History of Ceres's Cold Traps Based on Refined Shape Models
Erwan Mazarico
Numerous craters in the polar regions of Ceres are perennially shadowed. In a follow-up study to Ermakov et al. (2017, for which data products were previously shared here), shape models were created for specific polar craters of interest. The stereophotoclinometry (SPC) technique (Gaskell et al., 2008) was applied to nine craters: Bilwis, Damia, Enkimdu, Zatik, and five unnamed. This allowed careful consideration of the scattered light to extract topographic details in the deep shadows within these craters.
Shape Modeling
The shape models are to be archived at the NASA PDS Small Bodies Node (here). A specific URL to this archive will be added once the products are reviewed and made public.Shadow Modeling
We first conducted illumination simulations over the whole north polar region using the regional shape model obtained by applying stereophotogrammetric (SPG) methodology (Roatsch et al., 2016; archived on PDS here), in order to determine the extent of PSRs (perennially shadowed region here, rather than truly permanent).The SPG file (CE_HAMO_G_90N_000E_STE_DTM.IMG) was cropped to +/- 330 km around the north pole, in order to provide sufficient topographic padding for the horizon computations and given that few PSRs are expected that far away from the pole. Sequentially at each pixel (136.7m/px), the horizon mask was computed in all azimuthal directions (e.g., Mazarico et al., 2011).
The map of 'perennial shadow' (at a given obliquity) was computed following O'Brien and Byrne (2022) and confirmed with more standard time-averaged illumination maps. These computations were performed for a range of obliquity values, from 1 degree to 20 degrees with a step of 1 degree.
These results were then combined into a single map which reports the highest obliquity value for which a pixel was found to be in perennial shadow (that is, it never receives direct sunlight for the specified obliquity).
This map is shared here as a GeoTIFF (see the WKT georeferencing definition here).
This data file was used for Figure 1 of Schörghofer et al. (2024), and it is available to download here as a high-resolution PDF.
Second, we performed shadow modeling based on the regional SPC models created for each crater (40m/px or 100m/px). These should be more accurate than the global SPG model. The results, which employed a triangulated mesh and the model by Potter et al. (2023), are available on the Harvard Dataverse (here). Results are shown in graphical form in Figure 3 of the paper.
Thermal Modeling
Shadowed regions on the floor of polar craters receive energy indirectly from the sections of the crater wall that are in a direct line of sight (viewshed), both at infrared and visible wavelengths. A terrain irradiance model was used to quantify the energy input, using the computational model by Potter et al. (2023), which constructs a matrix of view factors and calculates the maximum direct and indirect energy input over a selected time period. The energy balance is then translated into equilibrium surface temperatures. The results are available at the same Harvard Dataverse repository (here). Results for the current obliquity of 4° equilibrium temperatures are available in the data archive for additional obliquity values.Data Usage Policy
Please cite the following references when using any of the products described above:Publication: Schörghofer, N., R. Gaskell, E. Mazarico, and J. Weirich. "History of Ceres's cold traps based on refined shape models." The Planetary Science Journal 5(4), 99, 2024, doi:10.3847/PSJ/ad3639.
Datasets:
• Northern PSR maps based on current global SPG model: this archive
Mazarico, E. (2024). History of Ceres's Cold Traps Based on Refined Shape Models [Data set]. NASA Goddard Space Flight Center Planetary Geodesy Data Archive. doi:10.60903/GSFCPGDA-CERESPSR
• New global and 9 local SPC models: PDS SBN
• PSR and equilibrium temperature maps based on local SPC models: Harvard Dataverse
Schorghofer, Norbert; Gaskell, Robert; Mazarico, Erwan; Weirich, John, 2023, "Replication Data for: History of Ceres's Cold Traps Based on Refined Shape Models", doi:10.7910/DVN/LDMMXS, Harvard Dataverse, V1
References
Ermakov, A. I. , E. Mazarico, S. E. Schröder, U. Carsenty, N. Schorghofer, F. Preusker, C. A. Raymond, C. T. Russell, and M. T. Zuber. "Ceres' obliquity history and its implications for the permanently shadowed regions." Geophysical Research Letters 44, 2652, 2017, doi:10.1002/2016GL072250
Mazarico, E., G. A. Neumann, D. E. Smith, M. T. Zuber, and M. H. Torrence. "Illumination conditions of the lunar polar regions using LOLA topography." Icarus 211(2): 1066-1081, 2011, doi:10.1016/j.icarus.2010.10.030
O'Brien, P. and S. Byrne. "Double shadows at the lunar poles." The Planetary Science Journal 3(11), 258, 2022, doi:10.3847/PSJ/ac9e5b
Potter, S. F., S. Bertone, N. Schorghofer, E. Mazarico. "Fast hierarchical low-rank view factor matrices for thermal irradiance on planetary surfaces." Journal of Computational Physics X 17, 100130, 2023, doi:10.1016/j.jcpx.2023.100130
Roatsch,T., E. Kersten,K.-D. Matz,F. Preusker, F. Scholten, S. Elgner, S.E. Schroeder, R. Jaumann, C.A. Raymond, C.T. Russell. " DAWN FC2 DERIVED CERES HAMO DTM SPG V1.0, DAWN-A-FC2-5-CERESHAMODTMSPG-V1.0." NASA Planetary Data System, 2016.
Schörghofer, N., R. Gaskell, E. Mazarico, and J. Weirich. "History of Ceres's cold traps based on refined shape models." The Planetary Science Journal 5(4), 99, 2024, doi:10.3847/PSJ/ad3639.