Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe non-convex shape of (234) Barbara, the first Barbarian
129
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Asteroid (234) Barbara is the prototype of a category of asteroids that has been shown to be extremely rich in refractory inclusions, the oldest material ever found in the Solar System. It exhibits several peculiar features, most notably its polarimetric behavior. In recent years other objects sharing the same property (collectively known as Barbarians) have been discovered. Interferometric observations in the mid-infrared with the ESO VLTI suggested that (234) Barbara might have a bi-lobated shape or even a large companion satellite. We use a large set of 57 optical lightcurves acquired between 1979 and 2014, together with the timings of two stellar occultations in 2009, to determine the rotation period, spin-vector coordinates, and 3-D shape of (234) Barbara, using two different shape reconstruction algorithms. By using the lightcurves combined to the results obtained from stellar occultations, we are able to show that the shape of (234) Barbara exhibits large concave areas. Possible links of the shape to the polarimetric properties and the object evolution are discussed. We also show that VLTI data can be modeled without the presence of a satellite.
rate research
Read More
Context. The so-called Barbarian asteroids share peculiar, but common polarimetric properties, probably related to both their shape and composition. They are named after (234) Barbara, the first on which such properties were identified. As has been suggested, large scale topographic features could play a role in the polarimetric response, if the shapes of Barbarians are particularly irregular and present a variety of scattering/incidence angles. This idea is supported by the shape of (234) Barbara, that appears to be deeply excavated by wide concave areas revealed by photometry and stellar occultations. Aims. With these motivations, we started an observation campaign to characterise the shape and rotation properties of Small Main- Belt Asteroid Spectroscopic Survey (SMASS) type L and Ld asteroids. As many of them show long rotation periods, we activated a worldwide network of observers to obtain a dense temporal coverage. Methods. We used light-curve inversion technique in order to determine the sidereal rotation periods of 15 asteroids and the con- vergence to a stable shape and pole coordinates for 8 of them. By using available data from occultations, we are able to scale some shapes to an absolute size. We also study the rotation periods of our sample looking for confirmation of the suspected abundance of asteroids with long rotation periods. Results. Our results show that the shape models of our sample do not seem to have peculiar properties with respect to asteroids with similar size, while an excess of slow rotators is most probably confirmed.
Classical global convergence results for first-order methods rely on uniform smoothness and the L{}ojasiewicz inequality. Motivated by properties of objective functions that arise in machine learning, we propose a non-uniform refinement of these notions, leading to emph{Non-uniform Smoothness} (NS) and emph{Non-uniform L{}ojasiewicz inequality} (NL{}). The new definitions inspire new geometry-aware first-order methods that are able to converge to global optimality faster than the classical $Omega(1/t^2)$ lower bounds. To illustrate the power of these geometry-aware methods and their corresponding non-uniform analysis, we consider two important problems in machine learning: policy gradient optimization in reinforcement learning (PG), and generalized linear model training in supervised learning (GLM). For PG, we find that normalizing the gradient ascent method can accelerate convergence to $O(e^{-t})$ while incurring less overhead than existing algorithms. For GLM, we show that geometry-aware normalized gradient descent can also achieve a linear convergence rate, which significantly improves the best known results. We additionally show that the proposed geometry-aware descent methods escape landscape plateaus faster than standard gradient descent. Experimental results are used to illustrate and complement the theoretical findings.
We report new photometric lightcurve observations of the Lucy Mission target (11351) Leucus acquired during the 2017, 2018 and 2019 apparitions. We use these data in combination with stellar occultations captured during five epochs (Buie et al. 2020) to determine the sidereal rotation period, the spin axis orientation, a convex shape model, the absolute scale of the object, its geometric albedo, and a model of the photometric properties of the target. We find that Leucus is a prograde rotator with a spin axis located within a sky-projected radius of 3{deg} (1$sigma$) from J2000 Ecliptic coordinates ($lambda=208deg$, $beta=+77deg$) or J2000 Equatorial Coordinates (RA=248$deg$, Dec=+58$deg$). The sidereal period is refined to $P_{sid}=445.683pm0.007$ h. The convex shape model is irregular, with maximum dimensions of (60.8, 39.1, 27.8) km. The convex model accounts for global features of the occultation silhouettes, although minor deviations suggest that local and global concavities are present. We determine a geometric albedo $p_V=0.043pm0.002$. The derived phase curve supports a D-type classification for Leucus.
Asteroid modeling efforts in the last decade resulted in a comprehensive dataset of almost 400 convex shape models and their rotation states. This amount already provided a deep insight into physical properties of main-belt asteroids or large collisional families. We aim to increase the number of asteroid shape models and rotation states. Such results are an important input for various further studies such as analysis of asteroid physical properties in different populations, including smaller collisional families, thermophysical modeling, and scaling shape models by disk-resolved images, or stellar occultation data. This provides, in combination with known masses, bulk density estimates, but constrains also theoretical collisional and evolutional models of the Solar System. We use all available disk-integrated optical data (i.e., classical dense-in-time photometry obtained from public databases and through a large collaboration network as well as sparse-in-time individual measurements from a few sky surveys) as an input for the convex inversion method, and derive 3D shape models of asteroids, together with their rotation periods and orientations of rotation axes. The key ingredient is the support of more that one hundred observers who submit their optical data to publicly available databases. We present updated shape models for 36 asteroids, for which mass estimates are currently available in the literature or their masses will be most likely determined from their gravitational influence on smaller bodies, which orbital deflection will be observed by the ESA Gaia astrometric mission. This was achieved by using additional optical data from recent apparitions for the shape optimization. Moreover, we also present new shape model determinations for 250 asteroids, including 13 Hungarias and 3 near-Earth asteroids.
Non-convex sparse minimization (NSM), or $ell_0$-constrained minimization of convex loss functions, is an important optimization problem that has many machine learning applications. NSM is generally NP-hard, and so to exactly solve NSM is almost impossible in polynomial time. As regards the case of quadratic objective functions, exact algorithms based on quadratic mixed-integer programming (MIP) have been studied, but no existing exact methods can handle more general objective functions including Huber and logistic losses; this is unfortunate since those functions are prevalent in practice. In this paper, we consider NSM with $ell_2$-regularized convex objective functions and develop an algorithm by leveraging the efficiency of best-first search (BFS). Our BFS can compute solutions with objective errors at most $Deltage0$, where $Delta$ is a controllable hyper-parameter that balances the trade-off between the guarantee of objective errors and computation cost. Experiments demonstrate that our BFS is useful for solving moderate-size NSM instances with non-quadratic objectives and that BFS is also faster than the MIP-based method when applied to quadratic objectives.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
