Browsing by Subject "G(1)"

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  • Martikainen, J.; Muinonen, K.; Penttilä, A.; Cellino, A.; Wang, X. -B. (2021)
    Aims. We perform light curve inversion for 491 asteroids to retrieve phase curve parameters, rotation periods, pole longitudes and latitudes, and convex and triaxial ellipsoid shapes by using the sparse photometric observations from Gaia Data Release 2 and the dense ground-based observations from the DAMIT database. We develop a method for the derivation of reference absolute magnitudes and phase curves from the Gaia data, allowing for comparative studies involving hundreds of asteroids.Methods. For both general convex shapes and ellipsoid shapes, we computed least-squares solutions using either the Levenberg-Marquardt optimization algorithm or the Nelder-Mead downhill simplex method. Virtual observations were generated by adding Gaussian random errors to the observations, and, later on, a Markov chain Monte Carlo method was applied to sample the spin, shape, and scattering parameters. Absolute magnitude and phase curve retrieval was developed for the reference geometry of equatorial illumination and observations based on model magnitudes averaged over rotational phase.Results. The derived photometric slope values showed wide variations within each assumed Tholen class. The computed Gaia G-band absolute magnitudes matched notably well with the V-band absolute magnitudes retrieved from the Jet Propulsion Laboratory Small-Body Database. Finally, the reference phase curves were well fitted with the H, G(1), G(2) phase function. The resulting G(1), G(2) distribution differed, in an intriguing way, from the G(1), G(2) distribution that is based on the phase curves corresponding to light curve brightness maxima.
  • 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.
  • Shevchenko, Vasilij G.; Belskaya, Irina N.; Mikhalchenko, Olga I.; Muinonen, Karri; Penttilä, Antti; Gritsevich, Maria; Shkuratov, Yuriy G.; Slyusarev, Ivan G.; Videen, Gorden (2019)
    The values of the phase integral q were determined for asteroids using a numerical integration of the brightness phase functions over a wide phase-angle range and the relations between q and the G parameter of the HG function and q and the G(1), G(2) parameters of the HG(1)G(2) function. The phase-integral values for asteroids of different geometric albedo range from 0.34 to 0.54 with an average value of 0.44. These values can be used for the determination of the Bond albedo of asteroids. Estimates for the phase-integral values using the G(1) and G(2) parameters are in very good agreement with the available observational data. We recommend using the HG(1)G(2) function for the determination of the phase integral. Comparison of the phase integrals of asteroids and planetary satellites shows that asteroids have systematically lower values of q.
  • 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.