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.     

Ellipsoidal geometry in asteroid thermal models: The standard radiometric model

This paper reports results of the incorporation of ellipsoidal geometry into the standard radiometric model for asteroids. For small departures from spherical shape the standard model using spherical geometry predicts fluxes in good agreement with ellipsoidal models. Large departures from spherical shape, however, can produce substantial differences in the calculated flux depending on the subsolar temperature and the wavelength of interest. The results derived here suggest that radiometric measurements of highly nonspherical, low-obliquity asteroids interpreted with spherical models result in systematically smaller diameter and higher albedos. In addition, non-spherical shape can also result in a systematic difference in the diameter of a particular asteroid derived from separate 10- and 20-μm flux measurements interpreted with spherical models. Thermal-infrared diurnal lightcurves calculated for ellipsoids have amplitudes that depend on wavelength as well as projected area, and phase curves calculated for ellipsoids are indistinguishable from those calculated for spheres.     

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.     

Equilibria and orbits around asteroid using the polyhedral model

In the current study, we use the polyhedral model to compute the potential of the asteroid. There are five equilibrium points in the gravitational field of the asteroid 283 Emma. We concluded that the zero-velocity surfaces and the equilibrium points change with the suppositive variation of the rotational speed of the asteroid. It is found that if the rotational speed equals a half as it is in present, the number of equilibrium points is also five. However, if the rotational speed equals twice as it is in present, there are only three equilibrium points left. Four different periodic orbits are calculated using the hierarchical grid searching method. We calculated characteristic multipliers of periodic orbits to investigate the stability of these periodic orbits. The orbit near the primary's equatorial plane is more likely to be stable when the separation/ primary-radius is a large number.     

Cassini-VIMS at Jupiter: solar occultation measurements using Io

We report unusual and somewhat unexpected observations of the jovian satellite Io, showing strong methane absorption bands. These observations were made by the Cassini VIMS experiment during the Jupiter flyby of December/January 2000/2001. The explanation is straightforward: Entering or exiting from Jupiter's shadow during an eclipse, Io is illuminated by solar light which has transited the atmosphere of Jupiter. This light, therefore becomes imprinted with the spectral signature of Jupiter's upper atmosphere, which includes strong atmospheric methane absorption bands. Intercepting solar light refracted by the jovian atmosphere, Io essentially becomes a “mirror” for solar occultation events of Jupiter. The thickness of the layer where refracted solar light is observed is so large (more than 3000 km at Io's orbit), that we can foresee a nearly continuous multi-year period of similar events at Saturn, utilizing the large and bright ring system. During Cassini's 4-year nominal mission, this probing technique should reveal information of Saturn's atmosphere over a large range of southern latitudes and times.     

Lunar occultation of Saturn. I. The diameters of Tethys,Dione, Rhea,Titan, and Iapetus

The diameters of Tethys, Dione, Rhea, Titan and Iapetus were determined from observations of their March 30, 1974, lunar occultations, made with the Mauna Kea 224 and 61 cm telescopes. Light curves were obtained simultaneously in four colors, and the difference between the time of occultation at the two telescopes provided a direct measurement of the slope of the lunar limb, found to be small in all cases. The satellite diameters were determined by least-squares fits of model occultation light curves to the data. In these fits the diameter and degree of limb darkening of the satellite are correlated variables, requiring the limb darkening to be specified before the diameter can be determined, or vice versa. However, for Titan the signal-to-noise ratio is sufficiently high to allow some assessment of the amount of limb darkening, which was found to be substantial. Titan's diameter must be at least 5800 km, much larger than the currently accepted value of 5000 km, making it the largest satellite in the solar system. This larger diameter implies a low mean density. For the other four satellites arguments are presented in favor of accepting the occultation diameters corresponding to limb darkened disks. Except for Titan, the lunar occultation diameters generally agree with previous diskmeter and radiometric determinations.     

Dynamical model of binary asteroid systems using binary octahedrons

We used binary octahedrons to investigate the dynamical behaviors of binary asteroid systems. The mutual potential of the binary polyhedron method is derived from the fourth order to the sixth order. The irregular shapes, relative orbits, attitude angles, as well as the angular velocities of the binary asteroid system are included in the model. We investigated the relative trajectory of the secondary relative to the primary, the total angular momentum and total energy of the system, the three-axis attitude angular velocity of the binary system, as well as the angular momentum of the two components. The relative errors of the total angular momentum and the total energy indicate that the calculation has a high precision. It is found that the influence of the orbital and attitude motion of the primary from the gravitational force of the secondary is obvious. This study is useful in understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system.     

Winds and the occultation experiment

The occulation experiment may be used to obtain dynamic meteorological information when performed from an orbiting spacecraft. It is shown that interpretation of refractivity data in this fashion does not require a composition, as normally used to obtain pressure, density and temperature profiles.     

Redetermination of the space weathering rate using spectra of Iannini asteroid family members

We have obtained moderate S/N (∼85) spectra at a realized resolution of R∼100 for 11 members of the Iannini family, until recently the youngest known family at under 5 million years of age [Nesvorný, D., Bottke, W.F., Levison, H.F., Dones, L., 2003. Astrophys. J. 591, 486-497, 720-771]. The spectra were acquired using the Echellette Spectrograph and Imager in its low-resolution prism mode on the Keck II telescope. The family members belong to the S-complex of asteroids with perhaps some K class members. The Iannini family members' average spectral slope, defined as the slope of the best-fit line constrained to pivot about 1 at 550 nm, is (0.30±0.04)/μm, matching the (0.26±0.03)/μm reported by Jedicke et al. [Jedicke, R., Nesvorný, D., Whiteley, R.J., Ivezi?, ?., Juri?, M., 2004. Nature 429, 275-277] using SDSS [Ivezi?, ?., Juri?, M., Lupton, R.H., Tabachnik, S., Quinn, T., 2002. In: Tyson, J.A., Wolff, S. (Eds.), Survey and Other Telescope Technologies and Discoveries. In: Proc. SPIE, vol. 4836. SPIE, Bellingham, pp. 98-103] color photometry. Using our spectra for this family as well as new observations of Karin family members [Vernazza, P., Birlan, M., Rossi, A., Dotto, E., Nesvorný, D., Brunetto, R., Fornasier, S., Fulchignoni, M., Renner, S., 2006. Astron. Astrophys. 460, 945-951] and new classifications of some older families we have revised the space weathering rate of S-complex asteroids originally determined by Jedicke et al. [Jedicke, R., Nesvorný, D., Whiteley, R.J., Ivezi?, ?., Juri?, M., 2004. Nature 429, 275-277]. Following Jedicke et al. [Jedicke, R., Nesvorný, D., Whiteley, R.J., Ivezi?, ?., Juri?, M., 2004. Nature 429, 275-277] we parameterize the space weathering rate of the principal component color of the spectrum (PC₁), which is correlated with the spectral slope, as PC₁(t)=PC₁(0)+ΔPC₁[1−exp−α(t/τ)]. Our revised rate suggests that the characteristic time scale for space weathering is τ=570±220 Myr and that new S-complex clusters will have an initial color of PC₁(0)=0.31±0.04. The revised time scale is in better agreement with lab measurements and our measurements support the use of space weathering as a dating method. Under the assumption that all the spectra should be identical, since the members all derive from the same parent body and are presumably covered with similar regolith, we combined them to obtain a high-S/N composite spectrum for the family. The combined spectrum is within the S-complex.     

Efficient intra- and inter-night linking of asteroid detections using kd-trees

The Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) under development at the University of Hawaii's Institute for Astronomy is creating the first fully automated end-to-end Moving Object Processing System (MOPS) in the world. It will be capable of identifying detections of moving objects in our solar system and linking those detections within and between nights, attributing those detections to known objects, calculating initial and differentially corrected orbits for linked detections, precovering detections when they exist, and orbit identification. Here we describe new kd-tree and variable-tree algorithms that allow fast, efficient, scalable linking of intra and inter-night detections. Using a pseudo-realistic simulation of the Pan-STARRS survey strategy incorporating weather, astrometric accuracy and false detections we have achieved nearly 100% efficiency and accuracy for intra-night linking and nearly 100% efficiency for inter-night linking within a lunation. At realistic sky-plane densities for both real and false detections the intra-night linking of detections into ‘tracks’ currently has an accuracy of 0.3%. Successful tests of the MOPS on real source detections from the Spacewatch asteroid survey indicate that the MOPS is capable of identifying asteroids in real data.     

Spots on asteroid surfaces: Research opportunities using ground-based instruments

We discuss possible mechanisms for the formation of albedo spots on asteroids. We infer that the most likely mechanisms are impact cratering and related processes. This is confirmed by the reflectance spectra of the asteroids 10 Hygiea, 135 Hertha, and 196 Philomela, the results of a spectral frequency analysis of the sizes of features on the surface of 4 Vesta and 21 Lutetia, and the estimates for the parameters of impact features.     

An analysis of Pluto occultation light curves using an atmospheric radiative-conductive model

We use a radiative-conductive model to least-squares fit Pluto stellar occultation light curve data. This model predicts atmospheric temperature based on surface temperature, surface pressure, surface radius, and CH₄ and CO mixing ratios, from which model light curves are to be calculated. The model improves upon previous techniques for deriving Pluto’s atmospheric thermal structure from stellar occultation light curves by calculating temperature (as a function of height) caused by heating and cooling by species in Pluto’s atmosphere, instead of a general assumption that temperature follows a power law with height or some other idealized function. We are able to fit for model surface radius, surface pressure, and CH₄ mixing ratio with one of the 2006 datasets and for surface pressure and CH₄ mixing ratio for other datasets from the years 1988, 2002, 2006, and 2008. It was not possible to fit for CO mixing ratio and surface temperature because the light curves are not sensitive to these parameters. We determine that the model surface radius, under the assumption of a stratosphere only (i.e. no troposphere) model in radiative-conductive balance, is . The CH₄ mixing ratio results are more scattered with time and are in the range of 1.8-9.4 × 10⁻³. The surface pressure results show an increasing trend from 1988 to 2002, although it is not as dramatic as the factor of 2 from previous studies.     

Planets in the asteroid belt

Abstract— The main asteroid belt has lost >99.9% of its solid mass since the time at which the planets were forming, according to models for the protoplanetary nebula. Here we show that the primordial asteroid belt could have been cleared efficiently if much of the original mass accreted to form planetsized bodies, which were capable of perturbing one another into unstable orbits. We provide results from 25 N‐body integrations of up to 200 planets in the asteroid belt, with individual masses in the range 0.017–0.33 Earth masses. In the simulations, these bodies undergo repeated close encounters which scatter one another into unstable resonances with the giant planets, leading to collision with the Sun or ejection from the solar system. In response, the giant planets' orbits migrate radially and become more circular. This reduces the size of the main‐belt resonances and the clearing rate, although clearing continues. If ～3 Earth masses of material was removed from the belt this way, Jupiter and Saturn would initially have had orbital eccentricities almost twice their current values. Such orbits would have made Jupiter and Saturn 10–100x more effective at clearing material from the belt than they are on their current orbits. The time required to remove 90% of the initial mass from the belt depends sensitively on the giant planets' orbits, and weakly on the masses of the asteroidal planets. 18 of the 25 simulations end with no planets left in the belt, and the clearing takes up to several hundred million years. Typically, the last one or two asteroidal planets are removed by interactions with planets in the terrestrial region     

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.     

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.     

The accurate determination of stellar angular diameters using broad-band stellar interferometry

The angular diameter of a star can be estimated from interferometric observations by fitting the data with the visibility function for a uniformly illuminated disc and then using published correction factors to convert the uniform-disc angular diameter to the limb-darkened angular diameter. The correction factors are strictly valid only for monochromatic light. We investigate the effect of using a broad bandwidth, and present a simple method for calculating broad-band correction factors from the monochromatic factors.
The technique of fitting the data with a uniform-disc visibility function is only useful for stars with compact atmospheres and 'typical' limb-darkening profiles. It should not be applied to stars with extended atmospheres or that show extreme limb darkening. These stars have visibility functions that are qualitatively different from a uniform-disc visibility function, so they can be distinguished observationally from compact-atmosphere stars.     

On the reduction of occultation light curves

In the first two sections of this paper, the two basic methods of reducing occultation light curves—curve fitting and inversion—are reviewed and compared. It is shown that the curve fitting methods have severe problems of nonuniqueness. In addition, in the case of occultation curves dominated by spikes, it is not clear that such solutions are meaningful. The inversion method does not suffer from these drawbacks. Methods of deriving temperature profiles from refractivity profiles are dealt with in the third section. It is shown that, although the temperature profiles are sensitive to small errors in the refractivity profile, accurate temperatures can be obtained, particularly at the deeper levels of the atmosphere. The final section contains a brief discussion of the ambiguities that arise when the occultation curve straddles the turbopause.     

An analysis of bending waves in Saturn's rings using voyager radio occultation data

The oblique geometry of the Voyager 1 radio occulation of Saturn's rings resulted in a strong coupling between the local slope of the ring midplane and the associated radio opacity (optical depth). We apply a model of this relationship to those regions of the rings where bending waves have been observed in the radio data. Using the Shu et al. linear model for a bending wave (F.H. Shu, J.N. Cuzzi, and J.J. Lissauer, 1983,Icarus53, 185–206), we obtain height profiles for the Mimas 5:3 and 7:4 bending waves. The first oscillation of the Mimas 5:3 bending wave has an amplitude of about 800 m, in agreement with the prediction of the Shu et al. model. However, the rest of the wave may be explained only by either a greatly decreased amplitude in the region beyond the second cycle, or by a significant enhancement in radio optical depth in the region of the bending wave. The shape of the enhancement necessary is similar to that of the enhancement at photopolarimetry wavelengths (L.W. Esposito, M. O'Callaghan, and R.A. West, 1983,Icarus56, 439–452), but differs in the region of the first cycle. Our solution gives 131,901±6 km as the resonance location, and a surface mass density of 35±6g cm⁻². The error bars on the resonance location do not include the uncertainty in the radial scale of the radio occultation data, which is approximately 10 km (R.A. Simpson, G.L. Tyler, and J.B. Holberg, 1983,Astron. J.88, 1531–1536). The Mimas 7:4 bending wave conforms more closely to the linear model, and requires no reduction in amplitude or enhancement in optical depth. We find a surface mass density of 30.5±9 g cm⁻², and resonance location at 127,765±7km.