Browsing by Subject "OPTIMIZATION METHODS"

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  • Muinonen, K.; Torppa, J.; Wang, X-B; Cellino, A.; Penttilä, A. (2020)
    Context. We assess statistical inversion of asteroid rotation periods, pole orientations, shapes, and phase curve parameters from photometric lightcurve observations, here sparse data from the ESA Gaia space mission (Data Release 2) or dense and sparse data from ground-based observing programs.Aims. Assuming general convex shapes, we develop inverse methods for characterizing the Bayesian a posteriori probability density of the parameters (unknowns). We consider both random and systematic uncertainties (errors) in the observations, and assign weights to the observations with the help of Bayesian a priori probability densities.Methods. For general convex shapes comprising large numbers of parameters, we developed a Markov-chain Monte Carlo sampler (MCMC) with a novel proposal probability density function based on the simulation of virtual observations giving rise to virtual least-squares solutions. We utilized these least-squares solutions to construct a proposal probability density for MCMC sampling. For inverse methods involving triaxial ellipsoids, we update the uncertainty model for the observations.Results. We demonstrate the utilization of the inverse methods for three asteroids with Gaia photometry from Data Release 2: (21) Lutetia, (26) Proserpina, and (585) Bilkis. First, we validated the convex inverse methods using the combined ground-based and Gaia data for Lutetia, arriving at rotation and shape models in agreement with those derived with the help of Rosetta space mission data. Second, we applied the convex inverse methods to Proserpina and Bilkis, illustrating the potential of the Gaia photometry for setting constraints on asteroid light scattering as a function of the phase angle (the Sun-object-observer angle). Third, with the help of triaxial ellipsoid inversion as applied to Gaia photometry only, we provide additional proof that the absolute Gaia photometry alone can yield meaningful photometric slope parameters. Fourth, for (585) Bilkis, we report, with 1-sigma uncertainties, a refined rotation period of (8.5750559 0.0000026) h, pole longitude of 320.6 degrees +/- 1.2 degrees, pole latitude of - 25.6 degrees +/- 1.7 degrees, and the first shape model and its uncertainties from convex inversion.Conclusions. We conclude that the inverse methods provide realistic uncertainty estimators for the lightcurve inversion problem and that the Gaia photometry can provide an asteroid taxonomy based on the phase curves.
  • Wang, Xiaobin; Muinonen, Karri (Astronomical Society of the Pacific, 2018)
    Astronomical Society of the Pacific Conference Series
    The ground-based photometric observations of asteroids still is the main source to understand their basic physical properties, even though some space mission and space-based instruments have been applied in physical studies of asteroids. Owing to developments on scattering theories and 3D shape models of asteroid, we can carry out determination for basic physical parameters of asteroids from the photometric data. Here, we present photometric observations for some selected asteroids and light inversion results for these asteroids. In detail, they are: (1) To determine photometric phase functions of asteroids (107)Camilla and (106) Dione considering an ellipsoid shape and a cellinoid shape respectively; and (2) To inverse convex shape of main-belt slow rotating asteroids (168) Sibylla and (346)Hermentaria and a near Earth asteroid (3200) Phaethon. Based on derived photometric phase functions, the geometric albedo, and even rough taxonomic classification of asteroids are inferred. With the virtual photometry Monta Carlo method, the uncertainties of spin parameters of selected asteroids were compared.
  • Wang, Ao; Wang, Xiaobin; Muinonen, Karri; Han, Xianming L. (2019)
    The shapes and rotational states of main-belt asteroids are important for understanding their formation and evolution. Available photometric data of asteroids are biased due to selection effects, including the relative paucity of analyses of slowly rotating objects. In order to get photometric data of slowly rotating asteroids, an international joint observation project has been carried out since 2015 using Chinese and SARA (Southeastern Association for Research in Astronomy) telescopes. In this paper, the photometric data of one of this project targets - (103) Hera were analyzed using the convex inversion method and Lommel-Seeliger ellipsoid model. Combining existing and new photometric data, we re-calculated the shape and spin parameters for (103) Hera. Using a convex shape method, a pair of poles are derived for (103) Hera - (83.0 degrees, 39.0 degrees) and (269 degrees, 56.8 degrees) in ecliptic frame. The spin periods corresponding to these poles are very close - 23.74264 h and 23.74267 h respectively. Meanwhile, the same data were analyzed using the Lommel-Seeliger ellipsoid inversion method and a pair of pole solutions - (74.1 degrees, 39.0 degrees) and (263.1 degrees, 51.0 degrees) with a spin period of 23.74262 h and 23.74263 h respectively are derived. Based on the derived shape of (103) Hera, we have fitted the H, G(1), G(2) phase function using the calibrated data after removing effects of aspheric shape. As a result, we estimated its absolute magnitude H = 8.92 mag with two phase function parameters G(1) = 0.13 and G(2) = 0.45.
  • Oszkiewicz, Dagmara; Kryszczynska, Agnieszka; Kankiewicz, Pawel; Moskovitz, Nicholas A.; Skiff, Brian A.; Leith, Thomas B.; Durech, Josef; Wlodarczyk, Ireneusz; Marciniak, Anna; Geier, Stefan; Fedorets, Grigori; Troianskyi, Volodymyr; Fohring, Dora (2019)
    Context. Asteroid (2579) Spartacus is a small V-type object located in the inner main belt. This object shows spectral characteristics unusual for typical Vestoids, which may indicate an origin deeper than average within Vesta or an origin from an altogether different parent body. Aims. Our main goal is to study the origin of Spartacus. We derive the spin of Spartacus and a convex shape model of Spartacus in order to increase the knowledge of the body's physical properties. The rotational parameters are then used to investigate dynamical evolution of the object as well as to distinguish regions sampled by spectral observations to determine whether its surface displays heterogeneity. Methods. We collected lightcurves available from the literature (oppositions of 2009, 2012) and obtained additional photometric observations at various telescopes in 2016, 2017, and 2018. We used the lightcurve inversion method to derive a spin and convex shape model. We have collected spectral observations over two rotational periods of Spartacus and determined its spectral parameters using the modified Gaussian model (MGM). We then dynamically integrated the orbital elements of Spartacus, taking into account existing information, including its thermal properties, size and the derived spin axis orientation. Results. We find two models for (2579) Spartacus: (a) lambda = 312 degrees +/- 5 degrees, beta = -57 degrees +/- 5 degrees and (b) lambda = 113 degrees +/- 5 degrees, beta = -60 degrees +/- 5 degrees both retrograde. We find that the drift direction for Spartacus is consistent with separation from Vesta, and after a backward integration of 1 Gyr the asteroid reaches the boundary of the family. We did not observe spectral variations with rotation, thus the body most likely has a homogeneous surface. Additionally, new spectral analysis indicates that the 1.0 and 2.0 mu m band centers are within ranges that are typical for Vestoids while the area ratio of these bands is about half that of typical Vestoids. Conclusions. The asteroid (2579) Spartacus is in retrograde rotation and has a drift direction consistent with an origin from Vesta. The revised spectral band centers are within ranges typical for Vestoids, while band area ratio (BAR) is unusually low compared to that of other V-types. The dynamical model shows that the asteroid could have migrated to its current location from the edges of the Vesta family within 1 Gyr, but an origin from an earlier impact on Vesta could also be plausible.