Considerations on the magnitude distributions of the Kuiper belt and of the Jupiter Trojans

By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-neptunian planetesimal disk. We develop a sketch model of the HDs in the inner and outer parts of the disk that is consistent with the observed distributions and with the dynamical evolution scenario known as the ‘Nice model’. This leads us to predict that the HD of the hot population should have the same slope of the HD of the cold population for 6.5<H<9, both as steep as the slope of the Trojans' HD. Current data partially support this prediction, but future observations are needed to clarify this issue. Because the HD of the Trojans rolls over at H∼9 to a collisional equilibrium slope that should have been acquired when the Trojans were still embedded in the primordial trans-neptunian disk, our model implies that the same roll-over should characterize the HDs of the Kuiper belt populations, in agreement with the results of Bernstein et al. [Bernstein, G.M., and 5 colleagues, 2004. Astron. J. 128, 1364-1390] and Fuentes and Holman [Fuentes, C.I., Holman, M.J., 2008. Astron. J. 136, 83-97]. Finally, we show that the constraint on the total mass of the primordial trans-neptunian disk imposed by the Nice model implies that it is unlikely that the cold population formed beyond 35 AU.     

The Caltech Wide Area Sky Survey

The first phase of the Caltech Wide Area Sky Survey occurred from lateNovember 2001 through mid-April 2003. We present preliminary resultsfrom this survey which has detected 28 bright Kuiper Belt Objects(KBOs) and 4 Centaurs, 19 of which were discovered in our surveyincluding Quaoar, the largest KBO, as well as 6 of the 10intrinsically brightest KBOs. We have surveyed 5108 square degrees ofthe sky nearest the invariable plane to a limiting red magnitude of20.7. Correcting for the overabundance of objects near the invariableplane, this represents 27% completeness in terms of KBO numbers.Thus, approximately 100 KBOs and Centaurs brighter than m_R = 20.7exist, about 3/4 of which remain undiscovered. The bright KBOs areconsistent with the canonical q=4 size distribution, suggesting thatabout ten 1000 km diameter KBOs and about one 2000 km diameter KBOexist. Additionally, we observe only 3 KBOs with low inclination(i < 7 degrees) with 67% of the sky available to these objectssurveyed. This is in sharp contrast with the known KBOs, of whichabout 60% of the ～ 800 observed objects (as of May 2003) have i< 7 degrees. Although we observe at systematically higher invariableplane latitudes than many deeper KBO surveys, such systematic biasescannot fully explain the lack of low inclination objects, ameasurement which is significant at the > 3 σ level. Thissuggests that the bright KBOs have a fundamentally different maximumsize than the fainter KBOs. A better characterization of the surveylimiting magnitude and a more thorough modeling of observational biaseffects of different classes of KBOs will be made in a future work.     

Photometric behavior of 20000 Varuna at very small solar phase angles

Six nights of R-band CCD observations of the classical Kuiper Belt Object (KBO) 20000 Varuna (2000 WR106) were obtained at the Palomar Mountain 60- and 200-in telescopes. The observations were scheduled to take advantage of a particularly favorable apparition which allowed us to sample down to extremely small solar phase angle (α=0.036°). After rotational lightcurve subtraction, we found that the KBO exhibited a strong opposition surge of ∼0.1 mag at phase angles α<0.1°. We modeled our composite solar phase curve of Varuna using both H-G parameterization and Hapke theory and concluded that similar opposition surges may be wide spread among KBOs and that the regolith of Varuna may be significantly more porous than a typical main-belt C-type asteroid. Wide-spread opposition surges lead to higher albedos than derived assuming linear phase behavior: on the whole KBOs may be brighter than previously assumed.     

On the Use of Meteor Camera Systems in the Detection of Kuiper Belt Objects Through Serendipitous Stellar Occultations

The direct detection of Kuiper Belt Objects (KBOs) by telescopic imaging is not currently practical for objects much less than 100 km in diameter. However, indirect methods such as serendipitous stellar occultations might still be employed to detect these bodies. The method of serendipitous stellar occultations has been previously used with some success in detecting KBOs—Roques et al. (Astron J 132(2):819–822, 2006) detected three Trans-Neptunian objects; Schlichting et al. (Nature 462(7275):895–897, 2009) and Schlichting et al. (Astrophys J 761:150, 2012) each detected a single object in archival Hubble Space Telescope data. However, previous assessments of KBO occultation detection rates have been calculated only for telescopes—we extend this method to video camera systems, and we apply this derivation to the automated meteor camera systems currently in use at the University of Western Ontario. We find that in a typical scenario we can expect one occultation per month. However recent studies such as those of Shankman et al. (Astrophys. J. Lett. 764. doi:10.1088/2041-8205/764/1/L2, 2013) and Gladman et al. (AAS/Division for Planetary Sciences Meeting Abstracts, 2012) which indicate that the population of small KBOs may be smaller than has been assumed in the past may result in a sharp reduction of these rates. Nonetheless, a survey for KBO occultations using existing meteor camera systems may provide valuable information about the number density of KBOs.     

Pluto's Atmosphere And A Targeted-Occultation Search For Other Bound Kbo Atmospheres

Processes relevant to Pluto's atmosphere are discussed,and our current knowledge is summarized, including results of two stellar occultationsby Pluto that were observed in 2002. The question of whether other Kuiper belt objects (KBOs)may have bound atmospheres is considered, and observational indicators for KBO atmospheresare described. The definitive detection of a KBO atmosphere could be established withtargeted stellar-occultation observations. These data can also establish accurate diametersfor these objects and be used to detect possible nearby companions. Strategies for acquiringoccultation data with portable, airborne, and fixed telescopes are evaluated in terms of thenumber of KBO occultations per year that should be observable. For the sample of 29 currentlyknown KBOs with H ≤ 5.2, (radius ≤ 300 km for a geometricalbedo of 0.04), we expect about 4 events per year would yield good results for a (stationary) 6.5-m telescope. A network of portable0.36-m telescopes should be able to observe 6 events per year, and a 2.5-m airborne telescopewould have about 200 annual opportunities to observe KBO occultations.     

The size distribution of trans-Neptunian bodies

The magnitude distribution of the trans-Neptunian bodies composed of the Kuiper Belt Objects (KBOs) and Scattered Disk Objects (SDOs) is determined for absolute magnitudes H?7, using maximum likelihood estimation methods. This is translated into a corresponding size distribution. This gave a differential size index of q=3.966±0.15 for KBOs and q=3.016±0.32 for SDOs. It was found that these two distributions were statistically different. The KBOs were further split into classical KBOs and Plutinos which had indices of q=4.074±0.18 and q=3.301±0.37, respectively. There was no statistical evidence that these are different populations. The classical KBOs were further split and examined for four different semi-major axis ranges and it was found that there was moderate evidence that the entire sample was not well represented by one index. The distribution indices of the SDOs were compared with the distributions of short period comets and found to be similar. It is likely that the scattered disk population is the source of the short period comets.     

A derivation of the luminosity function of the Kuiper belt from a broken power-law size distribution

We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 30<Db<90 km via a maximum-likelihood fit of our model to the observed luminosity function. We also confirm that the observed luminosity function for m(R)∼21-28 is consistent with a broken power-law size distribution, and exhibits a break at .     

The population of faint Jupiter family comets near the Earth

We study the population of faint Jupiter family comets (JFCs) that approach the Earth (perihelion distances q<1.3 AU) by applying a debiasing technique to the observed sample. We found for the debiased cumulative luminosity function (CLF) of absolute total magnitudes H₁₀ a bimodal distribution in which brighter comets (H₁₀?9) follow a linear relation with a steep slope α=0.65±0.14, while fainter comets follow a much shallower slope α=0.25±0.06 down to H₁₀∼18. The slope can be pushed up to α=0.35±0.09 if a second break in the H₁₀ distribution to a much shallower slope is introduced at H₁₀∼16. We estimate a population of about 10³ faint JFCs with q<1.3 AU and 10<H₁₀<15 (radii ∼0.1-0.5 km). The shallowness of the CLF for faint near-Earth JFCs may be explained either as: (i) the source population (the scattered disk) has an equally very shallow distribution in the considered size range, or (ii) the distribution is flattened by the disintegration of small objects before that they have a chance of being observed. The fact that the slope of the magnitude distribution of the faint active JFCs is very similar to that found for a sample of dormant JFCs candidates suggests that for a surviving (i.e., not disintegrated) object, the probability of becoming dormant versus keeping some activity is roughly size independent.     

On the detectability of lightcurves of Kuiper belt objects

We present a statistical study of the detectability of lightcurves of Kuiper belt objects (KBOs). Some Kuiper belt objects display lightcurves that appear “flat”; i.e., there are no significant brightness variations within the photometric uncertainties. Under the assumption that KBO lightcurves are mainly due to shape, the lack of brightness variations may be due to (1) the objects having very nearly spherical shapes or (2) their rotation axes coinciding with the line of sight. We investigate the relative importance of these two effects and relate it to the observed fraction of “flat” lightcurves. This study suggests that the fraction of KBOs with detectable brightness variations may provide clues about the shape distribution of these objects. Although the current database of rotational properties of KBOs is still insufficient to draw any statistically meaningful conclusions, we expect that, with a larger dataset, this method will provide a useful test for candidate KBO shape distributions.     

The color of the Kuiper belt Core

Recent dynamical analyses of the Kuiper belt have introduced a rigorous classification scheme, determined the mean orbital plane, and identified “Core” and “Halo” populations as a function of inclination with respect to this plane (Elliot, J.L., Kern, S.D., Clancy, K.B., Gulbis, A.A.S., Millis, R.L., Buie, M.W., Wasserman, L.H., Chiang, E.I., Jordan, A.B., Trilling, D.E., Meech, K.J., 2005. Astron. J. 129, 1117-1162). Here, we use new observations and existing data to investigate the colors of Kuiper belt objects (KBOs) within this framework. With respect to the bulk KBO color distribution (all objects for which we have B-V and V-R colors; median B-R=1.56), we find that the population of objects classified following (Elliot, J.L., Kern, S.D., Clancy, K.B., Gulbis, A.A.S., Millis, R.L., Buie, M.W., Wasserman, L.H., Chiang, E.I., Jordan, A.B., Trilling, D.E., Meech, K.J., 2005. Astron. J. 129, 1117-1162) as Classical tends to be red (B-R>1.56) while the Scattered Near population is mostly neutral (B-R<1.56). Colors of Scattered Extended and Resonant objects are consistent with the bulk distribution. Separating objects into specific resonances demonstrates that the color of the Resonant sample is dominated by KBOs in the 3:2 resonance, which is consistent with previous findings. Unlike the objects in the 3:2 resonance, however, the majority of objects in the 5:2 resonance are neutral and all but one of the objects in the 4:3, 5:3, 7:4, 2:1, and 7:3 resonances are red. In particular, the objects in the 7:4 resonance are remarkably red. We find that the colors of KBOs in the Core (low-inclination) and Halo (high-inclination) are statistically different, with Core objects being primarily red and Halo objects having a slight tendency to be neutral. Notably, virtually all of the non-Resonant Core objects are red. This combination of low inclination, unperturbed orbits and red colors in the Core may be indicative of a relic grouping of objects.     

Nuclear magnitudes and the size distribution of Jupiter family comets

We present a new catalog of absolute nuclear magnitudes of Jupiter family (JF) comets, which is an updated version of our previous catalog [Tancredi, G., Fernández, J.A., Rickman, H., Licandro, J., 2000. Astron. Astrophys. Suppl. Ser. 146, 73-90]. From the new catalog we find a linear cumulative luminosity function (CLF) of slope 0.54±0.05 for JF comets with q?2.5 AU. By considering this CLF combined with the few measured geometric albedos with their respective uncertainties, and assuming a canonical albedo of 0.035±0.012 for those comets with undetermined albedos, we derive a cumulative size distribution that follows a power-law of index −2.7±0.3. The slope is similar to that derived from some theoretical collisional models and from some populations of Solar System bodies like the trans-neptunian objects. We also discuss and compare our size distribution with those by other authors that have recently appeared in the literature. Some striking differences in the computed slopes are explained in terms of biases in the studied samples, the different weights given to the brightest members of the samples, and discrepancies in the values of a few absolute nuclear magnitudes. We also compute sizes and fractions of active surface area of JF comets from their estimated absolute nuclear magnitudes and their water production rates. With the outgassing model that we use, about 60% of the computed fractions f of active surface area are found to be smaller than 0.2, with one case (28P/Neujmin 1) of no more than 0.001, which suggests that JF comets may transit through stages of very low activity, or even dormancy. There is an indication that JF comets with radii RN?3 km have active fractions f?0.01, which might be due to the rapid formation of insulating dust mantles on larger nuclei.     

Photometric Light Curve for the Kuiper Belt Object 2000 EB173 on 78 Nights

Kuiper belt objects (KBOs) are generally very faint and cannot in practice be monitored with a well-sampled long-term light curve; so our discovery of the bright KBO 2000 EB₁₇₃ offers an excellent opportunity for synoptic studies. We present a well-sampled photometric time series (77 R and 29 V magnitudes on 78 nights) over a 225-day time span centered on the 2001 opposition. The light curve (corrected to the year 2001 opposition distance) varies from 19.11 to 19.39 mag with a single peak that is smooth, time symmetric, and coincident with opposition. All variations in the light curve are consistent with a linear opposition surge (R_OPP=19.083+0.125∗α, where α is the solar phase angle), while any rotational modulation must have a peak-to-peak amplitude of less than 0.097 mag. This is the first measured opposition surge for any KBO (other than Pluto). The V−R color is 0.63±0.02, with no apparent variation with phase at the few percent level. With R=19.11 at opposition, 2000 EB₁₇₃ remains the brightest known KBO and a prime target for future photometric and spectroscopic studies.     

Towards initial mass functions for asteroids and Kuiper Belt Objects

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

Solar infrared occultation observations by SPICAM experiment on Mars-Express: Simultaneous measurements of the vertical distributions of H2O, CO2 and aerosol

The infrared AOTF spectrometer is a part of the SPICAM experiment onboard the Mars-Express ESA mission. The instrument has a capability of solar occultations and operates in the spectral range of 1-1.7 μm with a spectral resolution of ∼3.5 cm⁻¹. We report results from 24 orbits obtained during MY28 at Ls 130°-160°, and the latitude range of 40°-55° N. For these orbits the atmospheric density from 1.43 μm CO₂ band, water vapor mixing ratio based on 1.38 μm absorption, and aerosol opacities were retrieved simultaneously. The vertical resolution of measurements is better than 3.5 km. Aerosol vertical extinction profiles were obtained at 10 wavelengths in the altitude range from 10 to 60 km. The interpretation using Mie scattering theory with adopted refraction indices of dust and H₂O ice allows to retrieve particle size (reff∼0.5-1 μm) and number density (∼1 cm⁻³ at 15-30 km) profiles. The haze top is generally below 40 km, except the longitude range of 320°-50° E, where high-altitude clouds at 50-60 km were detected. Optical properties of these clouds are compatible with ice particles (effective radius reff=0.1-0.3 μm, number density N∼10 cm−3) distributed with variance νeff=0.1-0.2 μm. The vertical optical depth of the clouds is below 0.001 at 1 μm. The atmospheric density profiles are retrieved from CO₂ band in the altitude range of 10-90 km, and H₂O mixing ratio is determined at 15-50 km. Unless a supersaturation of the water vapor occurs in the martian atmosphere, the H₂O mixing ratio indicates ∼5 K warmer atmosphere at 25-45 km than predicted by models.     

Short-lived asteroids in the 7/3 Kirkwood gap and their relationship to the Koronis and Eos families

A population of 23 asteroids is currently observed in a very unstable region of the main belt, the 7/3 Kirkwood gap. The small size of these bodies—with the notable exception of (677) Aaltje (∼30 km)—as well as the computation of their dynamical lifetimes (3<T_D<172 Myr) shows that they cannot be on their primordial orbits, but were recently injected in the resonance. The distribution of inclinations appears to be bimodal, the two peaks being close to 2° and 10°. We argue that the resonant population is constantly being replenished by the slow leakage of asteroids from both the Koronis (I∼2°) and Eos (I∼10°) families, due to the drift of their semi-major axes, caused by the Yarkovsky effect. Assuming previously reported values for the Yarkovsky mean drift rate, we calculate the flux of family members needed to sustain the currently observed population in steady state. The number densities with respect to semi-major axis of the observed members of both families are in very good agreement with our calculations. The fact that (677) Aaltje is currently observed in the resonance is most likely an exceptional event. This asteroid should not be genetically related to any of the above families. Its size and the eccentricity of its orbit suggest that the Yarkovsky effect should have been less efficient in transporting this body to the resonance than close encounters with Ceres.     

Cassini imaging of Saturn's rings: II. A wavelet technique for analysis of density waves and other radial structure in the rings

We describe a powerful signal processing method, the continuous wavelet transform, and use it to analyze radial structure in Cassini ISS images of Saturn's rings. Wavelet analysis locally separates signal components in frequency space, causing many structures to become evident that are difficult to observe with the naked eye. Density waves, generated at resonances with saturnian satellites orbiting outside (or within) the rings, are particularly amenable to such analysis. We identify a number of previously unobserved weak waves, and demonstrate the wavelet transform's ability to isolate multiple waves superimposed on top of one another. We also present two wave-like structures that we are unable to conclusively identify. In a multi-step semi-automated process, we recover four parameters from clearly observed weak spiral density waves: the local ring surface density, the local ring viscosity, the precise resonance location (useful for pointing images, and potentially for refining saturnian astrometry), and the wave amplitude (potentially providing new constraints upon the masses of the perturbing moons). Our derived surface densities have less scatter than previous measurements that were derived from stronger non-linear waves, and suggest a gentle linear increase in surface density from the inner to the mid-A Ring. We show that ring viscosity consistently increases from the Cassini Division outward to the Encke Gap. Meaningful upper limits on ring thickness can be placed on the Cassini Division (3.0 m at r∼118,800 km, 4.5 m at r∼120,700 km) and the inner A Ring (10-15 m for r<127,000 km).     

Orbital linkages of Comet 6P/d'Arrest based on its asymmetric light curve

We present an investigation of different models of the nongravitational acceleration on Comet 6P/d'Arrest, as used in orbital linkages spanning 150 years from the discovery of the comet in 1851 until the recent observations made in 2001. Some of our models use the time-shifted g-like function to represent the variation of outgassing rate, but the main thrust is on models using instead a production curve that is fitted to recent light curve observations—mainly those in 1976. We pay special attention to the proper scaling of such a production curve, when applied to other apparitions with a different perihelion distance q, and we find a best fit with a q^−1.6 power-law. Generally, the best fit is found with models, in which the acceleration components are expressed in terms of the angular parameters of the rotating nucleus. We thus find the orientation of the spin axis, and using the orbital evolution we are able to predict a variable time shift of the outgassing curve. The very best results are found when applying this time shift to the light-curve based, angular models. The totality of the 1851-2001 observations can then be linked with a mean residual of less than 4″. This may be brought down to ∼^2″ by solving for individual ‘activity parameters’ of all apparitions, which are multiplicative factors applied to the acceleration amplitudes. These turn out to be within 10% of unity for the best fit. We have also performed a linkage to the observations of Comet 1678 (La Hire) using our models. We find an indication of a secular increase of the amount of asymmetry of the outgassing with respect to perihelion, part of which is due to the variable time shift caused by the orbital evolution.     

Generation and emplacement of fine-grained ejecta in planetary impacts

We report here on a survey of distal fine-grained ejecta deposits on the Moon, Mars, and Venus. On all three planets, fine-grained ejecta form circular haloes that extend beyond the continuous ejecta and other types of distal deposits such as run-out lobes or ramparts. Using Earth-based radar images, we find that lunar fine-grained ejecta haloes represent meters-thick deposits with abrupt margins, and are depleted in rocks ?1 cm in diameter. Martian haloes show low nighttime thermal IR temperatures and thermal inertia, indicating the presence of fine particles estimated to range from ∼10 μm to 10 mm. Using the large sample sizes afforded by global datasets for Venus and Mars, and a complete nearside radar map for the Moon, we establish statistically robust scaling relationships between crater radius R and fine-grained ejecta run-out r^* for all three planets. On the Moon, r^* ∼ R^−0.18 for craters 5-640 km in diameter. For Venus, radar-dark haloes are larger than those on the Moon, but scale as r^* ∼ R^−0.49, consistent with ejecta entrainment in Venus’ dense atmosphere. On Mars, fine-ejecta haloes are larger than lunar haloes for a given crater size, indicating entrainment of ejecta by the atmosphere or vaporized subsurface volatiles, but scale as R^−0.13, similar to the ballistic lunar scaling. Ejecta suspension in vortices generated by passage of the ejecta curtain is predicted to result in ejecta run-out that scales with crater size as R^1/2, and the wind speeds so generated may be insufficient to transport particles at the larger end of the calculated range. The observed scaling and morphology of the low-temperature haloes leads us rather to favor winds generated by early-stage vapor plume expansion as the emplacement mechanism for low-temperature halo materials.     

V-type asteroids in the middle main belt

V-type asteroids are bodies whose surfaces are constituted of basalt. In the Main Asteroid Belt, most of these asteroids are assumed to come from the basaltic crust of Asteroid (4) Vesta. This idea is mainly supported by (i) the fact that almost all the known V-type asteroids are in the same region of the belt as (4) Vesta, i.e., the inner belt (semi-major axis 2.1<a<2.5 AU), (ii) the existence of a dynamical asteroid family associated to (4) Vesta, and (iii) the observational evidence of at least one large craterization event on Vesta's surface. One V-type asteroid that is difficult to fit in this scenario is (1459) Magnya, located in the outer asteroid belt, i.e., too far away from (4) Vesta as to have a real possibility of coming from it. The recent discovery of the first V-type asteroid in the middle belt (2.5<a<2.8 AU), (21238) 1995WV7 [Binzel, R.P., Masi, G., Foglia, S., 2006. Bull. Am. Astron. Soc. 38, 627; Hammergren, M., Gyuk, G., Puckett, A., 2006. ArXiv e-print, astro-ph/0609420], located at ∼2.54 AU, raises the question of whether it came from (4) Vesta or not. In this paper, we present spectroscopic observations indicating the existence of another V-type asteroid at ∼2.53 AU, (40521) 1999RL95, and we investigate the possibility that these two asteroids evolved from the Vesta family to their present orbits by a semi-major axis drift due to the Yarkovsky effect. The main problem with this scenario is that the asteroids need to cross the 3/1 mean motion resonance with Jupiter, which is highly unstable. Combining N-body numerical simulations of the orbital evolution, that include the Yarkovsky effect, with Monte Carlo models, we compute the probability that an asteroid of a given diameter D evolves from the Vesta family and crosses over the 3/1 resonance, reaching a stable orbit in the middle belt. Our results indicate that an asteroid like (21238) 1995WV7 has a low probability (∼1%) of having evolved through this mechanism due to its large size (D∼5 km), because the Yarkovsky effect is not sufficiently efficient for such large asteroids. However, the mechanism might explain the orbits of smaller bodies like (40521) 1999RL95 (D∼3 km) with ∼70-100% probability, provided that we assume that the Vesta family formed ?3.5 Gy ago. We estimate the debiased population of V-type asteroids that might exist in the same region as (21238) and (40521) (2.5<a?2.62 AU) and conclude that about 10 to 30% of the V-type bodies with D>1 km may come from the Vesta family by crossing over the 3/1 resonance. The remaining 70-90% must have a different origin.     

Initial sizes of planetesimals and accretion of the asteroids

The present size frequency distribution (SFD) of bodies in the asteroid belt appears to have preserved some record of the primordial population, with an excess of bodies of diameter D ∼ 100 km relative to a simple power law. The survival of Vesta’s basaltic crust also implies that the early SFD had a shallow slope in the range ∼10-100 km. (Morbidelli, A., Bottke, W.F., Nesvorny, D., Levison, H.F. [2009]. Icarus 204, 558-573) were unable to produce these features by accretion from an initial population of km-sized planetesimals. They concluded that bodies with sizes in the range ∼100-1000 km and a SFD similar to the current population were produced directly from solid particles of sub-meter scale, without experiencing accretion through intermediate sizes. We present results of new accretion simulations in the primordial asteroid region. The requisite SFD can be produced from an initial population of planetesimals of sizes ?0.1 km, smaller than the usual assumption of km-sized bodies. The bump at D ∼ 100 km is produced by a transition from dispersion-dominated runaway growth to a regime dominated by Keplerian shear, before the formation of large protoplanetary embryos. Thus, accretion of the asteroids from an initial population of small (sub-km) planetesimals cannot be ruled out.