Orbital evolution of the Gefion and Adeona asteroid families: close encounters with massive asteroids and the Yarkovsky effect

Asteroid families are groupings of minor planets identified by clustering in their proper orbital elements; these objects have spectral signatures consistent with an origin in the break-up of a common parent body. From the current values of proper semimajor axes a of family members one might hope to estimate the ejection velocities with which the fragments left the putative break-up event (assuming that the pieces were ejected isotropically). However, the ejection velocities so inferred are consistently higher than N-body and hydro-code simulations, as well as laboratory experiments, suggest. To explain this discrepancy between today’s orbital distribution of asteroid family members and their supposed launch velocities, we study whether asteroid family members might have been ejected from the collision at low speeds and then slowly drifted to their current positions, via one or more dynamical processes. Studies show that the proper a of asteroid family members can be altered by two mechanisms: (i) close encounters with massive asteroids, and (ii) the Yarkovsky non-gravitational effect. Because the Yarkovsky effect for kilometer-sized bodies decreases with asteroid diameter D, it is unlikely to have appreciably moved large asteroids (say those with D > 15 km) over the typical family age (1-2 Gyr).For this reason, we numerically studied the mobility of family members produced by close encounters with main-belt, non-family asteroids that were thought massive enough to significantly change their orbits over long timescales. Our goal was to learn the degree to which perturbations might modify the proper a values of all family members, including those too large to be influenced by the Yarkovsky effect. Our initial simulations demonstrated immediately that very few asteroids were massive enough to significantly alter relative orbits among family members. Thus, to maximize gravitational perturbations in our 500-Myr integrations, we investigated the effect of close encounters on two families, Gefion and Adeona, that have high encounter probabilities with 1 Ceres, by far the largest asteroid in the main belt. Our results show that members of these families spreads in a of less than 5% since their formation. Thus gravitational interactions cannot account for the large inferred escape velocities.The effect of close encounters with massive asteroids is, however, not entirely negligible. For about 10% of the simulated bodies, close encounters increased the “inferred” ejection velocities from sub-100 m/s to values greater than 100 m/s, beyond what hydro-code and N-body simulations suggest are the maximum possible initial ejection velocity for members of Adeona and Gefion with D > 15 km. Thus this mechanism of mobility may be responsible for the unusually high inferred ejection speeds of a few of the largest members of these two families.To understand the orbital evolution of the entire family, including smaller members, we also performed simulations to account for the drift of smaller asteroids caused by the Yarkovsky effect. Our two sets of simulations suggest that the two families we investigated are relatively young compared to larger families like Koronis and Themis, which have estimated ages of about 2 Byr. The Adeona and Gefion families seems to be no more than 600 and 850 Myr old, respectively.     

The shallow magnitude distribution of asteroid families

It is well known that asteroid families have steeper absolute magnitude (H) distributions for H < 12-13 values than the background population. Beyond this threshold, the shapes of the absolute magnitude distributions in the family/background populations are difficult to determine, primarily because both populations are not yet observationally complete. Using a recently generated catalog containing the proper elements of 106,284 main belt asteroids and an innovative approach, we debiased the absolute magnitude distribution of the major asteroid families relative to the local background populations. Our results indicate that the magnitude distributions of asteroid families are generally not steeper than those of the local background populations for H > 13 (i.e., roughly for diameters smaller than 10 km). In particular, most families have shallower magnitude distributions than the background in the range 15-17 mag. Thus, we conclude that, contrary to previous speculations, the population of kilometer-size asteroids in the main belt is dominated by background bodies rather than by members of the most prominent asteroid families. We believe this result explains why the Spacewatch, Sloan Digital Sky Survey, and Subaru asteroid surveys all derived a shallow magnitude distribution for the dimmer members of the main belt population.We speculate on a few dynamical and collisional scenarios that can explain this shallow distribution. One possibility is that the original magnitude distributions of the families (i.e., at the moment of the formation event) were very shallow for H larger than ∼ 13, and that most families have not yet had the time to collisionally evolve to the equilibrium magnitude distribution that presumably characterizes the background population. A second possibility is that family members smaller than about 10 km, eroded over time by collisional and dynamical processes, have not yet been repopulated by the break-up of larger family members. For this same reason, the older (and possibly characterized by a weaker impact strength) background population shows a shallow distribution in the range 15-60 km.     

The size distributions of asteroid families in the SDSS Moving Object Catalog 4

Asteroid families, traditionally defined as clusters of objects in orbital parameter space, often have distinctive optical colors. We show that the separation of family members from background interlopers can be improved with the aid of SDSS colors as a qualifier for family membership. Based on an ∼88,000 object subset of the Sloan Digital Sky Survey Moving Object Catalog 4 with available proper orbital elements, we define 37 statistically robust asteroid families with at least 100 members (12 families have over 1000 members) using a simple Gaussian distribution model in both orbital and color space. The interloper rejection rate based on colors is typically ∼10% for a given orbital family definition, with four families that can be reliably isolated only with the aid of colors. About 50% of all objects in this data set belong to families, and this fraction varies from about 35% for objects brighter than an H magnitude of 13 and rises to 60% for objects fainter than this. The fraction of C-type objects in families decreases with increasing H magnitude for H>13, while the fraction of S-type objects above this limit remains effectively constant. This suggests that S-type objects require a shorter timescale for equilibrating the background and family size distributions via collisional processing. The size distribution varies significantly among families, and is typically different from size distributions for background populations. The size distributions for 15 families display a well-defined change of slope and can be modeled as a “broken” double power-law. Such “broken” size distributions are twice as likely for S-type familes than for C-type families (73% vs. 36%), and are dominated by dynamically old families. The remaining families with size distributions that can be modeled as a single power law are dominated by young families (<1 Gyr). When size distribution requires a double power-law model, the two slopes are correlated and are steeper for S-type families. No such slope-color correlation is discernible for families whose size distribution follows a single power law. For several very populous families, we find that the size distribution varies with the distance from the core in orbital-color space, such that small objects are more prevalent in the family outskirts. This “size sorting” is consistent with predictions based on the Yarkovsky effect.     

Formation of Asteroid Families by Catastrophic Disruption: Simulations with Fragmentation and Gravitational Reaccumulation

This paper builds on preliminary work in which numerical simulations of the collisional disruption of large asteroids (represented by the Eunomia and Koronis family parent bodies) were performed and which accounted not only for the fragmentation of the solid body through crack propagation, but also for the mutual gravitational interaction of the resulting fragments. It was found that the parent body is first completely shattered at the end of the fragmentation phase, and then subsequent gravitational reaccumulations lead to the formation of an entire family of large and small objects with dynamical properties similar to those of the parent body. In this work, we present new and improved numerical simulations in detail. As before, we use the same numerical procedure, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational reaccumulation phase. However, this reaccumulation phase is now treated more realistically by using a merging criterion based on energy and angular momentum and by allowing dissipation to occur during fragment collisions. We also extend our previous studies to the as yet unexplored intermediate impact energy regime (represented by the Flora family formation) for which the largest fragment's mass is about half that of the parent body. Finally, we examine the robustness of the results by changing various assumptions, the numerical resolution, and different numerical parameters. We find that in the lowest impact energy regime the more realistic physical approach of reaccumulation leads to results that are statistically identical to those obtained with our previous simplistic approach. Some quantitative changes arise only as the impact energy increases such that higher relative velocities are reached during fragment collisions, but they do not modify the global outcome qualitatively. As a consequence, these new simulations confirm previous main results and still lead to the conclusion that: (1) all large family members must be made of gravitationally reaccumulated fragments; (2) the original fragment size distribution and their orbital dispersion are respectively steeper and smaller than currently observed for the real families, supporting recent studies on subsequent evolution and diffusion of family members; and (3) the formation of satellites around family members is a frequent and natural outcome of collisional processes.     

Reconstructing the orbital history of the Veritas family

The family of (490) Veritas is a young, dynamically heterogeneous asteroid family, located in the outer main belt. As such, it represents a valuable example for studying the effects of chaotic diffusion on the shape of asteroid families. The Veritas family can be decomposed into several groups, in terms of the principal mechanisms that govern the local dynamics, which are analyzed here. A relatively large spread in proper eccentricity is observed, for the members of two chaotic groups. We show that different types of chaos govern the motion of bodies within each group, depending on the extent of overlap among the components of the corresponding resonant multiplets. In particular, one group appears to be strongly diffusive, while the other is not. Studying the evolution of the diffusive group and applying statistical methods, we estimate the age of the family to be τ=(8.7±1.7) Myr. This value is statistically compatible with that of 8.3 Myr previously derived by Nesvorný et al. [Nesvorný, D., Bottke, W.F., Levison, H.F., Dones, L., 2003. Astrophys. J. 591, 486-497], who analyzed the secular evolution of family members on regular orbits. Our methodology, applied here in the case of the Veritas family, can be used to reconstruct the orbital history of other, dynamically complex, asteroid families and derive approximate age estimates for young asteroid families, located in diffusive regions of the main belt. Possible refinements of the method are also discussed.     

The Flora Family: A Case of the Dynamically Dispersed Collisional Swarm?

Asteroid families are believed to originate by catastrophic disruptions of large asteroids. They are nowadays identified as clusters in the proper orbital elements space. The proper elements are analytically defined as constants of motion of a suitably simplified dynamical system. Indeed, they are generally nearly constant on a 10⁷-10⁸-year time scale. Over longer time intervals, however, they may significantly change, reflecting the accumulation of the tiny nonperiodic evolutions provided by chaos and nonconservative forces. The most important effects leading to a change of the proper orbital elements are (i) the chaotic diffusion in narrow mean motion resonances, (ii) the Yarkovsky nongravitational force, and (iii) the gravitational impulses received at close approaches with large asteroids. A natural question then arises: How are the size and shape of an asteroid family modified due to evolution of the proper orbital elements of its members over the family age? In this paper, we concentrate on the dynamical dispersion of the proper eccentricity and inclination, which occurs due to (i), but with the help of (ii) and (iii). We choose the Flora family as a model case because it is unusually dispersed in eccentricity and inclination and, being located in the inner main belt, is intersected by a large number of effective mean motion resonances with Mars and Jupiter. Our results suggest that the Flora family dynamically disperses on a few 10⁸-year time scale and that its age may be significantly less than 10⁹ years. We discuss the possibility that the parent bodies of the Flora family and of the ordinary L chondrite meteorites are the same object. In a broader sense, this work suggests that the common belief that the present asteroid families are simple images of their primordial dynamical structure should be revised.     

Visible spectroscopic and photometric survey of L5 Trojans: investigation of dynamical families

In this paper we present results obtained in the framework of a visible spectroscopic and photometric survey of Trojan asteroids. We concentrated on bodies orbiting at the L5 Lagrangian point of Jupiter that are also members of dynamical families. Spectroscopy is a crucial tool that allows us to characterize the mineralogical composition of families and their parent bodies, gives evidence of ongoing space weathering, and confirms family membership. We have observed 18 objects belonging to the Aneas, Astyanax, Sarpedon, and Phereclos families as defined by Beaugé and Roig (2001, Icarus 53, 391). In addition, we have determined the spectroscopic properties of 8 background Jupiter Trojans. The observed spectra are reddish with a dominance of D-type asteroids. As expected, the spectra of the non-family members are more heterogeneous compared to the spectra of family members, with the exception of the members of the Aneas family. We also confirm the lack of absorption features in the visible region, as already reported by other authors.     

The peculiar case of the Agnia asteroid family

The Agnia asteroid family, a cluster of asteroids located near semimajor axis a=2.79 AU, has experienced significant dynamical evolution over its lifetime. The family, which was likely created by the breakup of a diameter D∼50 km parent body, is almost entirely contained within the high-order secular resonance z₁. This means that unlike other families, Agnia's full extent in proper eccentricity and inclination is a byproduct of the large-amplitude resonant oscillations produced by this resonance. Using numerical integration methods, we found that the spread in orbital angles observed among Agnia family members would have taken at least 40 Myr to create; this sets a lower limit on the family's age. To determine the upper bound on Agnia's age, we used a Monte Carlo model to track how the small members in the family evolve in semimajor axis by Yarkovsky thermal forces. Our results indicate the family is no more than 140 Myr old, with a best-fit age of 100⁺³⁰₋₂₀ Myr. Using two independent methods, we also determined that the D∼5 km fragments were ejected from the family-forming event at a velocity near 15 m/s. This velocity is consistent with results from numerical hydrocode simulations of asteroid impacts and observations of other similarly sized asteroid families. Finally, we found that 57% of known Agnia fragments were initially prograde rotators. The reason for this limited asymmetry is unknown, though we suspect it is a fluke produced by the stochastic nature of asteroid disruption events.     

Collisional origin of the asteroid families: Mass and velocity distributions

The origin of asteroid families in terms of collisional breakup is analyzed using the data by Williams (1979, in Asteroids (T. Gehrels, Ed.), pp. 1040–1063, Univ. of Arizona Press, Tucson). The distributions of mass and relative velocity of the minor family members with respect to the largest body are derived. These ditributions are then compared with the outcomes of catastrophic impacts, predicted from theoretical arguments and observed from laboratory experiments. The general features of the mass distributions can be interpreted in terms of collisional disruption of a parent body followed by self-gravitational reaccumulation on the largest remnant; no decisive evidence for multiple reaccumulations is found. The typical ejection velocities of the family members are of the same order as those of laboratory fragments; since the definition of families is based on purely dynamical arguments, this results gives direct observational support to the collisional formation hypothesis. The transition between collisional outcomes dominated by solid-state forces and by self-gravitatation, expected to occur at diameters D ～ 100 km on the basis of rotational studies and of theoretical estimates, is clearly confirmed by the present analysis. A “morphological” classification into three broad classes (asymmetric, dispersed, and intermediate) is introduced; it is based on the distribution of mass vs relative velocity, taking also into account the parent body's (and the largest remnant's) escape velocity. Finally some results are outlined which apparently do not fit the theoretical predictions: (1) the degree of fragmentation in real families is generally lower than that observed for experimental targets and (2) when the relative velocities are computed, including also proper eccentricity and inclination differences, values higher by about a factor 4 than those derived from semiaxes differences only are found. Further studies are proposed, including more observations, better proper elements computation and classification methods, and new investigations on the physics of hypervelocity impacts.     

The Asteroid Veritas: An intruder in a family named after it?

The Veritas family is located in the outer main belt and is named after its apparent largest constituent, Asteroid (490) Veritas. The family age has been estimated by two independent studies to be quite young, around 8 Myr. Therefore, current properties of the family may retain signatures of the catastrophic disruption event that formed the family. In this paper, we report on our investigation of the formation of the Veritas family via numerical simulations of catastrophic disruption of a 140-km-diameter parent body, which was considered to be made of either porous or non-porous material, and a projectile impacting at 3 or 5 km/s with an impact angle of 0° or 45°. Not one of these simulations was able to produce satisfactorily the estimated size distribution of real family members. Based on previous studies devoted to either the dynamics or the spectral properties of the Veritas family, which already treated (490) Veritas as a special object that may be disconnected from the family, we simulated the formation of a family consisting of all members except that asteroid. For that case, the parent body was smaller (112 km in diameter), and we found a remarkable match between the simulation outcome, using a porous parent body, and the real family. Both the size distribution and the velocity dispersion of the real reduced family are very well reproduced. On the other hand, the disruption of a non-porous parent body does not reproduce the observed properties very well. This is consistent with the spectral C-type of family members, which suggests that the parent body was porous and shows the importance of modeling the effect of this porosity in the fragmentation process, even if the largest members are produced by gravitational reaccumulation during the subsequent gravitational phase. As a result of our investigations, we conclude that it is very likely that the Asteroid (490) Veritas and probably several other small members do not belong to the family as originally defined, and that the definition of this family should be revised. Further investigations will be performed to better constrain the definitions and properties of other asteroid families of different types, using the appropriate model of fragmentation. The identification of very young families in turn will continue to serve as a tool to check the validity of numerical models.     

Computing with certainty individual members of families of periodic orbits of a given period

The accurate computation of families of periodic orbits is very important in the analysis of various celestial mechanics systems. The main difficulty for the computation of a family of periodic orbits of a given period is the determination within a given region of an individual member of this family which corresponds to a periodic orbit. To compute with certainty accurate individual members of a specific family we apply an efficient method using the Poincaré map on a surface of section of the considered problem. This method converges rapidly, within relatively large regions of the initial conditions. It is also independent of the local dynamics near periodic orbits which is especially useful in the case of conservative dynamical systems that possess many periodic orbits, often of the same period, close to each other in phase space. The only computable information required by this method is the signs of various function evaluations carried out during the integration of the equations of motion. This method can be applied to any system of celestial mechanics. In this contribution we apply it to the photogravitational problem.     

Families among high-inclination asteroids

We present a new classification of families identified among the population of high-inclination asteroids. We computed synthetic proper elements for a sample of 18,560 numbered and multi-opposition objects having sine of proper inclination greater than 0.295. We considered three zones at different heliocentric distances (inner, intermediate and outer region) and used the standard approach based on the Hierarchical Clustering Method (HCM) to identify families in each zone. In doing so, we used slightly different approach with respect to previously published methodologies, to achieve a more reliable and robust classification. We also used available SDSS color data to improve membership and identify likely family interlopers. We found a total of 38 families, as well as a significant number of clumps and clusters deserving further investigation.     

An analysis of the region of the Phocaea dynamical family

In this work, I conduct a preliminary analysis of the Phocaea family region. I obtain families and clumps in the space of proper elements and proper frequencies, study the taxonomy of the asteroids for which this information is available, analyse the albedo and absolute magnitude distribution of objects in the area, obtain a preliminary estimate of the possible family age, study the cumulative size distribution and collision probabilities of asteroids in the region, the rotation rate distribution and obtain dynamical map of averaged elements and Lyapunov times for grids of objects in the area.
Among my results, I identified the first clump visible only in the frequency domain, the (6246) Komurotoru clump, obtained a higher limit for the possible age of the Phocaea family of 2.2 Byr, identified a class of Phocaea members on Mars-crossing orbits characterized by high Lyapunov times and showed that an apparently stable region on time-scales of 20 Myr near the  ν₆  secular resonance is chaotic, possibly because of the overlapping of secular resonances in the region. The Phocaea dynamical group seems to be a real S-type collisional family, formed up to 2.2 Byr ago, whose members with a large semimajor axis have been dynamically eroded by the interaction with the local web of mean-motion and secular resonances. Studying the long-term stability of orbits in the chaotic regions and the stability of family and clumps identified in this work remain challenges for future works.     

A stability study of asteroid families near the 3:1 and 5:2 resonance with Jupiter

By using theD-criterion Lindblad (1992) has identified 14 asteroid families from a sample of 4100 numbered asteroids with proper elements from Milani and Kneevi (1990). Taxonomic types and other physical properties for a significant number of objects in five of the families show strong homogeneity within each family, further strengthening their internal relationship.To test the hypothesis of a common origin in, e.g., a catastrophic collision event, we have set out to integrate the orbits of the members of the Maria, Dora and Oppavia-Gefion families over some 10⁶ years. The mean distance for the Maria family is close to the 3:1 mean-motion resonance with Jupiter, while the other two families lie close to the 5:2 resonance.We used a simplified solar system model which included the perturbations by Jupiter and Saturn only and implemented Everhart's variable stepsize integrator RA15. All close encounters between the family members (within 0.1 AU) were recorded as well. Preliminary results from integrations over 4×10⁵ years are presented here.The statistics of close encounters show pronounced peaks for several members within each family, while for others no significant levels above the background of random encounters or even very low frequencies were found. This indicates a subclustering within the families. Quite a lot of very close (<0.005 AU) mutual encounters are found, which suggest that, at least for the larger members in a family, the mutual gravitational interactions could be of some importance for the real orbital evolutions.The encounter statistics between the Dora and Oppavia family members suggest a possible interrelationship between this two groups.     

Velocity Space of Galactic O-B Stars

Based on the Hipparcos proper motions and available radial velocity data of O-B stars, we have re-examined the local kinematical structure of the young disk population of-1500 O-B stars not including the Gould-belt stars. A systematic warping motion of the stars about the direction to the Galactic center has been reconfirmed. A negative K-term implying a systematic contraction of stars in the solar vicinity has been detected. Two different distance scales are used in order to find out their impact on the kinematical parameters, and we conclude that the adopted distance scale plays an important role in characterizing the kinematical parameters at the present level of the measurement uncertainty.     

Reanalysis of asteroid families structure through visible spectroscopy

The taxonomic properties of the main asteroid families are analyzed and discussed in the light of an updated definition of the families using a large proper elements database and the asteroids taxonomy derived from reflectance spectra recently obtained by two large visible spectroscopic surveys: the SMASS II and the S3OS2. Our analysis indicates that most families are quite homogeneous taxonomically and mineralogically—whenever there exists a mineralogical constraint—, being probably originated from homogeneous parent bodies. The exceptions are the Nysa family, that should likely be considered a clan, and the Eos family that encompasses a broad range of taxonomies, whose mineralogical relations cannot be completely ruled out. Only in a few cases the families may be taxonomically distinguished from the background population. That is the case of the Minerva/Gefion, Adeona, Dora, Merxia, Hoffmeister, Koronis, Eos, and Veritas families. Some of the families presented in this work show a larger spectral diversity than previously reported, as it is the case for the Maria and Koronis families. On the other hand, the Veritas family is found to be homogeneous, in sharp contrast with previous works. Mineralogical relations are reported whenever they could be found in the literature and we examine the possible constraints posed by the presence of different taxonomies in certain families.     

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.     

Polarimetric evidence of close similarity between members of the Karin and Koronis dynamical families

We present the results of a campaign of polarimetric observations of small asteroids belonging to the Karin and Koronis families, carried out at the ESO Cerro Paranal Observatory using the VLT-Kueyen 8-m telescope. The Karin family is known to be very young, having likely been produced by the disruption of an original member of the Koronis family less than 6 Myr ago. The purpose of our study was to derive polarimetric properties for a reasonable sample of objects belonging to the two families, in order to look for possible systematic differences between them, to be interpreted in terms of differences in surface properties, in particular albedo. In turn, systematic albedo differences might be caused by different times of exposure to space weathering processes experienced by the two groups of objects. The results of our analysis indicate that no appreciable difference exists between the polarimetric properties of Karin and Koronis members. We thus find that space-weathering mechanisms may be very efficient in affecting surface properties of S-class asteroids on very short timescales. This result complements some independent evidence found by recent spectroscopic studies of very young families.     

Near-infrared spectroscopy of primitive asteroid families

We compare 13 near-infrared (0.8-2.4 μm) spectra of two low albedo C complex outer-belt asteroid families: Themis and Veritas. The disruption ages of these two families lie at opposite extremes: 2.5 ± 1.0 Gyr and 8.7 ± 1.7 Myr, respectively. We found striking differences between the two families, which show a range of spectral shapes and slopes. The seven Themis family members (older surfaces) have “red” (positive) slopes in the 1.6-2.4 μm region; in contrast, the six Veritas members (younger surfaces) have significantly “flatter” slopes at these same wavelengths. Moreover, the two families are characterized by different concavity at shorter (1.0-1.5 μm) wavelengths with the Themis group being consistently flat or concave up (smile) and the Veritas group being consistently concave down (frown). Each family contains a broad range of diameters, suggesting our results are not due to comparisons of asteroids of different sizes. The statistically significant clustering of the two spectral groups could be explained by one of the following three possibilities or a combination of them: (1) space weathering effects, (2) differences in original composition, or (3) differences in thermal history perhaps as a result of the difference in parent body sizes. As a result of our analyses, we propose a new method to quantify broad and shallow structures in the spectra of primitive asteroids. We found reasonable matches between the observed asteroids and individual carbonaceous chondrite meteorites. Because these meteoritic fits represent fresh surfaces, space weathering is neither necessary nor ruled out as an explanation of spectral differences between families. The six Veritas family near-infrared (NIR) spectra represent the first NIR analysis of this family, thus significantly increasing our understanding of this family over these wavelengths.     

Self-resonant bifurcations of the Sitnikov family and the appearance of 3D isolas in the restricted three-body problem

The association of the Sitnikov family with families of multiple three-dimensional periodic orbits is studied. In particular, the families consisting of three-dimensional periodic orbits bifurcating from self-resonant orbits of the Sitnikov family at double, triple and quadruple period of the bifurcation orbit are considered. The branch families close upon themselves and remain 3D up to their terminations having two common members with the Sitnikov family. By varying the mass parameter we also study the evolution of some of the computed families and find that they become isolas and disappear gradually in three-dimensions by shrinking to point size.