The Yarkovsky effect is not responsible for small crater depletion on Eros and Itokawa

The near-Earth Asteroids Eros and Itokawa show a pronounced lack of small (?100 m) craters, the vast majority of which were formed during their time in the main belt, and this has been cited as possible evidence that small (?10 m) impactors are efficiently removed from the main belt by the Yarkovsky effect. Using well-tested models for the evolution of the main-belt size distribution and the evolution of crater populations on asteroid surfaces, I show that a pronounced lack of small impactors would require size-dependent removal far stronger than can result from the Yarkovsky effect (or any other known process). Furthermore, such strong removal would lead to wavelike perturbations in the main-belt and near-Earth asteroid size distributions that are inconsistent with their observed size distributions, as well as the cratering records on asteroid surfaces. A more likely explanation is that processes on asteroid surfaces, such as seismic shaking, are responsible for erasing small craters after they form.     

Millimeter and submillimeter measurements of asteroid (2867) Steins during the Rosetta fly-by

The European Space Agency Rosetta Spacecraft passed within 803 km of the main belt asteroid (2867) Steins on 5 September 2008. The Rosetta Spacecraft carries a number of scientific instruments including a millimeter and submillimeter radiometer and spectrometer. The instrument, named MIRO (Microwave Instrument for the Rosetta Orbiter), consists of a 30-cm diameter, offset parabolic reflector telescope followed by two heterodyne receivers. Center-band operating frequencies of the receivers are near 190 GHz (1.6 mm) and 562 GHz (0.53 mm). Broadband continuum channels are implemented in both frequency bands for the measurement of near surface temperatures and temperature gradients. A 4096 channel CTS (chirp transform spectrometer) having 180 MHz total bandwidth and ∼44 kHz resolution is also connected to the submillimeter receiver. We present the continuum observations of asteroid (2867) Steins obtained during the fly-by with the MIRO instrument. Spectroscopic data were also collected during the fly-by using the MIRO spectrometer fixed-tuned to rotational lines of several molecules. Results of the spectroscopic investigation will be the topic of a separate publication.Comparative thermal models and radiative transfer calculations for Steins are presented. Emissivities of Steins were determined to be 0.6-0.7 and 0.85-0.9 at wavelengths of 0.53 and 1.6 mm, respectively. The thermal inertia of Steins was estimated to be in the range 450-850 J/(m² s^0.5 K). Assuming that the emissivity of Steins is determined by the Fresnel reflection coefficients of the surface material, the area-averaged dielectric constant of the surface material is in the range 4-20. These values are rock-like, and are unlike the powdered-regolith surface of the Moon.     

The light curve of asteroid 2867 Steins measured by VIRTIS-M during the Rosetta fly-by

On 5 September 2008, the Rosetta spacecraft encountered the asteroid 2867 Steins on its way to the comet 67P/Churyumov-Gerasimenko. This was the first of two planned asteroid fly-bys performed by the probe, the second fly-by being with the much larger asteroid 21 Lutetia in July 2010. The VIRTIS imaging spectrometer (IFOV 0.250 mrad, overall spectral range 0.25-5.1 μm) onboard Rosetta acquired data of Steins already before the closest approach phase, when the target was spatially unresolved, in order to obtain a light curve of the asteroid in the infrared spectral range extending up to 5 μm, that was never explored before. The VIRTIS light curve campaign started at 11:30 UTC onboard time, when the spacecraft was about 221,377 km away from the target, and ended at 17:58 UTC, at a distance of 20,741 km away from Steins. During this timeframe, the solar phase angle of the asteroid was roughly constant, ranging from 38.2° to 36.3°.Assuming the most recent value derived for the rotational period of Steins (Lamy et al., 2008), the VIRTIS observations covered slightly more than one rotation of the asteroid. In this interval, VIRTIS collected 8 hyperspectral cubes where Steins was captured 119 times, both in the visual and in the infrared range. Given the low signal and the unresolved appearance of the source, for which the instrument was not designed, only a small subset of wavelengths turned out to be suitable to sample the light curve. Nevertheless, in both the VIS and NIR ranges we find a similar trend, with two different maxima and minima during one rotational period, and amplitudes consistent with the results in the visual range obtained in previous works, including the data set acquired by the OSIRIS camera onboard Rosetta. We also report the presence of a new broad feature centered at approximately 0.81-0.82 μm, which is seen in the visual data throughout the rotation of the asteroid.     

The fossilized size distribution of the main asteroid belt

Planet formation models suggest the primordial main belt experienced a short but intense period of collisional evolution shortly after the formation of planetary embryos. This period is believed to have lasted until Jupiter reached its full size, when dynamical processes (e.g., sweeping resonances, excitation via planetary embryos) ejected most planetesimals from the main belt zone. The few planetesimals left behind continued to undergo comminution at a reduced rate until the present day. We investigated how this scenario affects the main belt size distribution over Solar System history using a collisional evolution model (CoEM) that accounts for these events. CoEM does not explicitly include results from dynamical models, but instead treats the unknown size of the primordial main belt and the nature/timing of its dynamical depletion using innovative but approximate methods. Model constraints were provided by the observed size frequency distribution of the asteroid belt, the observed population of asteroid families, the cratered surface of differentiated Asteroid (4) Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr. Using CoEM, we solved for both the shape of the initial main belt size distribution after accretion and the asteroid disruption scaling law . In contrast to previous efforts, we find our derived function is very similar to results produced by numerical hydrocode simulations of asteroid impacts. Our best fit results suggest the asteroid belt experienced as much comminution over its early history as it has since it reached its low-mass state approximately 3.9-4.5 Ga. These results suggest the main belt's wavy-shaped size-frequency distribution is a “fossil” from this violent early epoch. We find that most diameter D?120 km asteroids are primordial, with their physical properties likely determined during the accretion epoch. Conversely, most smaller asteroids are byproducts of fragmentation events. The observed changes in the asteroid spin rate and lightcurve distributions near D∼100-120 km are likely to be a byproduct of this difference. Estimates based on our results imply the primordial main belt population (in the form of D<1000 km bodies) was 150-250 times larger than it is today, in agreement with recent dynamical simulations.     

Itokawa's cratering record as observed by Hayabusa: Implications for its age and collisional history

In this paper, we study cratering and crater erasure processes and provide an age estimate for the near-Earth Asteroid (25143) Itokawa, the target of the mission Hayabusa, based on its crater history since the time when it was formed in the main belt by catastrophic disruption or experienced a global resetting event. Using a model which was applied to the study of the crater history of Gaspra, Ida, Mathilde and Eros [O'Brien, D.P., Greenberg, R., Richardson, J.E., 2006. Icarus 183, 79–92], we calculate the time needed to accumulate the craters on Itokawa's surface, taking into account several processes which can affect crater formation and crater erasure on such a low-gravity object, such as seismic shaking. We use two models of the projectile population and two scaling laws to relate crater diameter to projectile size. Both models of the projectile population provide similar results, and depending on the scaling law used, we find that the time necessary to accumulate Itokawa's craters was at least ∼75 Myr, and maybe as long as 1 Gyr. Moreover, using the same model and similar parameters (scaled accordingly), we provide a good match not only to Itokawa's craters, but also to those of Eros, which has also been imaged at high enough resolution to give crater counts in a similar size range to those on Itokawa. We show that, as for Eros, the lack of small craters on Itokawa is consistent with erasure by seismic shaking, although for Itokawa, the pronounced deficiency of the smallest craters (<10 m in diameter) requires another process or event in addition to just seismic shaking. A small body such as Itokawa is highly sensitive to specific events that may occur during its history. For example, the two parts of Itokawa, called head and body, may well have joined each other by a low-velocity impact within the last hundred thousand years [Scheeres, D.J., Abe, M., Yoshikawa, M., Nakamura, R., Gaskell, R.W., Abell, P.A., 2007. Icarus 188, 425–429]. In addition to providing an erasure mechanism for small craters, the proposed timescale of that event is consistent with the timescale necessary in our model to form the current, depleted population of just a few small (<10 m) craters on Itokawa, suggesting that it may be the explanation for the discrepancy between Itokawa's cratering record and that obtained from our equilibrium seismic shaking model. Other explanations for the depletion of the smallest craters on Itokawa, such as armoring by boulders lying on the surface, cannot be ruled out.     

The global effects of impact-induced seismic activity on fractured asteroid surface morphology

Impact-induced seismic vibrations have long been suspected of being an important surface modification process on small satellites and asteroids. In this study, we use a series of linked seismic and geomorphic models to investigate the process in detail. We begin by developing a basic theory for the propagation of seismic energy in a highly fractured asteroid, and we use this theory to model the global vibrations experienced on the surface of an asteroid following an impact. These synthetic seismograms are then applied to a model of regolith resting on a slope, and the resulting downslope motion is computed for a full range of impactor sizes. Next, this computed downslope regolith flow is used in a morphological model of impact crater degradation and erasure, showing how topographic erosion accumulates as a function of time and the number of impacts. Finally, these results are applied in a stochastic cratering model for the surface of an Eros-like body (same volume and surface area as the asteroid), with craters formed by impacts and then erased by the effects of superposing craters, ejecta coverage, and seismic shakedown. This simulation shows good agreement with the observed 433 Eros cratering record at a Main Belt exposure age of 400±200 Myr, including the observed paucity of small craters. The lowered equilibrium numbers (loss rate = production rate) for craters less than ∼100 m in diameter is a direct result of seismic erasure, which requires less than a meter of mobilized regolith to reproduce the NEAR observations. This study also points to an upper limit on asteroid size for experiencing global, surface-modifying, seismic effects from individual impacts of about 70-100 km (depending upon asteroid seismic properties). Larger asteroids will experience only localized (regional) seismic effects from individual impacts.     

Yarkovsky/YORP chronology of asteroid families

Asteroid families are the byproducts of catastrophic collisions whose fragments form clusters in proper semimajor axis, eccentricity, and inclination space. Although many families have been observed in the main asteroid belt, only two very young families, Karin and Veritas, have well-determined ages. The ages of other families are needed, however, if we hope to infer information about their ejection velocity fields, space weathering processes, etc. In this paper, we developed a method that allows us to estimate the ages of moderately young asteroid families (approximately in between 0.1 and 1 Gyr). We apply it to four suitable cases—Erigone, Massalia, Merxia, and Astrid—and derive their likely ages and approximate ejection velocity fields. We find that Erigone and Merxia were produced by large catastrophic disruption events (i.e., parent body ?100 km) that occurred approximately 280 and 330 Myr ago, respectively. The Massalia family was likely produced by a cratering event on Asteroid (20) Massalia less than 200 Myr ago. Finally, the Astrid family, which was produced by the disruption of a 60-70 km asteroid, is 100-200 Myr old, though there is considerable uncertainty in this result. We estimate that the initial ejection velocities for these families were only a few tens of meters per second, consistent with numerical hydrocode models of asteroid impacts. Our results help to verify that asteroid families are constantly undergoing dynamical orbital evolution from thermal (Yarkovsky) forces and spin vector evolution from thermal (YORP) torques.     

On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection — II

The efficiency of absorption of X-rays generated by a nuclear explosion at the surface of an asteroid, estimated earlier, is used to calculate the explosion yield needed to deflect the orbit of an asteroid. Following the work of Ahrens &38; Harris, it is shown that a recoil velocity of 1 cm s⁻¹ is required to deflect an asteroid from a collision course with the Earth, and the necessary yield of explosion energy is estimated. If it is assumed that the scaling law between the energy and the diameter of the resulting crater, obtained from experiments carried out on the Earth, remains valid on the asteroid surface, where gravity is much weaker, an explosion energy of 8 and 800 megaton (Mton) equivalent of TNT would be required for asteroids of diameter 1 and 10 km respectively. If, on the other hand, the crater diameter is proportional to a certain power of the gravity g , the power being determined from a dimension analysis, 130 kton and 12 Mton would be required to endow asteroids of diameters 1 and 10 km with the required velocity, respectively. The result indicates that in order to estimate the required explosion energy, a better understanding of cratering under gravity much weaker than on the Earth would be required.     

Size-Frequency Distribution of Small Lunar Craters: Widening with Degradation and Crater Lifetime

The review and new measurements are presented for depth/diameter ratio and slope angle evolution during small (D < 1 km) lunar impact craters aging (degradation). Comparative analysis of available data on the areal cratering density and on the crater degradation state for selected craters, dated with returned Apollo samples, in the first approximation confirms Neukum’s chronological model. The uncertainty of crater retention age due to crater degradational widening is estimated. The collected and analyzed data are discussed to be used in the future updating of mechanical models for lunar crater aging.     

Nonuniform cratering of the Moon and a revised crater chronology of the inner Solar System

We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronology method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analytically, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth-Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Varying depths of this megaregolith between the mare and highlands is a plausible partial explanation for differences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.     

Search for Steins’ surface inhomogeneities from OSIRIS Rosetta images

We investigate the possible presence of heterogeneous surface features on asteroid (2867) Steins, using the G-mode multivariate statistical method (Coradini et al., 1977) applied to Rosetta/OSIRIS images. We analyze both NAC and WAC images obtained near around the closest approach that occurred on September 5th, 2008, through different filters centered on wavelengths ranging from 295 to 986 nm. The shape of Steins is modeled as a polyhedron of almost 58 000 facets. Photometric corrections were performed using Hapke's (2002) model to compensate for the variable illuminations conditions at the surface. The G-mode classification method was performed on all visible and illuminated facets, i.e. in a region limited to [−50°,+60°] in latitude and [−40°,+90°] in longitude, that represents almost 30% of the total surface. The analyzed set of facets does not show any significant difference in the reflected light content, suggesting no surface inhomogeneities larger than 4% at the 95% confidence level.     

Possible long-term decline in impact rates: 2. Lunar impact-melt data regarding impact history

Crater counts at lunar landing sites with measured ages establish a steep decline in cratering rate during the period ∼3.8 to ∼3.1 Gyr ago. Most models of the time dependence suggest a roughly constant impact rate (within factor ∼2) after about 3 Gyr ago, but are based on sparse data. Recent dating of impact melts from lunar meteorites, and Apollo glass spherules, clarifies impact rates from ∼3.2 to ∼2 Gyr ago or less. Taken together, these data suggest a decline with roughly 700 Myr half-life around 3 Gyr ago, and a slower decline after that, dropping by a factor ∼3 from about ∼2.3 Gyr ago until the present. Planetary cratering involved several phases with different time behaviors: (1) rapid sweep-up of most primordial planetesimals into planets in the first hundred Myr, (2) possible later effects of giant planet migration with enhanced cratering, (3) longer term sweep-up of leftover planetesimals, and finally (4) the present long-term “leakage” of asteroids from reservoirs such as the main asteroid belt and Kuiper belt. In addition, at any given point on the Moon, a pattern of “spikes” (sharp maxima of relatively narrow time width) will appear in the production rate of smaller craters (?500 m?), not only from secondary debris from large primary lunar impacts at various distances from the point in question, but also from asteroid breakups dotted through Solar System history. The pattern of spikes varies according to type of sample being measured (i.e., glass spherules vs impact melts). For example, several data sets show an impact rate spike ∼470 Myr ago associated with the asteroid belt collision that produced the L chondrites (see Section 3.6 below). Such spikes should be less prominent in the production record of craters of D? few km. These phenomena affect estimates of planetary surfaces ages from crater counts, as discussed in a companion paper [Quantin, C., Mangold, N., Hartmann, W.K., Allemand, P., 2007. Icarus 186, 1-10]. Fewer impact melts and glass spherules are found at ∼3.8 Gyr than at ∼3.5 Gyr ago, even though the impact rate itself is known to have been higher at 3.8 Gyr ago than 3.5 Gyr. This disproves the assertion by Ryder [Ryder, G., 1990. EOS 71, 313, 322-323] and Cohen et al. [Cohen, B.A., Swindle, T.D., Kring, D.A., 2000. Science 290, 1754-1756] that ancient impact melts are a direct proxy for ancient impact (cf. Section 3.3). This result raises questions about how to interpret cratering history before 3.8 Gyr ago.     

The flyby of Rosetta at asteroid Šteins - mission and science operations

The international Rosetta mission, a cornerstone mission of the european space agency scientific Programme, was launched on 2nd March 2004 on its 10 years journey towards a rendezvous with comet Churyumov-Gerasimenko (Gardini et al., 1999). During its interplanetary flight towards its target Rosetta crosses the asteroid belt twice with the opportunity to observe at close quarters two asteroids: (2867)-Šteins in 2008 and (21)-Lutetia in 2010. The spacecraft design was such that these opportunities could be fully exploited to deliver valuable data to the scientific community. The mission trajectory was controlled such that Rosetta would fly next to asteroid Šteins on the 5th of September 2008 with a relative speed of 8.6 km/s at a minimum distance of 800 km. Mission operations have been carefully planned to achieve the best possible flyby scenario and scientific outcome. The flyby scenario, the optical navigation campaign, and the planning of the scientific observations had to be adapted by the Mission and the Science Operations Centres to the demanding requirements expressed by the scientific community. The flyby was conducted as planned with a large number of successful observations.     

Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion

The main belt is believed to have originally contained an Earth mass or more of material, enough to allow the asteroids to accrete on relatively short timescales. The present-day main belt, however, only contains ∼5×¹⁰⁻⁴ Earth masses. Numerical simulations suggest that this mass loss can be explained by the dynamical depletion of main belt material via gravitational perturbations from planetary embryos and a newly-formed Jupiter. To explore this scenario, we combined dynamical results from Petit et al. [Petit, J. Morbidelli, A., Chambers, J., 2001. The primordial excitation and clearing of the asteroid belt. Icarus 153, 338-347] with a collisional evolution code capable of tracking how the main belt undergoes comminution and dynamical depletion over 4.6 Gyr [Bottke, W.F., Durda, D., Nesvorny, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111-140]. Our results were constrained by the main belt's size-frequency distribution, the number of asteroid families produced by disruption events from diameter D>100 km parent bodies over the last 3-4 Gyr, the presence of a single large impact crater on Vesta's intact basaltic crust, and the relatively constant lunar and terrestrial impactor flux over the last 3 Gyr. We used our model to set limits on the initial size of the main belt as well as Jupiter's formation time. We find the most likely formation time for Jupiter was 3.3±2.6 Myr after the onset of fragmentation in the main belt. These results are consistent with the estimated mean disk lifetime of 3 Myr predicted by Haisch et al. [Haisch, K.E., Lada, E.A., Lada, C.J., 2001. Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153-L156]. The post-accretion main belt population, in the form of diameter D?1000 km planetesimals, was likely to have been 160±40 times the current main belt's mass. This corresponds to 0.06-0.1 Earth masses, only a small fraction of the total mass thought to have existed in the main belt zone during planet formation. The remaining mass was most likely taken up by planetary embryos formed in the same region. Our results suggest that numerous D>200 km planetesimals disrupted early in Solar System history, but only a small fraction of their fragments survived the dynamical depletion event described above. We believe this may explain the limited presence of iron-rich M-type, olivine-rich A-type, and non-Vesta V-type asteroids in the main belt today. The collisional lifetimes determined for main belt asteroids agree with the cosmic ray exposure ages of stony meteorites and are consistent with the limited collisional evolution detected among large Koronis family members. Using the same model, we investigated the near-Earth object (NEO) population. We show the shape of the NEO size distribution is a reflection of the main belt population, with main belt asteroids driven to resonances by Yarkovsky thermal forces. We used our model of the NEO population over the last 3 Gyr, which is consistent with the current population determined by telescopic and satellite data, to explore whether the majority of small craters (D<0.1-1 km) formed on Mercury, the Moon, and Mars were produced by primary impacts or by secondary impacts generated by ejecta from large craters. Our results suggest that most small craters formed on these worlds were a by-product of secondary rather than primary impacts.     

Evidence for surface variegation in Rosetta OSIRIS images of asteroid 2867 Šteins

The OSIRIS camera onboard Rosetta successfully acquired images of asteroid 2867 Steins through a variety of color filters during the flyby on 5 September 2008. The best images of this 5 km diameter asteroid have a resolution of 78 m per pixel. We process the images by deconvolving with the point spread function and enlarging through the Mitchell-Netravali filter. The enhanced set is analyzed by means of various techniques (PCA, band ratios, stereo anaglyphs) to study surface morphology and search for variegation. We identify a landslide, which supports a YORP origin for Steins’ unusual diamond shape. In addition, we find that the interior of one of two large craters on the south pole is bluer than the rest of the body.     

Impact cratering records of the mid-sized, icy saturnian satellites

Resolution of Voyager 1 and 2 images of the mid-sized, icy saturnian satellites was generally not much better than 1 km per line pair, except for a few, isolated higher resolution images. Therefore, analyses of impact crater distributions were generally limited to diameters (D) of tens of kilometers. Even with the limitation, however, these analyses demonstrated that studying impact crater distributions could expand understanding of the geology of the saturnian satellites and impact cratering in the outer Solar System. Thus to gain further insight into Saturn’s mid-sized satellites and impact cratering in the outer Solar System, we have compiled cratering records of these satellites using higher resolution CassiniISS images. Images from Cassini of the satellites range in resolution from tens m/pixel to hundreds m/pixel. These high-resolution images provide a look at the impact cratering records of these satellites never seen before, expanding the observable craters down to diameters of hundreds of meters. The diameters and locations of all observable craters are recorded for regions of Mimas, Tethys, Dione, Rhea, Iapetus, and Phoebe. These impact crater data are then analyzed and compared using cumulative, differential and relative (R) size-frequency distributions. Results indicate that the heavily cratered terrains on Rhea and Iapetus have similar distributions implying one common impactor population bombarded these two satellites. The distributions for Mimas and Dione, however, are different from Rhea and Iapetus, but are similar to one another, possibly implying another impactor population common to those two satellites. The difference between these two populations is a relative increase of craters with diameters between 10 and 30 km and a relative deficiency of craters with diameters between 30 and 80 km for Mimas and Dione compared with Rhea and Iapetus. This may support the result from Voyager images of two distinct impactor populations. One population was suggested to have a greater number of large impactors, most likely heliocentric comets (Saturn Population I in the Voyager literature), and the other a relative deficiency of large impactors and a greater number of small impactors, most likely planetocentric debris (Saturn Population II). Meanwhile, Tethys’ impact crater size-frequency distribution, which has some similarity to the distributions of Mimas, Dione, Rhea, and Iapetus, may be transitional between the two populations. Furthermore, when the impact crater distributions from these older cratered terrains are compared to younger ones like Dione’s smooth plains, the distributions have some similarities and differences. Therefore, it is uncertain whether the size-frequency distribution of the impactor population(s) changed over time. Finally, we find that Phoebe has a unique impact crater distribution. Phoebe appears to be lacking craters in a narrow diameter range around 1 km. The explanation for this confined “dip” at D = 1 km is not yet clear, but may have something to do with the interaction of Saturn’s irregular satellites or the capture of Phoebe.     

Asteroid families: Current situation

Being the products of energetic collisional events, asteroid families provide a fundamental body of evidence to test the predictions of theoretical and numerical models of catastrophic disruption phenomena. The goal is to obtain, from current physical and dynamical data, reliable inferences on the original disruption events that produced the observed families. The main problem in doing this is recognizing, and quantitatively assessing, the importance of evolutionary phenomena that have progressively changed the observable properties of families, due to physical processes unrelated to the original disruption events. Since the early 1990s, there has been a significant evolution in our interpretation of family properties. New ideas have been conceived, primarily as a consequence of the development of refined models of catastrophic disruption processes, and of the discovery of evolutionary processes that had not been accounted for in previous studies. The latter include primarily the Yarkovsky and Yarkovsky-O’Keefe-Radzvieski-Paddack (YORP) effects—radiation phenomena that can secularly change the semi-major axis and the rotation state. We present a brief review of the current state of the art in our understanding of asteroid families, point out some open problems, and discuss a few likely directions for future developments.     

Dynamical erosion of the asteroid belt and implications for large impacts in the inner Solar System

The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters in the current asteroid belt. In a numerical analysis of the long-term evolution of test particles in the main asteroid belt region, we find that the dynamical loss history of test particles from this region is well described with a logarithmic decay law. In our simulations the loss rate function that is established at persists with little deviation to at least . Our study indicates that the asteroid belt region has experienced a significant amount of depletion due to this dynamical erosion—having lost as much as ∼50% of the large asteroids—since 1 Myr after the establishment of the current dynamical structure of the asteroid belt. Because the dynamical depletion of asteroids from the main belt is approximately logarithmic, an equal amount of depletion occurred in the time interval 10-200 Myr as in 0.2-4 Gyr, roughly ∼30% of the current number of large asteroids in the main belt over each interval. We find that asteroids escaping from the main belt due to dynamical chaos have an Earth-impact probability of ∼0.3%. Our model suggests that the rate of impacts from large asteroids has declined by a factor of 3 over the last 3 Gyr, and that the present-day impact flux of objects on the terrestrial planets is roughly an order of magnitude less than estimates currently in use in crater chronologies and impact hazard risk assessments.     

Towards initial mass functions for asteroids and Kuiper Belt Objects

Our goal is to understand primary accretion of the first planetesimals. Some examples are seen today in the asteroid belt, providing the parent bodies for the primitive meteorites. The primitive meteorite record suggests that sizeable planetesimals formed over a period longer than a million years, each of which being composed entirely of an unusual, but homogeneous, mixture of millimeter-size particles. We sketch a scenario that might help explain how this occurred, in which primary accretion of 10-100 km size planetesimals proceeds directly, if sporadically, from aerodynamically-sorted millimeter-size particles (generically “chondrules”). These planetesimal sizes are in general agreement with the currently observed asteroid mass peak near 100 km diameter, which has been identified as a “fossil” property of the pre-erosion, pre-depletion population. We extend our primary accretion theory to make predictions for outer Solar System planetesimals, which may also have a preferred size in the 100 km diameter range. We estimate formation rates of planetesimals and explore parameter space to assess the conditions needed to match estimates of both asteroid and Kuiper Belt Object (KBO) formation rates. For parameters that satisfy observed mass accretion rates of Myr-old protoplanetary nebulae, the scenario is roughly consistent with not only the “fossil” sizes of the asteroids, and their estimated production rates, but also with the observed spread in formation ages of chondrules in a given chondrite, and with a tolerably small radial diffusive mixing during this time between formation and accretion. As previously noted, the model naturally helps explain the peculiar size distribution of chondrules within such objects. The optimum range of parameters, however, represents a higher gas density and fractional abundance of solids, and a smaller difference between Keplerian and pressure-supported orbital velocities, than “canonical” models of the solar nebula. We discuss several potential explanations for these differences. The scenario also produces 10-100 km diameter primary KBOs, and also requires an enhanced abundance of solids to match the mass production rate estimates for KBOs (and presumably the planetesimal precursors of the ice giants themselves). We discuss the advantages and plausibility of the scenario, outstanding issues, and future directions of research.