Context. The complex shape of comet 67P and its oblique rotation axis cause pronounced seasonal effects. Irradiation and hence activity vary strongly. Aims. We investigate the insolation of the cometary surface in order to predict the sublimation of water ice. The strongly varying erosion levels are correlated with the topography and morphology of the present cometary surface and its evolution. Methods. The insolation as a function of heliocentric distance and diurnal (spin dependent) variation is calculated using >10 5 facets of a detailed digital terrain model. Shading, but also illumination and thermal radiation by facets in the field of view of a specific facet are iteratively taken into account. We use a two-layer model of a thin porous dust cover above an icy surface to calculate the water sublimation, presuming steady state and a uniform surface. Our second model, which includes the history of warming and cooling due to thermal inertia, is restricted to a much simpler shape model but allows us to test various distributions of active areas. Results. Sublimation from a dirty ice surface yields maximum erosion. A thin dust cover of 50 µm yields similar rates at perihelion. Only about 6% of the surface needs to be active to match the observed water production rates at perihelion. A dust layer of 1 mm thickness suppresses the activity by a factor of 4 to 5. Erosion on the south side can reach more than 10 m per orbit at active spots. The energy input to the concave neck area (Hapi) during northern summer is enhanced by about 50% owing to self-illumination. Here surface temperatures reach maximum values along the foot of the Hathor wall. Integrated over the whole orbit this area receives the least energy input. Based on the detailed shape model, the simulations identify "hot spots" in depressions and larger pits in good correlation with observed dust activity. Three-quarters of the total sublimation is produced while the sub-solar latitude is south, resulting in a distinct dichotomy in activity and morphology. Conclusions. The northern areas display a much rougher morphology than what is seen on Imhotep, an area at the equator that will be fully illuminated when 67P is closer to the Sun. Self-illumination in concave regions enhance the energy input and hence erosion. This explains the early activity observed at Hapi. Cliffs are more prone to erosion than horizontal, often dust covered, areas, which leads to surface planation. Local activity can only persist if the forming cliff walls are eroding. Comet 67P has two lobes and also two distinct sides. Transport of material from the south to the north is probable. The morphology of the Imhotep plain should be typical for the terrains of the yet unseen southern hemisphere.

a b s t r a c tWe developed a thermophysical model for cometary nuclei, which is based upon the assumption that comets form by the gravitational instability of an ensemble of dust and ice aggregates. Under this condition, the tensile strength of the ice-free outer layers of a cometary nucleus can be calculated, using the dust-aggregate collision and adhesion model of Weidling et al. (Weidling, R. et al. [2012]. Icarus, 218, 688-700). Based on available laboratory data on the gas permeability and thermal conductivity of ice-free dust layers, we derived the temperature and pressure at the dust-ice interface for pure water and pure carbon dioxide ice. Comparison of the vapor pressure below the dust crust with its tensile strength allows the prediction of dust release from cometary surfaces. Our model predicts dust activity for pure CO 2 ice and for heliocentric distances of K 3 AU, whereas pure H 2 O ice cannot explain the dust emission.

We present a non-invasive technique for measuring the thermal conductivity of fragile and sensitive materials. In the context of planet formation research, the investigation of the thermal conductivity of porous dust aggregates provide important knowledge about the influence of heating processes, like internal heating by radioactive decay of short-lived nuclei, e.g. 26 Al, on the evolution and growth of planetesimals. The determination of the thermal conductivity was performed by a combination of laboratory experiments and numerical simulations. An IR camera measured the temperature distribution of the sample surface heated by a well-characterized laser beam. The thermal conductivity as free parameter in the model calculations, exactly emulating the experiment, was varied until the experimental and numerical temperature distributions showed best agreement. Thus, we determined for three types of porous dust samples, consisting of spherical, 1.5 µm-sized SiO 2 particles, with volume filling factors in the range of 15% to 54%, the thermal conductivity to be 0.002 to 0.02 W m −1 K −1 , respectively. From our results, we can conclude that the thermal conductivity mainly depends on the volume filling factor. Further investigations, which are planned for different materials and varied contact area sizes (produced by sintering), will prove the appropriate dependencies in more detail.

Our knowledge about the physical processes determining the activity of comets were mainly influenced by several extremely successful space missions (Giotto, Deep Space I, Stardust, Deep Impact and EPOXI), the predictions of theoretical models and the results of laboratory experiments. However, novel computer models should not be treated in isolation but should be based on experimental results and should be verified and calibrated by experimental work. Therefore, a new experimental setup was constructed to investigate the temperature dependent sublimation properties of hexagonal water ice and the gas diffusion through a dry dust layer covering the ice surface. We show that this experimental setup is capable to reproduce known gas production rates of pure hexagonal water ice. The reduction of the gas production rate due to an additional dust layer on top of the ice surface was measured and compared to the results of another experimental setup in which the gas diffusion through dust layers at room temperature was investigated. We found that the relative permeability of the dust layer is inversely proportional to its thickness, which is also predicted by theoretical models. However, the measured absolute weakening of the gas flow was smaller than predicted by models. This lack of correspondence between model and experiment may be caused by an ill-determination of the boundary condition in the theoretical models, which further demonstrates the necessity of laboratory investigations. Furthermore, the impedance of the dust layer to the ice evaporation was found to be similar to the impedance at room temperature, which means that the temperature profile of the dust layer is not influencing the reduction of the gas production. Finally, we present the results of an extended investigation of the sublimation coefficient, which is an important factor for the description of the sublimation rate of water ice and, thus, an important value for thermophysical modeling of icy bodies in the solar system. The achieved results of this laboratory investigations demonstrate that experimental works are essential for the understanding of the origin of cometary activity.

Context. The ESA Rosetta spacecraft has been orbiting the nucleus of comet 67P/Churyumov-Gerasimenko since August 2014. The rotation axis of the irregularly shaped nucleus has a large obliquity (52 • ) and is oriented such that the southern hemisphere is insolated during perihelion. Aims. We calculate the change in the rotation period as a function of the cometary orbital position due to forces exerted by cometary activity. Methods. We used a detailed shape model of 67P with >10 5 facets. We calculated the efficiency of the facets to exert a torque based on their radial distance from the center of mass and their orientation. We applied our thermal model to calculate the diurnal water-ice sublimation rate from each facet. The reaction force per facet combined with its torque efficiency creates a torque and changes the angular momentum. The component of the torque parallel to the spin axis changes the rotation period. Results. Our model shows that the rotation period increases slightly during the approach of the comet to the Sun. It reaches a maximum shortly before equinox and drops rapidly during perihelion passage. The magnitude of the change depends on the actual sublimation rates. The change in sign mainly depends on the shape of the nucleus and not much on the sublimation variation. The roughness of the nucleus has little influence. Conclusions. For the given geometry of the rotation axis, the change in the rotation period is mainly influenced by the sublimation activity of the irregular shape of the nucleus. The rotation period increases until shortly before equinox in early May 2015, in good agreement with observations, and will then become shorter rapidly.

Context. The gas-driven dust activity of comets is still an unsolved question in cometary physics. Homogeneous dust layers composed of micrometer-sized grains possess tensile strengths of ∼1 kPa, which is far higher than typical gas pressures caused by the sublimation of the ices beneath the covering dust layer. This implies that the dust grains cannot be detached from the surface by the gas pressure of the sublimating ices. One possibility to avoid this problem is that the nucleus formed through the gravitational collapse of an ensemble of millimeter-to centimeter-sized aggregates. In this case, an aggregate layer with a tensile strength on the order of ∼1 Pa is formed on the surface of the nucleus, which allows for the release of the aggregates from the surface by the gas pressure build up at the ice-dust interface. Aims. We use the gravitational instability formation scenario of cometesimals to derive the aggregate size that can be released by the gas pressure from the nucleus of comet 67P/Churyumov-Gerasimenko for different heliocentric distances and different volatile ices. Methods. To derive the ejected aggregate sizes, we developed a model based on the assumption that the entire heat absorbed by the surface is consumed by the sublimation process of one volatile species. The calculations were performed for the three most prominent volatile materials in comets, namely, H 2 O ice, CO 2 ice, and CO ice. Results. We find that the size range of the dust aggregates able to escape from the nucleus into space widens when the comet approaches the Sun and narrows with increasing heliocentric distance, because the tensile strength of the aggregates decreases with increasing aggregate size. The activity of CO ice in comparison to H 2 O ice is capable to detach aggregates smaller by approximately one order of magnitude from the surface. As a result of the higher sublimation rate of CO ice, larger aggregates are additionally able to escape from the gravity field of the nucleus. Conclusions. Our model can explain the large grains (ranging from 2 cm to 1 m in radius) in the inner coma of comet 67P/ChuryumovGerasimenko that have been observed by the OSIRIS camera at heliocentric distances between 3.4 AU and 3.7 AU. Furthermore, the model predicts the release of decimeter-sized aggregates (trail particles) close to the heliocentric distance at which the gas-driven dust activity vanishes. However, the gas-driven dust activity cannot explain the presence of particles smaller than ∼1 mm in the coma because the high tensile strength required to detach these particles from the surface cannot be provided by evaporation of volatile ices. These smaller particles can be produced for instance by spin-up and centrifugal mass loss of ejected larger aggregates.

The physical properties of cometary nuclei observed today relate to their complex history and help to constrain their formation and evolution. In this article, we review some of the main physical properties of cometary nuclei and focus in particular on the thermal, mechanical, structural and dielectric properties, emphasizing the progress made during the Rosetta mission. Comets have a low density of 480 ± 220 kg m -3 and a low permittivity of 1.9 -2.0, consistent with a high porosity of 70 -80 %, are weak with a very low global tensile strength <100 Pa, and have a low bulk thermal inertia of 0 -60 J K -1 m -2 s -1/2 that allowed them to preserve highly volatiles species (e.g. CO, CO2, CH4, N2) into their interior since their formation. As revealed by 67P/Churyumov-Gerasimenko, the above physical properties vary across the nucleus, spatially at its surface but also with depth. The broad picture is that the bulk of the nucleus consists of a weakly bonded, rather homogeneous material that preserved primordial properties under a thin shell of processed material, and possibly covered by a granular material; this cover might in places reach a thickness of several meters. The properties of the top layer (the first meter) are not representative of that of the bulk nucleus. More globally, strong nucleus heterogeneities at a scale of a few meters are ruled out on 67P's small lobe.

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