the parameter retrieval. References[1] Kreidberg, L., Koll, D.D.B., Morley, C. et al. Nature 573, 87–90 (2019).[2] Ian J. M. Crossfield et al 2022 ApJL 937 L17[3] Greene, T.P., Bell, T.J., Ducrot, E. et al. Nature 618, 39–42 (2023).[4] Zieba, S., Kreidberg, L., Ducrot, E. et al. Nature 620, 746–749 (2023). [5] Wohlfarth, K., Wöhler, C., Hiesinger, H., Helbert, J. A&A 674 A69 (2023)[6] S. Zieba, L. Kreidberg, R. Hu, C. Morley, K. Wohlfarth, M. Tenthoff, and C. Wöhler. JWST Proposal 4008. https://www.stsci.edu/jwst/science-execution/program-information?id=4008. (2023)[7] Bruce Hapke. Journal of Geophysical Research: Solid Earth, 86(B4):3039–3054, (1981)

IntroductionSurface reconstruction of planetary bodies such as the Moon and Mercury is crucial for geomorphological analysis, reflectance normalization, thermal modeling, rover landing site planning, and outreach activities. Stereo algorithms and Shape-and-Albedo-from-Shading (SAfS) are well-established methods for planetary 3D reconstruction. The current state-of-the-art combines both methods. SAfS refines the surface slopes of a stereo digital elevation model (DEM) and typically yields 3D models at image resolution [1,2,3,4,5,6]. This approach is generally well-validated for scientifically calibrated instruments that observe the planetary body under favorable conditions. However, the limits of SAfS still need to be explored. This work applied the SAfS algorithm to planetary flyby images acquired with uncalibrated off-the-shelf cameras. We qualitatively and quantitatively assessed the algorithm's performance and found the method robust even under these challenging conditions.MethodsWe considered two images: First, a flyby image of Mercury (Figure 1, left), which was obtained with a monitoring camera during BepiColombo’s third flyby, and second, a flyby image of the Moon captured by a GoPro during the Artemis I mission (Figure 1, right). In both cases, off-the-shelf cameras without a proper radiometric calibration routine were used instead of scientific instruments. Therefore, it was necessary to calibrate the images before applying the SAfS algorithm. For calibration, we estimated a reflectance image of the region of interest with Hapke parameters from [7] to establish a relationship between the digital number output of the camera and the physical radiances. The resulting Mercury flyby DEM was evaluated qualitatively, compared to MDIS WAC images [8]. The lunar flyby DEM was compared to the SLDEM2015 (60-100 m/pixel) [9], which serves as a ground truth. Figure 1. Left: Flyby image from the BepiColombo mission [10]. Right: Flyby image from the Artemis I mission [11]. ResultsFigure 2 shows the color-coded SAfS DEM for the BepiColombo image. We found that the algorithm successfully reconstructed the surface in the center of the image but struggled with the more extremely illuminated sections at the edges. It is obvious that the algorithm reconstructed some details that are not visible in the input DEM and hence improved the resolution. Figure 3 compares a grey-scale representation of the SAfS DEM with MDIS WAC image EW0251718878F. Small craters in Izquierdo (the crater in the right half of the marked section), a few kilometers in diameter, become especially visible. Figure 4 shows the marked section in more detail. Due to the lack of high-resolution ground truth, a detailed algorithm evaluation was not possible for this image.Figure 2. Color-coded presentation of the reconstructed SAfS DEM from the BepiColombo image. Figure 3. Left: grey scale reconstructed SAfS DEM from the BepiColombo image. Right: wide-angle camera (WAC) image from MDIS [8]. The marked image section was evaluated in more detail (Fig. 4). Figure 4. Comparison of WAC image, input DEM, BepiColombo (BC) image and SAfS DEM. Below the images are the height and slope of the profile (red dashed line). However, the ground truth evaluation with the Artemis I image gives a quantitative measure under comparable conditions. Figure 5 shows the color-coded SAfS DEM of a region of interest (ROI) reconstructed from the flyby image. The results for the Artemis I image for all ROIs were of high quality. Figure 6 shows the elevation profile indicated by the dashed line in Figure 5. The algorithm refines the low-frequency initial DEM (dashed line), yielding a SAfS DEM (red line), which closely resembles the ground truth DEM (black line). The vertical RMSE between the reconstructed DEM and the ground truth is 523 m, lower than the pixel size of approximately 1500 m. However, there were inaccuracies near the ROIs’ edges, and a preferred direction aligned with the illumination direction became visible.Figure 5. Color-coded presentation of the reconstructed SAfS DEM from the Artemis image. The black dashed line marks the profile that was analyzed in detail (see Fig. 6). Figure 6. Height profile of a selected terrain profile (see black dashed line in Fig. 5). Red line: DEM generated with the SAfS algorithm. Black line: Ground truth DEM. Dashed line: Initial DEM (input for the SAfS algorithm). ConclusionIn conclusion, it is possible to obtain sharp results by applying our SAfS framework to flyby images. Both results show that, despite the challenging conditions, the SAfS algorithm could reconstruct the surface up to image resolution and increase the level of detail of the input DEM. The quality differences between the two images can mainly be attributed to the (spatial) resolution of the original images and the oblique illumination direction. Usually, the image center is distortion-free, and the illumination geometry is best suited for SAfS. We found that the surface reconstruction at the edge of the image is also possible, but the quality decreases significantly. All in all, our flyby-derived DEMs are accurate, and a previous version has been used for ESA outreach activities, similar to [12]:https://www.esa.int/Science_Exploration/Space_Science/BepiColombo/BepiColombo_s_third_Mercury_flyby_the_movie References[1] A. Grumpe, F. Belkhir, C. Wöhler. Advances in Space Research, 53(12):1735–1767, 2014.[2] C. Jiang, S. Douté, B. Luo, L. Zhang, P&RS,130, 2017 [3] O. Alexandrov, R. Beyer. Earth and Space Science, 5, 2018[4] B. Wu, W. C. Liu, A. Grumpe, C. Wöhler. P&RS, 140, 2018[5] M. Tenthoff, K. Wohlfarth, C. Wöhler. Remote Sensing, 12(23), 2020.[6] M. Hess, M. Tenthoff, K. Wohlfarth, and C. Wöhler. Journal of Imaging, 8(6), 2022.[7] J. Warell, Icarus, 167, 2,2004[8] Hawkins, S. Edward, et al. Space Science Reviews 131 (2007): 247-338.[9] M.K. Barker, E. Mazarico, G.A. Neumann, M.T. Zuber, J. Haruyama,...

. Introduction:Mercury is a fascinating planet for thermal modelers. With extreme temperatures ranging from 100 K at night to over 700 K during the day [1, 2], and its 3:2 spin-orbit resonance with the sun [3], modelling Mercury’s thermal environment presents a unique challenge. Because of its proximity to the Sun and the orbit-spin resonance, Mercury also experiences differences in regional temperature identified as “hot” and “cold” poles. Various factors influence the temperature on Mercury’s surface like the albedo variation of impact craters, topography, surface morphology, distance to the sun, density and conduction of the material etc.Over the years, many studies have attempted to model the thermal properties of Mercury, often by using the Moon as a reference due to both being an airless body [4, 5]. From Mariner 10 to BepiColombo, the accuracy of these thermal models for Mercury has significantly improved, thanks to mission data. However, due to limited knowledge about the surface composition and other constraints, thermal models still require further refinement.In this study, we present a thermal model aimed at improving our understanding of Mercury’s local temperature behavior, ahead of MERTIS’s arrival at Mercury.2. MERTIS and the observation area:MERTIS (Mercury Radiometer and Thermal infrared Imaging Spectrometer), onboard the ESA-JAXA mission BepiColombo, is a thermal infrared spectrometer (TIS) and radiometer (TIR) that is part of the Mercury Planetary Orbiter payload [6]. TIS has a spectral range of 7-14 μm with a resolution of 90 nm, and TIR, a radiometric range of 7-40 μm, divided into two bands - 8-14 μm and 7-40 μm [6].One of the primary objectives of MERTIS is to study surface temperature distribution on both day and night side of Mercury. It first observed Mercury during BepiColombo’s 5th flyby on 1st December, 2024. The spacecraft achieved its closest approach at 37,000 km and MERTIS was able to observe the planet, through its space baffle, for 37 minutes, with a pixel resolution of 27 km for TIS and 100 km for TIR.The observed area extended from 140°E to 230°E longitude on Mercury and covered major craters such as Bashō crater in the south and parts of Caloris Basin in the north including the hot pole at 180°. MERTIS was able to observe the planet with an incidence angle of as little as 0.2° to as high as 95.00°, where the Sun is below the horizon, covering therefore a large range of local time.3. Methodology:The thermal model in our study takes the energy balance thermal equation for airless bodies as a reference to calculate the temperature distribution within the observed area, where absorbed solar energy equals emitted thermal radiation.Equation 1: Energy balance equation for airless bodies.Where: T = Temperature A = Bond Albedo - 0.058 S = Solar Flux 𝜎 = Stefan-Boltzmann Constant 𝜀 = Surface emissivityThe incoming radiation, or solar flux is calculated using a constant bond albedo [2], the distance from the sun and the incidence angle. The incidence angles of more than 90° are ignored as this indicates that the sun is below the horizon.Equation 2: Incident solar energy or solar flux.Where:F0 = Solar constant for Mercury at distance from the sun.𝜃 = Incidence angle (