TY - JOUR A1 - Kramer, Tobias A1 - Noack, Matthias A1 - Baum, Daniel A1 - Hege, Hans-Christian A1 - Heller, Eric J. T1 - Homogeneous dust emission and jet structure near active cometary nuclei: the case of 67P/Churyumov-Gerasimenko N2 - We compute trajectories of dust grains starting from a homogeneous surface activity-profile on a irregularly shaped cometary nucleus. Despite the initially homogeneous dust distribution a collimation in jet-like structures becomes visible. The fine structure is caused by concave topographical features with similar bundles of normal vectors. The model incorporates accurately determined gravitational forces, rotation of the nucleus, and gas-dust interaction. Jet-like dust structures are obtained for a wide range of gas-dust interactions. For the comet 67P/Churyumov-Gerasimenko, we derive the global dust distribution around the nucleus and find several areas of agreement between the homogeneous dust emission model and the Rosetta observation of dust jets, including velocity-dependent bending of trajectories. Y1 - 2015 ER - TY - CHAP A1 - Noack, Matthias A1 - Reinefeld, Alexander A1 - Kramer, Tobias A1 - Steinke, Thomas T1 - DM-HEOM: A Portable and Scalable Solver-Framework for the Hierarchical Equations of Motion T2 - 2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), 19th IEEE Int. Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC 2018) N2 - Computing the Hierarchical Equations of Motion (HEOM) is by itself a challenging problem, and so is writing portable production code that runs efficiently on a variety of architectures while scaling from PCs to supercomputers. We combined both challenges to push the boundaries of simulating quantum systems, and to evaluate and improve methodologies for scientific software engineering. Our contributions are threefold: We present the first distributed memory implementation of the HEOM method (DM-HEOM), we describe an interdisciplinary development workflow, and we provide guidelines and experiences for designing distributed, performance-portable HPC applications with MPI-3, OpenCL and other state-of-the-art programming models. We evaluated the resulting code on multi- and many-core CPUs as well as GPUs, and demonstrate scalability on a Cray XC40 supercomputer for the PS I molecular light harvesting complex. Y1 - 2018 SN - 978-1-5386-5555-9 U6 - https://doi.org/10.1109/IPDPSW.2018.00149 N1 - Best Paper Award SP - 947 EP - 956 ER - TY - JOUR A1 - Kramer, Tobias A1 - Noack, Matthias A1 - Reinefeld, Alexander A1 - Rodríguez, Mirta A1 - Zelinskyi, Yaroslav T1 - Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with Distributed Memory HEOM (DM-HEOM) JF - Journal of Computational Chemistry N2 - Time- and frequency resolved optical signals provide insights into the properties of light harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the complex. The hierarchical equations of motion (HEOM) provide a unifying theory, which allows one to study the combined effects of system-environment dissipation and non-Markovian memory without making restrictive assumptions about weak or strong couplings or separability of vibrational and electronic degrees of freedom. With increasing system size the exact solution of the open quantum system dynamics requires memory and compute resources beyond a single compute node. To overcome this barrier, we developed a scalable variant of HEOM. Our distributed memory HEOM, DM-HEOM, is a universal tool for open quantum system dynamics. It is used to accurately compute all experimentally accessible time- and frequency resolved processes in light harvesting molecular complexes with arbitrary system-environment couplings for a wide range of temperatures and complex sizes. Y1 - 2018 U6 - https://doi.org/doi:10.1002/jcc.25354 VL - 39 IS - 22 SP - 1779 EP - 1794 PB - Wiley Periodicals, Inc. ER - TY - JOUR A1 - Kramer, Tobias A1 - Noack, Matthias A1 - Reimers, Jeffrey R. A1 - Reinefeld, Alexander A1 - Rodríguez, Mirta A1 - Yin, Shiwei T1 - Energy flow in the Photosystem I supercomplex: comparison of approximative theories with DM-HEOM JF - Chemical Physics N2 - We analyze the exciton dynamics in PhotosystemI from Thermosynechococcus elongatus using the distributed memory implementation of the hierarchical equation of motion (DM-HEOM) for the 96 Chlorophylls in the monomeric unit. The exciton-system parameters are taken from a first principles calculation. A comparison of the exact results with Foerster rates and Markovian approximations allows one to validate the exciton transfer times within the complex and to identify deviations from approximative theories. We show the optical absorption, linear, and circular dichroism spectra obtained with DM-HEOM and compare them to experimental results. Y1 - 2018 U6 - https://doi.org/10.1016/j.chemphys.2018.05.028 VL - 515 SP - 262 EP - 271 PB - Elsevier B.V. ER - TY - JOUR A1 - Heller, Eric J. A1 - Fleischmann, Ragnar A1 - Kramer, Tobias T1 - Branched Flow N2 - In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refractive index variations. "Primary" diffraction (by individual sub-wavelength features) is absent. Eventually the weak refraction leads to imperfect focal "cusps". Much later, a statistical regime characterized by momentum diffusion is manifested. An important intermediate regime is often overlooked, one that is diffusive only in an ensemble sense. Each realization of the ensemble possesses dramatic ray limit structure that guides the waves (in the same sense that ray optics is used to design lens systems). This structure is a universal phenomenon called branched flow. Many important phenomena develop in this intermediate regime. Here we give examples and some of the physics of this emerging field. Y1 - 2019 ER - TY - JOUR A1 - Kramer, Tobias A1 - Rodríguez, Mirta T1 - Effect of disorder and polarization sequences on two-dimensional spectra of light harvesting complexes JF - Photosynthesis Research N2 - Two-dimensional electronic spectra (2DES) provide unique ways to track the energy transfer dynamics in light-harvesting complexes. The interpretation of the peaks and structures found in experimentally recorded 2DES is often not straightforward, since several processes are imaged simultaneously. The choice of specific pulse polarization sequences helps to disentangle the sometimes convoluted spectra, but brings along other disturbances. We show by detailed theoretical calculations how 2DES of the Fenna-Matthews-Olson complex are affected by rotational and conformational disorder of the chromophores. Y1 - 2020 U6 - https://doi.org/10.1007/s11120-019-00699-6 VL - 144 SP - 147 EP - 154 ER - TY - CHAP A1 - Kramer, Tobias T1 - Transient capture of electrons in magnetic fields, or: comets in the restricted three-body problem T2 - Journal of Physics: Conference Series N2 - The motion of celestial bodies in astronomy is closely related to the orbits of electrons encircling an atomic nucleus. Bohr and Sommerfeld presented a quantization scheme of the classical orbits to analyze the eigenstates of the hydrogen atom. Here we discuss another close connection of classical trajectories and quantum mechanical states: the transient dynamics of objects around a nucleus. In this setup a comet (or an electron) is trapped for a while in the vicinity of parent object (Jupiter or an atomic nucleus), but eventually escapes after many revolutions around the center of attraction. Y1 - 2020 U6 - https://doi.org/10.1088/1742-6596/1612/1/012019 VL - 1612 SP - 012019 ET - Symmetries in Science XVIII ER - TY - JOUR A1 - Hoang, Margaux A1 - Garnier, Philippe A1 - Lasue, Jeremie A1 - Rème, Henri A1 - Capria, Maria Teresa A1 - Altwegg, Kathrin A1 - Läuter, Matthias A1 - Kramer, Tobias A1 - Rubin, Martin T1 - Investigating the Rosetta/RTOF observations of comet 67P/Churyumov-Gerasimenko using a comet nucleus model: Influence of dust mantle and trapped CO JF - Astronomy & Astrophysics N2 - Context. Cometary outgassing is induced by the sublimation of ices and the ejection of dust originating from the nucleus. Therefore measuring the composition and dynamics of the cometary gas provides information concerning the interior composition of the body. Nevertheless, the bulk composition differs from the coma composition, and numerical models are required to simulate the main physical processes induced by the illumination of the icy body. Aims. The objectives of this study are to bring new constraints on the interior composition of the nucleus of comet 67P/Churyumov-Gerasimenko (hereafter 67P) by comparing the results of a thermophysical model applied to the nucleus of 67P and the coma measurements made by the Reflectron-type Time-Of-Flight (RTOF) mass spectrometer. This last is one of the three instruments of the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA), used during the Rosetta mission. Methods. Using a thermophysical model of the comet nucleus, we studied the evolution of the stratigraphy (position of the sublimation and crystallisation fronts), the temperature of the surface and subsurface, and the dynamics and spatial distribution of the volatiles (H2O, CO2 and CO). We compared them with the in situ measurements from ROSINA/RTOF and an inverse coma model. Results. We observed the evolution of the surface and near surface temperature, and the deepening of sublimation fronts. The thickness of the dust layer covering the surface strongly influences the H2O outgassing but not the more volatiles species. The CO outgassing is highly sensitive to the initial CO/H2O ratio, as well as to the presence of trapped CO in the amorphous ice. Conclusions. The study of the influence of the initial parameters on the computed volatile fluxes and the comparison with ROSINA/RTOF measurements provide a range of values for an initial dust mantle thickness and a range of values for the volatile ratio. These imply the presence of trapped CO. Nevertheless, further studies are required to reproduce the strong change of behaviour observed in RTOF measurements between September 2014 and February 2015. Y1 - 2020 U6 - https://doi.org/10.1051/0004-6361/201936655 VL - 638 SP - A106 ER - TY - JOUR A1 - Läuter, Matthias A1 - Kramer, Tobias A1 - Rubin, Martin A1 - Altwegg, Kathrin T1 - The gas production of 14 species from comet 67P/Churyumov-Gerasimenko based on DFMS/COPS data from 2014-2016 JF - Monthly Notices of the Royal Astronomical Society N2 - The coma of comet 67P/Churyumov-Gerasimenko has been probed by the Rosetta spacecraft and shows a variety of different molecules. The ROSINA COmet Pressure Sensor and the Double Focusing Mass Spectrometer provide in-situ densities for many volatile compounds including the 14 gas species H2O, CO2, CO, H2S, O2, C2H6, CH3OH, H2CO, CH4, NH3, HCN, C2H5OH, OCS, and CS2. We fit the observed densities during the entire comet mission between August 2014 and September 2016 to an inverse coma model. We retrieve surface emissions on a cometary shape with 3996 triangular elements for 50 separated time intervals. For each gas we derive systematic error bounds and report the temporal evolution of the production, peak production, and the time-integrated total production. We discuss the production for the two lobes of the nucleus and for the northern and southern hemispheres. Moreover we provide a comparison of the gas production with the seasonal illumination. Y1 - 2020 U6 - https://doi.org/10.1093/mnras/staa2643 VL - 498 IS - 3 SP - 3995 EP - 4004 PB - Monthly Notices of the Royal Astronomical Society ER - TY - CHAP A1 - Läuter, Matthias A1 - Kramer, Tobias A1 - Rubin, Martin A1 - Altwegg, Kathrin T1 - Gas production for 14 species on comet 67P/Churyumov-Gerasimenko from 2014-2016 T2 - Europlanet Science Congress N2 - During a two year period between 2014 and 2016 the coma of comet 67P/Churyumov-Gerasimenko (67P/C-G) has been probed by the Rosetta spacecraft. Density data for 14 gas species was recorded with the COmet Pressure Sensor (COPS) and the Double Focusing Mass Spectrometer (DFMS) being two sensors of the ROSINA instrument. The combination with an inverse gas model yields emission rates on each of 3996 surface elements of a surface shape for the cometary nucleus. The temporal evolution of gas production, of relative abundances, and peak productions weeks after perihelion are investigated. Solar irradiation and gas production are in a complex relation revealing features differing for gas species, for mission time, and for the hemispheres of the comet. This characterization of gas composition allows one to correlate 67P/C-G to other solar and interstellar comets, their formation conditions and nucleus properties, see [Bodewits D., et al., 2020 Nature Astronomy]. Y1 - 2020 U6 - https://doi.org/10.5194/epsc2020-319 VL - 14 SP - EPSC2020-319 PB - Europlanet Science Congress ER - TY - CHAP A1 - Kramer, Tobias A1 - Läuter, Matthias T1 - Non-gravitational force model vs observation: the trajectory and rotation-axis of comet 67P/Churyumov-Gerasimenko T2 - Europlanet Science Congress N2 - The determination of non-gravitational forces based on precise astrometry is one of the main tools to establish the cometary character of interstellar and solar-system objects. The Rosetta mission to comet 67P/C-G provided the unique opportunity to benchmark Earth-bound estimates of non-gravitational forces with in-situ data. We determine the accuracy of the standard Marsden and Sekanina parametrization of non-gravitational forces with respect to the observed dynamics. Additionally we analyse the rotation-axis changes (orientation and period) of 67P/C-G. This comparison provides a reference case for future cometary missions and sublimation models for non-gravitational forces. Y1 - 2020 U6 - https://doi.org/10.5194/epsc2020-403 VL - 14 SP - EPSC2020-403 PB - Europlanet Science Congress ER - TY - JOUR A1 - Kramer, Tobias A1 - Noack, Matthias A1 - Baum, Daniel A1 - Hege, Hans-Christian A1 - Heller, Eric J. T1 - Dust and gas emission from cometary nuclei: the case of comet 67P/Churyumov-Gerasimenko JF - Advances in Physics: X N2 - Comets display with decreasing solar distance an increased emission of gas and dust particles, leading to the formation of the coma and tail. Spacecraft missions provide insight in the temporal and spatial variations of the dust and gas sources located on the cometary nucleus. For the case of comet 67P/Churyumov-Gerasimenko (67P/C-G), the long-term obser- vations from the Rosetta mission point to a homogeneous dust emission across the entire illuminated surface. Despite the homogeneous initial dis- tribution, a collimation in jet-like structures becomes visible. We propose that this observation is linked directly to the complex shape of the nucleus and projects concave topographical features into the dust coma. To test this hypothesis, we put forward a gas-dust description of 67P/C-G, where gravitational and gas forces are accurately determined from the surface mesh and the rotation of the nucleus is fully incorporated. The emerging jet-like structures persist for a wide range of gas-dust interactions and show a dust velocity dependent bending. Y1 - 2018 U6 - https://doi.org/10.1080/23746149.2017.1404436 VL - 3 IS - 1 SP - 1404436 ER - TY - JOUR A1 - Nkenke, Emeka A1 - Zachow, Stefan A1 - Benz, Michaela A1 - Maier, Tobias A1 - Veit, Klaus A1 - Kramer, Manuel A1 - Benz, St. A1 - Häusler, Gerd A1 - Neukam, Friedrich A1 - Lell, Michael T1 - Fusion of computed tomography data and optical 3D images of the dentition for streak artefact correction in the simulation of orthognathic surgery JF - Journal of Dento-Maxillofacial Radiology Y1 - 2004 U6 - https://doi.org/10.1259/dmfr/27071199 VL - 33 SP - 226 EP - 232 ER - TY - JOUR A1 - Kramer, Tobias A1 - Läuter, Matthias A1 - Rubin, Martin A1 - Altwegg, Kathrin T1 - Seasonal changes of the volatile density in the coma and on the surface of comet 67P/Churyumov-Gerasimenko JF - Monthly Notices of the Royal Astronomical Society N2 - Starting from several monthly data sets of Rosetta’s COmetary Pressure Sensor we reconstruct the gas density in the coma around comet 67P/Churyumov-Gerasimenko. The underlying inverse gas model is constructed by fitting ten thousands of measurements to thousands of potential gas sources distributed across the entire nucleus surface. The ensuing self-consistent solution for the entire coma density and surface activity reproduces the temporal and spatial variations seen in the data for monthly periods with Pearson correlation coefficients of 0.93 and higher. For different seasonal illumination conditions before and after perihelion we observe a systematic shift of gas sources on the nucleus. Y1 - 2017 U6 - https://doi.org/10.1093/mnras/stx866 VL - 469 SP - S20 EP - S28 ER - TY - JOUR A1 - Kramer, Tobias A1 - Rodriguez, Mirta T1 - Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria JF - Scientific Reports N2 - Advances in time resolved spectroscopy have provided new insight into the energy transmission in natural photosynthetic complexes. Novel theoretical tools and models are being developed in order to explain the experimental results. We provide a model calculation for the two-dimensional electronic spectra of Cholorobaculum tepidum which correctly describes the main features and transfer time scales found in recent experiments. From our calculation one can infer the coupling of the antenna chlorosome with the environment and the coupling between the chlorosome and the Fenna-Matthews-Olson complex. We show that environment assisted transport between the subunits is the required mechanism to reproduce the experimental two-dimensional electronic spectra. Y1 - 2017 U6 - https://doi.org/10.1038/srep45245 VL - 7 SP - 45245 ER - TY - JOUR A1 - Kramer, Tobias A1 - Noack, Matthias T1 - Prevailing Dust-transport Directions on Comet 67P/Churyumov–Gerasimenko JF - The Astrophysical Journal Letters N2 - Dust transport and deposition behind larger boulders on the comet 67P/Churyumov–Gerasimenko (67P/C–G) have been observed by the Rosetta mission. We present a mechanism for dust-transport vectors based on a homogeneous surface activity model incorporating in detail the topography of 67P/C–G. The combination of gravitation, gas drag, and Coriolis force leads to specific dust transfer pathways, which for higher dust velocities fuel the near-nucleus coma. By distributing dust sources homogeneously across the whole cometary surface, we derive a global dust-transport map of 67P/C–G. The transport vectors are in agreement with the reported wind-tail directions in the Philae descent area. Y1 - 2015 U6 - https://doi.org/10.1088/2041-8205/813/2/L33 VL - 813 IS - 2 SP - L33 ER - TY - GEN A1 - Kramer, Tobias A1 - Noack, Matthias A1 - Baum, Daniel A1 - Hege, Hans-Christian A1 - Heller, Eric J. T1 - Dust and gas emission from cometary nuclei: the case of comet 67P/Churyumov-Gerasimenko N2 - Comets display with decreasing solar distance an increased emission of gas and dust particles, leading to the formation of the coma and tail. Spacecraft missions provide insight in the temporal and spatial variations of the dust and gas sources located on the cometary nucleus. For the case of comet 67P/Churyumov-Gerasimenko (67P/C-G), the long-term obser- vations from the Rosetta mission point to a homogeneous dust emission across the entire illuminated surface. Despite the homogeneous initial dis- tribution, a collimation in jet-like structures becomes visible. We propose that this observation is linked directly to the complex shape of the nucleus and projects concave topographical features into the dust coma. To test this hypothesis, we put forward a gas-dust description of 67P/C-G, where gravitational and gas forces are accurately determined from the surface mesh and the rotation of the nucleus is fully incorporated. The emerging jet-like structures persist for a wide range of gas-dust interactions and show a dust velocity dependent bending. T3 - ZIB-Report - 17-78 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66338 SN - 1438-0064 ER - TY - CHAP A1 - Kramer, Tobias A1 - Läuter, Matthias T1 - Benchmarking the rotating jet model of cometary activity with the trajectory of comet 67P/Churyumov-Gerasimenko T2 - EPSC Abstracts N2 - An important tool to assess the composition and the spatial origin of cometary material is the analysis of its trajectory reflecting gravitational acceleration due to solar system bodies complemented by non-gravitational accelerations (NGA). Y1 - 2024 U6 - https://doi.org/10.5194/epsc2024-207 VL - 17 ER - TY - JOUR A1 - Attree, Nicholas A1 - Gutiérrez, Pedro A1 - Groussin, Olivier A1 - Bürger, Johanna A1 - Keller, Horst Uwe A1 - Kramer, Tobias A1 - LASAGNI MANGHI, RICCARDO A1 - Läuter, Matthias A1 - Lemos, Pablo A1 - Markkanen, Johannes A1 - Marschall, Raphael A1 - Schuckart, Christian T1 - Varying water activity and momentum transfer on comet 67P/Churyumov-Gerasimenko from its non-gravitational forces and torques JF - Astronomy and Astrophysics N2 - Aims. We investigate the ability of a simultaneous fitting of comet 67P/Churyumov-Gerasimenko’s non-gravitational forces, torques, and total water-outgassing rate, as observed by Rosetta, to constrain complex thermophysical models of cometary material. Methods. We extend the previous work of fitting geographically defined surface outgassing models to the Rosetta observations by testing the effects of a more detailed geomorphological mapping, the resolution of the shape-model used, self-heating by neighbouring facets on the shape-model, thermal inertia in the outgassing solution, and the variation in the momentum coupling between the gas and the nucleus. We also directly compare the non-gravitational acceleration curves available in the literature. Results. We correct an error in the calculation of pole-orientation in the previous paper. We find that, under the assumptions of the model, non-gravitational forces and torques are driven by water sublimation from the nucleus, thermal inertia and self-heating have only minor effects, spatially uniform activity cannot explain 67P’s non-gravitational dynamics, spatially uniform momentum transfer cannot explain 67P’s non-gravitational dynamics, and different terrain types have different instantaneous responses to insolation. Conclusions. Consolidated terrain facing south on 67P/Churyumov-Gerasimenko has a high outgassing flux, a steep response to insolation, and a large gas momentum transfer coefficient. Instead, that facing north behaves differently, producing little to no water outgassing, and with a lower momentum transfer efficiency. Dusty terrain also has a lower outgassing rate and momentum transfer efficiency, and either depletes its volatile component or is buried in fall-back as the comet approaches the Sun. Momentum transfer appears correlated with insolation, likely due to an increased enhancement in the gas temperature as the dust it flows through is heated. Y1 - 2024 U6 - https://doi.org/10.1051/0004-6361/202450728 VL - 690 SP - A82 ER - TY - CHAP A1 - Attree, Nicholas A1 - Gutiérrez, Pedro A1 - Groussin, Olivier A1 - Bürger, Johanna A1 - Keller, Horst Uwe A1 - Kramer, Tobias A1 - Lasagni Manghi, Riccardo A1 - Läuter, Matthias A1 - Lemos, Pablo A1 - Markkanen, Johannes A1 - Marschall, Raphael A1 - Schuckart, Christian T1 - The Results of ISSI Team #547: Understanding the Activity of Comets Through 67P's Dynamics T2 - EPSC Abstracts N2 - Understanding cometary activity gives us an insight into the materials properties, and therefore formation and evolution processes of these relatively pristine protoplanetary objects. We will present the results of an International Space Science Institute project to investigate the phenomenon through the effects of the outgassing activity on the orbit and spin-state of comet 67P/Churymov-Gerasimenko, e.g. its non-gravitational dynamics. This International Team gathered experts in orbital dynamics and trajectory reconstruction together with thermophysical modellers and comet observationalists, in order to compare the available extractions of 67P’s non-gravitational acceleration (NGA) from its trajectory. The team then fitted a combination of the NGA, the non-gravitational torque (NGT), and the total water-outgassing rate with a thermophysical activity model. The results of this model will be presented. In particular, it was found that: non-gravitational forces and torques are driven by water sublimation from the nucleus; thermal inertia and self-heating have only minor effects; spatially uniform activity cannot explain 67P's non-gravitational dynamics; spatially uniform momentum transfer cannot explain 67P's non-gravitational dynamics; and different terrain types have different instantaneous responses to insolation. The implications of these findings for the modelling of cometary material and the variety of surface types seen on 67P will be discussed. Y1 - 2024 U6 - https://doi.org/10.5194/epsc2024-82 VL - 17 ER - TY - JOUR A1 - Läuter, Matthias A1 - Kramer, Tobias T1 - Rotation dynamics and torque efficiency of cometary nuclei JF - Astronomy & Astrophysics N2 - The dynamics of a rigid cometary nucleus is described by the evolutions of its center-of-mass and of its rotation state. Solar irradiation that reaches the surface of a cometary nucleus causes the sublimation of volatiles that form the coma around the nucleus. The sublimation process transfers linear momentum and rotational angular momentum from the nucleus to the surrounding space, and thus affects the dynamics via nongravitational forces and nongravitational torques. With the exception of close approaches to planets, these torques exert the dominant influence on the rotation states of cometary nuclei. The Rosetta mission 2014-2016 accompanying comet 67P/Churyumov-Gerasimenko provides the longest continuous observational data to track its rotation state. In particular, the data set encompasses the direction of the angular velocity, denoted by ω, and the angular frequency |ω|over a time period of approximately 700 days. The observed change of the rotation state is not explained by a low heat conductivity thermophysical model in combination with a homogeneous surface ice coverage of comet 67P. Spatially and/or temporally varying weights for effective active fraction with respect to a prescribed set of surface regions provide a potential solution to this problem. Here, we present a methodology for classifying the surface based on vectorial efficiency of the torque. On any cometary surface without geometric symmetry, the methodology highlights the decomposition into eight characteristic regions that encode the signs of torque efficiency with respect to all vector components. This decomposition is divided into two subsets of four regions each of which is located in one of both hemispheric regions. We analyze in detail rotation states close to lowest energy and different thermophysical models, and we discuss how the uncertainties of observations affect the model parameters. We study the occurrence of these regions for an oblate ellipsoid, a nearprolate ellipsoid, a bilobed shape, and a shape model analogous to that of comet 67P. The sensitivity analysis for comet 67P indicates that the observations constrain only one of the eight weights uniquely. The other directions are poorly constrained and show the limitation of the rotational data to determine the regional activity on comet 67P. Y1 - 2025 U6 - https://doi.org/10.1051/0004-6361/202553845 VL - 699 SP - A75 ER - TY - JOUR A1 - Groussin, Olivier A1 - Jorda, L. A1 - Attree, N. A1 - Birch, S.P.D. A1 - Bürger, Johanna A1 - Gutiérrez, Pedro A1 - Jindal, Abhinav S. A1 - Keller, H.U. A1 - Kramer, Tobias A1 - Lasagni Manghi, Riccardo A1 - Läuter, Matthias A1 - Markkanen, J. A1 - Marschall, R. A1 - Schuckart, C. T1 - Thermal environment and erosion of comet 67P/Churyumov-Gerasimenko JF - Astronomy and Astrophysics N2 - Aims. This paper focuses on how insolation affects the nucleus of comet 67P/Churyumov-Gerasimenko over its current orbit. We aim to better understand the thermal environment of the nucleus, in particular its surface temperature variations, erosion, relationship with topography, and how insolation affects the interior temperature for the location of volatile species (H2O and CO2). Methods. We have developed two thermal models to calculate the surface and subsurface temperatures of 67P over its 6.45-year orbit. The first model, with high resolution (300 000 facets), calculates surface temperatures, taking shadows and self-heating into account but ignoring thermal conductivity. The second model, with lower resolution (10 000 facets), includes thermal conductivity to estimate temperatures down to ∼3 m below the surface. Results. The thermal environment of 67P is strongly influenced by its large obliquity (52◦), which causes significant seasonal effects and polar nights. The northern hemisphere is the coldest region, with temperatures of 210–300 K. H2O is found in the first few centimetres, while CO2 is found deeper (∼2 m) except during polar night around perihelion, when CO2 accumulates near the surface. Cliffs erode 3–5 times faster than plains, forming terraces. The equatorial region receives maximum solar energy (8.5×109 J m−2 per orbit), with maximum surface temperatures of 300–350 K. On the plains, H2O is found in the first few centimetres, while CO2 is found deeper (∼2 m) and never accumulates near the surface. In the southern hemisphere, a brief intense perihelion heating raises temperatures to 350–400 K, which is followed by a 5-year polar night when surface temperatures drop to 55 K. Here H2O remains in the first few centimetres, while CO2 accumulates shallowly during polar night, enriching the region. Erosion is maximal in the southern hemisphere and concentrated on the plains, which explains the observed overall flatness of this hemisphere compared to the northern one. Over one orbit, the total energy from self-heating is 17% of the total energy budget, and 34% for thermal conduction. Our study contributes to a better understanding of the surface changes observed on 67P. Y1 - 2025 U6 - https://doi.org/10.1051/0004-6361/202452260 VL - 694 SP - A21 ER -