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.     

Colors of dynamically associated asteroid pairs

Recent dynamical studies have identified pairs of asteroids that reside in nearly identical heliocentric orbits. Possible formation scenarios for these systems include dissociation of binary asteroids, collisional disruption of a single parent body, or spin-up and rotational fission of a rubble-pile. Aside from detailed dynamical analyses and measurement of rotational light curves, little work has been done to investigate the colors or spectra of these unusual objects. A photometric and spectroscopic survey was conducted to determine the reflectance properties of asteroid pairs. New observations were obtained for a total of 34 individual asteroids. Additional photometric measurements were retrieved from the Sloan Digital Sky Survey Moving Object Catalog. Colors or spectra for a total of 42 pair components are presented here. The main findings of this work are: (1) the components in the observed pair systems have the same colors within the uncertainties of this survey, and (2) the color distribution of asteroid pairs appears indistinguishable from that of all Main Belt asteroids. These findings support a scenario of pair formation from a common progenitor and suggest that pair formation is likely a compositionally independent process. In agreement with previous studies, this is most consistent with an origin via binary disruption and/or rotational fission.     

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.     

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.     

Simultaneous spectroscopic and photometric observations of binary asteroids

Abstract— We present results of visible wavelengths spectroscopic measurements (0.45 to 0.72 microns) of two binary asteroids, obtained with the 1‐m telescope at the Wise Observatory on January 2008. The asteroids 90 Antiope and 1509 Esclangona were observed to search for spectroscopic variations correlated with their rotation while presenting different regions of their surface to the viewer. Simultaneous photometric observations were performed with the Wise Observatory's 0.46 m telescope, to investigate the rotational phase behavior and possible eclipse events. 90 Antiope displayed an eclipse event during our observations. We could not measure any slope change of the spectroscopic albedo within the error range of 3%, except for a steady decrease in the total light flux while the eclipse took place. We conclude that the surface compositions of the two components do not differ dramatically, implying a common origin and history. 1509 Esclangona did not show an eclipse, but rather a unique lightcurve with three peaks and a wide and flat minimum, repeating with a period of 3.2524 hours. Careful measurements of the spectral albedo slopes reveal a color variation of 7 to 10 percent on the surface of 1509 Esclangona, which correlates with a specific region in the photometric lightcurve. This result suggests that the different features on the lightcurve are at least partially produced by color variations and could perhaps be explained by the existence of an exposed fresh surface on 1509 Esclangona.     

Rotational properties of asteroids: Correlations and selection effects

Rotational data on 321 asteroids observed as of late 1978 are analyzed. Selection effects within the sample are discussed and used to define a data set consisting of 134 main-belt, nonfamily asteroids having reliably determined periods and amplitudes based on photoelectric observations. In contrast to A. W. Harris and J. A. Burns (1979, Icarus40, 115–144) we found no significant correlation between rotational properties and compositional type. Smaller asteroids have a greater range of rotational amplitudes than the largest asteroids but are not, on the average, appreciably more elongated. While no definite relationship between asteroid size and rotation rate was found the distribution is not random. The largest asteroids have rotation periods near 7 hr compared with 10 hr for the smaller. A group of large, rapidly rotating, high-amplitude asteroids is recognized. A pronounced change in rotational properties occurs near this size range (diam = 200 ± 50 km) which also corresponds to the size at which a change of slope occurs in the size frequency distribution. We believe this size range represents a transition region between very large, rapidly rotating, low-amplitude (primordial?) objects and smaller ones having a considerably greater range of periods and amplitudes. Asteroids in this transition size range display an increase in rotational amplitude with increasing spin rate; other than this, however, there is no correlation between period and amplitude. The region of low spatial density in the asteroid belt centered near 2.9 AU and isolated from the inner and outer belt by the 2:5 and 3:7 commensurabilities is shown to be a region in which non-C or -S asteroids are overrepresented and which have marginally higher rotational amplitudes than those located in more dense regions. We attribute disagreements between our results and other studies of this type to the inclusion of non-main-belt asteroids and photographic data in the earlier analyses.     

Yarkovsky origin of the unstable asteroids in the 2/1 mean motion resonance with Jupiter

The 2/1 mean motion resonance with Jupiter, intersecting the main asteroid belt at ≈3.27  au, contains a small population of objects. Numerical investigations have classified three groups within this population: asteroids residing on stable orbits (i.e. Zhongguos), those on marginally stable orbits with dynamical lifetimes of the order of 100 Myr (i.e. Griquas), and those on unstable orbits. In this paper, we reexamine the origin, evolution and survivability of objects in the 2/1 population. Using recent asteroid survey data, we have identified 100 new members since the last search, which increases the resonant population to 153. The most interesting new asteroids are those located in the theoretically predicted stable island A, which until now had been thought to be empty. We also investigate whether the population of objects residing on the unstable orbits could be resupplied by material from the edges of the 2/1 resonance by the thermal drag force known as the Yarkovsky effect (and by the YORP effect, which is related to the rotational dynamics). Using N -body simulations, we show that test particles pushed into the 2/1 resonance by the Yarkovsky effect visit the regions occupied by the unstable asteroids. We also find that our test bodies have dynamical lifetimes consistent with the integrated orbits of the unstable population. Using a semi-analytical Monte Carlo model, we compute the steady-state size distribution of magnitude   H < 14  asteroids on unstable orbits within the resonance. Our results provide a good match with the available observational data. Finally, we discuss whether some 2/1 objects may be temporarily captured Jupiter-family comets or near-Earth asteroids.     

Asteroid observations at low phase angles. I. 50 Virginia, 91 Aegina and 102 Miriam

We present observations of magnitude-phase dependences of three low-albedo asteroids down to phase angles of 0.1–0.2°. Data were obtained during 40 nights from 1994 to 1995 within the joint observational program at ESO and Kharkiv Astronomical Observatories with the aim to reach as low phase angles as possible. All three low-albedo asteroids may display a small nonlinear increase in magnitude-phase dependence at subdegree phase angles. The phase curves of 50 Virginia and 102 Miriam are poorly approximated by the HG function. Rotation periods of the asteroids were also determined: 14.310±0.010 hours for 50 Virginia, 6.030±0.001 h for 91 Aegina and 15.789± 0.003 h for 102 Miriam.     

Asteroidal binary systems: Detection and formation

Recent occultation data and an analysis of some photometric lightcurves have shown the possible existence of asteroidal binary systems.A simple geometrical model taking into account mutual shadowing effects shows some peculiar features of the lightcurve which can be recovered in several previously observed objects; therefore the hypothesis of a relatively high frequency of binary asteroids should be seriously considered.On the other hand, while the rotational period distribution of large asteroids (D>200 km) is sharply peaked at about 5–8 hours, the surprisingly higher dispersion towards longer periods for intermediate size objects (50<D<150 km) could be connected with a larger probability of binary nature within this class.From a theoretical point of view, the collisional fragmentation of asteroids could originate gravitationally bound fragments, with a tidal transfer of rotational into orbital angular momentum, causing a rapid synchronization of the system. This kind of processes could more easily occur for intermediate objects since: (a) for large ones, very massive colliding bodies are needed for fragmentation, that means a very rare event; (b) for smaller asteroids, solid state interactions are stronger than the gravitational ones, so that a breakage probably causes a complete disruption of the gravitational binding. Further collisional events could disintegrate some systems, so that the present frequency of binary asteroids could be lower than that of the objects whose rotational period was increased by such processes.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Asteroid rotation: I. Tabulation and analysis of rates,pole positions and shapes

Data are presented for the 182 asteroids whose rotational properties are available in the literature. Plots are provided for the asteroid rotational frequency f and lightcurve amplitude Δm versus asteroid size; the latter is determined using standard methods if data are available but otherwise is estimated from asteroid albedos, selected depending on taxonomic type or orbital position. A linear least-squares fit to all the data shows that f increases with decreasing size, confirming McAdoo and Burns' (1973) result; this is demonstrated to be primarily caused by relatively more small non-C than C asteroids in our sample, coupled with a slower mean rotation rate for C asteroids (P ≈ 11 hr) than non-C asteroids (P ≈ 9 hr). In terms of the collisional theory of Harris (1979a), this means that the C's are less dense than the other minor planets. Any slight tendency for smaller asteroids to spin faster, even within a taxonomic type, could be due to selection effects; our data are not extensive enough to determine whether the very smallest (? 10-km diameter) spin especially fast. The minor planets of our survey become more irregular at smaller sizes, disputing the conclusions of Bowell (1977b), Degewij (1977), and Degewij et al. (1978), based on other, perhaps more complete, data; selection effects may account for this disagreement. Shapes do not appear to depend on taxonomic type. The dispersion of asteroid rotation rates from the mean is found to be in excellent agreement with a three-dimensional Maxwellian distribution, such as would be developed in a collisionally evolved system. The rotation axes, therefore, appear to be randomly oriented in space. Rotation pole positions are also tabulated and calculated to likely be constant in space over the extent of past observation. Observers are encouraged to measure the rotational properties of faint objects and asteroids of unusual taxonomic types, and to carry out long-time studies of asteroids which over short periods do not seem to vary.     

Asteroid Models from the Pan-STARRS Photometry

We present simulations on the asteroid photometric data that will be provided by the Pan-STARRS (Panoramic Survey Telescope and Rapid Response System). The simulations were performed using realistic shape and light-scattering models, random orientation of spin axes, and rotation periods in the range 2–24 h. We show that physical models of asteroids can be reconstructed from this data with some limitations (possible multiple pole solutions). We emphasize the potential of sparse photometric data to produce models of a large number of asteroids within the next decade and we outline further tests with fast and slow rotators, tumblers, and binary asteroids.     

Abodes for life in carbonaceous asteroids?

Thermal evolution models for carbonaceous asteroids that use new data for permeability, pore volume, and water circulation as input parameters provide a window into what are arguably the earliest habitable environments in the Solar System. Plausible models of the Murchison meteorite (CM) parent body show that to first-order, conditions suitable for the stability of liquid water, and thus pre- or post-biotic chemistry, could have persisted within these asteroids for tens of Myr. In particular, our modeling results indicate that a 200-km carbonaceous asteroid with a 40% initial ice content takes almost 60 Myr to cool completely, with habitable temperatures being maintained for ∼24 Myr in the center. Yet, there are a number of indications that even with the requisite liquid water, thermal energy sources to drive chemical gradients, and abundant organic “building blocks” deemed necessary criteria for life, carbonaceous asteroids were intrinsically unfavorable sites for biopoesis. These controls include different degrees of exothermal mineral hydration reactions that boost internal warming but effectively remove liquid water from the system, rapid (1-10 mm yr⁻¹) inward migration of internal habitable volumes in most models, and limitations imposed by low permeabilities and small pore sizes in primitive undifferentiated carbonaceous asteroids. Our results do not preclude the existence of habitable conditions on larger, possibly differentiated objects such as Ceres and the Themis family asteroids due to presumed longer, more intense heating and possible long-lived water reservoirs.     

Physical investigation of the potentially hazardous Asteroid (144898) 2004 VD17

In this paper we present the observational campaign carried out at ESO NTT and VLT in April and May 2006 to investigate the nature and the structure of the near-Earth object (144898) 2004 VD17. In spite of a great quantity of dynamical information, according to which it will have a close approach with the Earth in the next century, the physical properties of this asteroid are largely unknown. We performed visible and near-infrared photometry and spectroscopy, as well as polarimetric observations. Polarimetric and spectroscopic data allowed us to classify 2004 VD17 as an E-type asteroid. A good agreement was also found with the spectrum of the aubrite meteorite Mayo Belwa. On the basis of the polarimetric albedo (pv=0.45) and of photometric data, we estimated a diameter of about 320 m and a rotational period of about 2 h. The analysis of the results obtained by our complete survey have shown that (144898) 2004 VD17 is a peculiar NEO, since it is close to the breakup limits for fast rotator asteroids, as defined by Pravec and Harris [Pravec, P., Harris, A.W., 2000. Icarus 148, 12-20]. These results suggest that a more robust structure must be expected, as a fractured monolith or a rubble pile in a “strength regime” [Holsapple, K.A., 2002. Speed limits of rubble pile asteroids: Even fast rotators can be rubble piles. In: Workshop on Scientific Requirements for Mitigation of Hazardous Comets and Asteroids, Washington, September, 2002].     

Further evidence for collisions among asteroids

The 64 asteroids with reliably known rotational properties [rotation period P, magnitude B(1, 0) and maximum change of magnitude Δm] are studied. A plot of B(1,0) vs P illustrates that smaller asteroids tend to rotate faster than larger asteroids. The mean P for all 64 asteroids is 8.8 hr. The class of irregular asteroids (taken to be those with Δm >0.38, i.e., those whose axes differ by more than 40%) called group C are studied separately; they are shown to rotate much faster (mean P = 7.7 hr) than the remaining more regular asteroids (mean P = 9.2 hr). The smaller bodies are more irregular on the average. These results are interpreted in terms of a model in which collisions break asteroids into irregular fragments. Since angular momentum is transmitted in such collisions, significant increases in the mean can occur in the angular velocity of the largest fragment. The effect of interasteroid collisions on the mean orbital parameters is briefly discussed and is shown to be masked by selection effects.     

The rotation of small asteroids

The addition of the unbiased sample of R. P. Binzel and J. D. Mulholland (Icarus56, 519–533) nearly triples the sample size of photoelectrically determined rotational parameters for main belt asteroids with estimated diameters (D) ≤30 km. Nonparametric stattistical tests which require no assumptions about the distributions or variances of the samples are used to examine rotational parameters for all D ≤ 30 km asteroids. A comparison of photoelectric and photographic results shows that the techniques have a highly significant difference in the range of detected frequencies. This difference does not allow photographic and photoelectric observations to be combined for meaningful statistical tests since a photographic bias toward smaller sample variances can induce statistical results that appear overly significant. Photographic observations also show a highly significant bias toward detecting asteroids with larger lightcurve amplitudes. The fit of a Maxwellian to the observed rotational frequency distribution can be rejected at a highly significant confidence level but the observed distribution can be acceptably fit by two Maxwellian distributions, which is consistent with the hypothesis that there are separate populations of slow and fast rotating asteroids. The frequency distributions of <15 km main belt asteroids and Earth and Mars crossers are not found to differ significantly. However, the larger mean lightcurve amplitude of the Earth and Mars crossing asteroids is found to be statistically significant. This latter result is interesting in view of the lack of any strong inverse amplitude versus diameter relation for small asteroids. No significant diameter dependence on rotational frequency is seen among only D ≤ 30 km asteroids. However, the inverse frequency versus diameter relation for D ≤ 120 km asteroids found by S. F. Dermott, A. W. Harris, and C. D. Murray (Icarus, in press) is found to be statistically significant using a linear least-squares analysis of photoelectric data only. No significant diameter dependence on rotational lightcurve amplitude is seen using linear least-squares analysis of photoelectric data for D≤30 and D≤90 km asteroids. However, a significant inverse amplitude versus diameter relation is found when this analysis is extended to D≤120 km asteroids. This finding may be consistent with the hypothesis of Dermott et al. that near 120 km there is a transition between primordial asteroids and their collisional fragments.     

Spin rates of fast-rotating asteroids and fragments in impact disruption

We present a new experimental result of fragment spin-rate in impact disruption, using a thin glass plate. A cylindrical projectile impacts on a side (edge) of the plate. Dispersed fragments are observed using a high-speed camera and the spin rates of fragments are measured. We find that the measured fragment spin-rate decreases with increasing size. Assuming that the rotational energy of fragments is supplied from the residual stress, the spin rate ω decreases with increasing fragment size r as ω∼r−1, which explains the above experimental results. This size-dependence is similar to that of the observed spin rates of small fast-rotating asteroids. Our results suggest that spin rates of fragments of small asteroids immediately after disruption may have a similar size-dependence, and can provide constraints on the subsequent spin-state evolution of small asteroids due to thermal torques.     

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.     

YORP-Induced Long-Term Evolution of the Spin State of Small Asteroids and Meteoroids: Rubincam's Approximation

The rotation states of small asteroids and meteoroids are determined primarily by their collisions, gravitational torques due to the Sun and planets (in the case of close encounters), and internal dissipative effects (that relax the free-precession energy toward the fundamental state of principal-axis rotation). Rubincam has recently pointed out that thermal reemission on irregular-shaped bodies also results in a torque that may secularly change both the rotation rate and the orientation of the spin axis (the so-called YORP effect). Here we pursue investigation of this effect. Keeping the zero thermal-relaxation approximation of Rubincam and the assumption of the principal-axis rotation, we study the YORP effect both for precisely determined shapes of near-Earth asteroids and also for a large statistical sample of automatically generated shapes by the Gaussian-sphere technique of Muinonen. We find that the asymptotic state of the YORP evolution is characterized by an arbitrary value of the obliquity, with higher but nearly equal likelihood of 0°/180° and 90° states. At the adopted approximation, the most typical feature of this end state of the YORP evolution is secular deceleration of the rotation rate, which means that at some instant collisions will randomize the rotation state. In a minority of cases, the final state of the obliquity evolution leads to a permanent acceleration of the body's rotation, eventually resulting in rotational fission. The YORP-induced slow evolution may also play an important role in driving the rotation state of small asteroids toward the resonances between the forced precession due to the solar torque and perturbations of the orbital node and inclination. We find that for small Themis asteroids these resonances are isolated in the relevant range of frequencies, and the YORP evolving rotation may be either temporarily captured or rapidly jump across these resonances. In contrast, the possible values of the forced precession for small Flora asteroids may be resonant with clustered, nonisolated lines of the orbital perturbation. The individual rotation histories of small Flora asteroids may be thus very complicated and basically unpredictable. We comment on possible astronomical consequences of these results.     

First lightcurve observations and rotation of minor planet 127 Johanna

Photoelectric observations of the minor planet 127 Johanna were made in the UBV (RI)_c photometric system during its apparition in 1991 at the Piszkéstetõ mountain-station of Konkoly Observatory from August to December, when it showed a brightness variation with an amplitude of about 0.2 magnitude. The derived H, G values in the two-parameter magnitude system in V are 8.459 ± 0.013 and 0.114 ± 0.020, respectively. The determined V linear phase coefficient is of 0.036 ± 0.001 (mag/deg). The value of G and the observed values of color indices (U-B), (B-V) confirm that this asteroid belongs to the C taxonomic class as it was previously classified. The estimated effective diameter is between 96 and 118 km if the assumed V geometric albedo is of 0.06 and 0.04, respectively. The available data suggest a pure principal axis rotation mode. The mean synodic rotational period of the asteroid 127 Johanna is 6.94 ± 0.29 h. The uncertainty is due to the changing of aspect geometry. This value of the synodic rotation period means that this asteroid has an intermediate rotation period. The sense of rotation is prograde as indicated by the temporal evolution of the time derivative of the ecliptic longitude of the phase angle bisector as well as with the increasing synodic period of rotation during the same interval (October/November and December in 1991). The composite lightcurves created for short arc time data reveal structures with breakings and linear portions in V; this fact and the Fourier coefficients indicate a probably irregularly shaped body. There are slight indications that the B-V is redder close to the brightness minimum and the V-R_c is redder at the brightness maximum, and the periodic behavior cannot be proved in V-I_c. The less full rotational phase coverage of the observational data is insufficient to construct a shape model. The accurate pole orientation obviously cannot be determined using one opposition lightcurve data only. Further observations are required to get a more accurate knowledge of the physical parameters of this asteroid. For this purpose, a good opportunity to perform observations arose in December 1996, when this asteroid was in opposition at the northernmost declination.