The asteroid lightcurve database

The compilation of a central database for asteroid lightcurve data, i.e., rotation rate and amplitude along with ancillary information such as diameter and albedo (known or estimated), taxonomic class, etc., has been important to statistical studies for several decades. Having such a compilation saves the researcher hours of effort combing through any number of journals, some obvious and some not, to check on prior research. Harris has been compiling such data in the Asteroid Lightcurve Database (LCDB) for more than 25 years with Warner and Pravec assisting the past several years. The main data included in the LCDB are lightcurve rotation periods and amplitudes, color indices, H-G parameters, diameters (actual or derived), basic binary asteroid parameters, and spin axis and shape models. As time permits we are reviewing existing entries to enter data not previously recorded (e.g., phase angle data). As of 2008 December, data for 3741 asteroids based on more than 10650 separate detail records derived from entries in various journals were included in the LCDB. Of those 3741 asteroids, approximately 3100 have data of sufficient quality for statistical analysis, including 7 that have “dual citizenship” - meaning that they have (or had) asteroid designations as well comet designations. Here we present a discussion of the nature of LCDB data, i.e., which values are actually measured and which are derived. For derived data, we give our justification for specific values. We also present some analysis based on the LCDB data, including new default albedo (pV) and phase slope parameter (G) values for the primary taxonomic classes and a review of the frequency-diameter distribution of all asteroids as well as some selected subsets. The most recent version of data used in this analysis is available for download from the Collaborative Asteroid Lightcurve Link (CALL) site at http://www.MinorPlanetObserver.com/astlc/default.htm. Other data sets, some only subsets of the full LCDB, are available in the Ephemeris of Minor Planets, The Planetary Data System, and the Minor Planet Center web site.     

Combining asteroid models derived by lightcurve inversion with asteroidal occultation silhouettes

Asteroid sizes can be directly measured by observing occultations of stars by asteroids. When there are enough observations across the path of the shadow, the asteroid’s projected silhouette can be reconstructed. Asteroid shape models derived from photometry by the lightcurve inversion method enable us to predict the orientation of an asteroid for the time of occultation. By scaling the shape model to fit the occultation chords, we can determine the asteroid size with a relative accuracy of typically ∼10%. We combine shape and spin state models of 44 asteroids (14 of them are new or updated models) with the available occultation data to derive asteroid effective diameters. In many cases, occultations allow us to reject one of two possible pole solutions that were derived from photometry. We show that by combining results obtained from lightcurve inversion with occultation timings, we can obtain unique physical models of asteroids.     

Shapes and rotational properties of thirty asteroids from photometric data

We have analyzed photometric lightcurves of 30 asteroids, and present here the obtained shapes, rotational periods and pole directions. We also present new photometric observations of five asteroids. The shape models indicate the existence of many features of varying degrees of irregularity. Even large main-belt asteroids display such features, so the resulting poles and periods are more consistent than those obtained by simple ellipsoid-like models. In some cases the new rotational parameters are rather different from those obtained previously, and in a few cases there were no proper previous estimates at all.     

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.     

Determining asteroid spin states using radar speckles

Knowing the shapes and spin states of near-Earth asteroids is essential to understanding their dynamical evolution because of the Yarkovsky and YORP effects. Delay-Doppler radar imaging is the most powerful ground-based technique for imaging near-Earth asteroids and can obtain spatial resolution of <10 m, but frequently produces ambiguous pole direction solutions. A radar echo from an asteroid consists of a pattern of speckles caused by the interference of reflections from different parts of the surface. It is possible to determine an asteroid’s pole direction by tracking the motion of the radar speckle pattern. Speckle tracking can potentially measure the poles of at least several radar targets each year, rapidly increasing the available sample of NEA pole directions. We observed the near-Earth asteroid 2008 EV5 with the Arecibo planetary radar and the Very Long Baseline Array in December 2008. By tracking the speckles moving from the Pie Town to Los Alamos VLBA stations, we have shown that EV5 rotates retrograde. This is the first speckle detection of a near-Earth asteroid.     

Analysis of the Hungaria asteroid population

There are approximately 5000 known asteroids in the Hungaria orbital space, a region defined by orbits with high inclination (16° < i < 34°), low eccentricities (e < 0.18), and semi-major axes 1.78 < a < 2.0 AU. We argue that this region is populated by a large number of asteroids formed after a catastrophic collision involving (434) Hungaria, the presumptive largest fragment of the Hungaria collisional family. The remaining objects form a background population that share orbital characteristics with the family members. Due to the general dynamic stability of the region, it is likely that most asteroids in Hungaria space (the Hungaria “group”) have been in this region since the formation of the Solar System or at least since the planets assumed their current orbital configuration. Our examination of the Hungaria group included comparing rotation rates, taxonomic classification, and orbital dynamics to determine the characteristics of the family and background populations. We first found there is an excess of slow rotators among the group but, otherwise, the distribution of spin frequencies is essentially uniform, i.e., that a plot of the cumulative number of objects over the range of 1 d⁻¹ < f < 9 d⁻¹ is nearly a straight line or, put another way, if the distribution over the range is binned by equal intervals of f (1-2 d⁻¹, 2-3 d⁻¹, etc.), the number of objects in each bin is statistically the same.There is a distinct family within the Hungaria group, centered at a semi-major axis of 1.940 AU, with a dispersion range that increases with decreasing size of members, as expected of an evolved collisional family. The larger members with well-determined taxonomic class, including (434) Hungaria itself, have flat spectra, mostly likely type E or similar. The degree of spreading versus size of family members is consistent with that expected from Yarkovsky thermal drift in roughly 0.5 Gyr, suggesting that age for the family. The Asteroid (434) Hungaria is displaced in semi-major axis by 0.004 AU from the center of the Hungaria family. The collision event that produced the family should not have left the largest body displaced by more than 0.001 AU from the original orbit, thus we infer that the displacement of (434) Hungaria is mainly due to Yarkovsky drift, and is consistent with the expected drift for that size body in ∼0.5 Gyr. Below ∼1.93 AU heliocentric distance the Hungaria family is perturbed by at least two secular resonances, 2g − g₅ − g₆ and one of the family of 4th or 6th order secular resonances near s ∼ −22.25 ″/year. Their combined effect results in larger inclination dispersion of the family members.     

Spin vectors in the Koronis family: comprehensive results from two independent analyses of 213 rotation lightcurves

Observations of Koronis asteroid family members (158) Koronis, (277) Elvira, (311) Claudia, (321) Florentina, and (720) Bohlinia made during the period 1998-2001 yielded 61 new individual rotation lightcurves to augment previous surveys (R.P. Binzel, 1987, Icarus 72, 135-208; S.M. Slivan, R.P. Binzel, 1996, Icarus 124, 452-470) and allow determination of the senses of rotation and spin vector orientations for these objects. Spin vector reductions were performed on these five objects and also on family members (167) Urda, (208) Lacrimosa, (534) Nassovia, and (1223) Neckar using both a combination of amplitude-magnitude and epoch methods and a convex inversion method. A total of 213 individual lightcurves were analyzed to determine sidereal rotation periods, pole solutions and obliquities, associated photometric parameters, and model shapes for each object. We checked our methods and results using the (243) Ida Master Dataset of lightcurves (R. P. Binzel et al., 1993, Icarus 105, 310-325) and found that the true pole determined from the Galileo fly by of this irregularly shaped member of the Koronis family falls just at the edge of the estimated uncertainty of our own solution. Our findings for the spin vector distribution of 10 members within the Koronis family represent the first systematic study of spin states within a well-established Hirayama family, and provide observational constraints for models of the physics of family formation and spin vector evolution in the main belt.     

Photometry and spin rate distribution of small-sized main belt asteroids

Photometry results of 32 asteroids are reported from only seven observing nights on only seven fields, consisting of 34.11 cumulative hours of observations. The data were obtained with a wide-field CCD (^40.5′×^27.3′) mounted on a small, 46-cm telescope at the Wise Observatory. The fields are located within ±1.5° from the ecliptic plane and include a region within the main asteroid belt. The observed fields show a projected density of ∼23.7 asteroids per square degree to the limit of our observations. 13 of the lightcurves were successfully analyzed to derive the asteroids' spin periods. These range from 2.37 up to 20.2 h with a median value of 3.7 h. 11 of these objects have diameters in order of two kilometers and less, a size range that until recently has not been photometrically studied. The results obtained during this short observing run emphasize the efficiency of wide-field CCD photometry of asteroids, which is necessary to improve spin statistics and understand spin evolution processes. We added our derived spin periods to data from the literature and compared the spin rate distributions of small main belt asteroids (5>D>0.15 km) with that of bigger asteroids and of similar-sized NEAs. We found that the small MBAs do not show the clear Maxwellian-shaped distribution as large asteroids do; rather they have a spin rate distribution similar to that of NEAs. This implies that non-Maxwellian spin rate distribution is controlled by the asteroids' sizes rather than their locations.     

Ceres lightcurve analysis—Period determination

The sidereal period of Ceres is refined from 9.075 h to 9.074170±0.000002, making use of recent and historical lightcurves spanning almost 50 years. An observed increase in the amplitude of the lightcurve with solar phase angle is consistent with bright, discrete albedo features contributing a greater fraction of light as the defect of illumination increases. Observations near the same phase angle over this time span show no evidence of changes that would indicate active surface processes.     

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

A survey of small fast rotating asteroids among the near-Earth asteroid population

A survey of 62 small near-Earth asteroids was conducted to determine the rotation state of these objects and to search for rapid rotation. Since results for 9 of the asteroids were previously published (Pravec, P., Hergenrother, C.W., Whiteley, R.J., Šarounová, L., Kušnirák, P., Wolf, M. [2000]. Icarus 147, 477-486; Pravec, P. et al. [2005] Icarus 173, 108-131; Whiteley, R.J., Tholen, D.J., Hergenrother, C.W. [2002a]. Icarus 157, 139-154; Hergenrother, C.W., Whiteley, R.J., Christensen, E.J. [2009]. Minor Planet Bull. 36, 16-18.), this paper will present results for the remaining 53 objects. Rotation periods significantly less than 2 h are indicative of intrinsic strength in the asteroids, while periods longer than 2 h are typically associated with gravitationally bound aggregates. Asteroids with absolute magnitude (H) values ranging from 20.4 to 27.4 were characterized. The slowest rotator with a definite period is 2004 BW₁₈ with a period of 8.3 h, while 2000 DO₈ and 2000 WH₁₀ are the fastest with periods of 1.3 min. A minimum of two-thirds of asteroids with H > 20 are fast rotating and have periods significantly faster than 2.0 h. The percentage of rapid rotators increases with decreasing size and a minimum of 79% of H ? 24 objects are rapid rotators. Slowly-rotating objects, some with periods as long as 10-20 h, make up a small though significant fraction of the small asteroid population. There are three fast rotators with relatively large possible diameters (D): 2001 OE₈₄ with 470 ? D ? 820 m (Pravec, P., Kušnirák, P., Šarounová, L., Harris, A.W., Binzel, R.P., Rivkin, A.S. [2002b]. Large coherent Asteroid 2001 OE84. In: Warmbein, B. (Eds.), Proceedings of Asteroids, Comets, Meteors - ACM 2002. Springer, Berlin, pp. 743-745), 2001 FE₉₀ with 265 ? D ? 594 m (Hicks, M., Lawrence, K., Rhoades, H., Somers, J., McAuley, A., Barajas, T. [2009]. The Astronomer’s Telegrams, # 2116), and 2001 VF₂ with a possible D of 145 ? D ? 665 m. Using the diameters derived from nominal absolute magnitudes and albedos, the remainder of the fast rotating population is completely consistent with D ? 200 m. Even when taking into account the largest possible uncertainties in the determination of diameters, the remainder must all have D ? 400 m. With the exceptions of 2001 OE₈₄, this result agrees with previous upper diameter limits for fast rotators in Pravec and Harris (Pravec, P., Harris, A.W. [2000]. Icarus 148, 589-593) and Whiteley et al. (Whiteley, R.J, Tholen, D.J., Hergenrother, C.W. [2002a]. Icarus 157, 139-154.     

Global photometric properties of Asteroid (4) Vesta observed with Dawn Framing Camera

Dawn spacecraft orbited Vesta for more than one year and collected a huge volume of multispectral, high-resolution data in the visible wavelengths with the Framing Camera. We present a detailed disk-integrated and disk-resolved photometric analysis using the Framing Camera images with the Minnaert model and the Hapke model, and report our results about the global photometric properties of Vesta. The photometric properties of Vesta show weak or no dependence on wavelengths, except for the albedo. At 554 nm, the global average geometric albedo of Vesta is 0.38 ± 0.04, and the Bond albedo range is 0.20 ± 0.02. The bolometric Bond albedo is 0.18 ± 0.01. The phase function of Vesta is similar to those of S-type asteroids. Vesta’s surface shows a single-peaked albedo distribution with a full-width-half-max ∼17% relative to the global average. This width is much smaller than the full range of albedos (from ∼0.55× to >2× global average) in localized bright and dark areas of a few tens of km in sizes, and is probably a consequence of significant regolith mixing on the global scale. Rheasilvia basin is ∼10% brighter than the global average. The phase reddening of Vesta measured from Dawn Framing Camera images is comparable or slightly stronger than that of Eros as measured by the Near Earth Asteroid Rendezvous mission, but weaker than previous measurements based on ground-based observations of Vesta and laboratory measurements of HED meteorites. The photometric behaviors of Vesta are best described by the Hapke model and the Akimov disk-function, when compared with the Minnaert model, Lommel–Seeliger model, and Lommel–Seeliger–Lambertian model. The traditional approach for photometric correction is validated for Vesta for >99% of its surface where reflectance is within ±30% of global average.     

Lightcurves and poles of seven asteroids

The Asteroids 5 Astraea, 19 Fortuna, 51 Nemausa, 68 Leto, 138 Tolosa, 196 Philomela and 409 Aspasia have been studied using Strömgren photometry observations made in 1997. Simultaneous lightcurves in the uvby Strömgren filters of synodic periods of 0.70004±0.00020, 0.31013±0.00003, 0.32400±0.00020, 0.61910±0.00100, 0.42087±0.00009, 0.34750±0.00020 and 0.37576±0.00060 days, and amplitudes, in the y filter, of 0.^m16±0.^m05, 0.^m30±0.^m02, 0.^m15±0.^m04, 0.^m29±0.^m02, 0.^m43±0.^m03, 0.^m30±0.^m04 and 0.^m15±0.^m06 have been found for 5 Astraea, 19 Fortuna, 51 Nemausa, 68 Leto, 138 Tolosa, 196 Philomela and 409 Aspasia, respectively. Additional observations of 138 Tolosa and 196 Philomela during February 2000, show lightcurve amplitudes equal or greater than 0.^m15 for 138 Tolosa and of 0.^m45 for 196 Philomela in 2000 opposition.Solutions for the sense of rotation, sidereal period, pole orientation and shape properties have been proposed for the first time for 138 Tolosa and improved solutions have been obtained for 5 Astraea, 19 Fortuna, 51 Nemausa, 196 Philomela and 409 Aspasia.     

Visible spectroscopic and photometric survey of Jupiter Trojans: Final results on dynamical families

We present the results of a visible spectroscopic and photometric survey of Jupiter Trojans belonging to different dynamical families. The survey was carried out at the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory (La Silla, Chile) in April 2003, May 2004 and January 2005. We obtained data on 47 objects, 23 belonging to the L5 swarm and 24 to the L4 one. These data together with those already published by Fornasier et al. [Fornasier, S., Dotto, E., Marzari, F., Barucci, M.A., Boehnhardt, H., Hainaut, O., de Bergh, C., 2004a. Icarus 172, 221-232] and Dotto et al. [Dotto, E., Fornasier, S., Barucci, M.A., Licandro, J., Boehnhardt, H., Hainaut, O., Marzari, F., de Bergh, C., De Luise, F., 2006. Icarus 183, 420-434], acquired since November 2002, constitute a total sample of visible spectra for 80 objects. The survey allows us to investigate six families (Aneas, Anchises, Misenus, Phereclos, Sarpedon, Panthoos) in the L5 cloud and four L4 families (Eurybates, Menelaus, 1986 WD and 1986 TS6). The sample that we measured is dominated by D-type asteroids, with the exception of the Eurybates family in the L4 swarm, where there is a dominance of C- and P-type asteroids. All the spectra that we obtained are featureless with the exception of some Eurybates members, where a drop-off of the reflectance is detected shortward of 5200 Å. Similar features are seen in main belt C-type asteroids and commonly attributed to the intervalence charge transfer transition in oxidized iron. Our sample comprises fainter and smaller Trojans as compared to the literature's data and allows us to investigate the properties of objects with estimated diameter smaller than 40-50 km. The analysis of the spectral slopes and colors versus the estimated diameters shows that the blue and red objects have indistinguishable size distribution, so any relationship between size and spectral slopes has been found. To fully investigate the Trojans population, we include in our analysis 62 spectra of Trojans available in literature, resulting in a total sample of 142 objects. Although the mean spectral behavior of L4 and L5 Trojans is indistinguishable within the uncertainties, we find that the L4 population is more heterogeneous and that it has a higher abundance of bluish objects as compared to the L5 swarm. Finally, we perform a statistical investigation of the Trojans's spectra property distributions as a function of their orbital and physical parameters, and in comparison with other classes of minor bodies in the outer Solar System. Trojans at lower inclination appear significantly bluer than those at higher inclination, but this effect is strongly driven by the Eurybates family. The mean colors of the Trojans are similar to those of short period comets and neutral Centaurs, but their color distributions are different.     

Asteroid photometric and polarimetric phase curves: empirical interpretation

A method for interpretation of asteroid phase curves, based on empirical modeling and laboratory measurements, is outlined and preliminary results are presented. A linear-exponential function is used to describe the opposition peaks and negative polarization surges of various asteroids and laboratory samples and a statistical algorithm is used in parameter estimation. The linear-exponential function describes well the phase curves, but dense phase angle coverage, particularly at small phase angles must be obtained to improve the results. Major emphasis should also be put on laboratory study: with an extensive library of laboratory measurements, a stronger connection between the phase curve properties and surface characteristics is possible.     

Significance analysis of asteroid pairs

We have studied statistical significance of asteroid pairs residing on similar heliocentric orbits with distances (approximately the current relative encounter velocity between orbits) up to in the five-dimensional space of osculating elements. We found candidate pairs from the Hungaria zone through the entire main belt as well as outside the main belt, one among Hildas and one in the Cybele zone. We first determined probability that the candidate pairs are just coincidental couples from the background asteroid population. Those with estimated probability <0.3 were further investigated. In particular we computed synthetic proper elements for the relevant asteroids and used them to determine the three-dimensional distance of the members in candidate pairs. We consider small separation in the proper-element space as a signature of a real asteroid pair; conversely, cases with large separation in the proper-element space were rejected as spurious. Finally, we provide a list of candidate pairs that appear real, genetically related, to facilitate targeted studies, such as photometric and spectroscopic observations. As a by-product, we discovered six new compact clusters of three or more asteroids. Initial backward orbit integrations suggest that they are young families with ages <2 Myr.     

Photometric observations of 107P/Wilson-Harrington

We present lightcurve observations and multiband photometry for 107P/Wilson-Harrington using five small- and medium-sized telescopes. The lightcurve has shown a periodicity of 0.2979 day (7.15 h) and 0.0993 day (2.38 h), which has a commensurability of 3:1. The physical properties of the lightcurve indicate two models: (1) 107P/Wilson-Harrington is a tumbling object with a sidereal rotation period of 0.2979 day and a precession period of 0.0993 day. The shape has a long axis mode (LAM) of L₁:L₂:L₃ = 1.0:1.0:1.6. The direction of the total rotational angular momentum is around λ = 310°, β = −10°, or λ = 132°, β = −17°. The nutation angle is approximately constant at 65°. (2) 107P/Wilson-Harrington is not a tumbler. The sidereal rotation period is 0.2979 day. The shape is nearly spherical but slightly hexagonal with a short axis mode (SAM) of L₁:L₂:L₃ = 1.5:1.5:1.0. The pole orientation is around λ = 330°, β = −27°. In addition, the model includes the possibility of binary hosting. For both models, the sense of rotation is retrograde. Furthermore, multiband photometry indicates that the taxonomy class of 107P/Wilson-Harrington is C-type. No clear rotational color variations are confirmed on the surface.     

Photometric analysis of Eros from NEAR data

A photometric model of (433) Eros at wavelengths from 450 to 1050 nm is constructed using the combination of the images from the multispectral imager (MSI) obtained during the one-year long orbital phase of the NEAR mission, ground-based lightcurves from earlier observations, and our theoretical forward modeling simulations coupled with the NEAR shape model. The single scattering albedo is found to be 0.33±0.03 at 550 nm, which is smaller than past findings by 30%. The amplitude and width of the opposition effect are 1.4±0.1 and 0.010±0.004 from ground based lightcurves. It is confirmed that the asymmetry factor of the single-particle phase function and the surface roughness parameter do not depend on wavelength from 450 to 1050 nm, and their values are estimated to be −0.25±0.02 and 28°±3°, respectively, comparable with the earlier measurements from the NEAR NIS data. The geometric albedo and the Bond albedo at 550 nm are calculated to be 0.23 and 0.093, respectively, which make Eros less reflective than previous models, but still slightly more reflective than average S-type asteroids. The lower albedos of Eros are more consistent with our forward modeling simulations, as well as with its spectrum. Eros is a typical S-type asteroid like (951) Gaspra and (243) Ida, and has similar surface regolith properties. Combining the single-scattering albedo with the olivine composition of ordinary chondrites, taking into account space weathering darkening, we constrain the grain size of the regolith particles on Eros to a range of 50 to 100 μm.     

A three-parameter magnitude phase function for asteroids

We develop a three-parameter H, G₁, G₂ magnitude phase function for asteroids starting from the current two-parameter H, G phase function. We describe stochastic optimization of the basis functions of the magnitude phase function based on a carefully chosen set of asteroid photometric observations covering the principal types of phase dependencies. We then illustrate the magnitude phase function with a chosen set of observations. It is shown that the H, G₁, G₂ phase function systematically improves fits to the existing data and considerably so, warranting the utilization of three parameters instead of two. With the help of the linear three-parameter phase function, we derive a nonlinear two-parameter H, G₁₂ phase function, and demonstrate its applicability in predicting phase dependencies based on small numbers of observations.     

Collisional evolution of the asteroid belt

A new synthesis of asteroid collisional evolution is motivated by the question of whether most asteroids larger than ∼1 km size are strengthless gravitational aggregates (rubble piles). NEAR found Eros not to be a rubble pile, but a shattered collisional fragment, with a through-going fracture system, and an average of about 20 m regolith cover. Of four asteroids visited by spacecraft, none appears likely to be a rubble pile, except perhaps Mathilde. Nevertheless, current understanding of asteroid collisions and size-dependent strength, and the observed distribution of rotation rates versus size, have led to a theoretical consensus that many or most asteroids larger than 1 km should be rubble piles. Is Eros, the best-observed asteroid, highly unusual because it is not a rubble pile? Is Mathilde, if it is a rubble pile, like most asteroids? What would be expected for the small asteroid Itokawa, the MUSES-C sample return target? An asteroid size distribution is synthesized from the Minor Planet Center listing and results of the Sloan Digital Sky Survey, an Infrared Space Observatory survey, the Small Main-belt Asteroid Spectroscopic Survey and the Infrared Astronomical Satellite survey. A new picture emerges of asteroid collisional evolution, in which the well-known Dohnanyi result, that the size distribution tends toward a self-similar form with a 2.5-index power law, is overturned because of scale-dependent collision physics. Survival of a basaltic crust on Vesta can be accommodated, together with formation of many exposed metal cores. The lifetimes against destruction are estimated as 3 Gyr at the size of Eros, 10 Gyr at ten times that size, and 40 Gyr at the size of Vesta. Eros as a shattered collisional fragment is not highly unusual. The new picture reveals the new possibility of a transition size in the collisional state, where asteroids below 5 km size would be primarily collisional breakup fragments whereas much larger asteroids are mostly eroded or shattered survivors of collisions. In this case, well-defined families would be found in asteroids larger than about 5 km size, but for smaller asteroids, families may no longer be readily separated from a background population. Moreover, the measured boulder size distribution on Eros is re-interpreted as a sample of impactor size distributions in the asteroid belt. The regolith on Eros may result largely from the last giant impact, and the same may be true of Itokawa, in which case about a meter of regolith would be expected there. Even a small asteroid like Itokawa may be a shattered object with regolith cover.