Ejection Velocity Field Research Articles

Experimental study on rockburst of surrounding rock in an elliptical tunnel with different axial ratios

The effect of the ratio of long and short axes on the rockburst of an elliptical tunnel structure was investigated by performing a series of true triaxial tests on red sandstone cuboid samples containing seven types of elliptical holes with different long–short axial ratios, using a self-developed true triaxial compression equipment. The entire process of spalling was monitored and recorded using a miniature camera. According to the test results, the failure stress, geometrical characteristics of the rockburst notch, fragment characteristics, and ejection velocity field characteristics of the rockburst are summarized, and the influence of the axial ratios of the elliptical hole on the failure characteristics and stability of the tunnel are discussed in detail. The test results indicate that the rockburst process of elliptical tunnels with different axial ratios experiences four processes; namely, calm period, small particle ejection period, spalling, and rockburst. The shape of the failure area after the rockburst presents a V-shaped feature. With the increase of the axial ratio, the area, angle, and depth of the V-shaped area show a decreasing trend, the initial failure stress of the cavern and the rockburst failure stress exhibit a trend of first decreasing and then increasing; the tangential stress of the cavern shows an increasing trend; the mass percentage of micro, fine, and medium grain decreases; and the average ejection velocity first decreases and then increases. Under the same stress conditions, rockbursts are more likely to occur on circular sections. Under the same section conditions, the ellipse can bear larger loads when its major axis is parallel to the disturbance stress. These conclusions are helpful to the efficient design of the tunnel structure.

Identifying the population of stable ν6 resonant asteroids using large data bases

ABSTRACT Large observational surveys, like those that will be conducted at the Vera C. Rubin Observatory, are expected to discover up to one million new asteroids in the first year of operation. This will more than double the data base of known asteroids. New methods will be needed to handle the large influx of data. Here, we tested some of these new approaches by studying the population of asteroids on stable orbits inside the ν6 secular resonance. This resonance is one of the strongest mechanisms for destabilizing the orbits of main-belt bodies and producing Near-Earth Asteroids. Yet, stable orbital configurations where the asteroid pericenter is either aligned or anti-aligned with that of Saturn exist inside the resonance. The population of stable ν6 resonators is now the largest population of asteroids in stable orbits inside a secular resonance. Here, we obtained the largest sample of asteroids’ proper elements ever used. Clustering methods and the use of machine learning algorithms permitted the identification of the known asteroid families crossed by the ν6 resonance and of two entirely new groups: the Tiffanykapler and the 138605 QW177 families. The Tiffanykapler family is the first young asteroid family ever found in a linear secular resonance, with an age of 3.0 ± 1.2 My and an ejection velocity field parameter of $V_{\mathrm{ EJ}} = 15^{+6}_{-3}$ m s−1. We identify a population of high-eccentricity objects around the Tina family that may be the first example of an asteroid family ‘resonant halo’.

Clarissa Family Age from the Yarkovsky Effect Chronology

Abstract The Clarissa family is a small collisional family composed of primitive C-type asteroids. It is located in a dynamically stable zone of the inner asteroid belt. In this work we determine the formation age of the Clarissa family by modeling planetary perturbations as well as thermal drift of family members due to the Yarkovsky effect. Simulations were carried out using the SWIFT-RMVS4 integrator modified to account for the Yarkovsky and Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effects. We ran multiple simulations starting with different ejection velocity fields of fragments, varying proportion of initially retrograde spins, and also tested different Yarkovsky/YORP models. Our goal was to match the observed orbital structure of the Clarissa family which is notably asymmetrical in the proper semimajor axis, a p. The best fits were obtained with the initial ejection velocities ≲20 m s−1 of diameter D ≃ 2 km fragments, ∼4:1 preference for spin-up by YORP, and assuming that ≃80% of small family members initially had retrograde rotation. The age of the Clarissa family was found to be t age = 56 ± 6 Myr for the assumed asteroid density ρ = 1.5 g cm−3. Small variation of density to smaller or larger value would lead to slightly younger or older age estimates. This is the first case where the Yarkovsky effect chronology has been successfully applied to an asteroid family younger than 100 Myr.

The Zelima asteroid family: Resonant configuration and rotational fission clusters

Asteroid families are groups of asteroids that are identifiable in domains of proper elements. They may be the outcome of a collision, or the product of rotational fission. Among collisional families, young asteroid families are of interest because they preserve information on the original ejection velocity field with which the asteroid fragments were expelled, and because they may host a significant population of clusters produced by rotational fission among their members. The recently identified Zelima asteroid family is unique because, apart from its very young age of less than 3 Myr, is also interacting with the z1 secular resonance, making it the third asteroid family in this peculiar configuration, after the Agnia and Padua families, and the only one for which all members are in z1 librating states. Because of its extremely young age, the orbits of its members are still very clustered in the domain (σ,dσ/dt), with σ=ϖ−ϖ6+Ω−Ω6 the resonant argument of the z1 resonance. This allow for precisely dating the family with a method not available for any other main belt group. The Zelima family, based on this argument, should be 2.5±1.5 Myr old, and conserved quantities of the z1 secular resonance show that its ejection velocity field is in a range of 1.1−0.2+0.6 of the escape velocity from the parent body, in agreement with general results for cratering collisional families. Finally, 41.7% of the members of the Zelima family are also members of possible fission clusters, confirming the trend observed for other very young families, like the Jones and Lorre groups.

A dynamical study of the Gefion asteroid family

The Gefion asteroid family is a group of S-type asteroids located between the 8J:-3A and 5J:-2A mean-motion resonances. The 5J:-2A resonance seems to be responsible for the absence of the right side of the V-shape of this family. We aim in this work to present a detailed study on the Gefion family, motivated by the incompatibility found in previous family age estimations and the fact that this family could be seen as one of the most probable sources of L-chondrite meteorites. After eliminating all possible taxonomical and dynamical interlopers, we use a Monte Carlo method to analyze the semi-major axis evolution of several fictitious families under the influence of the Yarkovsky and Yarkovsky-O’Keefe-Radzievsky-Paddack (YORP) effects. We also perform simulations using symplectic integrators to account for the Yarkovsky effect (diurnal and seasonal versions) and the stochastic YORP effect. We make use of the distribution of the component of the ejection velocity field (vW) perpendicular to the orbital plane and the time dependence of the asymmetry of the distribution of the target function of a fictitious family generated with ejection velocity parameter 20+55−15m s−1to obtain an age estimate of 1030+19−67Myr. We find that 6.5% of asteroids from the Gefion family can reach orbits similar to particles in the current near-Earth objects space; 73% of them are among the Amors asteroids, and the remaining ones are among the Apollos. We only found 0.5% from the Gefion family reaching the Mars-crossing space.

The influence of Ceres on the dynamical evolution of the Zdenekhorsky/Nemesis asteroid family

The Nemesis family, also identified as the Zdenekhorsky family by some authors, is an “incomplete” asteroid family in the central main belt, characterized by an asymmetric distribution between its left and right side, with most of its members located in the left part of the family. It has been suggested that this asymmetry, as well as the shape of its left slope, could have been significantly affected by Ceres, either though close encounters or because of the effect of the nodal linear resonance ν1C. Several age estimates were also found for this family, ranging from a minimum of 150 ± 80 Myr to a maximum of 440 ± 20 Myr. Here we study the effect that Ceres may have had on the dynamical evolution of this family. For this purpose, we performed several numerical simulations that include the Yarkovsky effect and either consider or neglect Ceres as a massive body. We found that the asymmetric shape of this family does not seem to be a product of the local dynamics, but may be an intrinsic feature of the original ejection velocity field by which this family was created. If we assume that the current population of asteroids in librating states of the ν1C secular resonance is currently in a steady-state and originates from the Nemesis family, this population will no longer be sustainable on timescales of 200 Myr since the group formation, which sets an upper limit on the maximum possible family age.

On the age of the Beagle secondary asteroid family

The Beagle family is a C-type subgroup of the Themis family, in the outer main belt. Previous works suggested that it could be younger than 20 Myr and a possible source for the dust in the i≃1.4∘α zodiacal dust band. Here we took advantage of a much larger database for Beagle family members to revisit previous age estimates of this group. Standard dating techniques based on the family V-shape or on Monte Carlo methods of Yarkovsky and YORP mobility suggest that i) there might be a dichotomy for the inner and outer part of the Beagle family, which may be either two separate families or the product of an anisotropic ejection velocity field and that ii) the age of the possibly younger outer part of the Beagle family should be 35−35+65 Myr. The past convergence of Beagle longitude of the node is compatible with a family age of ≃14 Myr, when (1678) Glarona is used as a reference orbit. Without further information on Beagle members spin states, however, only very lower limits on the family age can be currently obtained when the Yarkovksy force is accounted for.

Initial velocity V-shapes of young asteroid families

Ejection velocity fields of asteroid families are largely unconstrained due to the fact that members disperse relatively quickly on Myr time-scales by secular resonances and the Yarkovsky effect. The spreading of fragments in $a$ by the Yarkovsky effect is indistinguishable from the spreading caused by the initial ejection of fragments. By examining families $<$20 Myrs-old, we can use the V-shape identification technique to separate family shapes that are due to the initial ejection velocity field and those that are due to the Yarkovsky effect. $<$20 Myr-old asteroid families provide an opportunity to study the velocity field of family fragments before they become too dispersed. Only the Karin family's initial velocity field has been determined and scales inversely with diameter, $D^{-1}$. We have applied the V-shape identification technique to constrain young families' initial ejection velocity fields by measuring the curvature of their fragments' V-shape correlation in semi-major axis, $a$, vs. $D^{-1}$ space. Curvature from a straight line implies a deviation from a scaling of $D^{-1}$. We measure the V-shape curvature of 11 young asteroid families including the \FYnospace, Aeolia, Brangane, Brasilia, Clarissa, Iannini, Karin, Konig, Koronis(2), Theobalda and Veritas asteroid families. We find that the majority of asteroid families have initial ejection velocity fields consistent with $\sim D^{-1}$ supporting laboratory impact experiments and computer simulations of disrupting asteroid parent bodies.

On the ages of resonant, eroded and fossil asteroid families

In this work we have estimated 10 collisional ages of 9 families for which for different reasons our previous attempts failed. In general, these are difficult cases that required dedicated effort, such as a new family classifications for asteroids in mean motion resonances, in particular the 1/1 and 2/1 with Jupiter, as well as a revision of the classification inside the 3/2 resonance.Of the families locked in mean motion resonances, by employing a numerical calibration to estimate the Yarkovsky effect in proper eccentricity, we succeeded in determining ages of the families of (1911) Schubart and of the “super-Hilda” family, assuming this is actually a severely eroded original family of (153) Hilda. In the Trojan region we found families with almost no Yarkovsky evolution, for which we could compute only physically implausible ages. Hence, we interpreted their modest dispersions of proper elements as implying that the Trojan asteroid families are fossil families, frozen at their proper elements determined by the original ejection velocity field. We have found a new family, among the Griquas locked in the 2/1 resonance with Jupiter, the family of (11097) 1994 UD1.We have estimated the ages of 6 families affected by secular resonances: families of (5) Astraea, (25) Phocaea, (283) Emma, (363) Padua, (686) Gersuind, and (945) Barcelona. By using in all these cases a numerical calibration method, we have shown that the secular resonances do not affect significantly the secular change of proper a. We have confirmed the existence of the family resulting from cratering on (5) Astraea by computing a new set of resonant proper elements adapted to the resonance g+g5−2g6: this new family has a much larger membership and has a shape compatible with simple collisional models.For the family of (145) Adeona we could estimate the age only after removal of a number of assumed interlopers.With the present paper we have concluded the series dedicated to the determination of asteroid ages with a uniform method. Overall we computed 53 ages for a total of 49 families. For the future work there remain families too small at present to provide reliable estimates, as well as some complex families (221, 135, 298) which may have more ages than we could currently estimate. Future improvement of some already determined family ages is also possible by increasing family membership, revising the calibrations, and using more reliable physical data.

The Hoffmeister asteroid family

The Hoffmeister family is a C-type group located in the central main belt. Dynamically, it is important because of its interaction with the ${\nu}_{1C}$ nodal secular resonance with Ceres, that significantly increases the dispersion in inclination of family members at lower semi-major axis. As an effect, the distribution of inclination values of the Hoffmeister family at semi-major axis lower than its center is significantly leptokurtic, and this can be used to set constraints on the terminal ejection velocity field of the family at the time it was produced. By performing an analysis of the time behaviour of the kurtosis of the $v_W$ component of the ejection velocity field (${\gamma}_2(v_W)$), as obtained from Gauss' equations, for different fictitious Hoffmeister families with different values of the ejection velocity field, we were able to exclude that the Hoffmeister family should be older than 335 Myr. Constraints from the currently observed inclination distribution of the Hoffmeister family suggest that its terminal ejection velocity parameter $V_{EJ}$ should be lower than 25~m/s. Results of a Yarko-YORP Monte Carlo method to family dating, combined with other constraints from inclinations and ${\gamma}_2(v_W)$, indicate that the Hoffmeister family should be $220^{+60}_{-40}$~Myr old, with an ejection parameter $V_{EJ}= 20\pm5$~m/s.

On the highly inclinedvWleptokurtic asteroid families

$v_W$ leptokurtic asteroid families are families for which the distribution of the normal component of the terminal ejection velocity field $v_W$ is characterized by a positive value of the ${\gamma}_2$ Pearson kurtosis, i.e., they have a distribution with a more concentrated peak and larger tails than the Gaussian one. Currently, eight families are known to have ${\gamma}_2(v_W) > 0.25$. Among these, three are highly inclined asteroid families, the Hansa, Barcelona, and Gallia families. As observed for the case of the Astrid family, the leptokurtic inclination distribution seems to be caused by the interaction of these families with node secular resonances. In particular, the Hansa and Gallia family are crossed by the $s-s_V$ resonance with Vesta, that significantly alters the inclination of some of their members. In this work we use the time evolution of ${\gamma}_2(v_W)$ for simulated families under the gravitational influence of all planets and the three most massive bodies in the main belt to assess the dynamical importance (or lack of) node secular resonances with Ceres, Vesta, and Pallas for the considered families, and to obtain independent constraints on the family ages. While secular resonances with massive bodies in the main belt do not significantly affect the dynamical evolution of the Barcelona family, they significantly increase the ${\gamma}_2(v_W)$ values of the simulated Hansa and Gallia families. Current values of the ${\gamma}_2(v_W)$ for the Gallia family are reached over the estimated family age only if secular resonances with Vesta are accounted for.

Constraints on the original ejection velocity fields of asteroid families

Asteroid families form as a result of large-scale collisions among main belt asteroids. The orbital distribution of fragments after a family-forming impact could inform us about their ejection velocities. Unfortunately, however, orbits dynamically evolve by a number of effects, including the Yarkovsky drift, chaotic diffusion, and gravitational encounters with massive asteroids, such that it is difficult to infer the ejection velocities eons after each family's formation. Here we analyze the inclination distribution of asteroid families, because proper inclination can remain constant over long time intervals, and could help us to understand the distribution of the component of the ejection velocity that is perpendicular to the orbital plane ($v_{W}$). From modeling the initial breakup, we find that the distribution of $v_{W}$ of the fragments, which manage to escape the parent body's gravity, should be more peaked than a Gaussian distribution (i.e., be leptokurtic) even if the initial distribution was Gaussian. We surveyed known asteroid families for signs of a peaked distribution of $v_{W}$ using a statistical measure of the distribution peakedness or flatness known as kurtosis. We identified eight families whose $v_{W}$ distribution is significantly leptokurtic. These cases (e.g. the Koronis family) are located in dynamically quiet regions of the main belt, where, presumably, the initial distribution of $v_{W}$ was not modified by subsequent orbital evolution. We suggest that, in these cases, the inclination distribution can be used to obtain interesting information about the original ejection velocity field.

Characterizing the original ejection velocity field of the Koronis family

An asteroid family forms as a result of a collision between an impactor and a parent body. The fragments with ejection speeds higher than the escape velocity from the parent body can escape its gravitational pull. The cloud of escaping debris can be identified by the proximity of orbits in proper element, or frequency, domains. Obtaining estimates of the original ejection speed can provide valuable constraints on the physical processes occurring during collision, and used to calibrate impact simulations. Unfortunately, proper elements of asteroids families are modified by gravitational and non-gravitational effects, such as resonant dynamics, encounters with massive bodies, and the Yarkovsky effect, such that information on the original ejection speeds is often lost, especially for older, more evolved families.It has been recently suggested that the distribution in proper inclination of the Koronis family may have not been significantly perturbed by local dynamics, and that information on the component of the ejection velocity that is perpendicular to the orbital plane (vW), may still be available, at least in part. In this work we estimate the magnitude of the original ejection velocity speeds of Koronis members using the observed distribution in proper eccentricity and inclination, and accounting for the spread caused by dynamical effects. Our results show that (i) the spread in the original ejection speeds is, to within a 15% error, inversely proportional to the fragment size, and (ii) the minimum ejection velocity is of the order of 50 m/s, with larger values possible depending on the orbital configuration at the break-up.

Analysis of the kinematics of ejecta created after a catastrophic collision

According to the results of hydrodynamical simulations, the creation of an asteroid dynamical family as the outcome of a high-energy collision consists of the partial or complete shattering of the parent body followed by re-accumulation of many fragments into larger bodies due to the mutual gravity. This scenario seems to reproduce satisfactorily the observed properties of the asteroid families, and in particular the size distribution of the members. In this paper we show a preliminary analysis of the ejection velocity fields predicted by hydrodynamical models, in comparison with the ejection velocity fields simulated by semi-empirical models, in order to identify the features of the velocity distribution that trigger or prevent the fragments’ gravitational re-accumulation.

Dynamical evolution and chronology of the Hygiea asteroid family

The asteroid (10) Hygiea is the fourth largest asteroid of the Main Belt, by volume and mass, and it is the largest member of its own family. Previous works investigated the long-term effects of close encounters with (10) Hygiea of asteroids in the orbital region of the family, and analyzed the taxonomical and dynamical properties of members of this family. In this paper we apply the high-quality SDSS-MOC4 taxonomic scheme of DeMeo and Carry (2013) to members of the Hygiea family core and halo, we obtain an estimate of the minimum time and number of encounter necessary to obtain a $3\sigma$ (or 99.7%) compatible frequency distribution function of changes in proper $a$ caused by close encounters with (10) Hygiea, we study the behavior of asteroids near secular resonance configurations, in the presence and absence of the Yarkovsky force, and obtain a first estimate of the age of the family based on orbital diffusion by the Yarkovsky and YORP effects with two methods. The Hygiea family is at least 2 Byr old, with an estimated age of $T = 3200^{+380}_{-120}$ Myr and a relatively large initial ejection velocity field, according to the approach of Vokrouhlick\'{y} et al. (2006a, b). Surprisingly, we found that the family age can be shortened by $\simeq$ 25% if the dynamical mobility caused by close encounters with (10) Hygiea is also accounted for, which opens interesting new research lines for the dynamical evolution of families associated with massive bodies. In our taxonomical analysis of the Hygiea asteroid family, we also identified a new V-type candidate: the asteroid (177904) (2005 SV5). If confirmed, this could be the fourth V-type object ever to be identified in the outer main belt.

Constraining asteroid dynamical models using GAIA data

GAIA is expected to greatly enhance our knowledge on the orbital, spin-state, spectral and size distribution of individual asteroids and asteroid families. Dynamical models, incorporating resonant phenomena and thermal (Yarkovsky/YORP) effects, can be used to understand the observations, in particular the orbital, size-frequency and spin-axis distributions in families and groups. Conversely, the GAIA data can be used to appropriately modify/constrain our models. Such work will necessarily involve an optimization procedure, for which a large number of dynamical experiments will typically be needed; this is clearly a limiting factor. We present here a preliminary version of a statistical model that describes asteroid transport due to gravitational perturbations in the 3-D space of proper elements, coupled with Yarkovsky drift effects. Computationally, the model is very efficient for studying the long-term evolution of large ensembles of asteroids (e.g. families). Thus, given a “final” distribution of orbits, spins and sizes, our model could be used in an iterative fashion, to derive e.g. an optimal guess of the initial ejection velocity field in a family-forming event.

On the first ν6 anti-aligned librating asteroid family of Tina

Asteroid families are groups of bodies identified in the space of proper elements or of frequencies that share a common origin in the collisional break-up of their progenitors. Their dynamical evolution is shaped by the interaction with the local web of mean-motion and secular resonances, and by non-gravitational effects, such as the 'Yarkovsky' and 'Yarkovsky-O'Keefe―Radzievskii―Paddack' (YORP) effects. Thus, obtaining information on their age and original ejection velocity field is generally a difficult task. Recently, two families were found to have a large fraction of members in the non-linear secular resonance z 1 : the Agnia and Padua families. Conserved quantities of the z 1 resonance allowed for a more precise determination of their ages and ejection velocity fields. So far, however, no family was known to be in a linear secular resonance, such as the v 6 resonance, although individual asteroids were known to be in v 6 anti-aligned librating states. The v 6 resonance occurs when there is a commensurability between the frequency of precession of the pericentre of an asteroid and that of Saturn. As a consequence, in librating states, the resonant argument oscillates around a stable point. In anti-aligned librating states, the resonant argument oscillates around the stable point at 180°. Here we show that the newly identified Tina family is characterized by having all its members in such a state, making it the only family in the asteroid belt known to be completely embedded in a secular resonance configuration. This rare dynamical configuration limits the maximum eccentricity of Tina members, preventing them from experiencing Martian close encounters and forming a stable island of a new dynamical type. The current dispersion of asteroid resonant elements suggests that the family should be at least 2.5 Myr old, while Monte Carlo simulations including the Yarkovsky and YORP effects suggest that the Tina family should be 170 +20 ―30 M yr old.

The (not so) peculiar case of the Padua family

The Agnia asteroid family was recently studied by Vokrouhlicky et al. because of its peculiar and, so far, unique relationship with the z 1 secular resonance. The Agnia family is almost entirely contained within the high-order secular resonance z 1 . Here, I study another family in the middle belt that is characterized by its interaction with the z 1 resonance, the Padua family. More than 75 per cent of its members are currently on z 1 librating orbits, and therefore several of the techniques used by Vokrouhlicky et al. can also be applied to this family. As for the case of the Agnia family, numerical integration methods and Monte Carlo models can be used to set lower and upper limits on the family age, and to obtain estimates on the fraction of prograde rotators. The constraints obtained on the family age and original ejection velocity field may be used to set limits on the dynamical mobility caused by low-energy collisions, that is dependent on the yet poorly known exponent a that best fits the size distribution of objects of less than 5 km in diameter. In this work, the Padua dynamical family was obtained in both the proper element and frequency domains. Numerical simulations of family members in the space of the z 1 resonance variable (σ, dσ/dt) suggest that the family is at least 25 Myr old. The conservation of the z 1 K' 2 conserved quantity implies that the original ejection velocity field was of V EJ = 35.0 ± 8.5 m s -1 . Monte Carlo models of the diffusion of the semimajor axis caused by the Yarkovsky and Yarkovsky-O'Keefe-Radzievsky-Paddack (YORP) effects also confirm the results obtained with the alternative approaches. The Padua family is 24 +28 -20 Myr old, and it was probably created by an impact that ejected fragments with average ejection velocities of V EJ = 30.0 +2.0 -4.0 m s -1 . The fact that the Padua family is at least 25 Myr old suggests that low-energy collisions as modelled by Dell'Oro & Cellino should have played a minor role in the semimajor axis diffusion of the family members. My results are at best consistent with a value of a equal to -2.3. Families interacting with secular resonances such as the Agnia and Padua families can provide useful information not only about their age and original ejection velocity field, but also on the yet poorly known cumulative size distribution of objects of diameters of 5 km and less.

Karin cluster formation by asteroid impact

Insights into collisional physics may be obtained by studying the asteroid belt, where large-scale collisions produced groups of asteroid fragments with similar orbits and spectra known as the asteroid families. Here we describe our initial study of the Karin cluster, a small asteroid family that formed 5.8 ± 0.2 Myr ago in the outer main belt. The Karin cluster is an ideal ‘natural laboratory’ for testing the codes used to simulate large-scale collisions because the observed fragments produced by the 5.8-Ma collision suffered apparently only limited dynamical and collisional erosion. To date, we have performed more than 100 hydrocode simulations of impacts with non-rotating monolithic parent bodies. We found good fits to the size–frequency distribution of the observed fragments in the Karin cluster and to the ejection speeds inferred from their orbits. These results suggest that the Karin cluster was formed by a disruption of an ≈33-km-diameter asteroid, which represents a much larger parent body mass than previously estimated. The mass ratio between the parent body and the largest surviving fragment, (832) Karin, is ≈0.15–0.2, corresponding to a highly catastrophic event. Most of the parent body material was ejected as fragments ranging in size from yet-to-be-discovered sub-km members of the Karin cluster to dust grains. The impactor was ≈ 5.8 km across. We found that the ejections speeds of smaller fragments produced by the collision were larger than those of the larger fragments. The mean ejection speeds of >3-km-diameter fragments were ≈ 10 m s −1 . The model and observed ejection velocity fields have different morphologies perhaps pointing to a problem with our modeling and/or assumptions. We estimate that ∼ 5 % of the large asteroid fragments created by the collision should have satellites detectable by direct imaging (separations larger than 0.1 arcsec). We also predict a large number of ejecta binary systems with tight orbits. These binaries, located in the outer main belt, could potentially be detected by lightcurve observations. Hydrocode modeling provides important constraints on the interior structure of asteroids. Our current work suggests that the parent asteroid of the Karin cluster may have been an unfractured (or perhaps only lightly fractured) monolithic object. Simulations of impacts into fractured/rubble pile targets were so far unable to produce the observed large gap between the first and second largest fragment in the Karin cluster, and the steep slope at small sizes (≈6.3 differential index). On the other hand, the parent asteroid of the Karin cluster was produced by an earlier disruptive collision that created the much larger, Koronis family some 2 – 3 Gyr ago. Standard interpretation of hydrocode modeling then suggests that the parent asteroid of the Karin cluster should have been formed as a rubble pile from Koronis family debris. We discuss several solutions to this apparent paradox.

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.