M. Brož

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.

Asteroid families in the first-order resonances with Jupiter

Asteroids residing in the first-order mean motion resonances with Jupiter hold important information about the processes that set the final architecture of giant planets. Here, we revise current populations of objects in the J2/1 (Hecuba-gap group), J3/2 (Hilda group) and J4/3 (Thule group) resonances. The number of multi-opposition asteroids found is 274 for J2/1, 1197 for J3/2 and three for J4/3. By discovering a second and third object in the J4/3 resonance (186024) 2001 QG207 and (185290) 2006 UB219, this population becomes a real group rather than a single object. Using both hierarchical clustering technique and colour identification, we characterize a collisionally born asteroid family around the largest object (1911) Schubart in the J3/2 resonance. There is also a looser cluster around the largest asteroid (153) Hilda. Using N-body numerical simulations we prove that the Yarkovsky effect (infrared thermal emission from the surface of asteroids) causes a systematic drift in eccentricity for resonant asteroids, while their semimajor axis is almost fixed due to the strong coupling with Jupiter. This is a different mechanism from main belt families, where the Yarkovsky drift affects basically the semimajor axis. We use the eccentricity evolution to determine the following ages: (1.7 ± 0.7) Gyr for the Schubart family and 4 Gyr for the Hilda family. We also find that collisionally born clusters in the J2/1 resonance would efficiently dynamically disperse. The steep size distribution of the stable population inside this resonance could thus make sense if most of these bodies are fragments from an event older than � 1 Gyr. Finally, we test stability of resonant populations during Jupiter’s and Saturn’s crossing of their mutual mean motion resonances. In particular, we find primordial objects in the J3/2 resonance were efficiently removed from their orbits when Jupiter and Saturn crossed their 1:2 mean motion resonance.

Did the Hilda collisional family form during the late heavy bombardment

We model the long-term evolution of the Hilda collisional family located in the 3/2 mean-motion resonance with Jupiter. Its eccentricity distribution evolves mostly due to the Yarkovsky/YORP effect and assuming that (i) impact disruption was isotropic and (ii) albedo distribution of small asteroids is the same as for large ones, we can estimate the age of the Hilda family to be 4 +0 −1 Gyr. We also calculate collisional activity in the J3/2 region. Our results indicate that current collisional rates are very low for a 200-km parent body such that the number of expected events over gigayears is much smaller than 1. The large age and the low probability of the collisional disruption lead us to the conclusion that the Hilda family might have been created during the late heavy bombardment (LHB) when the collisions were much more frequent. The Hilda family may thus serve as a test of orbital behaviour of planets during the LHB. We have tested the influence of the giant-planet migration on the distribution of the family members. The scenarios that are consistent with the observed Hilda family are those with fast migration time-scales � 0.3–3 Myr, because longer time-scales produce a family that is depleted and too much spread in eccentricity. Moreover, there is an indication that Jupiter and Saturn were no longer in a compact configuration (with period ratio PS/PJ > 2.09) at the time when the Hilda family was created.

An anisotropic distribution of spin vectors in asteroid families

Current amount of ~500 asteroid models derived from the disk-integrated photometry by the lightcurve inversion method allows us to study not only the spin-vector properties of the whole population of MBAs, but also of several individual collisional families. We create a data set of 152 asteroids that were identified by the HCM method as members of ten collisional families, among them are 31 newly derived unique models and 24 new models with well-constrained pole-ecliptic latitudes of the spin axes. The remaining models are adopted from the DAMIT database or the literature. We revise the preliminary family membership identification by the HCM method according to several additional criteria - taxonomic type, color, albedo, maximum Yarkovsky semi-major axis drift and the consistency with the size-frequency distribution of each family, and consequently we remove interlopers. We then present the spin-vector distributions for eight asteroidal families. We use a combined orbital- and spin-evolution model to explain the observed spin-vector properties of objects among collisional families. In general, we observe for studied families similar trends in the (a_p, \beta) space: (i) larger asteroids are situated in the proximity of the center of the family; (ii) asteroids with \beta>0{\deg} are usually found to the right from the family center; (iii) on the other hand, asteroids with \beta 0{\deg} or \beta<0{\deg}. Our numerical simulation of the long-term evolution of a collisional family is capable of reproducing well the observed spin-vector properties. Using this simulation, we also independently constrain the age of families Flora (1.0\pm0.5 Gyr) and Koronis (2.5-4 Gyr).

Eurybates — the only asteroid family among Trojans?

We study orbital and physical properties of Trojan asteroids of Jupiter. We try to discern all families previously discussed in literature, but we conclude there is only one significant family among Trojans, namely the cluster around asteroid (3548) Eurybates. It is the only cluster, which has all of the following characteristics: (i) it is clearly concentrated in the proper-element space; (ii) size-frequency distribution is different from background asteroids; (iii) we have a reasonable collisional/dynamical model of the family. Henceforth, we can consider it as a real collisional family. We also report a discovery of a possible family around the asteroid (4709) Ennomos, composed mostly of small asteroids. The asteroid (4709) Ennomos is known to have a very high albedo pV ≃ 0.15, which may be related to a hypothetical cratering e

The thermal emission from boulders on (25143) Itokawa and general implications for the YORP effect

Infrared radiation emitted from an asteroid surface causes a torque that can significantly affect rotational state of the asteroid. The influence of small topographic features on this phenomenon, called the YORP effect, seems to be of utmost importance. In this work, we show that a lateral heat diffusion in boulders of suitable sizes leads to an emergence of a local YORP effect which magnitude is comparable to the YORP effect due to the global shape. We solve a three-dimensional heat diffusion equation in a boulder and its surroundings by the finite element method, using the FreeFem++ code. The contribution to the total torque is inferred from the computed temperature distribution. Our general approach allows us to compute the torque induced by a realistic irregular boulder. For an idealized boulder, our result is consistent with an existing one-dimensional model. We also estimated (and extrapolated) a size distribution of boulders on (25143) Itokawa from close-up images of its surface. We realized that topographic features on Itokawa can potentially induce a torque corresponding to a rotational acceleration of the order 10−7 rad day−2 and can therefore explain the observed phase shift in light curves.

Large distance of ε Aurigae inferred from interstellar absorption and reddening

The long-period (P = 27.1 years) peculiar eclipsing binary e Aur, which has recently completed its two year-long primary eclipse, has perplexed astronomers for over a century. The eclipse arises from the transit of a huge, cool and opaque, disk across the face of the F0 Iab star. One of the principal problems with understanding this binary is that the very small parallax of p = (1.53 ± 1.29) mas, implying a distance range of d ∼ (0.4−4.0) kpc, returned by a revised reduction of the Hipparcos satellite observations, is so uncertain that it precludes a trustworthy estimate of the luminosities and masses of the binary components. A reliable distance determination would help solve the nature of this binary and distinguish between competing models. A new approach is discussed here: we estimate the distance to e Aur from the calibration of reddening and interstellar-medium gas absorption in the direction of the system. The distance to e Aur is estimated from its measured E(B −V) and the strength of the diffuse interstellar band 6613.56 A. Spectroscopy and UBV photometry of several B- and A-type stars (<1 ◦ of e Aur) were carried out. The distances of the reference stars were estimated from either measured or spectroscopic parallaxes. The range in distances of the reference stars is from 0.2 to 3.0 kpc. We find reasonably tight relations among E(B − V), EW, and Ic (6613 A feature) with distance. From these calibrations, a distance of d = (1.5 ± 0.5) kpc is indicated for e Aur. If e Aur is indeed at (or near) this distance, its inferred absolute visual magnitude of MV � (−9.1 ± 1.1) mag for the F-supergiant indicates that it is a very young, luminous and massive star. Noteworthy, the high luminosity inferred here is well above the maximum value of MV �− 6. m 2 expected for (less-massive) post asymptotic giant branch supergiant stars. Thus, based on the circumstantial evidence, the higher-mass model appears to best explain the properties of this mysterious binary system. As a by-product of this study, our spectroscopy led to the finding that two of the stars used in the distance calibrations, HD 31617 and HD 31894, are newly discovered spectroscopic binaries, and HD 32328 is a new radial-velocity variable.

Interaction of the Yarkovsky-Drifting Orbits with Weak Resonances: Numerical Evidence and Challenges

Long-term numerical simulations of main-belt meteoroid and small asteroid orbital evolution with the Yarkovsky effect resulted in several puzzling (and challenging) facts when the orbits got into interaction with weak resonances. Orbits of small asteroids, slowly drifting due to the Yarkovsky effect, may reside in the resonance zone for sufficiently long time. Thereupon the eccentricity and inclination may slowly evolve. Overlapping of close resonances, or multiplets of a single high-order resonance, may cause that the classical theory of capture in a single resonance (as previously applied to tidal evolution of satellites of PR-evolving dust orbits in low order exterior resonances with inner planets) is not applicable. Here we show few examples of these processes based on numerical simulations. Analytical estimation of the chaotic diffusion rate in eccentricity and inclination in these more complex dynamical situations is an important challenge for the future theory.

ξTauri: a unique laboratory to study the dynamic interaction in a compact hierarchical quadruple system

Context. Compact hierarchical systems are important because the effects caused by the dynamical interaction among its members occur ona human timescale. These interactions play a role in the formation of close binaries through Kozai cycles with tides. One such system is ξ Tauri: it has three hierarchical orbits: 7.14 d (eclipsing components Aa, Ab), 145 d (components Aa+Ab, B), and 51 yr (components Aa+Ab+B, C). Aims. We aim to obtain physical properties of the system and to study the dynamical interaction between its components. Methods. Our analysis is based on a large series of spectroscopic photometric (including space-borne) observations and long-baseline optical and infrared spectro-interferometric observations. We used two approaches to infer the system properties: a set of observation-specific models, where all components have elliptical trajectories, and an N -body model, which computes the trajectory of each component by integrating Newton’s equations of motion. Results. The triple subsystem exhibits clear signs of dynamical interaction. The most pronounced are the advance of the apsidal line and eclipse-timing variations. We determined the geometry of all three orbits using both observation-specific and N -body models. The latter correctly accounted for observed effects of the dynamical interaction, predicted cyclic variations of orbital inclinations, and determined the sense of motion of all orbits. Using perturbation theory, we demonstrate that prominent secular and periodic dynamical effects are explainable with a quadrupole interaction. We constrained the basic properties of all components, especially of members of the inner triple subsystem and detected rapid low-amplitude light variations that we attribute to co-rotating surface structures of component B. We also estimated the radius of component B. Properties of component C remain uncertain because of its low relative luminosity. We provide an independent estimate of the distance to the system. Conclusions. The accuracy and consistency of our results make ξ Tau an excellent test bed for models of formation and evolution of hierarchical systems.

A UNIFIED SOLUTION FOR THE ORBIT AND LIGHT-TIME EFFECT IN THE V505 Sgr SYSTEM

The multiple system V505 Sagittarii is composed of at least three stars: a compact eclipsing pair and a distant component, whose orbit is measured directly using speckle interferometry. In order to explain the observed orbit of the third body in V505 Sagittarii and also other observable quantities, namely the minima timings of the eclipsing binary and three different radial velocities (RVs) detected in the spectrum, we thoroughly test a fourth-body hypothesis—a perturbation by a dim, yet-unobserved object. We use an N-body numerical integrator to simulate future and past orbital evolution of three or four components in this system. We construct a suitable χ 2 metric from all available speckle-interferometry, minima-timings, and RV data and we scan a part of a parameter space to get at least some of the possible solutions. In principle, we are able to explain all observable quantities by the presence of a fourth body, but the resulting likelihood of this hypothesis is very low. We also discuss other theoretical explanations of the minima-timing variations. Further observations of the minima timings during the next decade or high-resolution spectroscopic data can significantly constrain the model.