Models of Twenty Asteroids from Photometric Data

We present models of the shapes and rotational states of selected asteroids based on data from the Uppsala Asteroid Photometric Catalogue. The results show a wide variety of shapes especially among the smaller asteroids. Few asteroids show clear signs of significant albedo variegation. Most rotational states are in reasonable agreement with those previously estimated with rough models. We discuss some practical aspects of photometric analysis and present a simple way of building one-spot models.     

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.     

Determination of rotational parameters of asteroid (360) Carlova

Information on the rotational parameters of asteroids may provide data for research on the collision and evolution of asteroids, or even the evolution of the solar system. We carried out new CCD photometric observation of the main belt carbon-type asteroid (360) Carlova with the 1-m telescope of Yunnan Observatory, and obtained the following results:. rotational sidereal period, 0.25780417 ± 0.00000003d, ecliptic coordinates of the rotating axis, (95°±3°, 40°±1°). These are found by using the epoch-method of retrieval with our and previously published photometric data. Our results are consistent with those of our predecessors, while being slightly more accurate.     

Observation Plan for Refining Shape Model of (6) HEBE

As the number of observatories located on the surface of Earth is increasing largely in decades more and more photometric data of asteroids is observed to make the research about their various physical and chemical characteristics. Compared with hundreds of thousands of asteroids found up to now, rare hundreds of three-dimensional shape models of asteroids have been built from the tremendous photometric data with incessant observations, i.e. lightcurves. For some specific asteroid already with many observed lightcurves, the unceasing observation is not too much valuable, nevertheless an additional lightcurve observed in a request viewing aspect can refine the shape model and other related parameters. This article taking the asteroid (6) HEBE for example, attempts to introduce a method to make the observation plan by combining the request of the shape model and the orbital limitation of asteroids. Through analyzing the distribution of lightcurves of (6) HEBE, small cabins without any lightcurve data are found, which can be filled by new observations at some specified dates when the positions of Asteroid, Sun, Earth are limited as the request geometry.     

Flattening,pole, and albedo features of 4 vesta from photometric data

A number of large asteroids show irregular lightcurves of relatively small amplitude and/or ambiguous rotational periods. These observations and the fact that their strong gravitational binding probably results in quasi-equilibrium shapes lead to model these bodies as axisymmetric, biaxial ellipsoids covered by albedo markings. We developed a general numerical algorithm for obtaining simulated lightcurves of “spotted” asteroids and varied the most critical geometrical and physical parameters (albedo contrast, size, and position of the spots; polar coordinates, and shape of the asteroid). We then analyzed the case of 4 Vesta by assuming an axisymmetric ellipsoidal shape with a large brighter region on one hemisphere, in agreement with the results of photometric and polarimetric observations. Fitting the numerical simulations to the available data, we obtained the flattening of the ellipsoid (0.79 ± 0.03), the albedo contrast and geometry of the brighter region, and the orientation of the polar axis. If the derived flattenning corresponds to the equilibrium shape of a nearly homogeneous body, a density of 2.4 ± 0.3 g cm⁻³ can be inferred. These results show satisfactory agreement with values by different techniques. We plan to apply the same method both to other large asteroids and to smaller, irregularly shaped ones; in the latter case, this will allow us to test the uncertainties in current pole determination methods.     

Near-infrared spectrophotometry of Asteroid 25143 Itokawa from NIRS on the Hayabusa spacecraft

A photometric analysis of the S-type Asteroid 25143 Itokawa is performed over multiple wavelengths ranging from 0.85 to 2.10 μm based on disk-resolved reflectance spectra obtained with the Hayabusa near-infrared spectrometer (NIRS). We derive the global photometric properties of Itokawa in terms of Hapke's photometric model. We find that Itokawa has a single-scatter albedo that is 35-40% less than that of Asteroid 433 Eros. Itokawa also has a single-particle phase function that is more strongly back-scattering than that of Eros. Despite its hummocky surface strewn with large boulders, Itokawa exhibits an opposition effect. However, the total amplitude of the opposition surge for Itokawa was estimated to be less than unity while Eros and other S-type asteroids have been found to have model values exceeding unity. The wavelength dependence of the opposition surge width reveals that coherent backscatter contributes to the opposition effect on Itokawa's surface. The photometric roughness of Itokawa is well constrained to a value of 26° ± 1° which is similar to Eros, suggesting that photometric roughness models the smallest surface roughness scale for which shadows exist.     

Shape, size and multiplicity of main-belt asteroids: I. Keck Adaptive Optics survey

This paper presents results from a high spatial resolution survey of 33 main-belt asteroids with diameters >40 km using the Keck II Adaptive Optics (AO) facility. Five of these (45 Eugenia, 87 Sylvia, 107 Camilla, 121 Hermione, 130 Elektra) were confirmed to have satellite. Assuming the same albedo as the primary, these moonlets are relatively small (∼5% of the primary size) suggesting that they are fragments captured after a disruptive collision of a parent body or captured ejecta due to an impact. For each asteroid, we have estimated the minimum size of a moonlet that can positively detected within the Hill sphere of the system by estimating and modeling a 2-σ detection profile: in average on the data set, a moonlet located at 2/100×RHill (1/4×RHill) with a diameter larger than 6 km (4 km) would have been unambiguously seen. The apparent size and shape of each asteroid was estimated after deconvolution using a new algorithm called AIDA. The mean diameter for the majority of asteroids is in good agreement with IRAS radiometric measurements, though for asteroids with a D<200 km, it is underestimated on average by 6-8%. Most asteroids had a size ratio that was very close to those determined by lightcurve measurements. One observation of 104 Klymene suggests it has a bifurcated shape. The bi-lobed shape of 121 Hermione described in Marchis et al. [Marchis, F., Hestroffer, D., Descamps, P., Berthier, J., Laver, C., de Pater, I., 2005c. Icarus 178, 450-464] was confirmed after deconvolution. The ratio of contact binaries in our survey, which is limited to asteroids larger than 40 km, is surprisingly high (∼6%), suggesting that a non-single configuration is common in the main-belt. Several asteroids have been analyzed with lightcurve inversions. We compared lightcurve inversion models for plane-of-sky predictions with the observed images (9 Metis, 52 Europa, 87 Sylvia, 130 Elektra, 192 Nausikaa, and 423 Diotima, 511 Davida). The AO images allowed us to determine a unique photometric mirror pole solution, which is normally ambiguous for asteroids moving close to the plane of the ecliptic (e.g., 192 Nausikaa and 52 Europa). The photometric inversion models agree well with the AO images, thus confirming the validity of both the lightcurve inversion method and the AO image reduction technique.     

Scattering Law Analysis Based on Hapke and Lommel-Seeliger Models for Asteroidal Taxonomy

In deriving the physical properties of asteroids from their photometric data, the scattering law plays an important role, although the shape variations of asteroids result in the main variations in lightcurves. By following the physical behaviors of light reflections, Hapke et al. deduced complex functions to represent the scattering process, however, it is very hard to accurately simulate the surface scattering law in reality. For simplicity, other numerical scattering models are presented for efficiently calculating the physical properties of asteroids, such as the Lommel-Seeliger(LS) model. In this article,these two models are compared numerically. It is found that in some numerical applications the LS model in simple form with four parameters can be exploited to replace the Hapke model in complex form with five parameters. Furthermore, the generated synthetic lightcurves by the Cellinoid shape model also show that the LS model can perform as well as the Hapke model in the inversion process. Finally, by applying the Principal Component Analysis(PCA) technique to the parameters of the LS model, we present an efficient method to classify C and S type asteroids, instead of the conventional method using the parameters of the Hapke model.     

The Rotational Periods of Three C-Type Asteroids 431, 521 and 524

The determination for asteroids’ spin parameters is very important for the physical study of asteroids and their evolution. Sometimes, the low amplitude of light curves and kinds of systematic errors in photometric data prevent the determination of the asteroids’ spin period. To solve such a problem, we introduced the de-correlation methods developed in searching for exoplanetary transit signal into the asteroid’s data reduction in this paper. By applying the principle of Collier Cameron (MNRAS 373:799–810, 2006) and Tamuz et al. (MNRAS 356:1466–1470, 2005)’s, we simulated the systematic effects in photometric data of asteroid, and removed those simulated errors from photometric data. Therefore the S/N of intrinsic signals of three selected asteroids are enhanced significantly. As results, we derived the new spin periods of 18.821 ± 0.011 h, 28.202 ± +0.071 h for (431) and (521) respectively, and refined the spin period of (524) as 14.172 ± 0.016 h.     

Asteroid photometric and polarimetric phase curves: Joint linear‐exponential modeling

Abstract— We present Markov‐Chain Monte‐Carlo methods (MCMC) for the derivation of empirical model parameters for photometric and polarimetric phase curves of asteroids. Here we model the two phase curves jointly at phase angles ≤25° using a linear‐exponential model, accounting for the opposition effect in disk‐integrated brightness and the negative branch in the degree of linear polarization. We apply the MCMC methods to V‐band phase curves of asteroids 419 Aurelia (taxonomic class F), 24 Themis (C), 1 Ceres (G), 20 Massalia (S), 55 Pandora (M), and 64 Angelina (E). We show that the photometric and polarimetric phase curves can be described using a common nonlinear parameter for the angular widths of the opposition effect and negative‐polarization branch, thus supporting the hypothesis of common physical mechanisms being responsible for the phenomena. Furthermore, incorporating polarimetric observations removes the indeterminacy of the opposition effect for 1 Ceres. We unveil a trend in the interrelation between the enhancement factor of the opposition effect and the angular width: the enhancement factor decreases with decreasing angular width. The minimum polarization and the polarimetric slope at the inversion angle show systematic trends when plotted against the angular width and the normalized photometric slope parameter. Our new approach allows improved analyses of possible similarities and differences among asteroidal surfaces.     

Asteroid spin‐axis longitudes from the Lowell Observatory database

By analyzing brightness variation with ecliptic longitude and using the Lowell Observatory photometric database, we estimate spin‐axis longitudes for more than 350,000 asteroids. Hitherto, spin‐axis longitude estimates have been made for fewer than 200 asteroids. We investigate longitude distributions in different dynamical groups and asteroid families. We show that asteroid spin‐axis longitudes are not isotropically distributed as previously considered. We find that the spin‐axis longitude distribution for Main Belt asteroids is clearly nonrandom, with an excess of longitudes from the interval 30°–110° and a paucity between 120° and 180°. The explanation of the nonisotropic distribution is unknown at this point. Further studies have to be conducted to determine if the shape of the distribution can be explained by observational bias, selection effects, a real physical process, or other mechanism.     

CCD-photometry and pole coordinates for eight asteroids

The long time photometric observations were carried out for eight asteroids: (122) Gerda, (153) Hilda, (190) Ismene, (221) Eos, (411) Xanthe, (679) Pax, (700) Auravictrix, (787) Moskva. New rotation periods have been determined for the asteroids (153) Hilda (5.959 h) and (411) Xanthe (11.408 h), and known rotation periods for some of the others have been confirmed. Using our data and others data we have estimated new pole coordinates for the observed asteroids.     

Current problems of dynamics of moons of planets and binary asteroids based on observations

The general approach to studying the dynamics of moons of planets and asteroids consists in developing more and more accurate models of motion based on observational data. Not only the necessary ephemerides, but also some physical parameters of planets and moons are obtained this way. It is demonstrated in the present study that progress in this field is driven not only by the increase in accuracy of observations. The accuracy of ephemerides may be increased by expanding the observation time interval. Several problems arise on the way toward this goal. Some of them become apparent only when the procedure of observational data processing and use is examined in detail. The method used to derive astrometric data by processing the results of photometric observations of mutual occultations and eclipses of planetary moons is explained below. The primary contribution to the error of astrometric results is produced by the unaccounted noise level in photometric readings and the inaccuracy of received values of the albedo of moons. It is demonstrated that the current methods do not allow one to eliminate the noise completely. Extensive additional photometric measurements should be performed at different angles of rotation of moons and in different spectral bands of the visible wavelength range in order to obtain correct values of the albedo of moons. Many new distant moons of the major planets have been discovered in the early 21st century. However, the observations of these moons are scarce and were performed over short time intervals; as a result, some of the moons were lost. The necessity of further observations of these Solar System bodies is pointed out in the present study. Insufficient knowledge of asteroid masses is an obstacle to improving the accuracy of the ephemerides of Mars. The basic method for determining the masses of large asteroids consists in analyzing their influence on the motion of Mars, the Earth, and spacecraft. The masses of more than 100 large asteroids were determined this way. One of the principal techniques for Earth-based measurement of the masses of asteroids involves astrometric observations of binary asteroids. The determination of relative coordinates is made rather difficult by the apparent proximity of components. The success of these efforts depends on the availability of instrumentation and the expertise of observers skilled in adaptive optics and speckle interferometry. Collaboration between different research teams and observers is absolutely necessary.     

Surface composition of Hilda asteroids from the analysis of the Sloan Digital Sky Survey colors

In this paper we search for photometric data of asteroids in the Hilda region in the Moving Object Catalogue of the Sloan Digital Sky Survey to find the spectral characteristics of small members of this group. We found that the correlation between size and spectral slope previously suggested for Hilda asteroids is correct only for large objects (H<12) but it is not supported by data obtained for the small ones. The best possibility to explain this behavior is that a space weathering process affecting the surface properties of these primitive objects is operating, modulated by a collisional resurfacing process affected by the lack of small projectiles in the population. Despite the intrinsic limitations of the few band photometry of the Sloan Digital Sky Survey, the analysis presented is based mainly in the detection of spectral slopes providing enough good indication about the taxonomic type of these asteroids and making us confident about our conclusions.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

Asteroid observations at low phase angles: III. Brightness behavior of dark asteroids

The results of photometric observations of eight main-belt asteroids with low surface albedo are presented. The magnitude-phase dependences including low phase angles (<1 deg) have been obtained for Asteroids 76 Freia (down to phase angle 0.1 deg, P-type), 190 Ismene (0.3 deg, P-type), 303 Josephina (0.2 deg, C-type), 309 Fraternitas (0.1 deg, C-type), 313 Chaldaea (0.1 deg, C-type), 444 Gyptis (0.8 deg, P-type), 615 Roswitha (0.1 deg, C-type), and 954 Li (0.03 deg, FCX-type). The behavior of brightness in the range of opposition effect is found to be practically linear for 190 Ismene with amplitude of opposition effect only 0.03 mag. Amplitudes of the opposition effect for other asteroids are close to a mean for this type. The obtained data allowed us also to determine the rotation periods of asteroids: 303 Josephina (12.497±0.001 h), 309 Fraternitas (11.205±0.005 h), 615 Roswitha (4.422±0.001 h) and 954 Li (7.207±0.002 h). The color indexes B-V, V-R and R-I have been determined for some asteroids.     

Physical characteristics of Hayabusa target Asteroid 25143 Itokawa

In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.     

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.     

Some results from the National Observatory of Turkey, Kazan State University, and Nikolaev Astronomical Observatory on small bodies of the solar system

A scientific collaboration between TÜB?TAK National Observatory (Turkey), Kazan State University (Russia) and Nikolaev Astronomical Observatory (Ukraine) involves observations of minor planets and near-Earth asteroids (NEAs) with the 1.5 m Russian-Turkish telescope (RTT150). Regular observations of selected asteroids in the range of 11-18 magnitudes began in 2004 with the view of determining masses of selected asteroids, improving the orbits of the NEAs, and studying physical characteristics of selected asteroids from photometric observations. More than 3000 positions of 53 selected asteroids and 11 NEAs have been obtained with an internal error in the range of 30-300 mas for a single determination. Photometric reductions of more than 4000 CCD frames are in progress. Masses of 21 asteroids were estimated through dynamical method using the ground-based optical observations, mainly from the RTT150 and Minor Planet Center. A comparison of the observational results from the RTT150 in 2004-2005 with observations of the same objects at other observatories allows us to conclude that RTT150 can be used for ground-based support in astrometry for the space mission GAIA.