J. Ďurech

DAMIT: a database of asteroid models

Context. Apart from a few targets that were directly imaged by spacecraft, remote sensing techniques are the main source of information about the basic physical properties of asteroids, such as the size, the spin state, or the spectral type. The most widely used observing technique ‐ time-resolved photometry ‐ provides us with data that can be used for deriving asteroid shapes and spin states. In the past decade, inversion of asteroid lightcurves has led to more than a hundred asteroid models. In the next decade, when data from all-sky surveys are available, the number of asteroid models will increase. Combining photometry with, e.g., adaptive optics data produces more detailed models. Aims. We created the Database of Asteroid Models from Inversion Techniques (DAMIT) with the aim of providing the astronomical community access to reliable and up-to-date physical models of asteroids ‐ i.e., their shapes, rotation periods, and spin axis directions. Models from DAMIT can be used for further detailed studies of individual objects, as well as for statistical studies of the whole set. Methods. Most DAMIT models were derived from photometric data by the lightcurve inversion method. Some of them have been further refined or scaled using adaptive optics images, infrared observations, or occultation data. A substantial number of the models were derived also using sparse photometric data from astrometric databases. Results. At present, the database contains models of more than one hundred asteroids. For each asteroid, DAMIT provides the polyhedral shape model, the sidereal rotation period, the spin axis direction, and the photometric data used for the inversion. The database is updated when new models are available or when already published models are updated or refined. We have also released the C source code for the lightcurve inversion and for the direct problem (updates and extensions will follow).

A study of asteroid pole-latitude distribution based on an extended set of shape models derived by the lightcurve inversion method

Context. In the past decade, more than one hundred asteroid models were derived using the lightcurve inversion method. Measured by the number of derived models, lightcurve inversion has become the leading method for asteroid shape determination. Aims. Tens of thousands of sparse-in-time lightcurves from astrometric projects are publicly available. We investigate these data and use them in the lightcurve inversion method to derive new asteroid models. By having a greater number of models with known physical properties, we can gain a better insight into the nature of individual objects and into the whole asteroid population. Methods. We use sparse photometry from selected observatories from the AstDyS database (Asteroids – Dynamic Site), either alone or in combination with dense lightcurves, to determine new asteroid models by the lightcurve inversion method. We investigate various correlations between several asteroid parameters and characteristics such as the rotational state and diameter or family membership. We focus on the distribution of ecliptic latitudes of pole directions. We create a synthetic uniform distribution of latitudes, compute the method bias, and compare the results with the distribution of known models. We also construct a model for the long-term evolution of spins. Results. We present 80 new asteroid models derived from combined data sets where sparse photometry is taken from the AstDyS database and dense lightcurves are from the Uppsala Asteroid Photometric Catalogue (UAPC) and from several individual observers. For 18 asteroids, we present updated shape solutions based on new photometric data. For another 30 asteroids we present their partial models, i.e., an accurate period value and an estimate of the ecliptic latitude of the pole. The addition of new models increases the total number of models derived by the lightcurve inversion method to ∼200. We also present a simple statistical analysis of physical properties of asteroids where we look for possible correlations between various physical parameters with an emphasis on the spin vector. We present the observed and de-biased distributions of ecliptic latitudes with respect to different size ranges of asteroids as well as a simple theoretical model of the latitude distribution and then compare its predictions with the observed distributions. From this analysis we find that the latitude distribution of small asteroids (D 60 km) exhibits an evident excess of prograde rotators, probably of primordial origin.

Thermo-physical properties of 162173 (1999 JU3), a potential flyby and rendezvous target for interplanetary missions

Context. Near-Earth asteroid 162173 (1999 JU3) is a potential flyby and rendezvous target for interplanetary missions because of its easy-to-reach orbit. The physical and thermal properties of the asteroid are relevant for establishing the scientific mission goals and also important in the context of near-Earth object studies in general. Aims. Our goal was to derive key physical parameters such as shape, spin-vector, size, geometric albedo, and surface properties of 162173 (1999 JU3). Methods. With three sets of published thermal observations (ground-based N-band, Akari IRC, Spitzer IRS), we applied a thermophysical model to derive the radiometric properties of the asteroid. The calculations were performed for the full range of possible shape and spin-vector solutions derived from the available sample of visual lightcurve observations. Results. The near-Earth asteroid 162173 (1999 JU3) has an effective diameter of 0.87 ± 0.03 km and a geometric albedo of 0.070 ± 0.006. The χ 2 -test reveals a strong preference for a retrograde sense of rotation with a spin-axis orientation of λ ecl = 73°, β ecl = -62° and P sid = 7.63 ± 0.01 h. The most likely thermal inertia ranges between 200 and 600 J m ―2 s ―0.5 K ―1 , about a factor of 2 lower than the value for 25143 Itokawa. This indicates that the surface lies somewhere between a thick-dust regolith and a rock/boulder/cm-sized, gravel-dominated surface like that of 25143 Itokawa. Our analysis represents the first time that shape and spin-vector information has been derived from a combined data set of visual lightcurves (reflected light) and mid-infrared photometry and spectroscopy (thermal emission).

Combining asteroid models derived by lightcurve inversion with asteroidal occultation silhouettes

Abstract 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.

Detection of the YORP effect in asteroid (1620) Geographos

Aims. The rotation state of small asteroids is affected by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) torque. The directly observable consequence of the YORP effect is the secular change of the asteroid’s rotation period. We carried out new photometric observations of asteroid (1620) Geographos in 2008 to extend the time line that, if long enough, would enable us to see possible deviations from a constant period rotation. Methods. We used the lightcurve inversion method to model the shape and spin state of Geographos. We assumed that the rotation rate evolves in time as ω(t) = ω0 + υt, where both the constant term of the rotation rate ω0 and the linear term υ are parameters to be optimized. In total, we used 94 lightcurves observed in 1969−2008. Results. We show that for υ = 0, a constant-period model, the whole dataset of lightcurves cannot be satisfactorily fitted. However, when relaxing υ in the optimization process we obtain an excellent agreement between the model and observations. The best-fit value υ = (1.15 ± 0.15) × 10 −8 rad d −2 implies that Geographos’ rotation rate accelerates by � 2. 7m s yr −1 . This is in agreement with the theoretically predicted value 1.4 × 10 −8 rad d −2 obtained from numerical integration of YORP torques acting on our convex shape model. Geographos is only the third asteroid (after (1862) Apollo and (54509) YORP) for which the YORP effect has been detected. It is also the largest object for which effects of thermal torques were revealed.

Photometric signatures of highly nonconvex and binary asteroids

We present an analysis of synthetic lightcurves of highly nonconvex single or synchronous binary asteroids, paying particular attention to the connection between the available solar phase angles and the observable degree of asteroid noncon- vexity. The measure of nonconvexity of an object is defined and computed for asteroids with known shapes. We discuss the possibility of recovering global nonconvexities or binary structure of an asteroid from its lightcurves. The importance of obser- vations at high solar phase angles is emphasized. For main-belt asteroids only binary or bifurcated shapes can be resolved (at least in a qualitative sense) - topologically star-like asteroids can be modelled as convex bodies. Concavities can be revealed only if an asteroid is observed at suciently high solar phase angles (>60) when shadowing eects from nonconvexities become important. This can be fulfilled only for near-Earth asteroids. Reconstruction of local topographic details is in practice precluded by the uncertainty of the light-scattering properties of the surface and the scarcity of very large phase angles.

Asteroid models from combined sparse and dense photometric data

Aims. Shape and spin state are basic physical characteristics of a n asteroid. They can be derived from disc-integrated photometry by the lightcurve inversion method. Increasing the number of asteroids with known basic physical properties is necessary to better understand the nature of individual objects as well as for studies of the whole asteroid population. Methods. We use the lightcurve inversion method to obtain rotation parameters and coarse shape models of selected asteroids. We combine sparse photometric data from the US Naval Observatory with ordinary lightcurves from the Uppsala Asteroid Photometric Catalogue and the Palmer Divide Observatory archive, and show that such combined data sets are in many cases suffi cient to derive a model even if neither sparse photometry nor lightcurves can be used alone. Our approach is tested on multiple-apparition lightcurve inversion models and we show that the method produces consistent results. Results. We present new shape models and spin parameters for 24 asteroids. The shape models are only coarse but describe the global shape characteristics well. The typical error in the pole directi on is∼ 10‐20 ◦ . For a further 18 asteroids, inversion led to a unique determination of the rotation period but the pole direction was not well constrained. In these cases we give only an estimate of the ecliptic latitude of the pole.

New photometric observations of asteroids (1862) Apollo and (25143) Itokawa - an analysis of YORP effect

Aims. Asteroid (1862) Apollo is one of two asteroids in which the YORP effect was detected. We carried out new photometric observations of Apollo in April 2007 to enlarge the time line and to derive a more precise shape and spin state model. We also observed another YORP-candidate, asteroid (25143) Itokawa, in December 2006 and January 2007 to obtain a longer time line. An estimation of the YORP strength on Itokawa based on its precise shape model from the Hayabusa mission predicted the deceleration to be already observable during the 2007 apparition. Methods. We used the lightcurve inversion method to model the shape and spin state of Apollo. For Itokawa, the shape and pole direction are known to a high degree of accuracy from the Hayabusa mission, so we used a modified version of lightcurve inversion with only two free parameters – the rotation period and its linear change in time. Results. The new model of Apollo confirms earlier results. The observed acceleration of Apollo’s rotation rate is (5.5 ± 1.2) × 10 −8 rad d −2 , which is in agreement with the theoretically predicted value. For Itokawa, the theoretical YORP value is sensitive to the resolution of the shape model and lies in the range from − 2t o−3 × 10 −7 rad d −2 . This is inconsistent with results of lightcurve inversion that place an upper limit to the change of Itokawa’s rotation rate ∼1.5 × 10 −7 rad d −2 .

Analysis of the rotation period of asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger - search for the YORP effect

Context. The spin state of small asteroids can change on a long timescale by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, the net torque that arises from anisotropically scattered sunlight and proper thermal radiation from an irregularly-shaped asteroid. The secular change in the rotation period caused by the YORP effect can be detected by analysis of asteroid photometric lightcurves. Aims. We analyzed photometric lightcurves of near-Earth asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger with the aim to detect possible deviations from the constant rotation caused by the YORP effect. Methods. We carried out new photometric observations of the three asteroids, combined the new lightcurves with archived data, and used the lightcurve inversion method to model the asteroid shape, pole direction, and rotation rate. The YORP effect was modeled as a linear change in the rotation rate in time dω/dt .V alues of dω/dt derived from observations were compared with the values predicted by theory. Results. We derived physical models for all three asteroids. We had to model Eger as a nonconvex body because the convex model failed to fit the lightcurves observed at high phase angles. We probably detected the acceleration of the rotation rate of Eger dω/dt = (1.4 ± 0.6) × 10 −8 rad d −2 (3σ error), which corresponds to a decrease in the rotation period by 4. 2m s yr −1 . The photometry of Cerberus and Ra-Shalom was consistent with a constant-period model, and no secular change in the spin rate was detected. We could only constrain maximum values of |dω/dt| < 8 × 10 −9 rad d −2 for Cerberus, and |dω/dt| < 3 × 10 −8 rad d −2 for Ra-Shalom.

Thermophysical modeling of asteroids from WISE thermal infrared data – Significance of the shape model and the pole orientation uncertainties

Abstract In the analysis of thermal infrared data of asteroids by means of thermophysical models (TPMs) it is a common practice to neglect the uncertainty of the shape model and the rotational state, which are taken as an input for the model. Here, we present a novel method of investigating the importance of the shape model and the pole orientation uncertainties in the thermophysical modeling – the varied shape TPM (VS-TPM). Our method uses optical photometric data to generate various shape models that map the uncertainty in the shape and the rotational state. The TPM procedure is then run for all these shape models. We apply the implementation of the classical TPM as well as our VS-TPM to the convex shape models of several asteroids together with their thermal infrared data acquired by the NASA’s Wide-field Infrared Survey Explorer (WISE) and compare the results. These show that the uncertainties of the shape model and the pole orientation can be very important (e.g., for the determination of the thermal inertia) and should be considered in the thermophysical analyses. We present thermophysical properties for six asteroids – (624) Hektor, (771) Libera, (1036) Ganymed, (1472) Muonio, (1627) Ivar, and (2606) Odessa.