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Planetesimals in the primordial disc may have experienced a collisional cascade. If so, the comet nuclei later placed in the Kuiper belt, scattered disc, and Oort Cloud would primarily be fragments and collisional rubble piles from that cascade. However, the heating associated with the collisions cannot have been strong enough to remove the hypervolatiles that are trapped within more durable ices, because comet nuclei are rich in hypervolatiles. This places constraints on the diameter of the largest bodies allowed to participate in collisional cascades, and limits the primordial disc lifetime or population size. In this paper, the thermophysical code NIMBUS is used to study the thermal evolution of planetesimals before, during, and after catastrophic collisions. The loss of CO during segregation of $\mathrm{CO_2:CO}$ mixtures and during crystallisation of amorphous $\mathrm{H_2O}$ is calculated, as well as mobilisation and internal relocation of $\mathrm{CO_2}$. If an amorphous $\mathrm{H_2O}$ host existed, and was protected by a $\mathrm{CO_2:CO}$ heat sink, only diameter $D<20\,\mathrm{km}$ (inner disc) and $D<64\,\mathrm{km}$ (outer disc) bodies could have been involved in a collisional cascade. If $\mathrm{CO_2}$ was the only CO host, the critical diameters drop to $D<20$-$32\mathrm{km}$. Avoiding disruption of larger bodies requires a primordial disc lifetime of $<9\,\mathrm{Myr}$ at $15\,\mathrm{au}$ and $<50$-$70\,\mathrm{Myr}$ at $30\,\mathrm{au}$. Alternatively, if a $450\,\mathrm{Myr}$ disc lifetime is required to associate the primordial disc disruption with the Late Heavy Bombardment, the disc population size must have been 6-60 times below current estimates., Comment: 20 pages, 11 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

Deriving properties of cometary nuclei from coma data is of significant importance for our understanding of cometary activity and has implications beyond. Ground-based data represent the bulk of measurements available for comets. Yet, to date these observations only access a comet's gas and dust coma at rather large distances from the surface and do not directly observe its surface. In contrast, spacecraft missions are one of the only tools that gain direct access to surface measurements. However, such missions are limited to roughly one per decade. We can overcome these challenges by recognising that the coma contains information about the nucleus's properties. In particular, the near-surface gas environment is most representative of the nucleus. It can inform us about the composition, regionality of activity, and sources of coma features and how they link to the topography, morphology, or other surface properties. The inner coma data is a particularly good proxy because it has not yet, or only marginally, been contaminated by coma chemistry or secondary gas sources. Additionally, the simultaneous observation of the innermost coma with the surface provides the potential to make a direct link between coma measurements and the nucleus. If we hope to link outer coma measurements obtained by Earth-based telescopes to the surface, we must first understand how the inner coma measurements are linked to the surface. Numerical models that describe the flow from the surface into the immediate surroundings are needed to make this connection. This chapter focuses on the advances made to understand the flow of the neutral gas coma from the surface to distances up to a few tens of nuclei radii. We describe both simple/heuristic models and state-of-the-art physically consistent models. Model limitations and what they each are best suited for are discussed., Comment: 29 pages, 9 figures, Chapter in press for the book Comets III, edited by K. Meech and M. Combi, University of Arizona Press

Kuiper-like belts of planetesimals orbiting stars other than the Sun are most commonly detected from the thermal emission of small dust produced in collisions. Emission from gas, most notably CO, highlights the cometary nature of these planetesimals. Here we present models for the release of gas from comet-like bodies in these belts, both due to their thermophysical evolution, most notably the decay of long-lived radioactive nuclides and collisional evolution, including catastrophic and gentler resurfacing collisions. We show that the rate of gas release is not proportional to the rate of dust release, if non-catastrophic collisions or thermal evolution dominate the release of CO gas. In this case, care must be taken when inferring the composition of comets. Non-catastrophic collisions dominate the gas production at earlier times than catastrophic collisions, depending on the properties of the planetesimal belt. We highlight the importance of the thermal evolution of comets, including crucially the decay of long-lived radioactive nuclides, as a source of CO gas around young (<50Myr) planetary systems, if large (10-100s kms) planetesimals are present., Comment: Accepted by MNRAS, 16 pages. Updated following review comments

The Aswan cliff on Comet 67P/Churyumov-Gerasimenko collapsed on 2015 July 10. Thereby, relatively pristine comet material from a depth of ~12 m was exposed at the surface. Observations of the collapse site by the microwave instrument Rosetta/MIRO have been retrieved from 8 months prior to collapse, as well as from 5, 7, and 11 months post-collapse. The MIRO data are analysed with thermophysical and radiative transfer models. The pre-collapse observations are consistent with a 30 MKS thermal inertia dust mantle with a thickness of at least 3 cm. The post-collapse data are consistent with: 1) a dust/water-ice mass ratio of 0.9$\pm$0.5 and a molar $\mathrm{CO_2}$ abundance of ~30 per cent relative to water; 2) formation of a dust mantle after ~7 months, having a thickness of a few millimetres or a fraction thereof; 3) a $\mathrm{CO_2}$ ice sublimation front at 0.4 cm that withdrew to 2.0 cm and later to 20$\pm$6 cm; 4) a thermal inertia ranging 10-45 MKS; 5) a gas diffusivity that decreased from $0.1\,\mathrm{m^2\,s^{-1}}$ to $0.001\,\mathrm{m^2\,s^{-1}}$; 6) presence of a solid-state greenhouse effect parts of the time. The data and the analysis provide a first empirical glimpse of how ice-rich cometary material ages and evolves when exposed to solar heating., Comment: 22 pages, 24 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

Between 2014 December 31 and 2015 March 17, the OSIRIS cameras on Rosetta documented the growth of a 140-m wide and 0.5-m deep depression in the Hapi region on Comet 67P/Churyumov–Gerasimenko. This shallow pit is one of several that later formed elsewhere on the comet, all in smooth terrain that primarily is the result of airfall of coma particles. We have compiled observations of this region in Hapi by the microwave instrument MIRO on Rosetta, acquired during October and November 2014. We use thermophysical and radiative transfer models in order to reproduce the MIRO observations. This allows us to place constraints on the thermal inertia, diffusivity, chemical composition, stratification, extinction coefficients, and scattering properties of the surface material, and how they evolved during the months prior to pit formation. The results are placed in context through long-term comet nucleus evolution modelling. We propose that (1) MIRO observes signatures that are consistent with a solid-state greenhouse effect in airfall material; (2) CO2 ice is sufficiently close to the surface to have a measurable effect on MIRO antenna temperatures, and likely is responsible for the pit formation in Hapi observed by OSIRIS; (3) the pressure at the CO2 sublimation front is sufficiently strong to expel dust and water ice outwards, and to compress comet material inwards, thereby causing the near-surface compaction observed by CONSERT, SESAME, and groundbased radar, manifested as the ‘consolidated terrain’ texture observed by OSIRIS. © 2022 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society.

Between 2014 December 31 and 2015 March 17, the OSIRIS cameras on Rosetta documented the growth of a 140m wide and 0.5m deep depression in the Hapi region on Comet 67P/Churyumov-Gerasimenko. This shallow pit is one of several that later formed elsewhere on the comet, all in smooth terrain that primarily is the result of airfall of coma particles. We have compiled observations of this region in Hapi by the microwave instrument MIRO on Rosetta, acquired during October and November 2014. We use thermophysical and radiative transfer models in order to reproduce the MIRO observations. This allows us to place constraints on the thermal inertia, diffusivity, chemical composition, stratification, extinction coefficients, and scattering properties of the surface material, and how they evolved during the months prior to pit formation. The results are placed in context through long-term comet nucleus evolution modelling. We propose that: 1) MIRO observes signatures that are consistent with a solid-state greenhouse effect in airfall material; 2) CO2 ice is sufficiently close to the surface to have a measurable effect on MIRO antenna temperatures, and likely is responsible for the pit formation in Hapi observed by OSIRIS; 3) the pressure at the CO2 sublimation front is sufficiently strong to expel dust and water ice outwards, and to compress comet material inwards, thereby causing the near-surface compaction observed by CONSERT, SESAME, and groundbased radar, manifested as the "consolidated terrain" texture observed by OSIRIS., Comment: 32 pages, 41 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

We here study the level of albedo variegation on the nucleus of Comet 67P/Churyumov-Gerasimenko. This is done by fitting the parameters of a standard photometric phase function model to disk-average radiance factor data in images acquired by the Rosetta/OSIRIS Narrow Angle Camera in the orange filter. Local discrepancies between the observed radiance factor and the disk-average solution are interpreted as a proxy W of the local single-scattering albedo. We find a wide range 0.02

The European Space Agency Rosetta/Philae mission to Comet 67P/Churyumov-Gerasimenko in 2014-2016 is the most complete and diverse investigation of a comet carried out thus far. Yet, many physical and chemical properties of the comet remain uncertain or unknown, and cometary activity is still not a well-understood phenomenon. We here attempt to place constraints on the nucleus abundances and sublimation front depths of H2O and CO2 ice, and to reconstruct how the nucleus evolved throughout the perihelion passage. We employ the thermophysical modelling code 'Numerical Icy Minor Body evolUtion Simulator', or NIMBUS, to search for conditions under which the observed H2O and CO2 production rates are simultaneously reproduced before and after perihelion. We find that the refractories to water-ice mass ratio of relatively pristine nucleus material is mu~1, that airfall material has mu~2, and that the molar abundance of CO2 relative H2O near 30 per cent. The dust mantle thickness is typically < 2 cm. The average CO2 sublimation front depths near aphelion were ~3.8 m and ~1.9 m on the northern and southern hemispheres, respectively, but varied substantially with time. We propose that airfall material is subjected to substantial fragmentation and pulverisation due to thermal fatigue during the aphelion passage. Sub-surface compaction of material due to CO2 activity near perihelion seems to have reduced the diffusivity in a measurable way., Comment: 22 pages, 19 figures. This is a pre--copyedited, author--produced PDF of an article accepted for publication in MNRAS following peer review

The Primordial Disk of small icy planetesimals, once located at 15-30 AU from the Sun, was disrupted by giant planet migration in the early Solar System. The Primordial Disk thereby became the source region of objects in the current-day Kuiper Belt, Scattered Disk, and Oort Cloud. I present the thermophysics code "Numerical Icy Minor Body evolUtion Simulator", or NIMBUS, and use it to study the thermophysical evolution of planetesimals in the Primordial Disk prior to its disruption. Such modelling is mandatory in order to understand the behaviour of dynamically new comets from the Oort Cloud, as well as the activity of Centaurs and short-period comets from the Scattered Disk, that return pre-processed to the vicinity of the Sun. I find that bodies in the midst of the Primordial Disk with diameters ranging 4-200 km lost all their CO ice on time-scales of order 0.1-10 Myr depending on size, through a combination of protosolar and long-lived radionuclide heating. CO and other hypervolatiles therefore require a less volatile host for their storage. I consider two possible hosts: amorphous water ice and CO2 ice. Because of the high luminosity of the protosun, some Primordial Disk bodies may have sustained significant crystallisation, CO:CO2 segregation, and CO2 sublimation in the uppermost few tens of meters. I discuss how this may affect coma abundance ratios and distant activity in dynamically new comets., Comment: 33 pages, 13 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

The observed presence of water molecules in the dayside lunar regolith was an unexpected discovery and remains poorly understood. Standard thermophysical models predict temperatures that are too high for adsorbed water to be stable. We propose that this problem can be caused by the assumption of locally flat surfaces that is common in such models. Here we apply a model that explicitly considers surface roughness, and accounts for solar illumination, shadows cast by topography, self-heating, thermal reradiation, and heat conduction. We couple the thermophysical model to a model of first-order desorption of lunar surface water and demonstrate that surface roughness substantially increases the capability of the Moon to retain water on its sunlit hemisphere at any latitude, and within $45^{\circ}$ of the poles, at any time of the lunar day. Hence, we show that lunar surface roughness has a strong influence on lunar water adsorption and desorption. Therefore, it is of critical importance to take account of surface roughness to get an accurate picture of the amount of water on the Moon's surface and in its exosphere., Comment: 9 pages, 10 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

Solar system bodies with surface and sub-surface volatiles will show observational evidence of activity when they reach a temperature where those volatiles change from solid to gas and are released. This is most frequently seen in comets, where activity is driven by the sublimation of water, carbon dioxide, or carbon monoxide ices. However, some bodies (notably the asteroid (3200) Phaethon) show initiation of activity at very small heliocentric distances, long after they have reached the sublimation temperatures of these ices. We investigate whether the sodium present in the mineral matrix could act as the volatile element responsible for this activity. We conduct theoretical modeling which indicates that sodium has the potential to sublimate in the conditions that Phaethon experiences, depending on the mineral phase it is held in. To test this, we then exposed samples of the carbonaceous chondrite Allende to varying heating events similar to what would be experienced by low perihelion asteroids. We measured the change in sodium present in each sample, and find that the highest temperature samples show a significant loss of sodium from specific mineral phases over a single heating event, comparable to a day on the surface of Phaethon. Under specific thermal histories possible for Phaethon, this outgassing could be sufficient to explain this object's observed activity. This effect would also be expected to be observed for other low-perihelia asteroids as well, and may act as a critical step in the process of disrupting small low-albedo asteroids., Comment: Published in PSJ with interactive figures

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From August 2014 to September 2016, the Rosetta spacecraft followed comet 67P/Churyumov-Gerasimenko along its orbit. After the comet passed perihelion, Rosetta performed a flyby manoeuvre over the Imhotep-Khepry transition in April 2016. The OSIRIS/Narrow-Angle-Camera (NAC) acquired 112 observations with mainly three broadband filters (centered at 480, 649, and 743 nm) at a resolution of up to 0.53 m/px and for phase angles between 0.095 degrees and 62 degrees. Aims. We have investigated the morphological and spectrophotometrical properties of this area using the OSIRIS/NAC high-resolution observations. Methods. We assembled the observations into coregistered color cubes. Using a 3D shape model, we produced the illumination conditions and georeference for each observation. We mapped the observations of the transition to investigate its geomorphology. Observations were photometrically corrected using the Lommel-Seeliger disk law. Spectrophotometric analyses were performed on the coregistered color cubes. These data were used to estimate the local phase reddening. Results. The Imhotep-Khepry transition hosts numerous and varied types of terrains and features. We observe an association between a feature's nature, its reflectance, and its spectral slopes. Fine material deposits exhibit an average reflectance and spectral slope, while terrains with diamictons, consolidated material, degraded outcrops, or features such as somber boulders present a lower-than-average reflectance and higher-than-average spectral slope. Bright surfaces present here a spectral behavior consistent with terrains enriched in water-ice. We find a phase-reddening slope of 0.064 +/- 0.001%/100 nm/degrees at 2.7 au outbound, similar to the one obtained at 2.3 au inbound during the February 2015 flyby. Conclusions. Identified as the source region of multiple jets and a host of water-ice material, the Imhotep-Khepry transition appeared in April 2016, close to the frost line, to further harbor several

Context. Since its arrival at the comet 67P/Churyumov-Gerasimenko in August 2014, the Rosetta spacecraft followed the comet as it went past the perihelion and beyond until September 2016. During this time there were many scientific instruments operating on board Rosetta to study the comet and its evolution in unprecedented detail. In this context, our study focusses on the distribution and evolution of exposed bright features that have been observed by OSIRIS, which is the scientific imaging instrument aboard Rosetta. Aims. We envisage investigating various morphologies of exposed bright features and the mechanisms that triggered their appearance. Methods. We co-registered multi-filter observations of OSIRIS images that are available in reflectance. The Lommel-Seeliger disk function was used to correct for the illumination conditions and the resulting colour cubes were used to perform spectrophotometric analyses on regions of interest. Results. We present a catalogue of 57 exposed bright features observed on the nucleus of the comet, all of which are attributed to the presence of HO ice on the comet. Furthermore, we categorise these patches under four different morphologies and present geometric albedos for each category. Conclusions. Although the nucleus of 67P/Churyumov-Gerasimenko appears to be dark in general, there are localised HO ice sources on the comet. Cometary activity escalates towards the perihelion passage and reveals such volatile ices. We propose that isolated HO ice patches found in smooth terrains in regions, such as Imhotep, Bes, and Hapi, result from frost as an aftermath of the cessation of the diurnal water cycle on the comet as it recedes from perihelion. Upon the comet's return to perihelion, such patches are revealed when sublimation-driven erosion removes the thin dust layers that got deposited earlier. More powerful activity sources such as cometary outbursts are capable of revealing much fresher, less contaminated HO ice that is preserved

Context. The camera OSIRIS on board Rosetta obtained high-resolution images of the nucleus of comet 67P/Churyumov-Gerasimenko (67P). Great parts of the nucleus surface are composed of fractured terrain. Aims. Fracture formation, evolution, and their potential relationship to physical processes that drive activity are not yet fully understood. Observed temperatures and gas production rates can be explained or interpreted with the presence of fractures by applying appropriate modelling methods. Methods. We followed a transient thermophysical model approach that includes radiative, conductive, and water-ice sublimation fluxes by considering a variety of heliocentric distances, illumination conditions, and thermophysical properties for a set of characteristic fracture geometries on the nucleus of 67P. We computed diurnal temperatures, heat fluxes, and outgassing behaviour in order to derive and distinguish the influence of the mentioned parameters on fractured terrain. Results. Our analysis confirms that fractures, as already indicated by former studies about concavities, deviate from flat-terrain topographies with equivalent properties, mostly through the effect of self-heating. Compared to flat terrain, illuminated cometary fractures are generally warmer, with smaller diurnal temperature fluctuations. Maximum sublimation rates reach higher peaks, and dust mantle quenching effects on sublimation rates are weaker. Consequently, the rough structure of the fractured terrain leads to significantly higher inferred surface thermal inertia values than for flat areas with identical physical properties, which might explain the range of measured thermal inertia on 67P. Conclusions. At 3.5 AU heliocentric distance, sublimation heat sinks in fractures converge to maximum values >50 W / m2 and trigger dust activity that can be related mainly to H2O. Fractures are likely to grow through the erosive interplay of alternating sublimation and thermal fatigue.

Aims. We aim to explore the behavior of the opposition effect as an important tool in optical remote sensing on the nucleus of comet 67P/Churyumov-Gerasimenko (67P), using Rosetta-OSIRIS images acquired in different filters during the approach phase, July-August 2014 and the close flyby images on 14 of February 2015, which contain the spacecraft shadow. Methods. We based our investigation on the global and local brightness from the surface of 67P with respect to the phase angle, also known as phase curve. The local phase curve corresponds to a region that is located at the Imhotep-Ash boundary of 67P. Assuming that the region at the Imhotep-Ash boundary and the entire nucleus have similar albedo, we combined the global and local phase curves to study the opposition-surge morphology and constrain the structure and properties of 67P. The model parameters were furthermore compared with other bodies in the solar system and existing laboratory study. Results. We found that the morphological parameters of the opposition surge decrease monotonically with wavelength, whereas in the case of coherent backscattering this behavior should be the reverse. The results from comparative analysis place 67P in the same category as the two Mars satellites, Phobos and Deimos, which are notably different from all airless bodies in the solar system. The similarity between the surface phase function of 67P and a carbon soot sample at extremely small angles is identified, introducing regolith at the boundary of the Imhotep-Ash region of 67P as a very dark and fluffy layer.

Aims. We aim to explore the behavior of the opposition effect as an important tool in optical remote sensing on the nucleus of comet 67P/Churyumov-Gerasimenko (67P), using Rosetta-OSIRIS images acquired in different filters during the approach phase, July-August 2014 and the close flyby images on 14 of February 2015, which contain the spacecraft shadow. Methods. We based our investigation on the global and local brightness from the surface of 67P with respect to the phase angle, also known as phase curve. The local phase curve corresponds to a region that is located at the Imhotep-Ash boundary of 67P. Assuming that the region at the Imhotep-Ash boundary and the entire nucleus have similar albedo, we combined the global and local phase curves to study the opposition-surge morphology and constrain the structure and properties of 67P. The model parameters were furthermore compared with other bodies in the solar system and existing laboratory study. Results. We found that the morphological parameters of the opposition surge decrease monotonically with wavelength, whereas in the case of coherent backscattering this behavior should be the reverse. The results from comparative analysis place 67P in the same category as the two Mars satellites, Phobos and Deimos, which are notably different from all airless bodies in the solar system. The similarity between the surface phase function of 67P and a carbon soot sample at extremely small angles is identified, introducing regolith at the boundary of the Imhotep-Ash region of 67P as a very dark and fluffy layer.© ESO, 2017.

Aims. We carried out an investigation of the surface variegation of comet 67P/Churyumov-Gerasimenko, the detection of regions showing activity, the determination of active and inactive surface regions of the comet with spectral methods, and the detection of fallback material. Methods. We analyzed multispectral data generated with Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) narrow angle camera (NAC) observations via spectral techniques, reflectance ratios, and spectral slopes in order to study active regions. We applied clustering analysis to the results of the reflectance ratios, and introduced the new technique of activity thresholds to detect areas potentially enriched in volatiles. Results. Local color inhomogeneities are detected over the investigated surface regions. Active regions, such as Hapi, the active pits of Seth and Ma'at, the clustered and isolated bright features in Imhotep, the alcoves in Seth and Ma'at, and the large alcove in Anuket, have bluer spectra than the overall surface. The spectra generated with OSIRIS NAC observations are dominated by cometary emissions of around 700 nm to 750 nm as a result of the coma between the comet's surface and the camera. One of the two isolated bright features in the Imhotep region displays an absorption band of around 700 nm, which probably indicates the existence of hydrated silicates. An absorption band with a center between 800-900 nm is tentatively observed in some regions of the nucleus surface. This absorption band can be explained by the crystal field absorption of Fe2+, which is a common spectral feature seen in silicates.

Context. Data derived from the reconstruction of the nucleus shape of comet 67P/Churyumov-Gerasimenko (67P) from images of the OSIRIS camera onboard ROSETTA show evidence that the nucleus rotates in complex mode. First, the orientation of the spin axis is not fixed in an inertial reference frame, which suggests a precessing motion around the angular momentum vector with a periodicity of approximately 257 h +/- 12 h. Second, periodograms of the right ascension and declination (RA/Dec) coordinates of the body-frame Z axis show a very significant (higher than 99.99%) periodicity at 276 h +/- 12 h, different from the rotational period of 12.40 h as previously determined from light-curve analysis. Aims. The main goal is to interpret the data and associated periodicities of the spin axis orientation in space. Methods. We analyzed the spin axis orientation in space and associated periodicities and compared them with solutions of Euler equations under the assumption that the body rotates in torque-free conditions. Statistical tests comparing the observationally derived spin axis orientation with the outcome from simulations were applied to determine the most likely inertia moments, excitation level, and periods. Results. Under the assumption that the body is solid-rigid and rotates in torque-free conditions, the most likely interpretation is that 67P is spinning around the principal axis with the highest inertia moment with a period of about 13 h. At the same time, the comet precesses around the angular momentum vector with a period of about 6.35 h. While the rotating period of such a body would be about 12.4 h, RA/Dec coordinates of the spin axis would have a periodicity of about 270 h as a result of the combination of the two aforementioned motions. Conclusions. The most direct and simple interpretation of the complex rotation of 67P requires a ratio of inertia moments significantly higher than that of a homogeneous body.

Heat transport and ice sublimation in comets are interrelated processes reflecting properties acquired at the time of formation and during subsequent evolution. The Microwave Instrument on the Rosetta Orbiter (MIRO) acquired maps of the subsurface temperature of comet 67P/Churyumov-Gerasimenko, at 1.6 mm and 0.5 mm wavelengths, and spectra of water vapor. The total H2O production rate varied from 0.3 kg s(-1) in early June 2014 to 1.2 kg s(-1) in late August and showed periodic variations related to nucleus rotation and shape. Water outgassing was localized to the "neck" region of the comet. Subsurface temperatures showed seasonal and diurnal variations, which indicated that the submillimeter radiation originated at depths comparable to the diurnal thermal skin depth. A low thermal inertia (similar to 10 to 50 J K-1 m(-2) s(-0.5)), consistent with a thermally insulating powdered surface, is inferred.

Spacecraft observations of atmosphereless Solar System bodies, combined with thermophysical modeling, provide important information about the thermal inertia and degree of surface roughness of these bodies. The thermophysical models rely on various methods of generating topography, the most common being the concave spherical segment. We here compare the properties of thermal emission for a number of different topographies - concave spherical segments, random Gaussians, fractals and parallel sinusoidal trenches - for various illumination and viewing geometries, degrees of surface roughness and wavelengths. We find that the thermal emission is strongly dependent on roughness type, even when the degrees of roughness are identical, for certain illumination and viewing geometries. The systematic usage of any single topography model may therefore bias determinations of thermal inertia and level of roughness. We outline strategies that may be employed during spacecraft observations to disentangle thermal inertia, level of roughness and type of topography. We also compare the numerically complex and time consuming full-scale thermophysical models with a simplified statistical approach, which is fairly easy to implement and quick to run. We conclude that the simplified statistical approach is similar to thermophysical models for cases tested here, which enables the user to analyze huge amounts of spectral data at a low numerical cost.

A thermophysical model is presented that considers surface roughness, cast shadows, multiple or single scattering of radiation, visual and thermal infrared self heating, as well as heat conduction in one or three dimensions. The code is suitable for calculating infrared spectral energy distributions for spatially resolved or unresolved minor Solar System bodies without significant atmospheres or sublimation, such as the Moon, Mercury, asteroids, irregular satellites or inactive regions on comet nuclei. It is here used to explore the effects of surface roughness on spatial scales small enough for heat conduction to erase lateral temperature gradients. Analytically derived corrections to one-dimensional models that reproduce the results of three-dimensional modeling are presented. We find that the temperature of terrains with such small-scale roughness is identical to that of smooth surfaces for certain types of topographies and non-scattering material. However, systematic differences between smooth and rough terrains are found for scattering materials, or topographies with prominent positive relief. Contrary to common beliefs, the roughness on small spatial scales may therefore affect the thermal emission of Solar System bodies.

Re-calibrated near-infrared spectroscopy of the resolved nucleus of Comet 9P/Tempel 1 acquired by the Deep Impact spacecraft has been analyzed by utilizing the post-Stardust-NExT nucleus shape model and spin pole solution, as well as a novel thermophysical model that explicitly accounts for small-scale surface roughness and thermal inertia. We find that the thermal inertia varies measurably across the surface, and that thermal emission from certain regions only can be reproduced satisfactory if surface roughness is accounted for. Particularly, a scarped/pitted terrain that experienced morning sunrise during the flyby is measurably rough (Hapke mean slope angle similar to 45 degrees) and has a thermal inertia of at most 50J m(-2) K-1 s(-1/2), but probably much lower. However, thick layered terrain and thin layered terrain experiencing local noon during the flyby have a substantially larger thermal inertia, reaching 150J m(-2) K-1 s(-1/2) if the surface is as rough as the scarped/pitted terrain, but 200J m(-2) K-1 s(-1/2) if the terrain is considered locally flat. Furthermore, the reddening of the nucleus near-infrared 1.5-2.2 gm spectrum varies between morphological units, being reddest for thick layered terrain (median value 3.4% k angstrom(-1)) and most neutral for the smooth terrain known to contain surface water ice (median value 3.1% k angstrom(-1)). Thus, Comet 9P/Tempel 1 is heterogeneous in terms of both thermophysical and optical properties, due to formation conditions and/or post-formation processing.

On July 4, 2005, the HRI-IR instrument onboard the Deep Impact spacecraft (NASA/Univ. of Maryland) acquired the first ever near-infrared spectra of a fully resolved comet nucleus, 9P/Tempel 1. Early attempts to estimate the thermal inertia of the surface material were inconclusive, due to negligence of small-scale surface roughness in the thermophysical models used to analyze the spectra. Following a substantial recalibration of the original dataset, we now reconsider the 9P/Tempel 1 spectra, using more realistic thermophysical models. In addition to largescale nucleus irregularity, these models now explicitly consider small-scale roughness and related phenomena such as shadowing and IR self heating. Furthermore, 3D heat conduction can be utilized when topographic features are similar in size to the thermal skin depth, or smaller. Estimates of the thermal inertia, degree of small-scale roughness and their levels of variation across the nucleus are presented.