Non-family Asteroids Research Articles

Dynamical evolution of the inner asteroid belt

ABSTRACT A determination of the dynamical evolution of the asteroid belt is difficult because the asteroid belt has evolved since the time of asteroid formation through mechanisms that include: (1) catastrophic collisions, (2) rotational disruption, (3) chaotic orbital evolution, and (4) orbital evolution driven by Yarkovsky radiation forces. The time-scales of these loss mechanisms are uncertain and there is a need for more observational constraints. In the inner main belt (IMB), the mean size of the non-family asteroids increases with increasing inclination. Here, we use that observation to show that all IMB asteroids originate from either the known families or from ghost families, that is, old families with dispersed orbital elements. We estimate that the average age of the asteroids in the ghost families is a factor of 1/3 less than the Yarkovsky orbital evolution time-scale. However, this orbital evolution time-scale is a long-term average that must allow for the collisional evolution of the asteroids and for stochastic changes in their spin directions. By applying these constraints on the orbital evolution time-scales to the evolution of the size-frequency distribution of the Vesta asteroid family, we estimate that the age of this family is greater than 1.3 Gyr and could be comparable with the age of the Solar system. By estimating the number of ghost families, we calculate that the number of asteroids that are the root sources of the meteorites and the near-Earth asteroids that originate from the IMB is about 20.

The common origin of family and non-family asteroids: Implications for meteorites and NEAs

AbstractThe observed size-frequency distributions (SFDs) of the five major asteroid families in the Inner Main Belt (IMB), defined by Nesvorný (2015) using the Hierarchical Clustering Method (Zappala et al. 1990), are distinctly different and deviate significantly from the linear log-log relation described by Dohnanyi (1969). The existence of these differences in the SFDs, and the fact that the precursor bodies of the major families have distinctly different eccentricities and inclinations, provides an explanation for the observations that the mean sizes of both the family and the non-family asteroids are correlated with their mean proper eccentricities and anti-correlated with their mean proper inclinations. We deduce from this, and from the fact that the SFDs of the family and the non-family asteroids are almost identical, that the family and most of the non-family asteroids in the IMB have a common origin (Dermott et al. 2018).

The common origin of family and non-family asteroids: Implications

AbstractBecause the number of asteroids in the IMB with absolute magnitude H<16.5 is effectively complete, the distributions of the sizes and the orbital elements of these asteroids must be devoid of observational selection effects. This allows us to state that the observed size-frequency distributions (SFDs) of the five major asteroid families in the IMB, defined by Nesvorný (2015) using the Hierarchical Clustering Method (Zappala et al. 1990), are distinctly different and deviate significantly from the linear log-log relation described by Dohnanyi (1969). The existence of these differences in the SFDs, and the fact that the precursor bodies of the major families have distinctly different eccentricities and inclinations, provides a simple explanation for the observations that the mean sizes of the family asteroids, taken as a whole, are correlated with their mean proper eccentricities and anti-correlated with their mean proper inclinations. While the latter observations do have a simple explanation, we observe that the mean sizes of the non-family asteroids in the IMB are also correlated with their mean proper eccentricities and anti-correlated with their mean proper inclinations. We deduce from this, and from the fact that the SFDs of the non-family and the family asteroids (again taken as a whole) are almost identical, that the family and most of the non-family and asteroids have a common origin. We estimate that ~85% of all the asteroids in the IMB with H<16.5 originate from the Flora, Vesta, Nysa, Polana and Eulalia families with the remaining ~15% originating from either the same families or, more likely, a few ghost families (Dermott et al. 2018).

The common origin of family and non-family asteroids

All asteroids are currently classified as either family, originating from the disruption of known bodies, or non-family. An outstanding question is the origin of these non-family asteroids. Were they formed individually, or as members of known families but with chaotically evolving orbits, or are they members of old ghost families, that is, asteroids with a common parent body but with orbits that no longer cluster in orbital element space? Here, we show that the sizes of the non-family asteroids in the inner belt are correlated with their orbital eccentricities and anticorrelated with their inclinations, suggesting that both non-family and family asteroids originate from a small number of large primordial planetesimals. We estimate that ~85% of the asteroids in the inner main belt originate from the Flora, Vesta, Nysa, Polana and Eulalia families, with the remaining ~15% originating from either the same families or, more likely, a few ghost families. These new results imply that we must seek explanations for the differing characteristics of the various meteorite groups in the evolutionary histories of a few, large, precursor bodies. Our findings also support the model that asteroids formed big through the gravitational collapse of material in a protoplanetary disk.

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.

Accretion of Interplanetary Dust Particles by the Earth

Analyses of hypervelocity micrometeoroid impact craters preserved in lunar material and on the panels of the Long Duration Exposure Facility (LDEF) indicate that each year Earth accretes about 3 × 107kg of interplanetary dust particles (IDPs) from the zodiacal cloud (E. Grünet al.1985,Astron. Astrophys.286, 915–924; S. G. Love and D. E. Brownlee, 1993,Science262, 550–553). The size distributions of these lunar and LDEF craters indicate that the mass distribution of IDPs encountering Earth peaks at about 200 μm diameter. This particle-size cutoff may be indicative of collisionally evolved asteroidal dust, where the collisional lifetime of dust particles larger than ∼100 μm is shorter than the time required for their orbits to decay under Poynting–Robertson light drag from the asteroid belt to Earth (B. Å. S. Gustafson, 1994,Annu. Rev. Earth Planet. Sci.22, 553–595). Additionally, analyses of IDPs collected from the stratosphere by high-flying aircraft reveal a diversity in chemical composition which is even narrower than that of the meteorites (G. J. Flynn, 1995,Nature376, 114). Together these findings suggest that IDPs present in the atmosphere and our collections may originate from very limited sources in the asteroid belt.The most abundant sources of dust to be unambiguously linked to the zodiacal cloud are the three asteroid families Eos, Themis, and Koronis—the progenitors of the ten-degree and low-latitude dust bands discovered by the Infrared Astronomical Satellite in 1984. We use direct numerical integration of the full equations of motion to model the orbital evolution of dust particles from these three families as well as from other nonfamily asteroids and from the population of known short period comets. Our simulations include gravitational perturbations from the planets, radiation pressure, and solar wind drag. We find that a large, and perhaps the dominant, fraction of the IDPs accreted by Earth comes from the asteroid families Eos, Themis, and Koronis and that probably fewer than 25% of accreted IDPs come from comets. We also find a seasonal variation in the distribution of ascending nodes of the Themis and Koronis dust particle orbits near Earth. Earth-orbiting instruments utilizing aero-gels could exploit these seasonal variations to collect and return intact samples of these two asteroid families.Finally, we demonstrate how the long-term accretion rate of asteroidal dust from all sources should be anti-correlated with Earth's changing orbital eccentricity.

The cometary bombardment on the primitive asteroid belt

In this paper, we estimate the number of catastrophic collisions between asteroids and comets scattered from the Uranus–Neptune zone during the process of planetary accretion.We found that the change in slope at ≈75 km in the size distribution for non-family asteroids could be produced by an intense bombardment of scattered comets in a short period of time after the accretion of Uranus and Neptune, provided that any asteroid with radius ≤130–150 km received a catastrophic collision by scattered comets. Larger asteroids have probably not received any catastrophic collision, due to the small number of large comets.We also estimate that the total amount of mass in the primitive asteroid belt, before the depletion produced by dynamical and collisional processes, was not less than ≈1800 times the present one.

The Three-Dimensional Structure of the Zodiacal Dust Bands

Using observations of the infrared sky brightness by the Cosmic Background Explorer (COBE)11The National Aeronautics and Space Administration/Goddard Space Flight Center (NASA/GSFC) is responsible for the design, development, and operation of the Cosmic Background Explorer (COBE). Scientific guidance is provided by the COBE Science Working Group. GSFC is also responsible for the development of the analysis software and for the production of the mission data sets.Diffuse Infrared Background Experiment (DIRBE) and Infrared Astronomical Satellite (IRAS), we have created maps of the surface brightness Fourier-filtered to suppress the smallest (< 1°) structures and the large-scale background (>15°). Dust bands associated with the Themis, Koronis, and Eos families are readily evident. A dust band associated with the Maria family is also present. The parallactic distances to the emitting regions of the Koronis, Eos, and Maria dust bands were found to be 1.4 to 2.5 AU. A weak dust band associated with the Eunomia/Io family is evident, together with another weak and previously unattributed dust band, which may split further into two band pairs, potentially associated with the Hygiea or Vesta family. The brightnesses of the blended Themis/Koronis bands and the Eos dust band vary with ecliptic longitude, such that the northern or southern component of the band pair becomes brighter when its tilt brings it into the ecliptic plane. We attribute the brightness variations to the motion of the Earth within the emitting region, and conclude that at least some dust-band particles are on Earth-crossing orbits. For the Themis and Koronis families, the tilt is sufficient that the Earth may pass to the edges of the emitting region, where the density is highest, leading to “glints” two or four times a year. We compared the observed distributions to theoretically motivated, empirical models for the three-dimensional distribution of asteroid family dust. In the torus model, the dust is distributed among the asteroid family members with the same distributions of proper orbital inclination and semimajor axis but a random ascending node. In the migrating model, particles are presumed to be under the influence of Poynting–Robertson drag, so that they are distributed throughout the inner Solar System. The migrating model is better able to match the parallactic variation of dust-band latitude as well as the 12- to 60-μm spectrum of the dust bands. The annual brightness variations can be explained only by the migrating model. Upper limits are placed on the dust density associated with the Nysa and Flora families—both of the large, inner-belt families with wide inclination dispersions. The association of five (and potentially seven) dust bands with the largest asteroid families suggests that dust bands are an integral part of asteroid families. If nonfamily asteroids produce dust at a rate similar to that of the families with the lowest dust density, then they can account for the brightness of the zodiacal light in the ecliptic.

Zodiacal Dust Bands

One of the outstanding problems in solar system science is the source of the particles that constitute the zodiacal cloud. The zodiacal dust bands discovered by IRAS have a pivotal role in this debate because, without doubt, they are the small, tail end products of asteroidal collisions. Geometrical arguments are probably the strongest and the plane of symmetry of the dust bands places their source firmly in the asteroid belt. A cometary source, Comet Encke for example, could exist at the distance of the mainbelt, but the dynamics of cometary orbits makes the formation of cometary dust bands impossible, unless, of course, there is a significant (comparable in volume to the asteroidal families) source of comets interior to the orbit of Jupiter with low (asteroidal) orbital eccentricities. We have suggested that the dust bands are associated with the prominent asteroidal families. The link with the Themis and Koronis families is good but the link with Eos remains to be proved. We show here by detailed modeling that even though the filtered infrared flux in the 25μm waveband associated with the dust bands is only ~1% of the total signal, this is only the “tip of the iceberg” and that asteroidal dust associated with the bands constitutes ~10% of the zodiacal cloud. This result, plus the observed size-frequency distribution of mainbelt asteroids and the observed ratio of the number of family to non-family asteroids allows us to estimate that asteroidal dust accounts for about one third of the zodiacal cloud. The discovery of the “leading-trailing” asymmetry of the zodiacal cloud in the IRAS data and our interpretation of this asymmetry in terms of a ring of asteroidal particles in resonant lock with the Earth is important for two reasons. (1) The existence of the ring strongly suggests that large (diameter ≥ 12μm) asteroidal particles (or particles with low orbital eccentricities) are transported to the inner solar system by drag forces. (2) The observed ratio of the trailing-leading asymmetry allows an independent estimate of the contribution of asteroidal particles to the zodiacal cloud. These new results have important implications for the source of the interplanetary dust particles (IDPs) collected at the Earth. Because asteroidal particles constitute about one third of the zodiacal cloud and are transported to the inner solar system by drag forces, gravitational focussing by the Earth that results in the preferential capture of particles from orbits with low inclinations and low eccentricities and the possible “funneling” effect of the ring itself, imply that nearly all of the unmelted IDPs collected at the Earth are asteroidal.

Mass distribution in the asteroid belt

The dependence of the cumulative number of numbered asteroids (up to 3720) on their absolute magnitude is investigated. The differential mass index k is derived from these relations for fainter asteroids. A steeper slope (2.2 < k < 2.4) is found in the four most populous asteroid familes (Flora, Koronis, Eos and Themis) and a flatter slope (1.3 < k < 1.6) for non-family asteroids. This indicates that there are two different asteroid populations in the asteorid belt. Total masses of the asteroid families may be greater than it is commonly accepted.

The size distribution of main-belt asteroids from IRAS data

The IRAS data base on asteroid albedos and diameters has been used to derive size distributions for a set of about 4000 numbered main-belt asteroids and for various subsets defined according to the semimajor axis range and family membership. Different procedures have been used to obtain albedo estimates for the (mostly small) members of the sample not observed by IRAS, allowing us to assess the sensitivity of the derived size distributions to the assumptions used for this purpose. The results show that, apart from the Flora zone in the inner belt, non-family asteroids always have size distributions characterized by a strong change in slope at diameters ≈ 150 km, with the differential power-law distribution exponent passing from values around 3 or more at large sizes, to ≈ 1 at smaller ones. In the Flora region, where the sample is complete down to about 18 km (contrasting with 44 km for the whole asteroid population), a steep slope is also observed at small sizes. A similar feature is typical of the most populous families. While the size distribution of large bodies has probably been little affected by collisional evolution, it seems likely that most family members and Flora asteroids are fragments from catastrophic impacts, with a size distribution close to that found after laboratory impact experiments. For the other main-belt asteroids, the flatter slope in the intermediate diameter range between ≈ 30 and 150 km is either due to the influence of self-gravity on the collisional outcomes, or is a remnant of the ‘primordial’ distribution. Collisional evolution models, however, can approximately reproduce the observed overall distribution starting from very different initial populations. Thus, the size distribution data alone do not effectively constrain the initial distribution and the intensity of the collisional process.

Collisional evolution in the Eos and Koronis asteroid families: Observational and numerical results

Recent observational results ( R.P. Binzel 1987, Icarus 22, 135–208) are analyzed to investigate the origin and evolution of the Eos and Koronis families. Rotation rates in the Eos family display a Maxwellian distribution implying a collisionally evolved population and are significantly faster than Koronis family and nonfamily asteroids. Observational and laboratory results suggest that the largest members in each family may still “remember” their parent-body rotation rates which were both in the range of 1–3 revolutions/ day. Results from a numerical model for the collisional evolution of rotational angular momentum are used to interpret the different rotational characteristics as possibly being due to different relative ages of the families. The age of the Eos family may be comparable with that of the Solar System while the Koronis family may be considerably younger. Koronis family members display a higher mean lightcurve amplitude and therefor may be more irregularly shaped. Alternatively, the higher amplitudes may be accounted for by a preferential low obliquity alignment of spin vectors, a testable hypothesis.

The asteroids as outcomes of catastrophic collisions

The role of catastrophic collisions in the evolution of the asteroids is discussed in detail, employing extrapolations of experimental results on the outcomrs of high-velocity impacts. We determine the range of the probable largest collision for target asteroids of different sizes during the solar system's lifetime, and we conclude that all the asteroids have undergone collisional events capable of overcoming the material's solid-state cohesion. Such events do not lead inescapably to complete disruption of the targets, because (i) for a previously unfractured target, experiments show that fragments of significant size can survive breakup, depending on the energy and geometry of the collision; (ii) self-gravitation can easily cause a reaccumulation of fragments for targets exceeding a critical size, which seems to be of the order of 100 km. In the intermediate diameter range 100⪅ D ⪅300 km, where formation of gravitationally bound “rubble piles” is frequent, the transfer of angular momentum can be large enough to produce objects with triaxial equilibrium shapes (Jacobi ellipsoids) or to cause fission into binary systems. In the same size range, low-velocity escape of collisional fragments can also occur, leading to the formation of dynamical families. Asteroids smaller than ∼100 km are mostly multigeneration fragments, while for D⪆300 km the collisional process produces nearly spheroidal objects covered by megaregoliths; whether their rotation is “primordial” or collisionally generated depends critically on the past flux of colliders. The complex and size-dependent phenomenology predicted by the theory compares satisfactorily with the observational evidence, as derived both by a classification of asteroids in terms of their size, spin rate, and lightcurve amplitude, and by a comparison between the rotational properties of family and nonfamily asteroids. The fundamental result of this investigation is that almost all asteroids are outcomes of catastrophic collisions, and that these events cause either complete fragmentation of the target bodies or, at least, drastic readjustments of their internal structure, shape, and spin rate.

Rotational properties of asteroids: Correlations and selection effects

Rotational data on 321 asteroids observed as of late 1978 are analyzed. Selection effects within the sample are discussed and used to define a data set consisting of 134 main-belt, nonfamily asteroids having reliably determined periods and amplitudes based on photoelectric observations. In contrast to A. W. Harris and J. A. Burns (1979, Icarus 40, 115–144) we found no significant correlation between rotational properties and compositional type. Smaller asteroids have a greater range of rotational amplitudes than the largest asteroids but are not, on the average, appreciably more elongated. While no definite relationship between asteroid size and rotation rate was found the distribution is not random. The largest asteroids have rotation periods near 7 hr compared with 10 hr for the smaller. A group of large, rapidly rotating, high-amplitude asteroids is recognized. A pronounced change in rotational properties occurs near this size range (diam = 200 ± 50 km) which also corresponds to the size at which a change of slope occurs in the size frequency distribution. We believe this size range represents a transition region between very large, rapidly rotating, low-amplitude (primordial?) objects and smaller ones having a considerably greater range of periods and amplitudes. Asteroids in this transition size range display an increase in rotational amplitude with increasing spin rate; other than this, however, there is no correlation between period and amplitude. The region of low spatial density in the asteroid belt centered near 2.9 AU and isolated from the inner and outer belt by the 2:5 and 3:7 commensurabilities is shown to be a region in which non- C or - S asteroids are overrepresented and which have marginally higher rotational amplitudes than those located in more dense regions. We attribute disagreements between our results and other studies of this type to the inclusion of non-main-belt asteroids and photographic data in the earlier analyses.