Study of photometric phase curve: assuming a cellinoid ellipsoid shape for asteroid(106) Dione

We carried out new photometric observations of asteroid(106) Dione at three apparitions(2004, 2012 and 2015) to understand its basic physical properties. Based on a new brightness model,new photometric observational data and published data of(106) Dione were analyzed to characterize the morphology of Dione's photometric phase curve. In this brightness model, a cellinoid ellipsoid shape and three-parameter(H, G_1, G_2) magnitude phase function system were involved. Such a model can not only solve the phase function system parameters of(106) Dione by considering an asymmetric shape of an asteroid, but also can be applied to more asteroids, especially those without enough photometric data to solve the convex shape. Using a Markov Chain Monte Carlo(MCMC) method, Dione's absolute magnitude of H = 7.66_(-0.03)~(+0.03) mag, and phase function parameters G_1= 0.682_(-0.077)~(+0.077) and G_2= 0.081_(-0.042)~(+0.042) were obtained. Simultaneously, Dione's simplistic shape, orientation of pole and rotation period were also determined preliminarily.     

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.     

Peculiar shapes of asteroids: Implications for light curves and periods of rotation

This paper presents some simple geometrical models of asteroids with theoretical light curves similar to the observed ones. In some cases the results suggest rotation periods to be double those one can obtain adopting two- or three-axial ellipsoids as models.A possible model, not in terms of a binary system, for asteroids with light curves like those of eclipsing binary stars, is also given.It should be stressed that the models studied in this paper are probably not very similar to real asteroids, but the principal conclusions should not be changed when more sophisticated models are considered.The work is to be a starting point for future researches on laboratory models of asteroids, in order to define, in a quantitative way, how the light curves are affected by the surface roughness and/or the large scale irregularities of the shape of an asteroid.     

Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite

Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body–full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (\fracbd, \fraccd){\left(\frac{b}{d}, \frac{c}{d}\right)} where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.     

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.     

Light Scattering from Regolith: Intensity Versus Particle Size Behavior

Nature of the photometric phase curves of the regolith like surfaces (like those of the asteroids) are believed to be dependent on the single particle characteristics like particle size, shape, composition etc. and physical characteristics of the surface like porosity and roughness. Most of the phase curves have a rapid surge of intensity at small phase angles (typically below 5^°) known as opposition effect, followed by a linear less decreasing trend at larger phase angles. Average intensity of the linear region has been found to be mostly dependent on the average particle size and its composition, in many laboratory observations. Generally, it is difficult to explain the nature of light scattering by an ensemble of irregular shaped inhomogeneous particles with a theoretical model, just by studying the phase curves. In the present work, we have investigated whether the theoretically expected variation of the scattered light intensity (at a given phase angle) with the average particle size of the grains constituting regoliths, for a given material of the particle is in agreement with the experimental results or not? If yes, this can be a simpler but efficient way to study light scattering by regolith like surfaces. For theoretical analysis, Hapke formula has been used with Mie theory for single particle phase function, where we have neglected the influence of porosity and roughness presently. The data are also fitted with an empirical formula. It has been found that this empirical formula may also be used to estimate the unknown average particle size of a real regolith with known composition.     

Stability of Surface Motion on a Rotating Ellipsoid

The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid.     

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.     

An Analysis of Gsc0008.324, Newly Discovered Binary Star

A separate solution of the R *light curves was carried out using the 1998version of the Wilson's synthetic light curve code. In this paper we considered observations of Robb et al. (1999) for analysis. The photometry showed that star exhibits variable and asymmetric light curve. The asymmetric in the light curve is fitted with a spot on the surface of the hotter component. The fundamental orbital and physical parameters of this system have determined. The mass ratio is defined to be always q ≤ 1. The results indicate that the system is a late-type detached binary so that the components seem to be a very close pair of dwarfs. This revised version was published online in July 2006 with corrections to the Cover Date.     

A computer study of EE Pegasi and CM Lacertae

Computer routines permit the solution of eclipsing binary light curves on the Russell Model. With additional automatic point plot routines, the operator has available all necessary supervisory control for an optimum solution. A solution of a synthetic light curve, whose parameters simulate those calculated for the physical system, is an important adjunct to test convergence properties of the physical system solution.Application to EE Peg determines values ofx _x andx _x even though secondary minimum is only 0.08 mag. deep. First order perturbation theory is used with the Russell Model to calculate a final triaxial ellipsoid model.Solution of the CM Lac light curve shows that the data require an occultation eclipse at primary minimum, in contrast to the available nomographic solution. The point plot routines demonstrate a substantial improvement effected by the computer solution and show that the latter technique can determine limb darkening coefficients in this partially-eclipsing system.Originally presented at the IAU Colloquium No. 16 held at the University of Pennsylvania, Philadelphia, U.S.A., September 8–11, 1971.     

An analysis of active close binaries (CB) based on photometric measurements

This is the first in a series of papers devoted to the actual problematics in the determination of orbital and physical parameters of active CB on the basis of the interpretation of photometric observations. One solves the problem in two stages: by obtaining a synthetic light curve in the case when the parameters of the corresponding CB model are givena priori (direct problem) and by determining the parameters of the given model for which the best fit between the synthetic light curve and the observations is achieved (inverse problem (see Djura?evi?, 1991). In the first article of the series one presents the basis of the model developed for the synthesis of asymmetric, deformed, light curves of active CB with spots on their components. The modelling of the CB systems is based on the principles orginated in the Wilson and Devinney (1971; hereafter referred to as WD) model for the synthesis of a light curve generalised to include also the case of a nonsynchronous rotation of the components. The shapes of the components correspond to the equipotentials in the Roche model so that the critical Roche limits can be filled up to an arbitrary degree. In a spherical-coordinate system the surfaces of the components are divided into a large number of elementary cells whose intensity and angular radiation distribution are determined by the star temperature. limb darkening, gravitational darkening, and by the effect of reflection in the system. The active regions are approximated with circular spots. The presence of spots (dark or hot) enables to explain the asymmetry and depressions on the light curves of active CB. The model enables to be also interpreted the light curves of classic CB (without spots).     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

DEM simulation of rotation-induced reshaping and disruption of rubble-pile asteroids

A Soft-Sphere Discrete Element Method (SSDEM) is used to simulate the rotational reshaping and disruption of cohesionless self-gravitating granular aggregates (as a representation of “rubble-pile” asteroids). Aggregates with spherical and ellipsoidal shapes are subjected to impulsive increments of their angular velocity to initiate a reshaping process leading up to the disruption of the aggregate. Internal stress fields are monitored during the process as well as critical angular velocities to initiate reshaping. In addition, the time evolution of other parameters such as filling fraction, angle of friction, mechanical energy, yield stress, semi-axes, density and mass dependence are also analysed. Several predictions from continuum theory are recovered in our simulations, in addition to further insight into the process by which cohesionless rubble piles can deform. Fundamentally different outcomes are found for frictionless grains and grains with surface friction modelled, verifying the importance of including such models in granular simulations. We find that the initiation of shape deformation is most consistently described by a Drucker–Prager failure criterion, which also provides an independent measure of the effective friction angle of our self-gravitating pile. Insight is also gained into the energetics of deformation, with most of the kinetic energy loss going into the deformation of the rubble pile, and a smaller component being internally dissipated. Finally, with this work we want to compare this computational approach with the theoretical predictions and, if possible, to mutually validate them.     

Modelling RR Lyrae pulsation: mission (im)possible?

In order to make an in-depth comparison between theory and observations, we analyse the light and velocity curves of various hydrodynamical models simulating RRab stars. The observations are represented by empirical formulae, derived in this and our earlier papers. It is shown that the overwhelming majority of the models tested do not follow the empirical relations regarding the shape of the light curves and the physical parameters. In almost all cases the luminosities predicted from the model light curves are significantly lower than the corresponding model values. The overall discrepancy of the models is an important indication of the limitation of the applicability of the present theoretical light and velocity curves in the determination of the physical parameters of these stars. In transforming the theoretical data to the observed light curves in V colour and in computing the observed radial velocities, it is shown that both bolometric correction and tracing the line-forming regions have considerable effects on the evaluation of the observed quantities. In an effort to resolve the discrepancy between theory and observations, it is suggested that a proper evaluation of the bolometric correction and radial velocity based on complete dynamical atmosphere models may be a useful step in this direction.     

Period variation and spot model for the W UMa type binary TY UMa

We present the full VRI light curves and the times of minima of TY UMa to provide a complete photometric solution and a long-term trend of period variation. The light curves show a high degree of asymmetry (the O'Connell effect). The maxima at 0.25 phase (Max I) are 0.021, 0.015, and 0.020 mag fainter than those at 0.75 phase (Max II) in V , R , and I , respectively. The period of TY UMa has varied in a sinusoidal way, superimposed on the long-term upward parabolic variation. The secularly increasing rate of the period is deduced as 1.83 s per century  ( P˙ / P =5.788×10^-10 d d^-1)  . The period of sinusoidal variation is about 57.4 yr. The spot model has been applied to fit the asymmetric light curves of TY UMa, to explain light variations. By changing only the spot parameters, the model light curves can fit the observed light curves for three epochs. This indicates that the variation of the spot location and size is the main reason for changing the shape of light curves, including two different maxima and the interchanging depths of occultation and transit minima.     

Shape of small solar system bodies

The morphometric parameters are examined for the shape of fragments of ordinary chondrites, iron meteorites, S- and C-class stony asteroids, metallic asteroids, and icy small bodies of the Solar System. All small Solar System bodies are shown to have, depending on their composition and, hence, physical and mechanical properties, a specific shape that is unique to a given composition. C-class asteroids, the strength of which is almost three times less than that of S asteroids, differ from the latter in their less elongated shape. No systematic change is observed in the morphometric parameters (increased roundness or sphericity) of small bodies of differing compositions depending on their mass, which suggests that the hypothesis of creep in small Solar System bodies is unlikely to be true. The absence of creep confirms that, regardless of their composition, all small Solar System bodies are solid elastic bodies having an ultimate strength (tensile strength and compressive strength) and a yield strength.     

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.     

Model orbits of asteroid 3040 Kozai

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.     

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.     

Laboratory simulation of photometric light curves of the asteroids

We report laboratory simulations of asteroid observations obtained using a specially designed apparatus SAM (the acronym stands for System for Asteroid Models).The aim of the experiment was to assess the geometrical and physical characteristics of an asteroidal body which may affect the shape of its light curve; and, in particular, the parameters which define asteroid orientation with respect to the observer, and the shape and surface morphology of the asteroids.The design and operation of the SAM is described in some detail and the first results obtained with models having a regular shape are presented and discussed.Istituto di Astrofisica Spaziale del CNR