Asteroid lightcurve inversion with Bayesian inference

Abstract

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-σ uncertainties, a refined rotation period of (8.5750559 ± 0.0000026) h, pole longitude of 320.6° ± 1.2°, pole latitude of − 25.6° ± 1.7°, 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.

Asteroid absolute magnitudes and phase curve parameters from Gaia photometry

“…In what follows, we summarize the key parts of the present model for the surface reflection coefficient (Muinonen et al 2020). The emergent intensity relates to the diffuse reflection coefficient, R, of an asteroid's surface element as…”

“…It follows that the parameters for the convex shapes are P = (P, λ, β, φ 0 , s 00 , ..., s l max l max , p, G 12 ) T , and for the triaxial ellipsoid shapes they are P = (P, λ, β, φ 0 , a, b, c, p, G 12 ) T . Additionally, since we are interested in the slope parameter, β S , we replace G 12 with β S , as previously demonstrated by Cellino et al (2009), Santana-Ros et al (2015, and Muinonen et al (2020). However, here we further take the phase-angle distribution of the observations into account (see Eq.…”

“…The triaxial ellipsoidal shape model, the general convex shape model, and the inverse methods, such as the virtualobservation Markov chain Monte Carlo (MCMC) sampling, used in this study are described in detail by Muinonen et al (2020).…”

“…As it is not possible to derive precise pole orientations from the photometry of GDR2 only (see Muinonen et al 2020;Cellino et al 2019), we performed the asteroid light curve inversion described in Sect. 2 for 491 asteroids using both the sparse photometric measurements from GDR2 and ground-based observations with initial rotation periods, longitudes, and latitudes from DAMIT.…”

“…We perform asteroid light curve inversion (see Muinonen et al 2020) using both triaxial ellipsoid shapes and general convex shapes to derive phase curve parameters for 491 asteroids by utilizing photometric measurements from GDR2 and from the Database of Asteroid Models from Inversion Techniques (DAMIT; Durech et al 2010). Unlike in the previously mentioned studies, our model takes the shape and the rotation of the asteroid into account to fit each photometric data point as precisely as possible.…”